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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 23:51:52 +0000The Kinetics of the Recombination of Methyl Radicals and Iodine Atoms
https://resolver.caltech.edu/CaltechAUTHORS:20150421-104908874
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Rice-O-K', 'name': {'family': 'Rice', 'given': 'O. K.'}}]}
Year: 1951
DOI: 10.1021/j150489a013
The process of recombination of free radicals may be formally regarded as proceeding via an intermediate complex (the so-called activated complex) in
which the radicals are more or less rigidly bound together to form an "active"
molecule. The term "active" here denotes a molecule containing a large excess
of vibrational energy arising from the formation of the new bond. This excess
energy must be removed through a deactivating collision, else it will reaccumulate in the new bond, and the molecule will decompose shortly after it has been formed.
This study treats the two main problems presented by radical recombinations:
the magnitude of the steric effects tending to reduce the rate below that calculated by the kinetic theory of collisions (this effect gives rise to the so-called "steric" factor) and the effect of pressure on the rate of recombination. For example, if the activated complex is a rigid structure, i.e., the radicals are
rigidly bound together, some of the rotational degrees of freedom of the radicals in their free state must be "frozen out" into bending vibrations of the new bond so that the activated complex may be formed. The relatively small probability of such a process results in a reduced chance of the formation of the activated complex and thus not every collision of radical and atom is effective in producing an active molecule. If, on the other hand, the activated complex has a loose structure, i.e., one in which the radicals rotate freely, then there will be no such restrictions on the rate of formation of the activated complex and every collision will be effective in producing an active molecule.https://authors.library.caltech.edu/records/cvh7m-ezx45Unimolecular dissociations and free radical recombination reactions
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp52b
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1952
DOI: 10.1063/1.1700424
The steric and pressure effects associated with the recombination of free radicals both depend on the nature of the activated complex, and are therefore intimately related. From a consideration of the reverse process of unimolecular dissociation, some equations are derived for these properties using an extension of earlier transition state and quasi-unimolecular theories. The present formalism differs from previous formulations of the latter in a number of ways, particularly in the expression used for the density of quantum states of the high energy molecules. Subsequent applications of the theory tentatively suggest that essentially all vibrational degrees of freedom of these molecules can contribute their energy to the vibrationally excited molecules. Consequently, vibrational anharmonicity would appear to be an important factor in intramolecular energy transfer. The present paper is an extension of a previously developed theory for the recombination of methyl radicals and iodine atoms.https://authors.library.caltech.edu/records/bzjse-q1z02Recombination of methyl radicals and atomic cracking of ethyl radicals
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp52a
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1952
DOI: 10.1063/1.1700425
The characteristics of this atomic cracking reaction and of the pressure and steric effects associated with the recombination of methyl radicals are all intimately related. The available data on these reactions are correlated by means of a previously developed theory. Some experimental results on the steric factor and the data on the remaining subjects appear to be consistent with the assumption that the methyl radicals must be highly oriented with respect to each other in order that recombination occur. However, experimental steric factors of unity have also been reported in the literature. The corresponding assumption of no orientation leads to disagreement with the remaining data unless some of the rotational degrees of freedom of the "active" molecule, in addition to the vibrations, are assumed to be "active." Even then, the difficulties are not completely removed. Further experimental work on these reactions is needed.https://authors.library.caltech.edu/records/98qpe-fsc85Lifetimes of active molecules. II
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp52c
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1952
DOI: 10.1063/1.1700423
Experimental data on the atomic cracking of propyl radicals and on the deuterization of methyl radicals are compared with some theoretical calculations. With the aid of some assumptions concerning intramolecular energy transfer in the dissociating molecules involved in these and other reactions and concerning the corresponding activated complexes, data on a number of free radical reactions are correlated.https://authors.library.caltech.edu/records/c0pn7-5rg83Lifetimes of Active Molecules. I
https://resolver.caltech.edu/CaltechAUTHORS:20140429-121818785
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1952
DOI: 10.1063/1.1700422
The specific dissociation constants for various vibrationally excited molecules (methane, ethane, and
propane) are inferred from an interpretation of experimental data on atomic cracking reactions and on the
deuterization of free radicals. As was to be expected, these dissociation constants decrease with increasing
number of degrees of freedom of the decomposing molecule.https://authors.library.caltech.edu/records/7beqh-00s44Studies on RDX and related compounds: X. Analysis for nitric acid in acetic acid-acetic anhydride media
https://resolver.caltech.edu/CaltechAUTHORS:20150422-163141762
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Winkler-C-A', 'name': {'family': 'Winkler', 'given': 'C. A.'}}]}
Year: 1953
DOI: 10.1139/v53-031
An analytical method has been developed for the estimation of nitric acid in acetic acid – acetic anhydride media, with a precision of 0.3%. The procedure involves the addition of a solution of potassium acetate in acetic acid to the sample. The excess is back-titrated conductometrically with a standard solution of nitric acid in acetic acid.https://authors.library.caltech.edu/records/33f4p-s2e23Studies of RDX and related compounds: XI. The conversion of PHX to AcAn
https://resolver.caltech.edu/CaltechAUTHORS:20150422-164115124
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Winkler-C-A', 'name': {'family': 'Winkler', 'given': 'C. A.'}}]}
Year: 1953
DOI: 10.1139/v53-083
The formation of AcAn from PHX, nitric acid, and acetic anhydride has been investigated at various temperatures. The effects of added acetic acid and added salts have been determined. While the reaction is first order with respect to PHX, it is of an order 2.6 with respect to nitric acid. The reaction rate is significantly decreased by small concentrations of sodium nitrate. The reaction is also characterized by a secondary salt effect and a low apparent activation energy of about 2 kcal. mole^(−1). A mechanism has been suggested in qualitative, and to some extent quantitative, agreement with the experimental data. It is postulated that the conversion of PHX involves a rate-controlling ionic reaction between PHX and nitric acid, and that this is followed by a rapid acetylation of the acidic intermediate to AcAn.https://authors.library.caltech.edu/records/rpjkz-r6z57Studies on Ion Exchange Resins. IX. Capacity and Specific Volumes of Quaternary Base Anion Exchange Resins
https://resolver.caltech.edu/CaltechAUTHORS:20150422-164715224
Authors: {'items': [{'id': 'Gregor-H-P', 'name': {'family': 'Gregor', 'given': 'Harry P.'}}, {'id': 'Belle-J', 'name': {'family': 'Belle', 'given': 'Jack'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1954
DOI: 10.1021/ja01636a085
The exchange capacities, wet weights and volumes of a quaternary ammonium anion exchange resin in a number of univalent anionic states including the halide, strong mineral acid anion, hydroxide, chloro-substituted acetate and benzene and naphthalene sulfonate states, were measured. The exchange capacity was the same for all anions, and showed the absence of appreciable adsorption effects. The swelled volume of the resin phase was correlated with the partial molal volumes of the exchange anions. Swelling appears to be determined, to a considerable extent, by ion-pair formation.https://authors.library.caltech.edu/records/cve1a-08f39Titration of Polyelectrolytes at Higher Ionic Strengths
https://resolver.caltech.edu/CaltechAUTHORS:20150422-165410484
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1954
DOI: 10.1021/j150518a008
The titration behavior of polyelectrolytes at higher ionic strengths is treated on the basis of the nearest neighbor interaction between the fixed ions. This point of view suggests a quantitative comparison of the behavior of polymeric and dibasic acids. The application of these considerations to existing work on the correlation of viscosity and titration curves of polymeric acids is briefly discussed.https://authors.library.caltech.edu/records/4xjjr-mj843Studies on Ion-exchange Resins. XIII. Selectivity Coefficients of Quaternary Base Anion-exchange Resins Toward Univalent Anions
https://resolver.caltech.edu/CaltechAUTHORS:20150424-092734637
Authors: {'items': [{'id': 'Gregor-H-P', 'name': {'family': 'Gregor', 'given': 'Harry P.'}}, {'id': 'Belle-J', 'name': {'family': 'Belle', 'given': 'Jack'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1955
DOI: 10.1021/ja01615a011
Selectivity coefficients of a quaternary base ammonium anion-exchange resin toward a number of univalent anions have been measured. In some systems the selectivity coefficients varied little with composition, while in others a marked dependence was observed. Examples of the former included systems made up of various pairs of ions from Group A-halide, acetate, iodate and nitrate, or of pairs of ions from Group B-thiocyanate, perchlorate, di- and trichlolroacetate, trifluoroacetate, toluenesulfonate and naphthalenesulfonate. Examples of systems where the selectivity coefficient changed markedly were made up of an anion from Group A with one from Group B. These data were interpreted in terms of two postulated types of specific interactions (ion-pair formation) of these ions with those of the resin matrix. The ion-pairs of Group A were assumed to be randomly distributed in the resin phase, while those of Group B were assumed to occur in the form of "patches," i.e., form clusters. The effect of temperature on the distribution coefficient was small; the concentration of the solution (when dilute) had a negligible effect upon the selectivity.https://authors.library.caltech.edu/records/wz40q-rex11Treatment of Isotopic Exchange Reactions Having Complex Mechanisms
https://resolver.caltech.edu/CaltechAUTHORS:20131218-134223600
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1955
DOI: 10.1063/1.1742197
The reaction rate vs time data of isotopic exchange reactions have been shown by previous work to obey a first‐order rate law, neglecting differences in isotopic reactivity. A simple method, of use in reactions having complex mechanisms, is developed for relating this first‐order rate constant to the rate constants of elementary steps in the process. The method involves examining the progress of specified atoms through the reaction sequence, and is applicable regardless of the number of exchange positions of the reactants, or of whether or not one isotope is present in tracer amounts. These results are used to reinterpret some data on the deuteration of diborane.https://authors.library.caltech.edu/records/93br9-bm687Calculation of Thermodynamic Properties of Polyelectrolytes
https://resolver.caltech.edu/CaltechAUTHORS:20140429-124648028
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1955
DOI: 10.1063/1.1742191
Expressions are derived which introduce an appreciable simplification into the calculation of the thermodynamic properties of solutions of polyelectrolytes in certain cases. For example, for a certain class of theoretical models of these systems it is found that the square of the mean ion activity coefficient of a uni-univalent salt in the presence of polymeric ions is V^2/∫e^(-eψ/kT)dV • ∫e^(eψ/kT)dV, the integration of the potential ψ being over a region whose volume is the volume of solution per macro-ion, V, and whose symmetry is that
assumed for the polyelectrolyte. The osmotic pressure of a salt-polyelectrolyte system is, ignoring the contribution of the macro-ion, estimated to be Σ_ic_i^skT, where Σ_ic_i^s is the sum of the concentrations of all ions at the surface bounding the previously defined volume V. Other relations and various applications are
given. The activity coefficient of salt in the presence of polyelectrolytes, calculated by extending the "parallel rod" picture of polymeric ions, is found to be in reasonable agreement with the experimental data. The use of the Poisson-Boltzmann equation to estimate ψ in these systems is shown not to render inconsistent several
alternative expressions for the electrostatic contribution to the free energy.https://authors.library.caltech.edu/records/h08mh-b7460Kinetic Study of the Reaction of Diborane with Phosphine
https://resolver.caltech.edu/CaltechAUTHORS:20131216-133447768
Authors: {'items': [{'id': 'Brumberger-H', 'name': {'family': 'Brumberger', 'given': 'H.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1956
DOI: 10.1063/1.1742601
The homogeneous gas phase reaction between diborane and phosphine at 0°C, yielding a solid product of composition BH_3PH_3, has been observed to give a linear relation between the initial rate of reaction and the pressure of either reactant, provided a certain pressure of each reactant, determined by the equilibrium constant and the pressure of the other gas, is exceeded. The reaction rate is independent of the amount of surface of the solid product or of the wall. When either reagent is in appreciable excess, the rate‐time data obey a pseudo first‐order equation.
These facts are consistent with a rate‐controlling reaction of diborane with phosphine to give BH_3PH_3 and BH_3, the borine reacting further with phosphine, and the BH_3PH_3 condensing rapidly to a solid. This mechanism leads to a rate equation which is in good agreement with the experimental evidence. The activation energy of the rate‐controlling step is 11.4±2.0 kcal mole^(-1).https://authors.library.caltech.edu/records/78xa7-wya29On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer. I
https://resolver.caltech.edu/CaltechAUTHORS:20140505-162124775
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1956
DOI: 10.1063/1.1742723
A mechanism for electron transfer reactions is described, in which there is very little spatial overlap of the electronic orbitals of the two reacting molecules in the activated complex. Assuming such a mechanism, a quantitative theory of the rates of oxidation‐reduction reactions involving electron transfer in solution is presented. The assumption of "slight‐overlap" is shown to lead to a reaction path which involves an intermediate state X* in which the electrical polarization of the solvent does not have the usual value appropriate for the given ionic charges (i.e., it does not have an equilibrium value). Using an equation developed elsewhere for the electrostatic free energy of nonequilibrium states, the free energy of all possible intermediate states is calculated. The characteristics of the most probable state are then determined with the aid of the calculus of variations by minimizing its free energy subject to certain restraints. A simple expression for the electrostatic contribution to the free energy of formation of the intermediate state from the reactants, ΔF*, is thereby obtained in terms of known quantities, such as ionic radii, charges, and the standard free energy of reaction.
This intermediate state X* can either disappear to reform the reactants, or by an electronic jump mechanism to form a state X in which the ions are characteristic of the products. When the latter process is more probable than the former, the over‐all reaction rate is shown to be simply the rate of formation of the intermediate state, namely the collision number in solution multiplied by exp(—ΔF*/kT). Evidence in favor of this is cited. In a detailed quantitative comparison, given elsewhere, with the kinetic data, no arbitrary parameters are needed to obtain reasonable agreement of calculated and experimental results.https://authors.library.caltech.edu/records/desqy-fmq55Electrostatic Free Energy and Other Properties of States Having Nonequilibrium Polarization. I
https://resolver.caltech.edu/CaltechAUTHORS:20140505-104019660
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1956
DOI: 10.1063/1.1742724
Various processes such as electron transferreactions, redox reactions at electrodes, and electronic excitation of dissolved ions may proceed by way of intermediate states whose electrical polarization is not in equilibrium with the field arising from the charges present. The usual expressions for the electrostatic-free energy and for the differential equation satisfied by the potential assume that the polarization and the field are in equilibrium. Accordingly, these equations are of but limited applicability to these processes. In the present paper equations are derived for various properties of systems having such nonequilibrium electrostatic configurations. These properties include the free energy, energy, and entropy of the nonequilibrium system, and the spacial dependence of the electrostatic potential. The free energy, for example, will be used to calculate the probability of formation of nonequilibrium states in certain problems of physical interest.https://authors.library.caltech.edu/records/fhhep-hnm65Relative Rates of Some Very Rapid Gaseous Bimolecular Reactions
https://resolver.caltech.edu/CaltechAUTHORS:DAEjcp57
Authors: {'items': [{'id': 'Daen-J', 'name': {'family': 'Daen', 'given': 'Jerome'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1957
DOI: 10.1063/1.1743243
The present paper describes a steady-state flow apparatus which permits the measurement of relative rates of rapid gas phase bimolecular association reactions at very low pressures. Using this apparatus, the relative reactivities of the methylamines with boron trifluoride were determined over the pressure range 0.009 to 0.04 mm Hg. Within the experimental error the ratio of rate constants, kCH3NH2/k(CH3)3N, was found to be pressure independent and to have a value of 1/12. A small number of experiments was made competing monomethylamine and dimethylamine for BF3; for this system the ratio of rate constants, kCH3NH2/k(CH3)2NH had an average value of 1/5. In addition to the above, experiments were made on various phenomena such as the sorption of BF3 on various surfaces, the selectivity of a diffusion pump, and the extent of base exchange reactions, insofar as these factors pertained to the understanding of the relative rate measurements.https://authors.library.caltech.edu/records/m7vmf-dy056On the theory of oxidation-reduction reactions and of related processes
https://resolver.caltech.edu/CaltechAUTHORS:20150421-095146212
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1957
Recent years have witnessed the elucidation of the mechanisms of many organic and inorganic chemical reactions. Several principal factors have contributed to this development. Among these may be listed the detailed kinetic study of numerous reactions, and the use of isotopic tracers, in some cases, to map the migration of specific atoms between the reacting molecules. Another factor is the deep insight into reaction mechanisms afforded by qualitative application of the ideas of modern valence theory, such as those embodied in the conception of the activated complex.
Oxidation-reduction reactions provide typical examples of this trend. Detailed kinetic studies have shown that they frequently involve a number of successive reaction steps. Attention has become focused on the rates and mechanisms of these elementary reactions, some of which are equilibria involving the formation, or disappearance, of the species participating in the actual redox step.
Similar remarks apply to electrode processes, whose slow rate is one cause of overvoltage and of polarographic irreversibility. Detailed studies of the mechanism of these processes, frequently by alternating current techniques, are comparatively fewer, but they have begun to reveal the complexities and trends involved. These processes, too, may involve several successive steps, some of which are associated with the formation or disappearance of the reacting particle undergoing electron or atom transfer with the electrode. Isotopic tracer techniques have been employed here also.https://authors.library.caltech.edu/records/zg3g6-jf279On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer. III. Applications to Data on the Rates of Organic Redox Reactions
https://resolver.caltech.edu/CaltechAUTHORS:20140505-141531708
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1957
DOI: 10.1063/1.1743424
A recently developed theory of oxidation‐reduction reactions (Part I) is used to calculate the rates of organic redox reactions whose mechanism involves the transfer of an electron from one reactant to the other. The theory can be used to discuss factors affecting the rates of these reactions. These factors include a standard free energy of reaction, the Coulombic interaction of the ionic charges of the reactants, and the solvation of the charged reactants. Attention is focused on the relation between the rate of the redox step in the over‐all process and the standard free energy change, ΔF^0, of this step, rather than on the more usual but less fundamental one between the corresponding quantities of the over‐all process itself.
An approximate method is described for applying the theory to a molecule whose charge is not located at its center. Essentially all organic molecules lie in this category.
As an example of these considerations, several typical reactions are discussed. These reactions involve the oxidation of a series of hydroquinones by ferric ions and of a series of leucoindophenols by dissolved oxygen. They are assumed to possess electron transfer, rather than atom transfer, mechanisms. Free energies and entropies of activation of the redox step are calculated using the theoretical equation. The calculated results are considered to be in reasonable agreement with the experimental data, no adjustable parameters being employed.https://authors.library.caltech.edu/records/n1dvg-fw104On the Theory of Oxidation-Reduction Reactions Involving Electron Transfer. II. Applications to Data on the Rates of Isotopic Exchange Reactions
https://resolver.caltech.edu/CaltechAUTHORS:20140505-144811265
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1957
DOI: 10.1063/1.1743423
The rates of some homogeneous isotopic exchange reactions in solution are considered in the light of a recently developed quantitative theory of redox processes (Part I). The relative importance of several factors influencing the rates of these reactions is discussed. These factors include the Coulombic repulsion between the ionic reactants and the extent of solvation of the ions. Free energies and entropies of activation of various reactions are calculated from the theory without the use of any adjustable parameters. The agreement with the experimental data is considered to be satisfactory.
On the basis of the theory and of earlier experiments in heavy water an experimental method is tentatively suggested for distinguishing electron and atom transfer mechanisms. This method applies to halide‐catalyzed exchange reactions of metal aquo-ions, and to other anion‐catalyzed reactions of this type not involving breakable OH bonds.https://authors.library.caltech.edu/records/r1qkb-fn033Some recent developments in the study of unstable species
https://resolver.caltech.edu/CaltechAUTHORS:20150424-091727767
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1957
DOI: 10.1111/j.1749-6632.1957.tb46083.x
The papers in this monograph reveal the considerable advances made during the past decade in the direct observation of free radicals, excited molecules, ions, and other reactive particles. These developments have followed the introduction of new techniques for producing large concentrations of these reactive species and have been facilitated by the use of relatively recent analytical devices and by the adaptation of older ones. However, to a large extent these developments are a direct consequence of the extensive studies, carried out during the past 30 years, in which the chemical properties of free radicals have been inferred primarily from an analysis of their chemical reaction products. These older methods are more indirect, but both approaches are required for a detailed understanding of unstable species and their reactions.https://authors.library.caltech.edu/records/akfqx-xt743Exploding Wire as a Light Source in Flash Photolysis
https://resolver.caltech.edu/CaltechAUTHORS:OSTjcp57a
Authors: {'items': [{'id': 'Oster-G-K', 'name': {'family': 'Oster', 'given': 'Gisela K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1957
DOI: 10.1063/1.1743665
The exploding wire technique has been developed for use as a light source in flash photolysis. The method consists of discharging a bank of condensers, via a mechanical switch through a thin Nichrome wire. The wire explodes, emitting light rich in the ultraviolet region in less than a millisecond. The luminous efficiency in the 200 to 330 mµ region is of the order of 10% of the input. The minimum electrical energy input necessary to produce an explosion is equal to the energy required to vaporize the wire. The light output of the exploding wire as measured by uranyl oxalate actinometry and acetone photolysis is proportional to the electrical energy input. It was found to be highly reproducible. It was further observed that the exploding wire behaves as a line source. Because of the absence of a quartz or Pyrex tube in this source, it may find application in the far as well as in the near ultraviolet and in the visible spectral regions.https://authors.library.caltech.edu/records/0kk94-j4z36Photochemical Studies in Flash Photolysis. I. Photolysis of Acetone
https://resolver.caltech.edu/CaltechAUTHORS:OSTjcp57b
Authors: {'items': [{'id': 'Oster-G-K', 'name': {'family': 'Oster', 'given': 'Gisela K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1957
DOI: 10.1063/1.1743749
The high-intensity flash photolysis of acetone was investigated using an exploding wire as a light source. Experiments were conducted with the unfiltered light of the flash, containing light in the near as well as in the far ultraviolet region of the spectrum. The results show that the C2H6/CO ratio in the reaction products is about 1.25 and is fairly insensitive to variation in acetone pressure. Addition of small amounts of biacetyl lowers the ratio still further. This is attributed to the deactivation of a long-lived excited acetone molecule formed in the ultraviolet region below 210 mµ. Addition of butane lowers the ratio far below unity. The CH4/CO ratio has the constant value of 0.1 for various light intensities, acetone pressures, pressures of added butane or of carbon dioxide. A convenient way of separating small amounts of ethane from very large amounts of carbon dioxide is described.https://authors.library.caltech.edu/records/nr5nv-mvr23Infrared Absorption Spectra of Nitric Acid and Its Solutions
https://resolver.caltech.edu/CaltechAUTHORS:20140501-160901110
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Fresco-J-M', 'name': {'family': 'Fresco', 'given': 'J. M.'}}]}
Year: 1957
DOI: 10.1063/1.1743769
Infrared spectra of reactive liquids such as anhydrous nitric and sulfuric acids were determined using silver chloride windows and, in some cases, Teflon spacers. The absorption frequencies of nitric acid agree well with those found from Raman spectra.
A nitronium ion frequency was observed at 2360 cm^(-1). The intensity of this band is enhanced by the addition of nitronium fluoborate, sulfuric acid, phosphorous pentoxide, or small amounts of acetic anhydride. It is reduced by addition of sodium nitrate, potassium dihydrogen phosphate, water, or larger amounts of acetic anhydride. Its behavior in these media provides information about pertinent equilibria. A nitronium ion combination band was observed near 3745 cm^(-1) when the concentration of this ion was particularly large. Bands arising from unionized nitric acid are completely absent when a small amount of nitric acid is added to 100% H_2SO_4.
Various bands found in aqueous nitric acid solutions are attributed to hydrogen‐bonded structures, both because of their behavior in different media and by analogy with effects observed in Raman studies.https://authors.library.caltech.edu/records/wvsjj-xdm28Studies of chemical reactions of excited species using intense light sources
https://resolver.caltech.edu/CaltechAUTHORS:20150811-114421577
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1958
DOI: 10.1139/v58-012
The use of measurements of the products of flash photolysis as a means for studying the reactions of electronically-excited molecules is discussed. With intense light sources the problem of isolating these reactions from others involving free radicals is simplified. The flash sources also have their limitations, and misleading information which can result from the presence of inert gases is noted. A diagnostic test is proposed for detecting the effects (if any) of a possible adiabatic temperature rise of the flash.
Some recent studies in the author's laboratory are summarized. Evidence is presented that in the flash photolysis of acetone acetyl radicals arise from an excited molecule. Several deactivation processes are described and compared with results from fluorescence studies.https://authors.library.caltech.edu/records/50kkh-kb990Ionic Polymerization. IX. The Effect of Water in the Cationic Polymerization of Styrene Catalyzed by Stannic Chloride
https://resolver.caltech.edu/CaltechAUTHORS:20150812-155806749
Authors: {'items': [{'id': 'Overberger-C-G', 'name': {'family': 'Overberger', 'given': 'C. G.'}}, {'id': 'Ehrig-R-J', 'name': {'family': 'Ehrig', 'given': 'R. J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1958
DOI: 10.1021/ja01543a028
This work was undertaken in order to obtain information on the mechanistic role of water on the polymerization of styrene catalyzed by stannic chloride. The polymerization and molecular weight were studied as a function of the concentration of water and of the other reagents in a nitrobenzene-carbon tetrachloride solvent medium at 25°. Unusually stringent drying conditions and a quantitative measure of water permitted the water content in these experiments to be known with high accuracy and allowed data to be obtained not available from previous work. A high vacuum technique was employed for introduction of all reagents, and the polymerization rate was following dilatometrically The initial rate of the reaction was observed to increase to a maximum and then decrease as the initial concentration of water was increased. The decrease in rate has been attributed partly to heterogeneity. At a constant initial water concentration, the reaction was found to be first order with respect to the stannic chloride concentration between 0.005 and 0.02 M, and approximately second order with respect to the monomer concentration between 1 and 3 M. The degree of polymerization of the resulting polymer increases with the initial monomer concentration, decreases with the water concentration, and is essentially independent of the catalyst concentration. A reaction mechanism has been proposed to account for these results, in which a monohydrate catalyst-cocatalyst complex is assumed. Termination is postulated to occur by a spontaneous unimolecular process and a bimolecular process involving water. A monomer transfer step is also indicated.https://authors.library.caltech.edu/records/j5xm7-mt182On the theory of electrochemical and chemical electron transfer processes
https://resolver.caltech.edu/CaltechAUTHORS:20150424-094237911
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1959
DOI: 10.1139/v59-022
Kinetic studies of simple electron transfer systems in solution and at electrodes have revealed a number of interesting and simplifying features. The chemical reactions also represent one of the very few cases in kinetics where it has been possible to make reasonable calculations of the absolute rate constant without introducing adjustable parameters or arbitrary assumptions. Because of their comparative simplicity, these processes also serve as a useful kinetic tool for investigating ion–solvent–electrode interactions.
In the present paper the writer's recent theoretical investigations are summarized and used to interpret data obtained from both solution and electrode studies. Various phenomena are discussed in the light of this theory and several predictions of behavior are made. The topics considered include effects of changing the overpotential or the standard free energy of reaction, the ionic structure, temperature, salt concentration, solvent, and electrode material. Both the parallelism between chemical and electrochemical transfers and the role played by the electrostatic image in the latter case are discussed. A classification of reactants is employed throughout, based in part on differences in the theoretical treatment.https://authors.library.caltech.edu/records/j6ehm-gxj85Exchange reactions and electron transfer reactions including isotopic exchange. Theory of oxidation-reduction reactions involving electron transfer. Part 4. -- A statistical-mechanical basis for treating contributions from solvent, ligands, and inert salt
https://resolver.caltech.edu/CaltechAUTHORS:20150812-160745521
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1960
DOI: 10.1039/DF9602900021
The mechanism for electron transfer is discussed in terms of an atomic motion on a potential-energy surface in many-dimensional atomic configuration space. In the absence of electronic coupling between the reactants, a surface for the reactants intersects one for the products. Electronic coupling causes the usual removal of this degeneracy and permits the products to be formed adiabatically or nonadiabatically by an atomic motion across the "intersection" surface.
The properties of a system on this latter surface are formulated in terms of statistical mechanics, in order to treat in a consistent manner the ligands microscopically and the exterior solvent macroscopically. A concept of "equivalent equilibrium distribution" is introduced to evaluate the surface integral. A macroscopic quantity is invoked only in the last step of the derivation, replacing its statistical-mechanical equivalent.
A relatively simple expression is obtained thereby for the reaction rate, which reduces to that obtained in part 1 when ligand and salt contributions are omitted. Applications can be made to a number of problems, such as prediction of non-isotopic electron-transfer rates from isotopic ones, relation between chemical and electrochemical electron transfers inert salt effects and possibility of an inverted chemical effect.https://authors.library.caltech.edu/records/h2ztx-ee849Activity coefficients of bipolar electrolytes. Silver succinate and sebacate in aqueous sodium nitrate
https://resolver.caltech.edu/CaltechAUTHORS:20150812-161351545
Authors: {'items': [{'id': 'Meeks-F-R', 'name': {'family': 'Meeks', 'given': 'F. R.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1961
DOI: 10.1021/j100820a029
Activity coeffxients of silver succinate and sebacate in aqueous sodium nitrate were determined by a solubility method. The silver ion concentration was measured potentiometrically in solutions of various ionic strengths wing an empirical calibration equation. A simple approximate theoretical model for these "bipolar" ions is observed to be in good agreement with results inferred from the electrostatic contribution to the activity coefficients. It treats a bipolar ion as two point charges separated by a fixed distance in the solvent. Its applicability to zwitterions is also considered. These studies are used to discuss the interaction of certain activated complexes of chemical reactions with their ionic atmospheres. Studies of bipolar ions also provide information about nearest neighbor interaction in polyelectrolyteshttps://authors.library.caltech.edu/records/pg2jm-n5f58Photochemical Studies in Flash Photolysis. II. Photolysis of Acetone with Filtered Light
https://resolver.caltech.edu/CaltechAUTHORS:20120829-151917599
Authors: {'items': [{'id': 'Slaag-N', 'name': {'family': 'Slagg', 'given': 'N.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1961
DOI: 10.1063/1.1731626
Flash photolysis was studied in the absence of wavelengths below 200 mμ. Effects of acetone pressure, light intensity, added biacetyl, temperature, and wavelength were investigated. The results are consistent with primary acts postulated previously on the basis of low‐intensity studies, but with the absence of complicating first‐order secondary reactions at these high radical concentrations. Deactivation of excited molecules explains the pressure effect on the C_2H_6/CO ratio, for wall effects are absent under flash conditions. A hot radical mechanism is suggested by the data for methane formation. The effect of wavelength on C_2H_6/CO ratio in regions centered near 260, 280, and 295 mμ is rather striking, and the results are compared with trends in low‐intensity studies in the same pressure region.https://authors.library.caltech.edu/records/r6w91-hxf11Kinetic Studies of Nitration with Nitronium Fluoroborate
https://resolver.caltech.edu/CaltechAUTHORS:20150812-162659549
Authors: {'items': [{'id': 'Ciaccio-L-L', 'name': {'family': 'Ciaccio', 'given': 'L. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1962
DOI: 10.1021/ja00869a014
Using nitronium fluoroborate as a nitrating agent, rates of nitration of nitrobenzene to m-dinitrobenzene were measured in methanesulfonic acid, in sulfuric acid and in acetonitrile. For comparison, the nitration rates were also determined with nitric acid in each of these solvents and with anhydrous nitric acid alone. The reaction was followed by polarographic analysis of quenched samples. Conditions for purification of the fluoroborate, analysis and preparation of kinetically reproducible methanesulfonic acid are described. The reaction is first order in nitrobenzene and first order in the nitrating agent (except for HNO_3 in CH_3SO_3H). Second order rate constants are about equal for the two nitrating agents in sulfuric acid and, when the HNO_3 data are extrapolated to zero HNO_3, in methanesulfonic acid. The rate constants in the two solvents are also comparable in magnitude. When a second order rate constant in anhydrous nitric acid is computed from the
estimated NO_2^+ concentration, its value at - 13° is about the same as those observed in the above acidic solvents at 25°, and its approximate value at room temperature is appreciably greater. In acetonitrile, the rate constant with NO_2BF_4 is much less, in qualitative agreement with the negligible content of free NO_2^+ in this medium as deduced from infrared spectra. The nitration rate with HNO_3 in acetonitrile is negligible. The study extends somewhat the range of solvents suitable for the investigation of medium effects on the attack of aromatics by NO_2^++.https://authors.library.caltech.edu/records/1p2eg-xcc63Photochemical Studies in Flash Photolysis IV. Intensity and Wavelength Effects
https://resolver.caltech.edu/CaltechAUTHORS:20150930-095907747
Authors: {'items': [{'id': 'Shilman-A', 'name': {'family': 'Shilman', 'given': 'A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1962
DOI: 10.1002/bscb.19620711105
Wavelength and intensity effects which we have observed in the flash photolysis of acetone are reviewed. Marked nonmonotonic wavelength effects occurred in the different regions investigated (260, 280 and 300 mμ) and serve to emphasize the problem of interpreting any data obtained with unfiltered light. The data at 300 mμ were compared with those obtained with continuous light sources 10^6 fold less intense. A considerable difference occurred in the C_2H_6/CO ratio. To investigate this intensity effect, flash photolyses were made over a wide range of reduced intensities, as low as 10^4 fold less than the maximum one, and the transition intensity region for change in C_2H_6/CO ratio and CO quantum yield was located. This phenomenon illustrates the more general fact that the apparent primary processes observed at typical flash intensities need not be the same as the primary processes found at low intensitieshttps://authors.library.caltech.edu/records/jpsta-gjr67Studies on Alternating Current Electrolysis. IV . Mathematical Treatment of Reversible Electron Transfer with Alternating Voltage Control and Distorted Current
https://resolver.caltech.edu/CaltechAUTHORS:20150812-162135095
Authors: {'items': [{'id': 'Remick-A-E', 'name': {'family': 'Remick', 'given': 'A. Edward'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1962
DOI: 10.1149/1.2425510
A mathematical treatment is developed which yields equations relating faradaic current, voltage, and time when an alternating voltage is applied to an electrolytic cell composed of a plane and auxiliary electrodes immersed in a solution containing initially supporting electrolyte and only reversibly oxidizable or reducible species. Both oxidant and reductant are taken to be soluble, and specific adsorption is assumed to be absent. The voltage across that branch of the equivalent circuit through which only faradaic current flows is assumed to be periodic with fixed amplitude and with or without an additional direct applied voltage component; the resultant current is distorted. Diffusion controlled kinetics is postulated, and it is assumed that equilibrium is essentially established at the electrode surface. The equations developed show that a "steady state" (i.e., a periodic state) is quickly attained, yield diagnostic tests of use in establishing the reversible mechanism, make it possible to determine the standard potential, and finally yield for the periodic state a relation between faradaic current and time. These results are then generalized so as to include systems in which the reversible electrochemical step is followed by a sufficiently slow secondary reaction step. One diagnostic result of interest in the latter connection is that the mean faradaic current vanishes in the periodic state, regardless of the amplitude or of the shape of the applied periodic potential, when the follow‐up reaction occurs to a negligible extent.https://authors.library.caltech.edu/records/f0yg0-y5965Photolysis of Diborane at 1849 Å
https://resolver.caltech.edu/CaltechAUTHORS:20120920-094428326
Authors: {'items': [{'id': 'Kreye-W-C', 'name': {'family': 'Kreye', 'given': 'W. C.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1962
DOI: 10.1063/1.1701337
The photolysis of diborane at 1849 Å has been studied in a specially constructed, internal‐type mercury‐vapor lamp. The products have been found to be H_2, B_(4)H_(10), B_(5)H_(11), and, at low pressures, a —BH— polymer. Reaction orders at 4°C have been obtained from linear plots of reaction products vs time for a range of diborane pressures from 0.08 to 80 cm, and at two light intensities. Linear relations between products and time existed only at very low conversions (∼1%), which required the development of a low‐temperature separation method for manipulating and analyzing the traces of B_(4)H_(10) and B_(5)H_(11). Because of the reactivity of these compounds, a detailed conditioning procedure was employed for the glass system.
A mechanism consistant with the kinetic data and suggested by the kinetic results of thermal and photosensitized decomposition of diborane is postulated: the B_(5)H_(11) is assumed to be formed from a dissociation of B_(2)H_6 into BH_3's, the latter arising from an excited molecule. The B_(4)H_(10) and polymer are assumed to be formed from a dissociation of B_(2)H_6 into B_(2)H_5 and H, followed by radical recombination. There is a significant difference between the kinetics of thermal and photochemical B_(5)H_(11) formation, a result which may be due to the considerable energy excess of the 1849 quantum over that needed for dissociation (∼125‐kcal excess). These kinetic results raise a number of interesting questions, questions which can only be resolved through further investigations of effects due to light intensity, added inert gases, and temperature. The primary quantum yield of the step forming B_(2)H_5 and H is about 10 times higher than that of the one forming BH_3's. A rather rough estimate suggests that the former is of the order of magnitude of unity.https://authors.library.caltech.edu/records/fm4h5-2yn87Dissociation and isomerization of vibrationally excited species. II. Unimolecular reaction rate theory and its application
https://resolver.caltech.edu/CaltechAUTHORS:WIEjcp62
Authors: {'items': [{'id': 'Wieder-G-M', 'name': {'family': 'Wieder', 'given': 'Grace M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1962
DOI: 10.1063/1.1733376
Data on quasi-unimolecular reactions have usually been compared with theoretical equations based on classical treatments, because the expressions are simpler than those obtained on the basis of a quantum model. The quantum reformulation of the RRK theory in Part I is used to compute the pressure dependence of the rate constants and the limiting low-pressure rates for a variety of unimolecular reactions without employing adjustable parameters. An asymptotic expansion of the integral for the limiting low-pressure second-order rate constant provides a very simple expression for this quantity.The errors inherent in corresponding classical calculations are estimated by comparing these results with those obtained from the theory in its classical limit. The error is temperature dependent and at low pressures increases from a factor of about three (under typical experimental conditions) for small reactants such as O3 and N2O to 105 or more for large molecules such as cyclopropane, C2H6, and N2O5. In most cases the rates calculated from the quantum form are in reasonable agreement with those obtained experimentally when all of the reactant oscillators are assumed effective in intramolecular energy transfer.https://authors.library.caltech.edu/records/te3ce-hqw29Highly Sensitive Low Temperature Fractionation Method for Separation and Measurement of Boron Hydrides
https://resolver.caltech.edu/CaltechAUTHORS:20150812-163645793
Authors: {'items': [{'id': 'Kreye-W-C', 'name': {'family': 'Kreye', 'given': 'W. C.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1962
DOI: 10.1021/ac60192a049
A highly sensitive method capable of detecting quantities of the boron hydrides, B_4H_(10) and B_5H_(11), as small as 0.02 µmole was required for the analysis of the products of a very low conversion kinetic study of the photolysis of diborane. Various analytical methods have been described in the literature for boron hydrides: infrared absorption, neutron absorption, gas chromatography, low temperature fractionation, and mass spectroscopy. Neutron absorption was used to determine total B^(10) content of individual boron hydrides for use in isotopic exchange studies. Gas chromatography was used successfully for B_4H_(10) and B_5H_9, though not for B_5H_(11) because of the latter's instability. Minimum detectable amounts for mixtures were given only for the infrared absorption method, where they were about 0.5 µmole of B_4H_(10) and B_5H_(11), so that the method was too insensitive for much of our investigation. A method was needed where a minimum detectable amount in the presence of large amounts of B_2H_6 was as low as 5 x 10^(-4) mole per cent. It is necessary in certain studies with boron hydrides to proceed to very low per cent conversions to avoid complications due to the reactions of the products.https://authors.library.caltech.edu/records/cbh5w-3m948Interactions in polar media. I. Interparticle interaction energy
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp63a
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1963
DOI: 10.1063/1.1733854
Using permanent plus induced charge distributions on particles a Hartree method is used to compute the polar contribution to the interparticle interaction energy. Each particle may be a single molecule or a collection of molecules, a whole electrode or an entire medium for example. The total interparticle interaction energy is taken to be the sum of this polar term and of an interparticle electron correlation term. The second of these includes effects due to interparticle London dispersion and exchange repulsion forces. A symmetry property associated with a quantum mechanical operator characterizing the induced charge distribution is obtained in a compact way using a projection operator. The polar term is also calculated from classical electrostatics and shown to be the same as the one above. The present work is a generalization of earlier treatments in which the particles were single molecules interacting via permanent and induced dipoles.An application of this work is the more general formulation of theories associated with polar interactions in condensed phases, such as the theory of electron transfer rates in solution and at electrodes, and the theory of electronic spectral shifts and band broadening of polar solutes in polar media.https://authors.library.caltech.edu/records/2bxcy-8w161On the theory of oxidation—Reduction reactions involving electron transfer. V. Comparison and properties of electrochemical and chemical rate constants
https://resolver.caltech.edu/CaltechAUTHORS:20150812-164543423
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1963
DOI: 10.1021/j100798a033
Using a theory of electron transfers which takes cognizance of reorganization of the medium outside the inner coordination shell and of changes of bond lengths inside it, relations between electrochemical and related chemical rate constants are deduced and compared with the experimental data. A correlation is found, without the use of arbitrary parameters. Effects of weak complexes with added electrolytes are included under specified conditions. The deductions offer a way of coordinating a variety of data in the two fields, internally as well as with each other, and a way of predicting results in one field from those in another. For example, the rate of oxidation or reduction of a series of related reactants by one reagent is correlated with that of another and with that of the corresponding electrochemical oxidation-reduction reaction, under certain specified conditions. These correlations may also provide a test for distinguishing an electron from an atom transfer mechanism.https://authors.library.caltech.edu/records/ap2a4-pax89Free energy of nonequilibrium polarization systems. II. Homogeneous and electrode systems
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp63b
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1963
DOI: 10.1063/1.1733886
The polar contribution to the free energy is calculated for a system containing "particles" imbedded in a continuum having nonequilibrium dielectric polarization. Each particle may either be a single molecule or a whole collection of molecules (such as an electrode) at specified nuclear configuration and may possess a general permanent and induced charge distribution. Thereby, the results of Part I of this series are extended to a variety of systems. It is also shown that the polar contribution to the free energy can be written as the sum of free energies of equilibrium polarization systems, thereby permitting the immediate application of literature expressions for the latter to calculating the former. This expression is also derived for systems possessing partial dielectric unsaturation under a certain typical condition. Applications are made to the theory of electron-transfer reactions in solution and at electrodes and to the theory of the shift of electronic spectra of polar solutes by polar solvents.https://authors.library.caltech.edu/records/32tag-pz022Interactions in Polar Media. II. Continua
https://resolver.caltech.edu/CaltechAUTHORS:20120829-105204970
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1963
DOI: 10.1063/1.1734270
It is shown that the electronically polarizable continuum model of a particle satisfies the equations of part I, after suitable choice of operator A_i appearing there. The proof is given for the case where the system is regarded as composed of particles and treated statistically mechanically. It is also given for the case where several particles receive special attention and the remainder of the system (the "medium") is treated as an orientationally and electronically polarizable continuum. For the second case it was necessary to extend the results of Part I, so as to include several particles in the presence of the above "medium" and to compute the free energy of such systems. Calculations are given for media possessing equilibrium and nonequilibrium dielectric polarization.
It follows from the foregoing proofs that a wide variety of models assumed in the literature for treating polar interactions are special cases of the model in Part I and of the extension to particle‐medium systems in this paper. Electrode systems, for example, are included, even when the electrode is treated in the usual dielectric continuum manner. The relation and relative merits of the two models for the induced charge distribution that are standard in the literature, both special cases of Part I, are discussed. These models are the induced dipole and the electronically polarizable continuum. Possible direct experimental investigation of the second of these by scattering experiments is examined.https://authors.library.caltech.edu/records/zh824-mrq67Photochemical Studies in Flash Photolysis. III. Photolysis of Acetone in Different Wavelength Regions
https://resolver.caltech.edu/CaltechAUTHORS:20120829-143226417
Authors: {'items': [{'id': 'Shilman-A', 'name': {'family': 'Shilman', 'given': 'A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1963
DOI: 10.1063/1.1734403
The flash photolysis of acetone was studied at wavelength regions centered around 260, 280, and 300 mμ, using absorbed intensities of the order of 10^(19) quanta/cc/sec for each wavelength region. The light source was an exploding wire, and the maximum temperature increase per flash was calculated to be not more than 5°C. The products, analyzed by gas chromatography using a sensitive electric discharge detector, consisted of C_2H_6, CO, biacetyl, and, in smaller amounts, CH_4. A search was made for other products as well, and detection limits are given.
The C_2H_6/CO ratio decreased with increasing acetone pressure at all wavelength regions and was independent of light intensity in the range investigated. The R_(CO)/p_(acet) ratio, measured over a wide pressure range, was pressure‐independent at 260 and 300 mμ but increased appreciably with pressure at 280 mμ. At low pressures, where the C_2H_6/CO ratio approached a limiting value, the ratio decreased with wavelength according to the order 280>260>300 mμ.
The lifetime of the excited acetone molecules at the respective wavelengths was estimated, from a steady‐state treatment, to be 0.6×10^(—9), 1×10^(—9), and 4×10^(—9) sec at 260, 280, and 300 mμ, assuming a collision deactivation efficiency of unity. At 300 mμ there was a marked difference in value of C_2H_6/CO at flash and low intensities: certain second‐order reactions involving excited states appear to occur completely at the relatively high concentrations prevailing under flash conditions. The transition region of intensity effects is described in subsequent papers of this series.https://authors.library.caltech.edu/records/6tdsh-3gj72Free Energy of Non equilibrium Polarization Systems. III. Statistical Mechanics of Homogeneous and Electrode Systems
https://resolver.caltech.edu/CaltechAUTHORS:20120829-105437675
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1963
DOI: 10.1063/1.1734522
A statistical mechanical treatment is given for homogeneous and electrochemical systems having nonequilibrium dielectric polarization. A relation between the free energy of these systems and those of related equilibrium ones is deduced, having first been derived in Part II by a dielectric continuum treatment. The results can be applied to calculating polar contributions in the theory of electron transfers and in that of shifts of electronic spectra in condensed media. The effect of differences in polarizability (of a light emitting or absorbing molecule in its initial and final electronic states) on the polar term in the shift is included by a detailed statistical analysis, thereby extending Part II. Throughout, the "particle" description of the entities contributing to these phenomena is employed, so as to derive the results for rather general potential energy functions.https://authors.library.caltech.edu/records/zf9wg-phy02Separation of Sets of Variables in Quantum Mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20120829-110758360
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1964
DOI: 10.1063/1.1725934
Separation of the Schrödinger equation for molecular dynamics into sets of variables can sometimes be performed when separation into individual variables is neither possible nor for certain purposes necesary. Sufficient conditions for such a separation are derived. They are the same as those found by Stäckel for the corresponding Hamilton—Jacobi problem, with an additional one which is the analog of the Robertson condition for one‐dimensional sets. Expressions are also derived for operators whose eigenvalues are the separation constants. They provide a variational property for these constants. For use in aperiodic problems an expression is obtained for the probability current in curvilinear coordinates in an invariant form. Application of these results to reaction rate theory is made elsewhere.https://authors.library.caltech.edu/records/ghj94-9fc51Local Approximation of Potential‐Energy Surfaces by Surfaces Permitting Separation of Variables
https://resolver.caltech.edu/CaltechAUTHORS:20120827-154914666
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1964
DOI: 10.1063/1.1725935
In the immediate vicinity of a potential‐energy minimum or of a saddle point, it is shown that major topographical features of a "nonseparable" potential‐energy surface can be imitated by those of a surface permitting separation of variables. For each extremal path of descent or ascent to the cited critical point of the surface, there is an exact match of the tangent, the first curvature vector in configuration space, and the force constant along that path provided that the known curvature vector satisfies an equation containing the metric tensor of the selected coordinate system and known force constants. Because of the wide choice of coordinate systems available for selection, it is anticipated that this relation may be fulfilled for each extremal path, partly by choice of the coordinate system and partly by subsequent choice of the curvilinear coordinates of the critical point. There are several possible applications of this local approximation, including those to problems involving anharmonic coupling of normal modes and those involving n‐dimensional tunneling and other calculations in reaction‐rate theory. Use will be made of the formalism to extend the activated complex theory in chemical kinetics. As a preliminary test of the local‐approximation concept, literature data on n‐ and one‐dimensional tunneling rates are compared. They are found to be fairly similar when proper cognizance is taken of zero‐point energies.https://authors.library.caltech.edu/records/rrpaz-qt708Chemical and Electrochemical Electron-Transfer Theory
https://resolver.caltech.edu/CaltechAUTHORS:20131211-091846715
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1964
DOI: 10.1146/annurev.pc.15.100164.001103
One of the active areas in reaction kinetics during the post-war years has
been that of electron-transfer reactions. These reactions constitute one type
of oxidation-reduction process and include both chemical and electrochemical
systems. Many rate constants have now been measured (1-8) and
they have stimulated a variety of theoretical studies (9-37). The field has
been characterized by a strong interplay of theory and experiment, which
now includes the testing of theoretically predicted quantitative correlations
(34). Because of a certain unique feature of the purely electron-transfer
reactions--the absence of bond rupture in the reaction step--these correlations
are unusual. They do not have the arbitrary parameters that occur
in theoretical studies of most other reactions in chemical kinetics. This review
will be limited to purely electron transfer reactions.https://authors.library.caltech.edu/records/sdc43-te159Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment
https://resolver.caltech.edu/CaltechAUTHORS:20120827-131805519
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1964
DOI: 10.1063/1.1726330
In its usual classical form, activated‐complex theory assumes a particular expression for the kinetic energy of the reacting system, one being associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic‐energy expression. A rate equation of the customary form is obtained: k_rate = (kT/h)exp[−(F‡−F^r)/kT], where F‡ is the free energy of a system constrained to exist on a hypersurface in n‐dimensional space and Fr is the free energy of the reactants. The usual derivation is then reinterpreted, in terms of geodesic normal coordinates, to be somewhat more general than it appears.
Normally, rotation—vibration interaction is neglected, as in the above derivation, although not in treatments of some special reactions in the literature for which the centrifugal potential is important. A derivation is given which includes the influence of this centrifugal potential but which omits Coriolis effects.https://authors.library.caltech.edu/records/173qa-9vb58Generalization of the Activated Complex Theory of Reaction Rates. I. Quantum Mechanical Treatment
https://resolver.caltech.edu/CaltechAUTHORS:20120829-112000188
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1964
DOI: 10.1063/1.1726329
In its usual form activated complex theory assumes a quasiequilibrium between reactants and activated complex, a separable reaction coordinate, a Cartesian reaction coordinate, and an absence of interaction of rotation with internal motion in the complex. In the present paper a rate expression is derived without introducing the Cartesian assumption. The expression bears a formal resemblance to the usual one and reduces to it when the added assumptions of the latter are introduced. The new equation for the transmission coefficient contains internal centrifugal terms. The fourth assumption can also be weakened and a rotational interaction included in the formalism. In applications of the rate equation use can be made of the recent finding that in the immediate vicinity of a saddle point or a minimum, a potential energy surface can be imitated in some major topographical respects by a surface permitting separation of variables. The separated wave equation for the reaction coordinate is then curvilinear because of the usual curvature of the path of steepest ascent to the saddle point. Calculations of transmission coefficients and rates can be made and compared with those obtainable from the usual one‐dimensional Cartesian‐like calculations on the one hand and with some based on the numerical integration of the n‐dimensional Schrödinger equation on the other. An application to a common three‐center problem is discussed.https://authors.library.caltech.edu/records/0qg50-q1y26Ion-Ion and Ion-Neutral Interactions in Solution and Measurements of Dielectric Constants
https://resolver.caltech.edu/CaltechAUTHORS:20120829-113816153
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1965
DOI: 10.1063/1.1696486
Data on dielectric constants of electrolyte solutions are used to evaluate directly the r^(−4) term in the asymptotic expression for the free energy of interaction of two ions in solution for large separation distance r. Use is made of the fact that for large separations each ion is in a uniform field due to the other, and that information about ions in uniform fields is obtainable from measurements of dielectric constants. For a Z:Z electrolyte, for example, the r^(−4) term is found to be Z^2e^2δ/8πϵ_0r^4, assuming the effect of overlapping solvent structures to be of shorter range; ϵ_0 is the dielectric constant of the solvent and δ is the measured decrement in dielectric constant per unit concentration of added electrolyte. A similar result obtained when one of the particles is uncharged, δ now referring to the decrement observed when the neutral is added to solution. Typical values of the term are given for various substances using the data on δ's. This determination of the r^(−4) term permits some evaluation of ion—image force theories.https://authors.library.caltech.edu/records/55zkr-wnh28On the Theory of Electron-Transfer Reactions. VI. Unified Treatment for Homogeneous and Electrode Reactions
https://resolver.caltech.edu/CaltechAUTHORS:20120829-113949714
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1965
DOI: 10.1063/1.1696792
A unified theory of homogeneous and electrochemical electron‐transfer rates is developed using statistical mechanics. The treatment is a generalization of earlier papers of this series and is concerned with seeking a fairly broad basis for the quantitative correlations among chemical and electrochemical rate constants predicted in these earlier papers. The atomic motions inside the inner coordination shell of each reactant are treated as vibrations. The motions outside are treated by the "particle description," which emphasizes the functional dependence of potential energy and free energy on molecular properties and which avoids, thereby, some unnecessary assumptions about the molecular interactions.https://authors.library.caltech.edu/records/4b08d-m6a24On the Theory of Shifts and Broadening of Electronic Spectra of Polar Solutes in Polar Media
https://resolver.caltech.edu/CaltechAUTHORS:20120829-115335864
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1965
DOI: 10.1063/1.1696913
When a polar‐solute molecule undergoes an electronic transition and forms a state of different polarity, the Franck—Condon principle shows that the new system is first formed in a nonequilibrium thermodynamic state. An expression for the spectral shift and broadening by a series of solvents of differing polarity is derived in the present paper in terms of thermodynamic properties of certain equilibrium distribution systems. For this purpose use is made of a recent particle description of nonequilibrium and equilibrium polar media, which emphasizes functional dependence and avoids, thereby, the usual more specific assumptions. A relation between the broadening and the shift is then deduced under certain conditions. Expressions are also derived for the effect of pressure and temperature on the shift, in terms of the polar contribution to the volume and entropy of solvation, respectively, and for the influence of applied electrical fields. An expression is obtained for the solvent‐reversal shift of Brooker in terms of the polarizability difference of the initial and final states of the solute. Introduction of more specific assumptions is then made for purposes of comparison with earlier works, which constitute special cases of the present one, and for estimation of dipole moments and polarizabilities of excited states from spectral and electrical shifts.https://authors.library.caltech.edu/records/nt4t7-td936Generalization of Activated-Complex Theory. III. Vibrational Adiabaticity, Separation of Variables, and a Connection with Analytical Mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20120829-134411768
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1965
DOI: 10.1063/1.1696977
In Part I, activated‐complex theory was extended by including the possibility of a curvilinear reaction coordinate. A separation‐of‐variables approximation was made in the neighborhood of the activated‐complex region of configuration space. In the present paper a more general yet simpler derivation of the final equation is given. It permits subsequent introduction of analytical mechanics in the above neighborhood in a variety of ways such as separation of variables, vibrational adiabaticity, or a method combining certain features of both, the separable—adiabatic approximation. The relationship of these methods is discussed.
Some numerical quantum‐ and classical‐mechanical results obtained for transmission coefficients of nonrotating atom‐transfer reactions (linear complexes), using computers, are interpreted in terms of an adiabatic approximation with reasonable agreement. Attention is also called to a modified WBK expression for the transmission coefficient, which generalizes the usual WBK formula in a simple way.https://authors.library.caltech.edu/records/5rsh2-ezr89On the Theory of Chemiluminescent Electron-Transfer Reactions
https://resolver.caltech.edu/CaltechAUTHORS:20120829-135513417
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1965
DOI: 10.1063/1.1697190
A mechanism is described for chemiluminescent electron‐transfer reactions. It is shown that in the case of very exothermic homogeneous electron‐transfer reactions, the intersection of the potential‐energy surface of the reactants with that of electronically unexcited products occurs only at high energies. The rate of formation of unexcited products then becomes slow. A numerical estimate of this slowness is made using known homogeneous rate constants for ordinary electron‐exchange reactions. An intersection occurs at lower energies when one of the products of a highly exothermic electron transfer is electronically excited, thereby reducing the exothermicity. The product may emit light or subsequently form a state that does.
A rather different situation is shown to occur at electrodes: the system can now reduce the "exothermicity" by having the electron transfer into a high unoccupied level of the conduction band or from a low occupied level of the latter. The large width of the conduction band in metals permits much latitude in reducing the exothermicity thereby.
These results are compared with present experimental findings that chemiluminescent electron transfers occur in solution rather than on electrode surfaces.https://authors.library.caltech.edu/records/4wt79-2xr32Dissociation and Isomerization of Vibrationally Excited Species. III
https://resolver.caltech.edu/CaltechAUTHORS:20120827-131950075
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1965
DOI: 10.1063/1.1697191
The equations of Part I for the specific and over‐all unimolecular reaction‐rate constants are extended slightly by including centrifugal effects in a more detailed way and by making explicit allowance for possible reaction‐path degeneracy (optically or geometrically isomeric paths). The expression for reaction‐path degeneracy can be applied to other types of reactions in discussions of statistical factors in reaction rates.https://authors.library.caltech.edu/records/kva5n-r4122Additivity of Heats of Combustion, LCAO Resonance Energies, and Bond Orders of Conformal Sets of Conjugated Compounds
https://resolver.caltech.edu/CaltechAUTHORS:20120827-132206413
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1965
DOI: 10.1063/1.1697189
The notion of "conformal sets" of aromatic and other conjugated compounds is introduced. To a good approximation, it is found that the sum of the heats of combustion of the compounds in one set equals the sum for the compounds in the other set. Similar additivity occurs for their LCAO‐calculated total π‐electron energies, LCAO bond orders and free valences. Bond lengths and dissociation energies are also considered. Conformal sets are defined in terms of their number and quality of self‐returning random walks on the atoms of the conjugated compounds. Even‐electron nonalternant and alternant compounds are included, as are, in certain cases, radicals. Some insight into the additivity for LCAO properties is obtained by relating the coefficients in LCAO secular equations to random walks and using contour integral formulas connecting LCAO properties with secular determinantshttps://authors.library.caltech.edu/records/tyvgw-q7697Theory of Electron-Transfer Reaction Rates of Solvated Electrons
https://resolver.caltech.edu/CaltechAUTHORS:20120829-112527649
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1965
DOI: 10.1063/1.1696504
A theory of electron‐transfer reactions of solvated electrons is described. Using an electron‐transfer theory formulated elsewhere and using polaron theory the rate constant is related to the standard reduction potentials of the two reactants, spectral and other data for the solvated electron, and rate data on ordinary chemical or electrochemical electron‐transfer reactions of the second reactant. This calculated rate constant appears in a boundary condition in a diffusion‐reaction differential equation. When that constant is high the reaction becomes diffusion controlled, but when the constant is low it becomes the observed rate constant itself. Some comparison is made with existing data. Conditions for possible but as yet unobserved chemiluminescence are also considered. Solvent‐electron polarization in the vicinity of a solvated electron is also examined, by application of polaron theory for a high lattice frequency continuum.https://authors.library.caltech.edu/records/k8kc5-cym67Chemical‐Reaction Cross Sections, Quasiequilibrium, and Generalized Activated Complexes
https://resolver.caltech.edu/CaltechAUTHORS:20120827-131500257
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1966
DOI: 10.1063/1.1727899
A quasiequilibrium expression is given relating sums over reaction cross sections to properties of activated complexes. When applied to recent classical‐mechanical computer data on the H+H_2 reaction to test the quasiequilibrium assumption, reasonable agreement is found over the range considered. Suggestions are made with respect to extending the range and to presenting the computer data in a modified form. The latter would permit testing a stronger statement of the hypothesis. The equations are used elsewhere to formulate a statistical‐dynamical theory for chemical‐reaction cross sections.https://authors.library.caltech.edu/records/tv8nn-0gr98On the Theory of Chemical-Reaction Cross Sections. I. A Statistical-Dynamical Model
https://resolver.caltech.edu/CaltechAUTHORS:20120829-145327891
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1966
DOI: 10.1063/1.1727983
A statistical‐dynamical model is formulated for total chemical‐reaction cross sections as a function of the relative velocity and the vibrational and the rotational state of the reactants. It is derived for reactions for which activated‐complex configurations can be defined; reactions with or without steric and activation barriers. A quasiequilibrium is postulated between reacting pairs and activated complexes of the same energy and angular momentum. An integral equation is obtained which is solved for the reaction cross section by introduction of a second postulate: The reaction probability is a function of the excess initial energy along the reaction coordinate (in excess of potential energy barrier, centrifugal potential barrier, and vibrational adiabatic requirements). A possible dynamical origin of the postulates is considered in later papers.https://authors.library.caltech.edu/records/jk25h-g8f29On the Analytical Mechanics of Chemical Reactions. Quantum Mechanics of Linear Collisions
https://resolver.caltech.edu/CaltechAUTHORS:20120829-145531942
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1966
DOI: 10.1063/1.1727528
The analytical quantum mechanics of chemically reactive linear collisions is treated in the vibrationally near‐adiabatic approximation. The "reaction coordinate" in this approximation is found to be the curve on which the classical local vibrational and internal centrifugal forces balance. Expressions are obtained for the calculation of transmission coefficients for these nonseparable systems. Some implications for tunneling calculations in the literature are noted. Expressions for nonadiabatic corrections are derived, the latter being associated with vibrational transitions undergone by the transmitted and reflected waves. When the system does not have enough energy to react, the last results refer to the vibration—translation energy‐transfer problem in linear collisions.
Two novel features are the introduction of an actual coordinate system which passes smoothly from one suited to reactants to one suited to products and the introduction of an adiabatic‐separable method, a method which includes curvilinear effects. Extensions to collisions in higher dimensions are given in later papers.https://authors.library.caltech.edu/records/snq85-fpa65On the Analytical Mechanics of Chemical Reactions. Classical Mechanics of Linear Collisions
https://resolver.caltech.edu/CaltechAUTHORS:20120829-110842187
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1966
DOI: 10.1063/1.1727529
The classical mechanics of chemically reactive linear collisions is investigated for vibrationally near‐adiabatic reactions. A coordinate system which passes smoothly from one suited to the reactants to one suited to the products is used. The Hamilton—Jacobi equation is then solved in the adiabatic approximation by introduction of an "adiabatic‐separable" method. Nonadiabatic corrections, which describe the probability of vibrational transitions, are also calculated. They involve the Fourier component of local internal centrifugal and vibration frequency‐change terms. The reaction coordinate for the adiabatic system is shown to be that curve on which local vibrational and internal centrifugal forces balance pointwise. Applications can be made to the role of translational—vibrational energy interchange in reactions, reaction‐cross‐section theory, bobsled effect, and other topics. The results may be compared with electronic computer calculations as they become available.https://authors.library.caltech.edu/records/bjkvb-dhc74Analytical mechanics and almost vibrationally-adiabatic chemical reactions
https://resolver.caltech.edu/CaltechAUTHORS:20150813-154622095
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1967
DOI: 10.1039/DF9674400007
Co-ordinates and "vibrationally-adiabatic" approximations are described for reactions in three dimensions. Some reactions may demonstrate a fairly strict adiabaticity for certain degrees of freedom and a statistical adiabaticity for others. Some will simply be strongly vibrationally-nonadiabatic. Several topics in kinetics are considered from the viewpoint of vibrational-adiabaticity or mild non-adiabaticityhttps://authors.library.caltech.edu/records/8e315-mdf48On the Theory of Chemical-Reaction Cross Sections. II. Application to the H + H_2 Reaction
https://resolver.caltech.edu/CaltechAUTHORS:20120827-160539777
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1967
DOI: 10.1063/1.1840833
The statistical—dynamical model formulated in Paper I is applied to the H+H_(2)→H_(2)+H reaction and compared with the exact three‐dimensional classical‐mechanical computer calculations of reaction cross sections. Encouraging agreement is obtained in the low‐to‐moderate relative velocity range, without the use of adjustable parameters. At very high velocities the comparison indicates the occurrence of some vibrational nonadiabaticity. Calculations are presently in progress to see if this nonadiabaticity equals that expected from a companion paper on analytical mechanics of certain collisions. Applications are also made to several topics: relations between classical and quantum computer calculations of cross sections, between activation energy and the recently reported threshold energy of reaction (D+H_(2)_→DH+H), and tests of activated‐complex theory.https://authors.library.caltech.edu/records/8c489-3cm73Electrode reactions of organic compounds. General introduction
https://resolver.caltech.edu/CaltechAUTHORS:20150817-124649604
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1039/DF9684500007
The last Faraday Society Discussions on Electrode Processes were held in 1947 and marked the onset of an extensive fruitful post-war development of fast reaction techniques in electrochemistry. Considerable information has since been obtained on rate constants of simple inorganic electron transfers, paralleling a similar development in homogeneous reactions, and on electron transfer theory. A theoretically-based relation exists between the two areas.
It has often been noted that the Faraday Society Discussions have marked a turning point in a field. The area of organic reactions at electrodes has been somewhat on the periphery of the field of organic chemistry, its relation to the subject of metal-catalyzed organic syntheses notwithstanding. The papers of the present Discussions illustrate, perhaps for the first time as a body, the rich variety of studies in the present field and a role for current organic concepts.https://authors.library.caltech.edu/records/96914-n0n80Kinetics of ferrocyanide reduction of quinones
https://resolver.caltech.edu/CaltechAUTHORS:20150812-165217873
Authors: {'items': [{'id': 'Levison-S-A', 'name': {'family': 'Levison', 'given': 'S. A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1021/j100847a071
We describe here the kinetics of ferrocyanide reduction of 2,5-dichloro-, benzo-, and 2,5-dimethylquinones (denoted below by I, II, III) in 1 M KCl. Reagent materials were used where available and the hydroquinones of I and III were synthesized by SnCl_2 reduction and recrystallization. Slightly alcoholic solutions of quinone in 1 M KCl were deoxygenated, placed in blackened vessels at 27°, and then in a 10-cm path Beckman cell. Buffered 1 M KCl ferrocyanide at 27° was added and the rate was measured from ferrocyanide disappearance at 420 mµ or disappearance of I at 275 mµ, using a Beckman.https://authors.library.caltech.edu/records/qzr6j-3ts07Theoretical relations among rate constants, barriers, and Brønsted slopes of chemical reactions
https://resolver.caltech.edu/CaltechAUTHORS:20150814-143930437
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1021/j100849a019
A simple relation, ΔF* = (λ(1 + Δ/λ)^2)/4, derived originally for weak-overlap electron transfers, is explored in a slightly modified version for reactions with considerable resonance splitting, such as atom transfers, proton transfers, and strong-overlap electron transfers. A useful additivity property, λ_(12) = ((λ_(11) + λ_(22))/2, permits barriers ΔF* for cross-reactions to be computed from those of exchange reactions, λ_(ii)/4. Some 45 barriers, calculated from some ten others, agreed with BEBO results, within a few kilocalories per mole. The agreement is analyzed and more general models for which it might occur are considered. A functional relationship between barrier and a degree-of-reaction parameter is devised to avoid commitment to too specific a model. An example where breakdown should occur is also given. Experimental data, as well as quantum mechanical calculations of barriers, will permit further tests. Corollaries of the relation include: (1) a classification of reaction barriers in terms of intrinsic (λ_(ii)) and extrinsic (ΔF^0') contributions, (2) a rate-constant relation k_(12) ≃ (k_(11)k_(22)K_(12)f_(12))^(1/2) and modifications thereof, (3) a calculation of the local Brønsted slope α from the intercept of the ΔF* vs. ΔF^0' plot, α = (1 + Δ/λ)/2, (4) a relation between k_H/k_D vs. ΔF^0' plots and local α's, and ( 5 ) other relations among rate constants. Throughout, ΔF* and ΔF^0' refer to an elementary step.https://authors.library.caltech.edu/records/xnks4-y0h56Electron transfer at electrodes and in solution: Comparison of theory and experiment
https://resolver.caltech.edu/CaltechAUTHORS:20150812-155404718
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1016/0013-4686(68)80031-3
Detailed quantitative information about different theoretical aspects of electron-transfer rates in solution and at electrodes can be obtained from appropriate experiments. Recent theoretical work has predicted certain quantitative correlations between rates of crossed-redox reactions and rates of isotopic exchange, and between homogeneous and electrochemical rates. Experimental tests of these predictions yield insight into "intrinsic" and "driving force" factors.
The intrinsic factor is related to differences in properties of oxidized and reduced species (eg, differences in corresponding bond lengths and differences in solvent orientation polarization). The driving force term is related to the standard free energy of reaction in the homogeneous reaction and to the activation overpotential in the electrode reaction.
Measurements of temperature coefficients of rates in dilute solution provide some information about adiabatic and dielectric-saturation effects. Absolute rates, in conjunction with knowledge of bond-length differences and bond-force constants, provide some insight into the over-all picture, (instrinsic, adiabatic, unsaturation factors etc). Study of the cited quantitative correlations permits the cancellation of many effects, and so can reveal others.
The present state of experimental information on these theoretical topics is described.https://authors.library.caltech.edu/records/mzxz3-82w66Recent developments in theoretical chemical kinetics
https://resolver.caltech.edu/CaltechAUTHORS:20150817-095902384
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1021/ed045p356
In the post-war years there have been a variety of new experiments in kinetics, and these have stimulated new theoretical developments. In the present brief article I have listed some of these experiments, and considered some selected topics and new questions in theoretical kinetics.https://authors.library.caltech.edu/records/s5d1v-13m78Analytical Mechanics of Chemical Reactions. IV. Classical Mechanics of Reactions in Two Dimensions
https://resolver.caltech.edu/CaltechAUTHORS:20120829-145721907
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1063/1.1670461
The natural collision coordinates of Part III are used to treat the analytical mechanics of chemical reactions, AB + C→A + BC. Other than in Part II, the classical analytical mechanics of chemical reactions on a smooth potential surface have not been explored previously in the literature. A Hamilton–Jacobi formalism is used, apparently for the first time in calculating a reaction rate. The "vibrationally adiabatic" reaction serves as the zeroth‐order approximation and nonadiabatic corrections are obtained. Theoretical expressions yield the rotational and vibrational energy distribution of reaction products, angular distribution, and reaction probability, as a function of impact parameter, initial translational velocity of relative motion, and initial rotational–vibrational state of reactants. The results are not intended to apply to reactions which show very large excursions from vibrational adiabaticity. In the zeroth approximation (vibrational adiabaticity), an adiabatic separation of variables is achieved. Here, the vibrational action is constant; however, the rotational–orbital action changes by a known increment from one constant value to another, on transition of that motion into a bending vibration. The resulting "adiabatic" correlation shows several interesting features. For reactions in which there are no large mass ratios, the state of vibration of AB, of rotation of AB, and of orbital motion of AB + C correlate with the state of vibration of BC, of rotation of BC, and of orbital motion of A + BC, respectively. For reactions with unusual mass ratios, such as H + Cl_(2)→HCl + Cl, the correlation equations show instead the "adiabatic" transformation of Cl_2 rotation into HCl + Cl orbital motion, thereby reflecting the expected result of angular momentum conservation. Had the rotational–orbital cross term in the kinetic energy been neglected, an incorrect correlation would have resulted in the latter case. Extension of the present work to three dimensions involves an added approximation, to be given in a subsequent paper. The expressions and method also permit comparison of one‐ and two‐dimensional computer results on a more similar basis and, because of certain similarities in computer results for energy distributions in two and three dimensions, perhaps comparison with experimental results on energy distributions. In conjunction with the computer results information can be obtained on various approximations, such as near adiabaticity. The present theory can also be used to analyze and perhaps extend various statistical‐type theories in the literature.https://authors.library.caltech.edu/records/2vj3j-91940Analytical Mechanics of Chemical Reactions. III. Natural Collision Coordinates
https://resolver.caltech.edu/CaltechAUTHORS:20120828-155547899
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1063/1.1670460
The coordinates of earlier papers of this series are extended from linear collisions to reactions in three dimensions. Termed "natural collision coordinates," they have a unique property of passing smoothly from those suited to reactants to those suited to products. Potential applications to bimolecular reactions are described.https://authors.library.caltech.edu/records/grx2z-w2q18On the slope of free energy plots in chemical kinetics
https://resolver.caltech.edu/CaltechAUTHORS:20150817-152550488
Authors: {'items': [{'id': 'Cohen-A-O', 'name': {'family': 'Cohen', 'given': 'Audrey O.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1021/j100858a052
In current electron-transfer theory, an activation free energy term, ΔF*, depends in a simple way on the "standard" free energy of reaction, ΔF^0', in the prevailing medium. Namely, ΔF* = (1/4)λ[1 + (ΔF^0'/λ)]^2, apart from small work terms; λ/4 is ΔF_0*, the value of ΔF* at (ΔF^0' = 0; and λ obeys a simple additivity property. As an exploratory step an equation of the same functional form is applied in the present paper to data on Brønsted slopes of 16 proton- and atom-transfer reaction series. Thereby, the instantaneous slope of a ΔF* vs. ΔF^0' plot is calculated to be (1/2)[1 + (ΔF^0'/4 ΔF_0*)]. Thus far the experimental results are consistent with this equation, but more data are needed. Other applications of the ΔF* equation, including one to the kinetic isotope effect, are also discussed. A rather approximate derivation of the above equation for atom and other transfers was given in an earlier paper of this series.https://authors.library.caltech.edu/records/adpqk-tcp81Classical Mechanics of Rotational–Translational and Other Energy Transfer. I. A Hamilton–Jacobi (Action-Angle) Treatment
https://resolver.caltech.edu/CaltechAUTHORS:COHjcp68
Authors: {'items': [{'id': 'Cohen-A-O', 'name': {'family': 'Cohen', 'given': 'Audrey O.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1968
DOI: 10.1063/1.1669904
The classical-mechanical equations of motion describing collisional energy transfer are converted to a form involving constants of the elastic collision, using a Hamilton–Jacobi formalism. These constants frequently vary only slowly during an inelastic collision. An approximate version of the transformed equations, related to a variation of constants procedure, is next introduced. The collision of an atom with a rigid linear diatomic molecule is considered in some detail. Several desirable features of the approximation are that the change in rotational angular momentum is obtained directly, all initial orientations of particles and angular momenta occur outside the integrals, an approximate error estimate can be made, results can be calculated relatively quickly, and further insight is obtained into the energy-transfer process. Because of the close relationship of Hamilton–Jacobi and Schrödinger formalisms, a comparison of exact and approximate classical results is also expected to provide estimates of range of validity of some commonly used approximations in the quantum case.https://authors.library.caltech.edu/records/t5sc5-k8x30Rapid Gas-Phase Reactions. Amines and Boron Trifluoride. II. Pressure Dependence of Rate Constant
https://resolver.caltech.edu/CaltechAUTHORS:20150810-161259699
Authors: {'items': [{'id': 'Glicker-S', 'name': {'family': 'Glicker', 'given': 'Sol'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1969
DOI: 10.1021/ja50001a013
Relative rate constants for reaction of monomethylamine and trimethylamine with boron trifluoride are reported for the pressure range 0.04-600 Torr. The limiting ratio at low pressure is about 0.836, and the extrapolated high-pressure ratio is of the order 4. The half-pressure for quasi-bimolecular behavior of the monomethylamine-boron trifluoride system is in the vicinity of 70 Torr. When the data are combined with those of Kistiakowsky, et al., individual pressure-dependent rate constants can be estimated. The amine-BF_3 series has loose activated complexes and low energy for redistribution among internal modes, making it an unusual candidate for theoretical unimolecular study.https://authors.library.caltech.edu/records/4t05f-1dj16Unusual slopes of free energy plots in kinetics
https://resolver.caltech.edu/CaltechAUTHORS:20150817-154034498
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1969
DOI: 10.1021/ja01054a003
Theoretical equations are used to comment on the relation between the slope of activation free energy-standard free energy of reaction plots and the concept of the position of the transition state along the reaction coordinate. The equations are then used to consider some recent experimental findings of unusual Brønsted coefficients.https://authors.library.caltech.edu/records/wew6q-35t88Vibrational–Translational Energy Transfer in the Near-Adiabatic Approximation
https://resolver.caltech.edu/CaltechAUTHORS:ATTjcp70
Authors: {'items': [{'id': 'Attermeyer-M', 'name': {'family': 'Attermeyer', 'given': 'Mary'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1970
DOI: 10.1063/1.1672698
Vibrational–translational energy transfer is examined in the near-adiabatic (or perturbed stationary states) approximation. The results are classical, and the method used is related to that of Marcus [J. Chem. Phys. 49, 2617 (1968)]. The results are compared with those of the more usual ("static") approximation and with the exact results. The PSS results were good at low energies at all mass ratios studied, unlike the static results. For certain mass ratios the static approximation fails badly, even at very low transition probabilities. For other mass ratios, the results are of comparable accuracy except at high energies where the static one is somewhat better. Reasons for the above behavior are discussed, and implications regarding existing infinite-order distorted wave and semiclassical calculations are noted. The relation to a recent correction of the Jackson–Mott calculation is described.https://authors.library.caltech.edu/records/yvv32-46317Rotational–Translational Energy Transfer. II. Comparison of Action-Angle Solution in the Near-Static Approximation with Exact Results
https://resolver.caltech.edu/CaltechAUTHORS:COHjcp70
Authors: {'items': [{'id': 'Cohen-A-O', 'name': {'family': 'Cohen', 'given': 'Audrey O.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1970
DOI: 10.1063/1.1673450
In Part I, the differential equations for molecular rotational–vibrational–translational energy transfer were re-expressed in terms of action-angle variables. In the present paper, approximate integral solutions and exact results for rotational–translational transfer are compared for a wide range of collisional and molecular parameters at small fractional changes in translational energy. The results are in good agreement over the range investigated except at low moments of inertia. Thereby, conditions where the present approximation is best correspond to some which are least accessible by approximate or numerical quantum mechanical methods. The present approximation employs for zeroth order a classical analog of the static approximation in quantum mechanics, rather than the adiabatic approximation, and the results have implications for the ranges of molecular parameters where each should be preferable in the quantum case.https://authors.library.caltech.edu/records/5c9n9-yv030High‐Order Time‐Dependent Perturbation Theory for Classical Mechanics and for Other Systems of First‐Order Ordinary Differential Equations
https://resolver.caltech.edu/CaltechAUTHORS:20120802-085756570
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1970
DOI: 10.1063/1.1673715
A time‐dependent perturbation solution is derived for a system of first‐order nonlinear or linear ordinary differential equations. By means of an ansatz, justified a posteriori, the latter equations can be converted to an operator equation which is solvable by several methods. The solution is subsequently specialized to the case of classical mechanics. For the particular case of autonomous equations the solution reduces to a well‐known one in the literature. However, when collision phenomena are treated and described in a classical "interaction representation" the differential equations are typically nonautonomous, and the more general solution is required. The perturbation expression is related to a quantum mechanical one and will be applied subsequently to semiclassical and classical treatments of collisions.https://authors.library.caltech.edu/records/9atr9-egk22Relation between State‐Selected or State‐Averaged Cross Sections of Endothermic Reactions and Rate Constants of Exothermic Reactions. Application of Bimolecular Microcanonical Activated Complex Theory
https://resolver.caltech.edu/CaltechAUTHORS:20120802-133824399
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1970
DOI: 10.1063/1.1674034
An expression is derived relating state‐selected or state‐averaged molecular beam reaction cross sections of endothermic reactions to observed rate constants for the inverse (exothermic) reactions. An approximation of Anlauf, Maylotte, Polanyi, and Bernstein is used, together with bimolecular microcanonical activated complex theory [R. A. Marcus, J. Chem. Phys. 45, 2138 (1966)].https://authors.library.caltech.edu/records/3wh5k-9q908Fourth Picture in Quantum Mechanics
https://resolver.caltech.edu/CaltechAUTHORS:20120808-095251007
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1970
DOI: 10.1063/1.1674179
A quantum‐mechanical counterpart to the classical mechanical variation of constants method is derived, with initial values of coordinates and momenta as "constants." Use is made of a formal operator solution for nonautonomous or autonomous systems in classical mechanics, which we published earlier, and of the correspondence between Poisson brackets and commutators. An alternative unified Lie‐algebraic derivation is also given. It is shown that the Schrödinger, Heisenberg, and interaction pictures in quantum mechanics do not correspond directly to the method of classical mechanical variation of these "constants." A fourth picture, termed "mixed interaction," is introduced and shown to so correspond. It complements the previous three in a symmetrical manner, bearing the same relation to the Heisenberg picture that the Schrödinger picture bears to the interaction one. The group‐theoretic relationship to the interaction picture is noted, as is the relation to the usual variation‐of‐constants method in wave mechanics. For completeness, the classical counterparts of the Heisenberg and interaction pictures are also given. The present results arose from a comparison of quantum and classical treatments of collisions.https://authors.library.caltech.edu/records/krze0-q9r23Theory of Reactive Collisions: Conformal Transformation
https://resolver.caltech.edu/CaltechAUTHORS:CONjcp70
Authors: {'items': [{'id': 'Connor-J-N-L', 'name': {'family': 'Connor', 'given': 'J. N. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1970
DOI: 10.1063/1.1674468
Conformal mapping techniques are applied to the Schrödinger equation for a bimolecular exchange reaction, with all three atoms lying on a line. For the case of a very heavy central mass, the extension of the theory to three dimensions is indicated. An angle-shaped region of the potential-energy surface is mapped onto an infinite strip in order to simplify the theoretical treatment of the boundary conditions. The mapping function is determined with the help of the Schwarz–Christoffel formula, and its properties described. The transformed Schrödinger equation is converted into an integral equation using the method of Green's functions, and integral representations for the reflection and transmission coefficients are obtained.https://authors.library.caltech.edu/records/fy0zf-30c69Analytical Mechanics of Chemical Reactions. V. Application to the Linear Reactive H +H_2 Systems
https://resolver.caltech.edu/CaltechAUTHORS:20120814-085632625
Authors: {'items': [{'id': 'Wu-S-F', 'name': {'family': 'Wu', 'given': 'Shiou-Fu'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1970
DOI: 10.1063/1.1673874
Natural collision coordinates and a zeroth‐order vibrational–adiabatic approximation are used to treat linear reactive collisions. Nonadiabatic effects on barrier transmission and on vibrational state of products are calculated. The present results are classical and are compared with exact classical numerical results for the H+H_2 reaction in the range 7–20 kcal/mol of initial relative translational energy. The agreement is encouraging and the results support the concepts introduced earlier of statistical adiabaticity and of nonadiabatic leak. At low energies the reaction is adiabatic on the average (initial vibrational phase average), thus justifying activated complex theory for this system. The relative importance of reaction path curvature and of vibrational frequency variation along the reaction path in inducing nonadiabatic effects is described. Implications for a quantum treatment, activated complex theory, and highly nonadiabatic systems are noted.https://authors.library.caltech.edu/records/6kam5-33j79Extension of the WKB method to wave functions and transition probability amplitudès (S-matrix) for inelastic or reactive collisions
https://resolver.caltech.edu/CaltechAUTHORS:20150708-112530300
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1970
DOI: 10.1016/0009-2614(70)80164-6
A WKB-type method is used to calculate the wave function and S-matrix for these collisions directly, instead of applying WKB to the customary infinite set of coupled differential equations. Action-angle variables and exact or approximate classical trajectories are used.https://authors.library.caltech.edu/records/0bq0e-3s218Theory of Semiclassical Transition Probabilities (S Matrix) for Inelastic and Reactive Collisions
https://resolver.caltech.edu/CaltechAUTHORS:20120806-131425987
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1971
DOI: 10.1063/1.1675453
In the present paper the time‐independent Schrödinger equation for inelastic collisions is solved directly in the WKB approximation, using action‐angle variables and the method of characteristics. A single wavefunction, consisting of an ingoing and an outgoing term, is thereby derived, describing all collision channels and so avoiding the application of WKB methods to an infinite set of coupled differential equations. An integral is obtained for the S matrix, and asymptotic methods (e.g., steepest descents, stationary phase) are used for its evaluation. The expressions can be calculated using numerical data on classical trajectories or using approximations. To facilitate the latter and to show the connection with approximations in the literature, a canonical perturbation theory is described for the wave phase and amplitude, in a form suited to collisions, and used to relate the theory to those approximations. The topic of collisional selection rules is also considered. The extension of the method employed in the present paper to the direct calculation of differential and total inelastic cross sections, rather than via the S matrix, is briefly described, and the extension to reactive cross sections is also noted. The method can also be used to treat time‐dependent problems, and so is not restricted to collisions. These topics and other applications will be described in later papers of this series.https://authors.library.caltech.edu/records/q4e44-czd95Theory of Semiclassical Transition Probabilities for Inelastic and Reactive Collisions. II Asymptotic Evaluation of the S Matrix
https://resolver.caltech.edu/CaltechAUTHORS:CONjcp71
Authors: {'items': [{'id': 'Connor-J-N-L', 'name': {'family': 'Connor', 'given': 'J. N. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1971
DOI: 10.1063/1.1675732
The asymptotic evaluation of the integral representation for an S matrix element in a previously developed semiclassical theory of molecular collisions is considered. The integral representation is evaluated asymptotically by the method of Chester, Friedman, and Ursell to give a uniform approximation for the S matrix element which is valid for classically accessible and classically inaccessible transitions. The results unify and extend those previously derived, which were restricted to the simple semiclassical and Airy function cases. A comparison is made with the simple, Airy, and uniform semiclassical approximations that occur in Miller's semiclassical theory of molecular collisions. Although the starting point of the two theories is different, it is concluded that their asymptotic results are essentially identical. In addition, a simpler derivation of the integral representation for an S matrix element from the semiclassical wavefunction is given, one which avoids the use of Green's theorem.https://authors.library.caltech.edu/records/4va3h-c4227Semiclassical transition probabilities (S matrix) of vibrational—translational energy transfer
https://resolver.caltech.edu/CaltechAUTHORS:WONjcp71a
Authors: {'items': [{'id': 'Wong-W-H', 'name': {'family': 'Wong', 'given': 'W. H.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1971
DOI: 10.1063/1.1675736
Uniformized coordinates and an integral expression for the semiclassical S matrix, derived elsewhere, are described and applied to vibrational transition probabilities. The expression obeys microscopic reversibility. The numerical results are compared with the exact quantum mechanical results of Secrest and Johnson.https://authors.library.caltech.edu/records/af846-yzs62Concept of Minimum State Density in the Activated Complex Theory of Bimolecular Reactions
https://resolver.caltech.edu/CaltechAUTHORS:20120813-141020948
Authors: {'items': [{'id': 'Wong-W-H', 'name': {'family': 'Wong', 'given': 'W. H.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1971
DOI: 10.1063/1.1675730
In some bimolecular reactions, for example, certain low potential‐energy barrier reactions, the saddle‐point choice for the position of the activated complex is vague and sometimes incorrect. In these and in some others a different choice is needed. The concept of minimum state density for this purpose, its relation to adiabatic transition state theory and to the maximum free energy criterion, are discussed. It is shown how it may be applied to bimolecular reactions using microcanonical activated complex theory for these reactions.https://authors.library.caltech.edu/records/508rd-9w897Theory of Semiclassical Transition Probabilities (S Matrix) for Inelastic and Reactive Collisions. III. Uniformization Using Exact Trajectories
https://resolver.caltech.edu/CaltechAUTHORS:20120813-093140548
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1972
DOI: 10.1063/1.1676866
A canonical transformation of coordinates in Part I is made using exact trajectories. The transformation tends to uniformize all coordinates including that for the radial motion, thus removing the singularities in the simple semiclassical exponential wavefunction in typical cases. The new coordinates are "time" and certain constants of the motion. A symmetrical choice for the transformation then yields an integral expression for the S matrix satisfying the principle of microscopic reversibility. Topics discussed include semiclassical unitary transformations and time‐reversal properties of action‐angle variables and of semi‐classical wavefunctions. Applications and numerical tests of the integral expression for S_(mn) are in progress.https://authors.library.caltech.edu/records/wg3nz-q3618Theory of Semiclassical Transition Probabilities (S Matrix) for Inelastic and Reactive Collisions. Uniformization with Elastic Collision Trajectories
https://resolver.caltech.edu/CaltechAUTHORS:20120808-160240177
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1972
DOI: 10.1063/1.1677730
A canonical transformation is described for uniformizing the coordinates used in Paper I of this series.
For comparison with the results of Paper III, which based a uniformization on exact trajectories, the
present article describes one based on elastic collision trajectories. The question of invariance of S-matrix
elements with respect to semiclassical unitary transformations is also discussed.https://authors.library.caltech.edu/records/anxqn-7fk07Analytical Mechanics of Chemical Reactions. VI. Rotational and Vibrational Distributions of the H + H_2 Reaction in a Plane
https://resolver.caltech.edu/CaltechAUTHORS:20120727-105943941
Authors: {'items': [{'id': 'Wu-S-F', 'name': {'family': 'Wu', 'given': 'Shiou-Fu'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1972
DOI: 10.1063/1.1677727
Rotational and vibrational distributions for the exchange reaction H+H_(2)→H_(2)+H are obtained numerically for reaction in a plane and compared with the vibrationally adiabatic solutions. Evidence is obtained regarding the two adiabatic solutions for the final rotational state predicted earlier and for the disappearance of one of these at higher initial relative velocity. Good agreement between calculations based on natural collision coordinates and these based on Cartesian coordinates was found, where tested. The vibrational motion for reaction in a plane is fairly adiabatic on the average at energies of thermal interest. Connections with other properties are noted. The results support the idea of statistical adiabaticity suggested earlier in this series and thus support a derivation of activated complex theory based on this concept.https://authors.library.caltech.edu/records/sjvev-wct78Theory of semiclassical transition probabilities for inelastic and reactive collisions. IV. Classically-inaccessible transitions calculated by integration along complex-valued trajectories
https://resolver.caltech.edu/CaltechAUTHORS:20150708-150702676
Authors: {'items': [{'id': 'Stine-J-R', 'name': {'family': 'Stine', 'given': 'J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1972
DOI: 10.1016/0009-2614(72)80366-X
We calculate semiclassical S-matrix elements S_(mn) by numerical integration along complex-valued trajectories, by avoiding (simply) previously reported trajectory divergences. Now, one can numerically calculate even ❘S_(mn)❘ ≈ 10^(−11) for the Secrest-Johnson system (their lowest ❘S_(mn)❘^2), instead of only ❘S_(mn)❘^2 > 10^(−3). Agreement is excellent.https://authors.library.caltech.edu/records/6wmwq-8b492Theory of Semiclassical Transition Probabilities for Inelastic and Reactive Collisions. V. Uniform Approximation in Multidimensional Systems
https://resolver.caltech.edu/CaltechAUTHORS:20120808-155748280
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1972
DOI: 10.1063/1.1678161
An integral semiclassical expression for the S matrix of inelastic and reactive collisions was formulated
earlier in this series. In the present paper a uniform approximation for the expression is derived for the
case of multidimensional systems. The method is an extension of that employed in Part II for the case
of one internal coordinate. The final result, Eq. (2), is highly symmetrical, thus making some of its properties
immediately clear.https://authors.library.caltech.edu/records/pawnb-5px22Semiclassical Theory for Collisions Involving Complexes (Compound State Resonances) and for Bound State Systems
https://resolver.caltech.edu/CaltechAUTHORS:20150930-120150893
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1973
DOI: 10.1039/DC9735500034
Semiclassical theory for bound states is discussed and a method is described for calculating the eigenvalues for systems not permitting separation of variables. Trajectory data are supplemented by interpolation to connect open ends of quasi-periodic trajectories. The method is also applied to quasi-bound states.
Previously, semiclassical S-matrix theory has focused on "direct" reactions. Processes involving complexes (compound state resonances) are treated in the present paper and an expression is derived for the S-matrix. Use is made of the above analysis of quasi-bound states and of trajectories connecting those states with open channels. The result deduced for the S-matrix has the expected factorization property, and expressions are given for computing the quantities involved. Some extensions and applications will be described in later papers. An implication for classical trajectory calculations of complexes is noted.https://authors.library.caltech.edu/records/v34zx-ng8601. Theoretical. The theoretical approach
https://resolver.caltech.edu/CaltechAUTHORS:20150810-165824675
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1973
DOI: 10.1039/DC9735500009
There are a number of areas in chemical kinetics where generalizations have been helpful in interpreting and correlating a large body of experimental data in gas phase or solution reactions. I am reminded here of Bronsted's relation between rate constants and equilibrium constants, Eyring's and Evans and Polanyi's work on transition state theory, Rice, Ramsperger and Kassel's work on unimolecular reaction, later augmented to RRKM, treatments of the curve crossing problems, Hammett's σρ relation and acidity function, and the subsequent equations they stimulated, theories of three-body recombination of atoms and of electron transfers in solution and at electrodes, simple BEBO calculations on activation energies, the Woodward-Hoffman rules and their implications for activation energies, Breit-Wigner and later treatments of resonances, models for ion-molecule reactions, to name a few. In the case of inelastic non-reactive collisions one would include the SSH theory, distorted wave theory for some systems, the Anderson theory of spectral line broadening and its later extensions.
The interested observer, as well as the seasoned practitioner, might well ask which of these generalizations of analytical thought apply to current problems of molecular dynamics, what new ones have been developed, or what experimental generalizations are there, if any, which literally cry out for a theoretical answer. He might ask, too, whether the present field is sufficiently different from the previous ones that the approximate analytical theory will be literally swept under by a Spartan-like phalanx of exact classical trajectories and their semiclassical and quantum mechanical counterparts, with much analytical thought going into this army.
We shall not attempt to answer all of these questions here, but shall summarize instead some of the trends which appear to be developing in the field. Calculations in the area are diverse, and some classification would be useful. A possible scheme for dynamical calculations is proposed in this introductory paper.https://authors.library.caltech.edu/records/vqryh-c3t28Semiclassical theory of molecular spectral line shapes in gases
https://resolver.caltech.edu/CaltechAUTHORS:20120802-120133804
Authors: {'items': [{'id': 'Fitz-D-E', 'name': {'family': 'Fitz', 'given': 'D. E.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1973
DOI: 10.1063/1.1680636
A semiclassical theory of the width and shift of molecular spectral lines is developed for gases. Overlapping
and nonoverlapping lines are considered, within the framework of the impact approximation. Use is made of
"exact" semiclassical theory of molecular collisions, recently developed by Miller and by Marcus, and of
developments in the quantum mechanical theory of spectral line shapes, by introducing the former into the
latter. Comparison is made with a classical-like approach.https://authors.library.caltech.edu/records/87xmb-xev65Semiclassical transition probabilities by an asymptotic evaluation of the S matrix for elastic and inelastic collisions. Bessel uniform approximation
https://resolver.caltech.edu/CaltechAUTHORS:20120802-162507229
Authors: {'items': [{'id': 'Stine-J-R', 'name': {'family': 'Stine', 'given': 'J. R.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1973
DOI: 10.1063/1.1680733
It has been observed in the past that the usual Airy uniform approximation gives probabilities greater than one, especially for near elastic collisions. By mapping the phase onto −ζ cos y + ky + A rather than (1∕3)y^3 − ζy + A one obtains a uniform approximation involving Bessel functions of the first kind, which approaches unity for the elastic collision. This Bessel uniform approximation is no more complicated than the Airy and also gives good agreement with exact quantum results, even if probabilities are large.https://authors.library.caltech.edu/records/6c3g2-az461Semiclassical S-matrix theory. VI. Integral expression and transformation of conventional coordinates
https://resolver.caltech.edu/CaltechAUTHORS:20120808-095709866
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1973
DOI: 10.1063/1.1680732
Sometimes, as in reactive systems, action‐angle variables are not conveniently defined at all points of the trajectory and recourse must be made to conventional coordinates. A simple canonical transformation converts the latter to coordinates of which one is time and the remainder are constant along the trajectory. The transformation serves to remove the singularities of the semiclassical wavefunction at the turning points of the trajectory. It yields, thereby, an integral expression for the S matrix by having produced wavefunctions which can be integrated over all space. The result supplements that of Paper III [R. A. Marcus, J. Chem. Phys. 56, 311 (1972)], which was derived for systems for which action‐angle variables could be defined throughout the collision.https://authors.library.caltech.edu/records/q8c6r-s2h39Compound state resonances in the collinear collision of an atom with a diatomic oscillator
https://resolver.caltech.edu/CaltechAUTHORS:EASjcp73
Authors: {'items': [{'id': 'Eastes-W', 'name': {'family': 'Eastes', 'given': 'Walter'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1973
DOI: 10.1063/1.1680688
Compound state resonance effects are reported in exact, numerical calculations of the collinear collision of a particle with a harmonic oscillator with a Morse interaction potential. They are shown to be due to the formation of a long-lived complex or quasibound state and are much more narrow than resonances reported previously for this type of system. The stable eigenvalues resulting from a variational calculation with a bound state basis set are found to be in excellent agreement with the resonance energies, and such a variational calculation is a good way of locating these resonances.https://authors.library.caltech.edu/records/y2pdy-br165Semiclassical collision theory. Multidimensional integral method
https://resolver.caltech.edu/CaltechAUTHORS:20120809-112855158
Authors: {'items': [{'id': 'Kreek-H', 'name': {'family': 'Kreek', 'given': 'H.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1974
DOI: 10.1063/1.1682492
Numerical results on the integral expression for the semiclassical S matrix are compared with exact quantum results for a multidimensional problem. The collision of a rigid rotor with an atom is treated. The integral method proves to be easy to apply. Within its range of maximum validity (no sign changes in the pre‐exponential factor of the semiclassical wavefunction) the agreement was typically within 20%. When sign changes occurred, the agreement was about a factor of 2 or better. Conditions affecting sign changes are described.https://authors.library.caltech.edu/records/29rem-ff740Semiclassical calculation of bound states of a multidimensional system
https://resolver.caltech.edu/CaltechAUTHORS:EASjcp74
Authors: {'items': [{'id': 'Eastes-W', 'name': {'family': 'Eastes', 'given': 'Walter'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1974
DOI: 10.1063/1.1681734
The semiclassical quantum conditions for bound states are studied for a nonseparable system of two coupled oscillators which possesses a collection of quasiperiodic trajectories. The semiclassical energy levels are found to be in excellent agreement with the exact quantum levels. This treatment differs from previous work in that periodic trajectories are not needed and in that the potential surface is smooth and nonseparable in all regions.https://authors.library.caltech.edu/records/6gyy1-hcw42Semiclassical collision theory. Multidimensional Bessel uniform approximation
https://resolver.caltech.edu/CaltechAUTHORS:20120809-135352662
Authors: {'items': [{'id': 'Kreek-H', 'name': {'family': 'Kreek', 'given': 'H.'}}, {'id': 'Ellis-R-L', 'name': {'family': 'Ellis', 'given': 'R. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1974
DOI: 10.1063/1.1681771
A multidimensional Bessel uniform approximation for the semiclassical S matrix is derived for the case of four real stationary phase points. A formula is also developed for the particular case when four stationary phase points may be considered to be well separated in pairs. The latter equation is then used in the treatment of two real and two complex stationary phase points.https://authors.library.caltech.edu/records/wsr2y-mtf23Semiclassical S matrix theory for a compound state resonance in the reactive collinear H + H_2 collision
https://resolver.caltech.edu/CaltechAUTHORS:20150708-113321594
Authors: {'items': [{'id': 'Stine-J-R', 'name': {'family': 'Stine', 'given': 'J. R.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1974
DOI: 10.1016/0009-2614(74)85095-5
The broad compound state resonance found in quantum mechanical calculations of the collinear H + H_2 reaction is shown to correspond semiclassically to multiple collisions of the atoms within the collision complex. The quantitative agreement between QM and SC results is quite reasonable.https://authors.library.caltech.edu/records/zadp6-m4z09Electron-transfer reactions with unusual activation parameters. Treatment of reactions accompanied by large entropy decreases
https://resolver.caltech.edu/CaltechAUTHORS:20150810-163729417
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Sutin-N', 'name': {'family': 'Sutin', 'given': 'N.'}}]}
Year: 1975
DOI: 10.1021/ic50143a051
The activation enthalpies for the oxidation of Fe(H_2O)_6^(2+) by poly(pyridine)iron(III) and -ruthenium(III) complexes (reactions 1 and 2, for example) are small or slightly negative.
Fe(H_2O)_6^(2+-) + Fe(bipy)_3^(3+) → Fe(H_2O)_6^(3+) + Fe(bipy)_3^(2+) (1)
Fe(H_2O)_6^(2+) + Ru(bipy)_3^(3+) → Fe(H_2O)_6^(3+) + Ru(bipy)_3^(2+) (2)
This has led to the suggestion that these reactions occur by a "non-Marcus" path which includes at least one distinctive feature not considered in a current outer-sphere electron-transfer model. We wish to point out that small or even negative activation enthalpies are in themselves not necessarily inconsistent with this model and indeed are predicted by it for the systems under consideration.https://authors.library.caltech.edu/records/b8720-28g87Semiclassical collision theory. Application of multidimensional uniform approximations to the atom-rigid-rotor system
https://resolver.caltech.edu/CaltechAUTHORS:20120809-141336648
Authors: {'items': [{'id': 'Kreek-H', 'name': {'family': 'Kreek', 'given': 'H.'}}, {'id': 'Ellis-R-L', 'name': {'family': 'Ellis', 'given': 'R. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1975
DOI: 10.1063/1.430543
The multidimensional Bessel and Airy uniform approximations developed earlier in this series for the semiclassical S matrix are applied to the atom rigid−rotor system. The need is shown for (a) using a geoemetrical criterion for determining whether a stationary phase point (s.p.pt) is a maximum, minimum, or saddle point; (b) choosing a proper quadrilateral configuration of the s.p.pts. with the phases as nearly equal as possible; and (c) choosing a unit cell to favor near−separation of variables. (a) and (b) apply both to the Airy and to the Bessel uniform approximations, and (c) to the Bessel. The use of a contour plot both to understand and to facilitate the search in new cases is noted. The case of real and complex−valued stationary phase points is also considered, and the Bessel uniform−in−pairs approximation is applied. Comparison is made with exact quantum results. As in the one−dimensional case, the Bessel is an improvement over the Airy for ''k = 0'' transitions, while for other transitions they give similar results. Comparison in accuracy with the results of the integral method is also given. As a whole, the agreement can be considered to be reasonable. The improvement of the present over various more approximate results is shown.https://authors.library.caltech.edu/records/pcc2t-gy745On the theory of energy distributions of products of molecular
beam reactions involving transient complexes
https://resolver.caltech.edu/CaltechAUTHORS:20120809-114611280
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1975
DOI: 10.1063/1.430649
Theoretical energy distributions of reaction products in molecular beam systems are described for reactions proceeding via transient complexes. Loose and tight transition states are considered for the exit channel. For a loose transition state and the case of l ≫ j, the result is the same as of Safron et al. For the case of a tight transition state exit channel effects are included analogous to steric effects for the reverse reaction. It is shown how, via one mechanism, bending vibrational energy of that transition state can contribute to the translational energy of the reaction products. Expressions are derived for the energy distributions of the products when l ≫ j and j ≫ l.https://authors.library.caltech.edu/records/arev3-vrh07Semiclassical calculation of bound states in a multidimensional system. Use of Poincaré's surface of section
https://resolver.caltech.edu/CaltechAUTHORS:NOIjcp75
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1975
DOI: 10.1063/1.430777
A method utilizing integration along invariant curves on Poincaré's surfaces of section is described for semiclassical calculation of eigenvalues. The systems treated are dynamically nonseparable and are quasiperiodic. Use is also made of procedures developed in the previous paper of this series. The calculated eigenvalues for an anharmonically coupled pair of oscillators agree well with the exact quantum values. They also agree with the previous semiclassical calculations in this laboratory, which instead used integrations along the caustics. The present paper increases the number of systems capable of being treated. Using numerical counter examples for nondegenerate systems, it is also shown that an alternative view in the literature, which assumes that periodic trajectories alone suffice, leads to wrong results for the individual eigenvalues.https://authors.library.caltech.edu/records/x3cdp-z6357Energetic and Dynamical Aspects of Proton Transfer Reactions in Solution
https://resolver.caltech.edu/CaltechAUTHORS:20150930-121201711
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1975
DOI: 10.1039/FS9751000060
Several energetic and dynamical aspects of proton transfers are treated. The effect of intrinsic barrier asymmetry on BEBO calculated Brönsted plots is investigated, and contributions to work terms are also considered. The dynamics of transfer of a light particle between two heavier ones is discussed for a particular potential energy surface, making use of classical trajectories, semiclassical concepts, and a previous quantum study. The question of nonequilibrium polarization of solvent is also considered.https://authors.library.caltech.edu/records/xmnvj-h7t63Semiclassical theory of spectral line shapes. II. Applications to CO, HCl, and OCS, broadened by inert gases
https://resolver.caltech.edu/CaltechAUTHORS:20120731-082134863
Authors: {'items': [{'id': 'Fitz-D-E', 'name': {'family': 'Fitz', 'given': 'D. E.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1975
DOI: 10.1063/1.430930
The semiclassical theory of spectral line broadening developed in the previous paper of this series is used to calculate the half‐widths and shifts of nonoverlapping rotational spectral lines of CO, HCl, and OCS, broadened by inert gases. Comparisons are made with the available experimental data and with related theoretical analyses, and reasonable agreement is obtained. The method used applies both to fairly quantum systems as well as to the relatively classical ones. A symmetrized semiclassical expression for Wigner 6‐j symbols is given and applied.https://authors.library.caltech.edu/records/nacv6-yb876Theory of the relaxation matrix and its relation to microwave transient phenomena. II. Semiclassical calculations for systems of OCS and nonpolar collision partners
https://resolver.caltech.edu/CaltechAUTHORS:LIUjcp75b
Authors: {'items': [{'id': 'Liu-Wing-ki', 'name': {'family': 'Liu', 'given': 'Wing-ki'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1975
DOI: 10.1063/1.431056
Cross sections corresponding to relaxation times T1 and T2 measured in microwave transient experiments are calculated for systems of OCS and nonpolar collision partners, employing the recently developed semiclassical theory of molecular collisions. Cases in the presence and absence of static Stark field are described. The over-all agreement with existing experimental results is encouraging. Similarities and differences between T1/T2 values in microwave transient experiments and in molecular beam maser experiments are discussed, together with a role of semiclassical collisional selection rules.https://authors.library.caltech.edu/records/s2st0-m2a49On the theory of the relaxation matrix and its application to microwave transient phenomena
https://resolver.caltech.edu/CaltechAUTHORS:LIUjcp75a
Authors: {'items': [{'id': 'Liu-Wing-ki', 'name': {'family': 'Liu', 'given': 'Wing-Ki'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1975
DOI: 10.1063/1.431055
The phenomenological relaxation times T1 and T2 measured in microwave transient experiments are expressed in terms of specific molecular relaxation matrix elements. Conditions for this simple T1, T2 description are also given. The system is described in terms of a kinetic equation for the density matrix, which provides a unified treatment of the microwave transient behavior, spectral line shapes, and double resonance phenomena. Spatial degeneracy of the states and m dependence of T1 and T2 are discussed in detail. The recently developed semiclassical theory of molecular collisions is then applied to obtain expressions for the relevant relaxation times.https://authors.library.caltech.edu/records/044v2-e1573Classical trajectory study of internal energy distributions in unimolecular processes
https://resolver.caltech.edu/CaltechAUTHORS:MCDjcp76
Authors: {'items': [{'id': 'McDonald-J-D', 'name': {'family': 'McDonald', 'given': 'J. D.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1976
DOI: 10.1063/1.433374
The method of classical trajectories has been used to study the flow of energy in a molecular system (similar to the molecules CD3Cl and CD3H) representing a chemical activation experiment. Energy distributions are obtained both before and after the breakup of the activated molecule by means of a correlation function technique. Four different potential energy surfaces are employed. It is found that the initial distribution of energy in the activated molecule may or may not be random, depending on the details of the particular surface. This distribution becomes random in less than 5×10−12 sec. The distribution of energy in the final product (CD3) is found to be randomly distributed (as predicted by RRKM theory including angular momentum considerations) for a surface with no exit channel barrier or strong intermode couplings. When these special forces are present nonrandom energy distributions result. Product channel barriers result in an excess of translational energy and exit channel intermode couplings result in nonrandom vibrational distributions. Angular momentum considerations are found to be important in matching the predictions of RRKM theory with the calculations.https://authors.library.caltech.edu/records/06ad2-e7669Energy Distributions in Unimolecular Reactions
https://resolver.caltech.edu/CaltechAUTHORS:20150729-110232282
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1977
DOI: 10.1002/bbpc.19770810226
The present paper describes results on modes of anharmonically coupled oscillators in a molecule, the role of energy exchange and near-degeneracy.
and quasi-periodic versus ergodic theory of unimolecular reactions. The quasi-periodic one is a formal generalization of Slater's
harmonic oscillator theory. Spectral decomposition of a classical trajectory for the molecule provides insight into the molecular spectrum.
both in the low(quasi-periodic) and high (ergodic) energy regimes. The role of quantization of transition states in unimolccular reactions and
a relation to vibrational adiabaticity are analyzed. Results obtained on energy distribution of translational energy of molecular beam reactions
involving intermediate complexes and tight exit channel transition states are described together with the relation to intramolecular
energy randomization.https://authors.library.caltech.edu/records/3jcxq-2ha34Classical and quantum centrifugal decoupling approximations for HCl–Ar
https://resolver.caltech.edu/CaltechAUTHORS:TARjcp77
Authors: {'items': [{'id': 'Tarr-S-M', 'name': {'family': 'Tarr', 'given': 'Susan M.'}}, {'id': 'Rabitz-H', 'name': {'family': 'Rabitz', 'given': 'Herschel'}}, {'id': 'Fitz-D-E', 'name': {'family': 'Fitz', 'given': 'D. E.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1977
DOI: 10.1063/1.434343
The centrifugal decoupling approximation previously employed in quantum mechanics is extended to classical mechanics. Both classical and quantum centrifugal decoupling (CCD and CD, respectively) calculations are performed for HCl–Ar. Total cross sections are obtained from the CCD and CD calculations. The CCD and CD total cross sections are shown to be in good agreement with the corresponding exact classical trajectory (EC) and close coupled (CC) cross sections, respectively. The conservation of the projection (Omega) of the rotational angular momentum along the body-fixed z-axis is studied as a possible explanation for the success of the CCD and CD approximations in predicting total cross sections. By examining the CC body-fixed S-matrix elements and studying the behavior of Omega during the course of an exact classical trajectory, it is found that Omega is conserved only under very limited conditions. Detailed examination of the calculations shows that the CD approximation may be good even when Omega varies rapidly.https://authors.library.caltech.edu/records/myvgr-80e45Semiclassical calculation of bound states in a multidimensional system for nearly 1:1 degenerate systems
https://resolver.caltech.edu/CaltechAUTHORS:NOIjcp77b
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1977
DOI: 10.1063/1.434911
The method is devised to calculate eigenvalues semiclassically for an anharmonic system whose two unperturbed modes are 1:1 degenerate, by introducing a curvilinear Poincaré surface of section. The results are in reasonable agreement with the quantum ones. The classical trajectories also frequently show a large energy exchange among the two unperturbed normal modes. Implications for Slater's theory of unimolecular reactions, which neglects this effect, and for "quantum ergodicity" are described.https://authors.library.caltech.edu/records/wavr5-ant04A spectral analysis method of obtaining molecular spectra from classical trajectories
https://resolver.caltech.edu/CaltechAUTHORS:NOIjcp77a
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1977
DOI: 10.1063/1.434901
Vibrational classical trajectories of anharmonic molecules are used here to obtain the classical vibrational autocorrelation function and, via a Fourier transform, the power (or infrared) spectrum of the dynamical variables. In the vibrationally quasiperiodic regime the spectrum consists of sharp lines, for any given initial amplitude. The initial amplitudes are chosen semiclassically. The spectral lines are compared with quantum mechanical calculations for systems with two and three coordinates, with excellent agreement. The method is also useful for obtaining a classical spectrum in the ergodic regime; the spectral lines are then ''broad'' rather than narrow. The method can be used in the analysis of trajectories for unimolecular reactions, infrared multiphoton dissociations, and for obtaining molecular spectra from force fields. The spectral analysis itself has implications for the theory of unimolecular reactions.https://authors.library.caltech.edu/records/rmx8c-q4f89On the theory of translational energy distributions of product molecules of molecular beam reactions involving transient complexes. II
https://resolver.caltech.edu/CaltechAUTHORS:WORjcp77
Authors: {'items': [{'id': 'Worry-G', 'name': {'family': 'Worry', 'given': 'Gary'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1977
DOI: 10.1063/1.434996
A statistically adiabatic model for chemical reactions involving a tight or loose transition state in the exit channel was used in Part I to obtain an integral equation for the individual reaction probabilities, i.e., for the magnitude of the S matrix elements. In the present paper this integral equation is explicitly solved for the general case of product orbital (l) and rotational (j) angular momenta constrained only by energy and angular momentum conservation. The reaction probabilities are shown to be related to a contour integral of a product of canonical partition functions. The theory includes an effect of the evolution of the bending vibrations of the transition state into free rotations of the product molecules. The distribution of final translational energy for the general (l,j) case is then obtained by averaging the reaction probabilities over various quantum states of the product molecules. The results are compared with the special cases in the literature for which (i) the transition state in the exit channel is loose (''phase space theory''), (ii) this case but with l>>j, and (iii) tight transition state theory with l>>j (Part I). The results are also compared with experimental data obtained from the molecular beam reaction F+(CH3)2C=CH2 -->F(CH3)2CCH2*-->CH3+FCH3C=CH2. The data and the theoretical results are now in better agreement. In the treatment described here and in Part I a loose transition state in the entrance channel was assumed. Expressions for the energy distribution are also given for the case when the entrance channel transition state is tight. Finally, a statistically adiabatic S matrix, which is useful for reactions proceeding through long-lived collision complexes having tight transition states, is described, and its possible application to angular distributions and angular momentum polarization experiments is discussed.https://authors.library.caltech.edu/records/npfkg-6mw32A study of the entropic and electrolyte effects in electron transfer reactions
https://resolver.caltech.edu/CaltechAUTHORS:20150708-114400041
Authors: {'items': [{'id': 'Waisman-E', 'name': {'family': 'Waisman', 'given': 'Eduardo'}}, {'id': 'Worry-G', 'name': {'family': 'Worry', 'given': 'Gary'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1977
DOI: 10.1016/S0022-0728(77)80248-9
The entropy of activation ΔS^‡ for electron transfer reactions occurring in concentrated electrolyte solutions is calculated, taking into account the electrostatic and electronic contributions. By applying the mean spherical and exponential approximations to treat a simple model of electrolytes (hard charged spheres in a dielectric continuum), the pair distribution function is calculated. These approximations are also used to calculate the electrolyte reorganization term, since both quantities contribute to the electrostatic part of ΔS^‡. Numerical application is made to the ferrous-ferric exchange reaction in 0.55 M HClO_4. Results of a preliminary electron tunneling calculation for the electron transfer are included. Reasonable agreement between observed and calculated ΔS^‡ is obtained.https://authors.library.caltech.edu/records/p2tza-k4e73A new tunneling path for reactions such as H+H_2→H_2+H
https://resolver.caltech.edu/CaltechAUTHORS:20120808-095605393
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Coltrin-M-E', 'name': {'family': 'Coltrin', 'given': 'Michael E.'}}]}
Year: 1977
DOI: 10.1063/1.435172
The standard tunneling path in transition state theory for reactions such as H+H_2→H_2+H has been the so‐called reaction path, namely the path of steepest ascent to the saddle point. This path is now known to give numerical results for the reaction probability which are in disagreement with the exact quantum mechanical ones by an order of magnitude at low tunneling energies. A new tunneling path corresponding to a line of vibrational endpoints is proposed. It is much shorter and is shown to give results in agreement with the quantum ones to within about a factor of two. A semiclassical basis for choosing this new path is given.https://authors.library.caltech.edu/records/gks7y-gjq74Classical trajectory study of infrared multiphoton photodissociation
https://resolver.caltech.edu/CaltechAUTHORS:20150708-111641365
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'McDonald-J-D', 'name': {'family': 'McDonald', 'given': 'J. D.'}}]}
Year: 1977
DOI: 10.1016/0009-2614(77)85420-1
Classical trajectories on a realistic model potential energy surface (approximating one dissociation channel of CD_3Cl) driven by an external force have been used to model infrared multiphoton dissociation. This model predicts a reasonable energy density threshold behavior, and generally (except at extremely high power densities) shows random (RRKM-like) behavior of the highly excited molecules, although non-random effects are evident immediately after the field is turned on.https://authors.library.caltech.edu/records/chqx8-w8442Semiclassical theory of the effects of collisions between rotors on molecular spectral lineshapes. II. Calculations for several systems
https://resolver.caltech.edu/CaltechAUTHORS:TURjcp77b
Authors: {'items': [{'id': 'Turfa-A-F', 'name': {'family': 'Turfa', 'given': 'Alexander F.'}}, {'id': 'Liu-Wing-ki', 'name': {'family': 'Liu', 'given': 'Wing-ki'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1977
DOI: 10.1063/1.434587
The T2 (microwave line broadening) and T1 (microwave transient experiments) collisional cross sections are obtained by Monte Carlo trajectory evaluations of semiclassical (WKB) expressions for those quantities derived in a previous paper in this series. The calculated values of the cross sections presented here yields the relation T1~T2 (within standard error) for the systems OCS–OCS, OCS–N2, OCS–H2, OCS–CO2, and HCN–HCN, a result which agrees with recent experimental findings. Reasonable agreement was also found between the calculated values of the T2 cross section and those observed spectroscopically.https://authors.library.caltech.edu/records/ew7af-24f35Semiclassical theory of the effects of collisions between rotors on molecular spectral line shapes. I
https://resolver.caltech.edu/CaltechAUTHORS:TURjcp77a
Authors: {'items': [{'id': 'Turfa-A-F', 'name': {'family': 'Turfa', 'given': 'Alexander F.'}}, {'id': 'Fitz-D-E', 'name': {'family': 'Fitz', 'given': 'D. E.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1977
DOI: 10.1063/1.434586
The semiclassical (WKB) limit of the quantum mechanical expression for the collisional line broadening cross section of the microwave spectrum of gaseous molecules is derived. For the present purpose of considering binary collisions between such species as OCS and CO2, action-angle-like variables for the classical mechanics of two interacting rotors are developed. Applications can be made to the evaluation of T2 (microwave line broadening) and T1 (microwave transient experiments) cross sections and to calculations of rotational and vibrational energy transfer for linear molecule–linear molecule systems.https://authors.library.caltech.edu/records/0z2we-z3616Collisional broadening and spectral line shape of an entire
rotational band
https://resolver.caltech.edu/CaltechAUTHORS:20120803-072601444
Authors: {'items': [{'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1978
DOI: 10.1063/1.435812
The impact approximation is applied to the classical binary collision operator making it possible to derive an expression for the dipole correlation function for real systems in a form which is computationally tractable and contains no adjustable parameters. Trajectory calculations are performed (in order to evaluate the microscopic expression for the relaxation parameter in the correlation function) for the system CO in dense Ar gas. Comparison is made with experimental data and excellent agreement is found for certain densities when a quantum correction is included. At higher densities (i.e., ρ^(−1/3)< "the range of the potential") one approximation is not valid and comparison with experiment illustrates this point.https://authors.library.caltech.edu/records/t0ak2-wbh86Vibrational nonadiabaticity and tunneling effects in transition state theory
https://resolver.caltech.edu/CaltechAUTHORS:20150810-162529916
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1979
DOI: 10.1021/j100464a027
The usual quantum mechanical derivation of transition state theory is a statistical one (a quasi-equilibrium is assumed) or dynamical. The typical dynamical one defines a set of internal states and assumes vibrational adiabaticity. Effects of nonadiabaticity before and after the transition state are included in the present derivation, assuming a classical treatment of the reaction coordinate. The relation to a dynamical derivation of classical mechanical transition state theory is described, and tunneling effects are considered.https://authors.library.caltech.edu/records/r3r91-14k26Rotational energy transfer in hydrogen halide molecules at supersonic beam velocities
https://resolver.caltech.edu/CaltechAUTHORS:TURjcp79
Authors: {'items': [{'id': 'Turfa-A-F', 'name': {'family': 'Turfa', 'given': 'Alexander F.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1979
DOI: 10.1063/1.437789
Rotational energy transfer cross sections are calculated for HCl–HCl and HCl–HF collisions using classical trajectories. The exponential model for the rotational results is compared with transitions j-->j[prime] in collisions of a supersonic HCl molecular beam with a thermal beam. Reasonable agreement with the functional form of that model is obtained. The trajectory results indicate that some modification is needed in the exponential formula, to account for microscopic reversibility in rotor–rotor collisions. Using a simple intermolecular potential without adjustable parameters, in which the only anisotropic terms are of the dipolar and dispersion type (i.e., long range), reasonable agreement is obtained with the experimental constant for HCl–HCl in the exponential. Calculations are also described for HCl–HI and HCl–HBr collisions. Microscopic reversibility for the averaged cross sections is discussed in connection with the exponential model.https://authors.library.caltech.edu/records/d6cgg-aw541Semiclassical comparison of quasi-classical and quantum moments of distribution of state in molecular collisions
https://resolver.caltech.edu/CaltechAUTHORS:20150810-163053434
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1979
DOI: 10.1021/j100471a013
State-to-state transition probabilities for molecular collisions are often computed from classical trajectories by equating quasi-classical and quantum moments of the final energy distributions and using some functional form to relate the transition probabilities to the quantum moments. The equality between quantum and quasi-classical moments in examined using semiclassical theory.https://authors.library.caltech.edu/records/675p9-6ky38On spin-exchange and electron-transfer rates in bacterial photosynthesis
https://resolver.caltech.edu/CaltechAUTHORS:HABpnas79.873
Authors: {'items': [{'id': 'Haberkorn-R', 'name': {'family': 'Haberkorn', 'given': 'R.'}}, {'id': 'Michel-Beyerle-M-E', 'name': {'family': 'Michel-Beyerle', 'given': 'M. E.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1979
A discrepancy is explored regarding the spin exchange integral estimated from magnetic field effects on recombination of the bacteriochlorophyll dimer cation (Bchl)2+ and the bacteriopheophytin anion Bph- and the measured electron transfer rate between Bph and electronically excited (Bchl)2. In one explanation considered here there are two sites for the electron or for the hole, with a hopping between sites.https://authors.library.caltech.edu/records/rzq7t-73p77Semiclassical calculation of bound states in multidimensional systems with Fermi resonance
https://resolver.caltech.edu/CaltechAUTHORS:NOIjcp79
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1979
DOI: 10.1063/1.438677
A method is devised to calculate eigenvalues semiclassically for an anharmonic system whose two unperturbed modes are 2:1 degenerate. For some special states the periodic energy exchange between unperturbed modes is found to be very large. The quantum mechanical wave functions are examined and a correlation with the classical trajectories is described, both for quasiperiodic and the stochastic cases. A method used in the literature for calculating the stochastic limit is tested and found to break down when the present anharmonic system is separable.https://authors.library.caltech.edu/records/srjjv-qzp05Properties of vibrational energy levels in the quasi periodic and stochastic regimes
https://resolver.caltech.edu/CaltechAUTHORS:NOIjcp80a
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Tabor-M', 'name': {'family': 'Tabor', 'given': 'M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1063/1.439075
Several aspects of the quantal energy spectrum are explored for the Henon–Heiles Hamiltonian system: a striking and initially unexpected continuation of sequences of eigenvalues from the quasiperiodic to the stochastic regime, the origin of large second differences Delta2Ei of eigenvalues arising from variation of a parameter, the comparison of classical and quantal spectra, and a comparison of the "classical" and quantal number of states. In the study of the second differences we find both "crossings" and "avoided crossings" of the eigenvalues. We discuss the importance of overlapping avoided crossings as a basis for a possible theory of "quantum stochasticity".https://authors.library.caltech.edu/records/ekct9-sbg17Semiclassical calculation of eigenvalues for a three-dimensional system
https://resolver.caltech.edu/CaltechAUTHORS:NOIjcp80b
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Moszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1063/1.439886
A method utilizing integration along invariant curves on Poincaré's surfaces of section is described for the semiclassical calculation of eigenvalues for three and higher dimensional systems, supplementing thereby our previous work in two dimensions. The eigenvalues calculated for anharmonically coupled oscillators agree well with the exact quantum eigenvalues.https://authors.library.caltech.edu/records/3egwt-jhb76Calculations related to quantum stochasticity, an example of overlapping avoided crossings
https://resolver.caltech.edu/CaltechAUTHORS:20150629-105634283
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1016/0009-2614(80)80370-8
In plots of eigenvalues of the Schrödinger equation versus a perturbation parameter, many avoided crossings are found in the classically stochastic regime for the system studied. None were observed in the classically quasi-periodic regime. Overlapping avoided crossings are suggested as a mechanism for making the vibrational wavefunction a "statistical" one.https://authors.library.caltech.edu/records/tg5g9-ef548Molecular Vibration and the Normal Mode Approximation
https://resolver.caltech.edu/CaltechAUTHORS:20150629-150931220
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1021/ed057p624
The conventional ideas about normal modes and molecular
vibration are currently undergoing closer examination for
highly vibrationally-excited systems. The standard method
involves calculating normal modes with the GF matrix technique. Normal modes assume a harmonic potential and.
in fact, in high energy systems local anharmonic modes have
given a better description of the spectrum than (harmonic)
normal modes of the molecules as a whole.https://authors.library.caltech.edu/records/kenea-x3781The role of vibrational–rotational coupling in V–V and V–R,T energy transfer
https://resolver.caltech.edu/CaltechAUTHORS:COLjcp80a
Authors: {'items': [{'id': 'Coltrin-M-E', 'name': {'family': 'Coltrin', 'given': 'M. E.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1063/1.440412
The effect of neglecting vibrational–rotational coupling in energy transfer calculations is studied for collisions of HF (v=1–7) with HF (v=0). An analog of a "classical path" method is considered in which rigid-rotor trajectories are used to determine a time-dependent forcing term on the vibrational motion of each molecule. The results are compared with our quasiclassical calculations in which no such approximation was used. At higher vibrational states the rigid-rotor forced-oscillator model is found to predict substantially smaller V–R,T rate constants than those found in the exact study.https://authors.library.caltech.edu/records/09ger-c8a30Cross-correlation trajectory study of V-V energy transfer
in HF-HF and DF-DF
https://resolver.caltech.edu/CaltechAUTHORS:20120718-155309804
Authors: {'items': [{'id': 'Coltrin-M-E', 'name': {'family': 'Coltrin', 'given': 'M. E.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1063/1.440591
Results of a fully three‐dimensional classical trajectory calculation of vibrational energy transfer are presented for the collision of HF(v=1) with HF(v=1) and its deuterium analog. A cross‐correlation method, together with quasiclassical trajectories, is introduced to relate the changes in vibrational states of the two molecules to probabilities and rate constants. Multiple collisions are found to make an important contribution to the vibrational energy transfer cross‐sections for the present potential surface. Vibrational anharmonicity is shown to decrease the energy transfer rate constant by a factor of ten, by causing the process to be further from exact resonance. Excellent agreement with experiment is obtained for the HF–HF and DF–DF systems.https://authors.library.caltech.edu/records/e76vs-tk842Cross‐correlation trajectory study of vibrational relaxation of HF (v=1–7) by HF (v=0)
https://resolver.caltech.edu/CaltechAUTHORS:20150617-110252744
Authors: {'items': [{'id': 'Coltrin-M-E', 'name': {'family': 'Coltrin', 'given': 'M. E.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1063/1.440653
Results are presented for a three‐dimensional quasiclassical trajectory study of the vibrational deactivation of vibrationally excited HF (v=1–7) by ground vibrational HF. A cross‐correlation method of analysis is used to calculate probabilities and rate constants for V–V and V–RT transitions using trajectory results. Comparisons are made of calculated total deactivation rate constants (V–V plus V–R T) with experimental values. The V–R T dominates the relaxation for higher v states, and increases particularly rapidly with increasing v. Comparisons are made with recent classical‐path calculations for this system, and in the use of Morse versus equivalent harmonic oscillator potentials.https://authors.library.caltech.edu/records/hq162-fk924Semiclassical quantization of multidimensional systems
https://resolver.caltech.edu/CaltechAUTHORS:RAMjcp80
Authors: {'items': [{'id': 'Ramaswamy-R', 'name': {'family': 'Ramaswamy', 'given': 'Ramakrishna'}}, {'id': 'Siders-P', 'name': {'family': 'Siders', 'given': 'P.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1063/1.439939
Low order classical perturbation theory is used to obtain semiclassical eigenvalues for a system of three anharmonically coupled oscillators. The results in the low energy region studied here agree well with the "exact" quantum values. The latter had been calculated by matrix diagonalization using a large basis set.https://authors.library.caltech.edu/records/wadez-m8w59Molecular Behavior in the Quasi-Periodic and Stochastic Regimes
https://resolver.caltech.edu/CaltechAUTHORS:20150702-102727259
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1980
DOI: 10.1111/j.1749-6632.1980.tb29685.x
Nonlinear dynamics has been applied to chemistry in a variety of ways, for example, in the analysis of spatial and temporal oscillations in chemical reactions. The
equations for the reaction rate at various regions of space are nonlinear in such cases. Several other papers in this volume touch upon this subject. Nonlinear dynamics has
also been used to treat collisions between molecules by solving Hamilton's equations for their motion. Many recent experimental data that have become available on
collisions and reaction dynamics have been treated in this way.https://authors.library.caltech.edu/records/9stkw-56091Perturbative examination of avoided crossings
https://resolver.caltech.edu/CaltechAUTHORS:RAMjcp81b
Authors: {'items': [{'id': 'Ramaswamy-R', 'name': {'family': 'Ramaswamy', 'given': 'Ramakrishna'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1981
DOI: 10.1063/1.441201
Quantum perturbation theory is used to examine the eigenvalues of a nonseparable Hamiltonian system in the classically regular and irregular regimes. As a function of the perturbation parameter, the eigenvalues obtained by exact (matrix diagonalization) methods undergo an avoided crossing. In the present paper perturbation theory is used as an approximate method to predict the locations of such avoided crossings in energy-parameter space. The sparsity of such avoided crossings in the Hénon–Heiles system is seen to produce regular sequences in the eigenvalues even when the classical motion is predominantly chaotic.https://authors.library.caltech.edu/records/rm3e9-m1j40On the onset of chaotic motion in deterministic systems
https://resolver.caltech.edu/CaltechAUTHORS:RAMjcp81a
Authors: {'items': [{'id': 'Ramaswamy-R', 'name': {'family': 'Ramaswamy', 'given': 'Ramakrishna'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1981
DOI: 10.1063/1.441202
In the present paper the classical counterpart of the quantum avoided crossing method for detecting chaos is described using classical (Lie-transform) perturbation theory and a grid of action variables. The results are applied to two systems of coupled oscillators with cubic and quartic nonlinearities. The plots of energy of members of the grid versus the perturbation parameter provide a visual description for predicting the onset of chaos.https://authors.library.caltech.edu/records/x9tvx-1gm30Quantum effects for electron-transfer reactions in the "inverted region"
https://resolver.caltech.edu/CaltechAUTHORS:20150624-121444071
Authors: {'items': [{'id': 'Siders-P', 'name': {'family': 'Siders', 'given': 'P.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1981
DOI: 10.1021/ja00394a004
Quantum effects in outer-sphere electron transfer reactions in the inverted region are considered. The results of quantum, "semiclassical", and classical calculations on model systems are presented. A series of highly exothermic reactions of tris(bipyridyl) complexes involving electronically excited reactants is discussed with regard to the possible importance of quantum effects and of alternate reaction pathways in understanding the failure of the series of reactions to exhibit pronounced "inverted" behavior. Electronically excited products or alternate atom-transfer mechanisms provide possible explanations for the large discrepancy.https://authors.library.caltech.edu/records/774am-ces10Dynamics of hydrogen atom and proton transfer reactions. Symmetric case
https://resolver.caltech.edu/CaltechAUTHORS:BABjcp81
Authors: {'items': [{'id': 'Babamov-V-K', 'name': {'family': 'Babamov', 'given': 'V. K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1981
DOI: 10.1063/1.441267
A method is devised for treating the transfer of a light particle such as a hydrogen atom or a proton between two heavy particles, for the case of a collinear symmetric reaction AH+A-->A+HA. Polar coordinates (rho,theta) with origin at the origin of the usual mass-weighted skewed-angle potential energy contour plot are employed to simplify the calculation. Symmetric and antisymmetric vibrationally adiabatic states are obtained at each rho. They provide an effective potential for the rho motion and are used to obtain the elastic adiabatic phase shifts for the rho motion and from them the transfer probability. The rho motion corresponds approximately to that of the heavy particles and the theta to that of the light one. Semiclassical limiting expressions are obtained and provide a description of light particle tunneling at low energies for heavy–light–heavy particle systems. Numerical results are given and the present approximation is good for the systems investigated.https://authors.library.caltech.edu/records/9ekp0-4q915On correlation functions and the onset of chaotic motion
https://resolver.caltech.edu/CaltechAUTHORS:KOSjcp81
Authors: {'items': [{'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Tabor-M', 'name': {'family': 'Tabor', 'given': 'M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1981
DOI: 10.1063/1.441323
A variety of correlation functions computed over a microcanonical ensemble for the Hénon–Heiles system are investigated. We find the general trend is that of a gradual change to some form of decaying behavior as the motion becomes predominantly chaotic. The decay of a mode energy correlation function indicates a time scale for intramolecular energy redistribution.https://authors.library.caltech.edu/records/nfprf-f6v27A simple classical model of infrared multiphoton dissociation
https://resolver.caltech.edu/CaltechAUTHORS:RAMjcp81c
Authors: {'items': [{'id': 'Ramaswamy-R', 'name': {'family': 'Ramaswamy', 'given': 'Ramakrishna'}}, {'id': 'Siders-P', 'name': {'family': 'Siders', 'given': 'Paul'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1981
DOI: 10.1063/1.441683
The classical mechanics of a system of two nonlinearly coupled oscillators driven by an oscillating electric field is studied. The presence of quasiperiodic and chaotic motion in the unforced system is shown to influence the nature of energy absorption. Two essentially different types of behavior are observed. In the first, energy is exchanged in a multiply periodic manner between the system and the forcing field. In the second regime, the energy exchange is erratic and a statistical analysis of a family of trajectories shows the role of the chaotic motion in the unforced system in the dissociation process. A theory for rate of photodissociation is presented and results are compared with those obtained from an ensemble of exact classical trajectories.https://authors.library.caltech.edu/records/cwh70-74p91On the frequency factor in electron transfer reactions and its role in the highly exothermic regime
https://resolver.caltech.edu/CaltechAUTHORS:20150629-144809463
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1981
DOI: 10.1002/kin.550130910
Consideration of current information on the dependence of the electron transfer rate on the radial separation distance and on the reactants′ radial distribution function suggests for adiabatic transfers a frequency factor closer to 10^(12)M^(−1) s^(−1) than to 10^(11)M^(−1) s^(−1). One effect is to raise the λ values estimated from self-exchange rate constants, and to extend thereby the range of ΔG°'s in which the "inverted region′" is masked by a diffusion-controlled reaction rate.https://authors.library.caltech.edu/records/5pfa4-mns58Quasiperiodic and Stochastic Behavior in Molecules
https://resolver.caltech.edu/CaltechAUTHORS:20120718-164823177
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1981
DOI: 10.1146/annurev.pc.32.100181.001411
The extent and rate of intramolecular energy transfer play a role in a variety of problems in chemical dynamics. Examples are unimolecular reactions (1 a,b), chemical activation (2a,b), vibrational-rotational-translation
energy distribution of the products of a dissociating species (3, 4), infrared multiphoton decomposition of molecules (5a,b, 6), internal conversion and intersystem crossing of electronically excited states (7a-d), dissociation of vibrationally excited state-selected van der Waals complexes (8), fluorescence spectra of electronically and vibrationally excited molecules
(9a,b, 10a,b), chemiluminescent spectra of vibrationally excited molecules (11), reactions induced by excitation of high overtones of a bond vibration (12a-c), and high overtone spectra (13a,b). The present article reviews
recent theoretical studies on the quasiperiodic and chaotic dynamical aspects of vibrational states and describes how those studies may be related to intramolecular randomization.https://authors.library.caltech.edu/records/0d0an-wys34The second R. A. Robinson Memorial Lecture. Electron, proton and related transfers
https://resolver.caltech.edu/CaltechAUTHORS:MARfdcs82
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1982
DOI: 10.1039/DC9827400007
Past and current developments in electron and proton transfer and in related fields are described. Broad classes of reactions have been considered from a unified viewpoint which offers a variety of experimental predictions. This introductory lecture considers various aspects of this many-faceted field. A simple equation is given for a highly exothermic electron-transfer reaction.https://authors.library.caltech.edu/records/eje5s-2c489Theory of highly exothermic electron transfer reactions
https://resolver.caltech.edu/CaltechAUTHORS:20150626-132435823
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Siders-P', 'name': {'family': 'Siders', 'given': 'Paul'}}]}
Year: 1982
DOI: 10.1021/j100394a009
The theory of highly exothermic homogeneous outer-sphere electron transfer reactions is discussed for transfers
occurring over a range of distances. A finite rate of diffusion of reactants and their long-range force are treated
by solving the diffusion equation numerically for the reactant pair distribution function. Steady-state solutions
for the bimolecular rate constant are compared with experimental data as well as with our recent approximate
analytic solution, which is found to agree in the present case. On the basis of short-time solutions, it is proposed
that experiments which measure electron transfer rates at short times following the onset of reaction improve
the possibility of observing the inverted effect in bimolecular systems. The chance of seeing it in linked systems
(unimolecular reactions) is even greater. The relation between the prediction of an "inverted region" in the
rate constant vs. ΔG° plot and the existence of a maximum in charge transfer spectral plots of intensity vs.
absorption frequency is pointed out.https://authors.library.caltech.edu/records/qbvk2-0ne63Cross-correlation trajectory study of vibrational relaxation of DF(v = 1 to 7) by DF(v = 0) and of HF by HF
https://resolver.caltech.edu/CaltechAUTHORS:COLjcp82
Authors: {'items': [{'id': 'Coltrin-M-E', 'name': {'family': 'Coltrin', 'given': 'M. E.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1982
DOI: 10.1063/1.443265
Three-dimensional quasiclassical trajectories and a cross-correlation method of analysis are used to study the vibrational relaxation of DF(v1 = 1 to 7) by DF(v2 = 0). Rate constants are calculated for V–V and V–R, T energy transfer. As was seen in earlier studies on HF–HF, the V–R, T mechanism becomes increasingly important at higher initial v1, as the V–V transfer moves further off resonance and also becomes increasingly endothermic. Both factors contribute to the decrease of V–V transfer rates with increasing v1 for the higher values of v1. Comparisons are made with results of a classical path study of vibrational relaxation in DF–DF and with experiment where possible. New results on the HF–HF V–V transfer rates are presented.https://authors.library.caltech.edu/records/kwrz0-pq497Semiclassical theory of intensities of vibrational fundamentals, overtones, and combination bands
https://resolver.caltech.edu/CaltechAUTHORS:20150624-092349300
Authors: {'items': [{'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Nold-D-W', 'name': {'family': 'Nold', 'given': 'D. W.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1982
DOI: 10.1021/j100209a001
Quantum mechanical and semiclassical results are compared for the spectrum of the Morse oscillator. When
an average quantum number [(n + m)/2] trajectory is employed for an n → m transition, good agreement is
obtained between the quantum and semiclassical intensities and between the frequencies, for the fundamental
and the overtones studied. Spectra of nonrotating OCS in the quasiperiodic and chaotic regions are presented,
and the intensities of a number of overtones and combination bands are calculated. Even very low intensity
transitions are observed.https://authors.library.caltech.edu/records/64qm8-a6k88Heavy mass barrier to intramolecular energy transfer
https://resolver.caltech.edu/CaltechAUTHORS:20150617-140457025
Authors: {'items': [{'id': 'Lopez-V', 'name': {'family': 'Lopez', 'given': 'V.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1982
DOI: 10.1016/0009-2614(82)80129-2
The dynamics of a collection of seven Morse or harmonic oscillators are investigated to model a molecule in which two halves are separated by a heavy atom. The results are related to a recent experiment on intramolecular dynamics and suggest an extension of the anharmonic local mode concept to groups.https://authors.library.caltech.edu/records/vnj6k-xf588Statistical Theory of Unimolecular Reactions and Intramolecular Dynamics
https://resolver.caltech.edu/CaltechAUTHORS:MARlc83
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1983
DOI: 10.1155/LC.2.203
In the present lecture we review experimental and theoretical developments in the field of intramolecular dynamics during the past sixty years. In a concluding section we consider possible implications for intramolecular laser selective chemistry.https://authors.library.caltech.edu/records/29dq3-mph98On the Theory of Intramolecular Energy Transfer
https://resolver.caltech.edu/CaltechAUTHORS:20120713-072845152
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1983
DOI: 10.1039/DC9837500103
We consider the distinguishing features of two main types of classical anharmonic motion in molecules, their quantum parallels, and conditions that classical chaos also be sufficient for "quantum chaos". Implications are considered for experimental reaction rates, R.R.K.M. theory, spectra and a possible type of system for intramolecular laser-selective chemistry. A theory of intramolecular energy transfer between two ligands of a heavy atom is described for a system which may contain many coordinates. It is partly statistical and, for the modes of each ligand which communicate through the heavy atom, dynamical.https://authors.library.caltech.edu/records/vhedx-qc791Comparison of quantal, classical, and semiclassical behavior at an isolated avoided crossing
https://resolver.caltech.edu/CaltechAUTHORS:20150617-105122572
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1983
DOI: 10.1063/1.445127
The quantal and classical/semiclassical behavior at an isloated avoided crossing are compared. While the quantum mechanical eigenvalue perturbation parameter plots exhibit the avoided crossing, the corresponding primitive semiclassical eigenvalue plots pass through the intersection. Otherwise, the eigenvalues agree well with the quantum mechanical values. The semiclassical splitting at the intersection is calculated from an appropriate Fourier transform. In the quasiperiodic regime, a quantum state near an avoided crossing is seen to exhibit typically more delocalization than the classical state. However, trajectories near the ''separatrix'' display a quasiperiodic ''transition'' between two zeroth order classical states.https://authors.library.caltech.edu/records/kqjbj-4hk97Dynamics of hydrogen atom and proton transfer reactions. Nearly degenerate asymmetric case
https://resolver.caltech.edu/CaltechAUTHORS:BABjcp83
Authors: {'items': [{'id': 'Babamov-V-K', 'name': {'family': 'Babamov', 'given': 'V. K.'}}, {'id': 'Lopez-V', 'name': {'family': 'Lopez', 'given': 'V.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1983
DOI: 10.1063/1.445442
A method for approximate treatment of collinear H atom or proton transfer reactions AH+B → A+HB which involve two nearly degenerate vibrational states is developed. The method is based on constructing a diabatic representation of the problem, i.e., one in which the reactant and the product vibrational states are distinguished as such throughout the collision. The diabatic representation is constructed with the aid of the adiabatic one discussed in an earlier paper. The treatment can also be applied to symmetric exchange reactions, in which case it yields good agreement with other results.https://authors.library.caltech.edu/records/t69wj-pc630Unimolecular reactions at low energies and RRKM behavior: isomerization and dissociation
https://resolver.caltech.edu/CaltechAUTHORS:20150624-095555455
Authors: {'items': [{'id': 'Khundkar-L-R', 'name': {'family': 'Khundkar', 'given': 'L. R.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Zewail-A-H', 'name': {'family': 'Zewail', 'given': 'A. H.'}}]}
Year: 1983
DOI: 10.1021/j100237a008
Rates of isomerization of electronically excited trans-stilbene and of the dissociation of isoquinoline-solvent
complexes in jet beams are compared with those expected from RRKM theory as a function of energy; the
comparison is made at low vibrational energies (~1200-3000 cm^(-1)). The jet result for the threshold energy
of the isomerization is compared with the activation energy for the reaction in solution. The two values are
in good agreement.https://authors.library.caltech.edu/records/ke6kd-bkk49Methods tor Plotting Trajectories tor Triatomic Molecules and Visualizing the Caustics
https://resolver.caltech.edu/CaltechAUTHORS:20150624-090603005
Authors: {'items': [{'id': 'Nold-D-W', 'name': {'family': 'Nold', 'given': 'D. W.'}}, {'id': 'Wardlaw-D-M', 'name': {'family': 'Wardlaw', 'given': 'D. M.'}}, {'id': 'Koszykowski-M-L', 'name': {'family': 'Koszykowski', 'given': 'M. L.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1983
DOI: 10.1021/j100238a011
A simple and efficient computational method is introduced for visualizing the structure of three-dimensional
classical trajectories. Examples are presented for Hamiltonians with incommensurate frequencies, as well as
with 1:1 and 2:1 resonances. Results are also presented for several states of OCS, one of which shows an accidental
4:1 resonance. Implications of this method for path integral quantization and perturbation methods are discussed.https://authors.library.caltech.edu/records/1586t-2yh53Densities of vibrational states of given symmetry species and their use in statistical estimates involving Coriolis and anharmonic effects
https://resolver.caltech.edu/CaltechAUTHORS:20150623-145825505
Authors: {'items': [{'id': 'Lederman-S-M', 'name': {'family': 'Lederman', 'given': 'Steven M.'}}, {'id': 'Runnels-J-H', 'name': {'family': 'Runnels', 'given': 'John H.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1983
DOI: 10.1021/j100245a011
A simple approximate statistical formula for densities of vibrational states of given symmetry is presented.
The formula becomes increasingly exact at higher vibrational energies. Application to Coriolis and anharmonic
effects is discussed.https://authors.library.caltech.edu/records/ab9qx-h0s44Uniform semiclassical theory of avoided crossings
https://resolver.caltech.edu/CaltechAUTHORS:20120712-144920694
Authors: {'items': [{'id': 'Uzer-T', 'name': {'family': 'Uzer', 'given': 'T.'}}, {'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1983
DOI: 10.1063/1.446326
A voided crossings influence spectra and intramolecular redistribution of energy. A semiclassical theory
of these avoided crossings shows that when primitive semiclassical eigenvalues are plotted vs a parameter
in the Hamiltonian they cross instead of avoiding each other. The trajectories for each are connected by a
classically forbidden path. To obtain the avoided crossing behavior, a uniform semiclassical theory of
avoided crossings is presented in this article for the case where that behavior is generated by a classical
resonance. A low order perturbation theory expression is used as the basis for a functional form for the
treatment. The parameters in the expression are evaluated from canonical invariants (phase integrals)
obtained from classical trajectory data. The results are compared with quantum mechanical results for
the splitting, and reasonable agreement is obtained. Other advantages of the uniform method are
described.https://authors.library.caltech.edu/records/k0ydj-d1f75Dynamics of hydrogen atom and proton transfer reactions. Simplified analytic two-state formulae
https://resolver.caltech.edu/CaltechAUTHORS:20150629-111957983
Authors: {'items': [{'id': 'Babamov-V-K', 'name': {'family': 'Babamov', 'given': 'Vasil K.'}}, {'id': 'Lopez-V', 'name': {'family': 'Lopez', 'given': 'Vicente'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1983
DOI: 10.1016/0009-2614(83)87024-9
Analytical formulae for the threshold region of the reaction probability curve for a nearly degenerate H-atom transfer are given and shown to yield good agreement with exact results for a two-state model system. Application to H and H+ transfer in complex systems is discussed.https://authors.library.caltech.edu/records/jb0na-9h943Comparison of multichannel and two-state calculations for H-atom transfer between two nearly degenerate states
https://resolver.caltech.edu/CaltechAUTHORS:20150617-134009275
Authors: {'items': [{'id': 'Abusalbi-N', 'name': {'family': 'Abusalbi', 'given': 'N.'}}, {'id': 'Kouri-D-J', 'name': {'family': 'Kouri', 'given': 'D. J.'}}, {'id': 'Lopez-V', 'name': {'family': 'Lopez', 'given': 'Vicente'}}, {'id': 'Babamov-V-K', 'name': {'family': 'Babamov', 'given': 'Vasil K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1016/0009-2614(84)85276-8
Multichannel and two-state calculations are made for a collinear H-atom transfer between two heavy masses. The particular reaction studied is on where the initial vibrational state of the reactants is nearly degenerate with a vibrational state of the products. The two sets of results for the reaction probability are in good agreement with each other.https://authors.library.caltech.edu/records/j9dqz-01y80Semiclassical and Quantum Vibrational Intensities
https://resolver.caltech.edu/CaltechAUTHORS:20150629-122749538
Authors: {'items': [{'id': 'Wardlaw-D-M', 'name': {'family': 'Wardlaw', 'given': 'D. M.'}}, {'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1021/j150647a044
The semiclassical theory of infrared vibrational intensities is extended and applied to multidimensional systems. The validity and utility of the semiclassical approach is assessed by comparison with perturbative and exact quantum results for one nonresonant and two resonant model Hamiltonian systems. Approximate mean trajectories are found to provide intensities accurate to within ~20% and frequencies accurate to within ~ 1% for almost all transitions studied. More accurate semiclassical results can be obtained by using exact mean trajectories and, for intensities in the nonresonant system, trajectories determined by an improved correspondence rule. The advantages and limitations of the semiclassical method are summarized.https://authors.library.caltech.edu/records/8wvv9-d2c74An exponentiated DWBA formula for H-atom transfers. Extensions to lower barrier potentials and to higher energies
https://resolver.caltech.edu/CaltechAUTHORS:BABjcp84
Authors: {'items': [{'id': 'Babamov-V-K', 'name': {'family': 'Babamov', 'given': 'Vasil K.'}}, {'id': 'Lopez-V', 'name': {'family': 'Lopez', 'given': 'Vicente'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1063/1.446939
Analytic formulas obtained earlier for the probability of H-atom transfer between two heavy particles in the threshold region are extended to higher energies and to systems with lower barrier potentials. The calculated reaction probability vs energy curve is in good agreement with numerical results for the model system investigated involving transfer between two nearly degenerate states.https://authors.library.caltech.edu/records/gjbk4-6kd23Eigenvalues of the Schrödinger equation for a periodic potential with nonperiodic boundary conditions: A uniform semiclassical analysis
https://resolver.caltech.edu/CaltechAUTHORS:CONjcp84
Authors: {'items': [{'id': 'Connor-J-N-L', 'name': {'family': 'Connor', 'given': 'J. N. L.'}}, {'id': 'Uzer-T', 'name': {'family': 'Uzer', 'given': 'T.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Smith-A-D', 'name': {'family': 'Smith', 'given': 'A. D.'}}]}
Year: 1984
DOI: 10.1063/1.446581
A uniform semiclassical expression for the eigenvalues of a one dimensional periodic Schrödinger equation with nonperiodic boundary conditions has been derived. The potential energy function can have any number of symmetric or asymmetric barriers and wells. The treatment is uniform in that the classical turning points can come close together, coalesce, and move into the complex plane as the energy passes through a barrier maximum. A detailed application is made to Mathieu functions of integer order; the equations themselves include the case of fractional order. Approximate semiclassical expressions are derived for the widths of the energy bands and the energy gaps of the periodic Mathieu equation when these quantities are small. The semiclassical results give a physical interpretation to formulas present in the mathematical literature and to the decrease in the splitting of a sequence of avoided crossings with increasing quantum numbers in coupled oscillator systems. Numerical calculations are reported to illustrate the high accuracy of the semiclassical formulas.https://authors.library.caltech.edu/records/ps2k9-4mk51RRKM reaction rate theory for transition states of any looseness
https://resolver.caltech.edu/CaltechAUTHORS:20150629-102705959
Authors: {'items': [{'id': 'Wardlaw-D-M', 'name': {'family': 'Wardlaw', 'given': 'David M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1016/0009-2614(84)85219-7
Unimolecular rate theory for various types of reactions is implemented for any looseness of transition state. Quantum states are counted for all but the "transitional" modes, their phase space being counted via Monte Carlo sampling. The rate constant k_(EJ) is then weighted with the initial E and J distributions.https://authors.library.caltech.edu/records/5y65q-txj64A simple DWBA ("Franck–Condon") treatment of H-atom transfers between two heavy particles
https://resolver.caltech.edu/CaltechAUTHORS:LOPjcp84
Authors: {'items': [{'id': 'Lopez-V', 'name': {'family': 'Lopez', 'given': 'Vicente'}}, {'id': 'Babamov-V-K', 'name': {'family': 'Babamov', 'given': 'Vasil K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1063/1.448135
A simple DWBA (Franck–Condon) method for calculating the probability of transferring a light particle between two heavy ones in a collinear collision at energies below and around the reaction threshold is presented. The region is the important one for the thermal reaction rates. The method is tested for two different model LEPS surfaces for H-atom transfer with moderately high barriers. The results are in good agreement with those of accurate multichannel calculations.The transition probability is calculated as an overlap integral over the reactants' and products' wave functions and the interaction potential. The reactants' and products' wave functions are calculated from their respective distortion potentials as one-term adiabatically separable approximations. Both the distortion potentials and the interaction potentials are extracted straightforwardly from the LEPS surface. The novel feature of the approach is that for the first time accurate results for the absolute values of the reaction probability are obtained from a simple overlap of single-channel approximate wave functions obtained directly from the respective parts of the potential energy surface for the reaction.https://authors.library.caltech.edu/records/bvqs6-6mv65Nonadiabatic processes involving quantum-like and classical-like coordinates with applications to nonadiabatic electron transfers
https://resolver.caltech.edu/CaltechAUTHORS:20120629-141832137
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1063/1.447418
Nonadiabatic processes may involve both classical‐like and quantum‐like coordinates. A semiclassical analysis is used to treat the contribution of the former to the Franck–Condon factor in the reaction rate expression, thereby avoiding the usual harmonic oscillator approximation. Microcanonical and canonical rate constants are calculated, yielding an expression which includes contributions from both types of coordinates. The results are applied to nonadiabatic electron transfer reactions in solution, and show how ΔG^0 enters the final rate expression, even though ΔE^0 is present in the initial Golden Rule nonadiabatic formula. This result avoids an approximation which has arisen in the nonadiabatic electron transfer literature.https://authors.library.caltech.edu/records/x5qz3-16p80RRKM and non-RRKM behavior in chemical activation and related studies
https://resolver.caltech.edu/CaltechAUTHORS:20150629-153003387
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Hase-W-L', 'name': {'family': 'Hase', 'given': 'William L.'}}, {'id': 'Swamy-K-N', 'name': {'family': 'Swamy', 'given': 'Kandadai N.'}}]}
Year: 1984
DOI: 10.1021/j150670a040
An expression is derived for the pressure dependence of a chemical activation unimolecular rate constant at a fixed total energy and angular momentum in terms of the distribution of unimolecular lifetimes. This rate constant is shown to have a certain insensitivity at low pressures to the form of the lifetime distribution. A kinetic model is then introduced based on a finite rate of intramolecular vibrational energy redistribution. The model provides an analytical explanation of a recent finding in a trajectory calculation for a particular chemical activation system, that the chemical activation unimolecular rate constant at low pressures equals the 7 = 0 microcanonical value even though the unimolecular lifetime distribution is highly non-RRKM. A similar result is predicted for a class of such systems. Implications are described.https://authors.library.caltech.edu/records/ca3s3-fd212Quantization with operators appropriate to shapes of trajectories and classical perturbation theory
https://resolver.caltech.edu/CaltechAUTHORS:20120703-092820677
Authors: {'items': [{'id': 'Uzer-T', 'name': {'family': 'Uzer', 'given': 'T.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1063/1.447487
Quantization is discussed for molecular systems having a zeroth order pair of doubly degenerate
normal modes. Algebraic quantization is employed using quantum operators appropriate to the
shape of the classical trajectories or wave functions, together with Birkhoff-Gustavson
perturbation theory and the W eyl correspondence for operators. The results are compared with a
previous algebraic quantization made with operators not appropriate to the trajectory shape.
Analogous results are given for a uniform semiclassical quantization based on Mathieu functions of fractional order. The relative sensitivities of these two methods (AQ and US) to the use of operators and coordinates related to and not related to the trajectory shape is discussed. The
arguments are illustrated using principally a Hamiltonian for which many previous results are available.https://authors.library.caltech.edu/records/j20fw-74218The highly excited C-H stretching states of CHD_3, CHT_3, and CH_3D
https://resolver.caltech.edu/CaltechAUTHORS:20120703-093554866
Authors: {'items': [{'id': 'Voth-G-A', 'name': {'family': 'Voth', 'given': 'Gregory A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Zewail-A-H', 'name': {'family': 'Zewail', 'given': 'A. H.'}}]}
Year: 1984
DOI: 10.1063/1.447650
Unlike many other molecules having local modes, the highly excited C-H stretching states of
CHD_3 show well resolved experimental spectra and simple Fermi resonance behavior. In this
paper the local mode features in this prototype molecule are examined using a curvilinear
coordinate approach. Theory and experiment are used to identify the vibrational state coupling.
Both kinetic and potential terms are employed in order to characterize the coupling of the C-H
stretch to various other vibrational modes, notably those including D-C-H bending. Predictions
are also made for CHT_3 and the role of dynamical coupling on the vibrational states of CH_3D
explored. Implications of these findings for mode-specific and other couplings are discussed.https://authors.library.caltech.edu/records/rkn3k-ehn24Densities of vibrational states of given symmetry species. Linear molecules and rovibrational states of nonlinear molecules
https://resolver.caltech.edu/CaltechAUTHORS:LEDjcp84
Authors: {'items': [{'id': 'Lederman-S-M', 'name': {'family': 'Lederman', 'given': 'Steven M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1063/1.447663
A simple statistical expression is given for the density of states of any symmetry species for linear molecules. Molecules with one and two pairs of doubly degenerate bending modes are considered. The results of our previous paper for vibrational states of nonlinear molecules are also extended to include density of rotational-vibrational states by symmetry species. The various expressions are tested by comparing with exact counts of states.https://authors.library.caltech.edu/records/76c0y-d5c66A model for orientation effects in electron‐transfer reactions
https://resolver.caltech.edu/CaltechAUTHORS:20120629-141911399
Authors: {'items': [{'id': 'Siders-P', 'name': {'family': 'Siders', 'given': 'Paul'}}, {'id': 'Cave-R-J', 'name': {'family': 'Cave', 'given': 'Robert J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1984
DOI: 10.1063/1.447665
A method for solving the single‐particle Schrödinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on TBA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells.https://authors.library.caltech.edu/records/vhh02-0d305Semiclassical Dressed State Theory for the Vibrational Excitation of a Morse Oscillator by Radiation
https://resolver.caltech.edu/CaltechAUTHORS:20150629-101153293
Authors: {'items': [{'id': 'Voth-G-A', 'name': {'family': 'Voth', 'given': 'Gregory A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1985
DOI: 10.1021/j100257a015
A uniform semiclassical theory is developed to treat the interaction of a Morse oscillator with a monochromatic radiation field. The correspondence with quantum-mechanical dressed state theory for the Rabi and resonant excitation frequencies is demonstrated, and the semiclassical theory is used to describe resonant one- and two-photon absorption processes. The results are extended to state-to-state vibrational excitation in a polyatomic species.https://authors.library.caltech.edu/records/gytjb-jfx41Semiclassical theory of Fermi resonance between stretching
and bending modes in polyatomic molecules
https://resolver.caltech.edu/CaltechAUTHORS:20120629-080822904
Authors: {'items': [{'id': 'Voth-G-A', 'name': {'family': 'Voth', 'given': 'Gregory A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1985
DOI: 10.1063/1.448847
Approximate semiclassical solutions are developed for a system of a Morse oscillator coupled to a harmonic oscillator via a nonlinear perturbation. This system serves as a model for the interaction of an excited stretching mode with a bending mode in a polyatomic molecule. Three semiclassical methods are used to treat this model. In particular, a matrix diagonalization, a two‐state model, and a uniform semiclassical approximation (USC) based on Mathieu functions are each used to determine the splittings and state mixing involved in these stretch–bend Fermi resonances. For small perturbations, approximate analytic semiclassical expressions are obtained for the system treated. These analytic expressions are given for the splittings using a two‐state or USC method and for the overlaps of the zeroth order states with the eigenstates of the molecule using a USC method.https://authors.library.caltech.edu/records/4dazv-xgr96Electron transfers in chemistry and biology
https://resolver.caltech.edu/CaltechAUTHORS:20150623-101844650
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Sutin-N', 'name': {'family': 'Sutin', 'given': 'Norman'}}]}
Year: 1985
DOI: 10.1016/0304-4173(85)90014-X
Electron-transfer reactions between ions and
molecules in solution have been the subject of
considerable experimental study during the past
three decades. Experimental results have also been
obtained on related phenomena, such as reactions
between ions or molecules and electrodes, charge-transfer
spectra, photoelectric emission spectra of
ionic solutions, chemiluminescent electron transfers,
electron transfer through frozen media, and
electron transfer through thin hydrocarbon-like
films on electrodes.https://authors.library.caltech.edu/records/84y1j-pmb45Unimolecular reaction rate theory for transition states of partial looseness. II. Implementation and analysis with applications to NO2 and C2H6 dissociations
https://resolver.caltech.edu/CaltechAUTHORS:WARjcp85
Authors: {'items': [{'id': 'Wardlaw-D-M', 'name': {'family': 'Wardlaw', 'given': 'David M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1985
DOI: 10.1063/1.449151
Implementation of RRKM theory for unimolecular dissociations having transition states of any degree of looseness is described for reactions involving dissociation into two fragments. The fragments may be atomic, diatomic, or polyatomic species. Action-angle and internal coordinates for the transitional modes of the reaction, transformations to Cartesian coordinates, and other calculational aspects are described. Results for the NO2-->NO+O reaction are presented, including the dependence of the microcanonical rate constant on the bond fission and bending potentials for model potential energy surfaces. Illustrative calculations for the C2H6-->2CH3 reaction are also given.https://authors.library.caltech.edu/records/n395v-bk832The Relation Between the Barriers for Thermal and Optical Electron Transfer Reactions in Solution
https://resolver.caltech.edu/CaltechAUTHORS:20150630-112955684
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Sutin-N', 'name': {'family': 'Sutin', 'given': 'Norman'}}]}
Year: 1986
DOI: 10.1080/02603598608072279
The relation between the energy of the intervalence (or metal-to-metal charge-transfer) transition in mixed-valence systems and the magnitude of the barrier to thermally activated electron transfer is described. We note that, contrary to what has frequently been assumed, the relation is in terms of free energies rather than internal energies or enthalpies. It is also shown, from plots of the enthalpies of the reactants and products versus the reaction coordinate, that negative activation enthalpies are a natural consequence when the standard enthalpy change for the reaction is sufficiently negative.https://authors.library.caltech.edu/records/063p9-wbm71Quantum and classical energy transfer between ligands of a heavy metal atom
https://resolver.caltech.edu/CaltechAUTHORS:20150629-101605534
Authors: {'items': [{'id': 'Lederman-S-M', 'name': {'family': 'Lederman', 'given': 'Steven M.'}}, {'id': 'Lopez-V', 'name': {'family': 'Lopez', 'given': 'Vicente'}}, {'id': 'Voth-G-A', 'name': {'family': 'Voth', 'given': 'Gregory A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1016/0009-2614(86)85020-5
Quantum and classical vibrational energy transfer between two ligands separated by a heavy atom are compared for a model system, one ligand being vibrationally excited initially and the other unexcited. Similarities and differences of quantum and classical results are noted. The approximate separability of certain modes simplifies the interpretation.https://authors.library.caltech.edu/records/zqrq5-g2a07Adiabatically reduced coupled equations for intramolecular dynamics calculations
https://resolver.caltech.edu/CaltechAUTHORS:20120627-095307849
Authors: {'items': [{'id': 'Voth-G-A', 'name': {'family': 'Voth', 'given': 'Gregory A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.450388
"Adiabatically reduced" coupled equations are derived to obtain an approximate quantum mechanical solution for the dynamics of nonstationary states in isolated polyatomic molecules. Under suitable conditions, the number of such equations is considerably less than the number of coupled equations needed in practice for the exact calculation. The relationship of the present technique to several other methods, including the partitioning method, is discussed, and specific applications of the present treatment are given.https://authors.library.caltech.edu/records/x06nv-3re18A semiclassical model for orientation effects in electron transfer reactions
https://resolver.caltech.edu/CaltechAUTHORS:CAVjcp86
Authors: {'items': [{'id': 'Cave-R-J', 'name': {'family': 'Cave', 'given': 'Robert J.'}}, {'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.450290
An approximate solution to the single-particle Schrödinger equation with an oblate spheroidal potential well of finite depth is presented. The electronic matrix element HBA for thermal electron transfer is calculated using these wave functions, and is compared with values of HBA obtained using the exact solution of the same Schrödinger equation. The present method yields accurate results for HBA, within the oblate spheroidal potential well model, and is useful for examining the orientational effects of the two centers on the rate of electron transfer.https://authors.library.caltech.edu/records/9jnrm-z7289Mutual orientation effects on electron transfer between porphyrins
https://resolver.caltech.edu/CaltechAUTHORS:20150626-144609048
Authors: {'items': [{'id': 'Cave-R-J', 'name': {'family': 'Cave', 'given': 'Robert J.'}}, {'id': 'Siders-P', 'name': {'family': 'Siders', 'given': 'Paul'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1021/j100398a044
Mutual orientation effects on the rate of nonadiabatic electron transfer between several diporphyrin pairs of experimental
interest are examined. The electronic matrix element for electron transfer is calculated within a one-electron spheroidal
model for a variety of states and orientations which are relevant to both biological and synthetic electron-transfer systems.
Both the mutual orientation of the pairs and the nodal structure of the donor and acceptor orbitals can have large effects
on calculated rates.https://authors.library.caltech.edu/records/vmp1h-6w067Dielectric relaxation and intramolecular electron transfers
https://resolver.caltech.edu/CaltechAUTHORS:SUMjcp86a
Authors: {'items': [{'id': 'Sumi-H', 'name': {'family': 'Sumi', 'given': 'H.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.450804
Intramolecular charge transfer are considered for the case that the motion of the system is on a single potential energy surface. The case where this motion occurred on two surfaces was considered elsewhere. The former is shown to be much preferable for studies of solvent dynamics. Several aspects of the relation between "constant charge" dielectric relaxation time of the polar solvent and the experimental decay time of emission from the polar excited state of the solute are discussed for hydrogen-bonded systems.https://authors.library.caltech.edu/records/t0j52-a0c08Dynamical effects in electron transfer reactions
https://resolver.caltech.edu/CaltechAUTHORS:SUMjcp86b
Authors: {'items': [{'id': 'Sumi-H', 'name': {'family': 'Sumi', 'given': 'H.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.449978
A theoretical treatment is given for the effect of intramolecular vibrational and diffusive solvent orientational motions on the rate of electron transfer reactions. Four limiting cases are considered for the two-electronic state problem: slow reaction, wide and narrow reaction window, and nondiffusing limits. With the aid of a decoupling approximation, an expression is derived for the reaction rate which reduces to the appropriate expression for each limiting case when the latter is approached. Under certain conditions the time dependence of the survival probability is multiexponential rather than single exponential. Because of this behavior two average survival times are defined and expressions for each are obtained. Experimental data are considered with the present treatment in mind. One feature of the present work is a more general analysis for the case that both vibrational and solvent diffusive motion contribute to the activation process. The relation to previous works in the literature is described.https://authors.library.caltech.edu/records/p877e-kc451Local group modes and the dynamics of intramolecular energy transfer across a heavy atom
https://resolver.caltech.edu/CaltechAUTHORS:LOPjcp86
Authors: {'items': [{'id': 'Lopez-V', 'name': {'family': 'Lopez', 'given': 'Vicente'}}, {'id': 'Fairen-V', 'name': {'family': 'Fairen', 'given': 'Victor'}}, {'id': 'Lederman-S-M', 'name': {'family': 'Lederman', 'given': 'Steven M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.449906
The dynamics of energy transfer is discussed for a model system in which two ligands are separated by a heavy atom. Numerical and analytical results are given for the case that each ligand is a CC. In the quasiperiodic regime, the dynamics are interpreted using perturbation theory. Local group modes involved in an intramolecular energy localization which can occur in this regime are identified. An approximate separation of the primarily ligand–ligand motions from the primarily ligand–metal–ligand ones occurs in the clearly quasiperiodic regime and also at an energy where the power spectra of the bond coordinates are "grassy." The overall analysis is used to make predictions for systems with larger ligands, when the primarily metal atom–ligand modes are, as above, approximately separable from the primarily intraligand ones.https://authors.library.caltech.edu/records/pz8k6-61q43Solvent dynamics and vibrational effects in electron transfer reactions
https://resolver.caltech.edu/CaltechAUTHORS:20150617-130217766
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Sumi-H', 'name': {'family': 'Sumi', 'given': 'H.'}}]}
Year: 1986
DOI: 10.1016/0022-0728(86)80507-1
Intramolecular vibrational effects can modify considerably the effect of solvent dynamics on the rates of electron transfer reactions, even for a fixed free energy barrier. Results of a previous paper by the authors are applied in an approximate way to provide a simplified formula for the reaction rate. The formula includes these effects and reduces to a well-known one of Kramers under a appropriate conditions and when, in addition, vibrational effects are absent.https://authors.library.caltech.edu/records/y8rx3-6wc70Theory, experiment, and reaction rates. A personal view
https://resolver.caltech.edu/CaltechAUTHORS:20150629-110344836
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1021/j100407a001
Occasionally as scientists we have the good fortune to stumble
onto problems whose significance and solution turn out to be more
far-reaching than may have been anticipated at the time. Such
proved to be the case in my own experience with unimolecular
and electron-transfer reactions and, to a lesser degree, with a few
other problems as well. I am particularly indebted to the organizers
of this issue for their recognition of 35 years of "RRKM"
theory and 30 years of the electron-transfer theory. Also, I am
especially indebted to my many colleagues who have contributed
to the field and to this issue.https://authors.library.caltech.edu/records/nn4q7-5k237A test of two approximate two-state treatments for the dynamics of H-atom transfers between two heavy particles
https://resolver.caltech.edu/CaltechAUTHORS:KLIjcp86a
Authors: {'items': [{'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Babamov-V-K', 'name': {'family': 'Babamov', 'given': 'Vasil K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.451835
Reactive transition probabilities and Boltzmann-averaged reactive transition probabilities for a slightly off-resonant model H-atom transfer system with an appreciable energy barrier are calculated using the approximate methods of Babamov et al. and of Crothers–Stückelberg. Both are compared with the corresponding quantities obtained from a numerical two-state treatment of the same model system. The method of Babamov et al. is seen to give more accurate results for the transition probabilities at energies below and around the reaction threshold, and much more accurate results for the Boltzmann-averaged probabilities in a wide range of temperatures than the second method. The relative merits of the two formulas are discussed.https://authors.library.caltech.edu/records/40mf5-8q532Semiclassical calculation of eigenvalues for higher order resonances in nonseparable oscillator systems
https://resolver.caltech.edu/CaltechAUTHORS:NOIjcp86
Authors: {'items': [{'id': 'Noid-D-W', 'name': {'family': 'Noid', 'given': 'D. W.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.450951
It is shown how the "trajectory-close method" introduced in earlier papers of this series can be used to treat other resonant systems semiclassically. The method, which does not involve the use of any curvilinear coordinate system, is illustrated for two coupled oscillators which have 3:1, 4:1, 5:1, 3:2, and 5:2 internal resonances. It is readily executed and it is shown how it can be extended to the three-oscillator case. This work supplements our earlier studies of 1:1, 2:1, and 3:1 resonant systems using this technique. Shapes of eigentrajectories and of corresponding quantum mechanical wave functions are compared for each of these systems. The paper also contains a survey of and comparison with other semiclassical methods which have been applied to systems with internal resonanceshttps://authors.library.caltech.edu/records/qrcc6-4gz70Unimolecular reaction rate theory for transition states of any looseness. 3. Application to methyl radical recombination
https://resolver.caltech.edu/CaltechAUTHORS:20150629-124940889
Authors: {'items': [{'id': 'Wardlaw-D-M', 'name': {'family': 'Wardlaw', 'given': 'David M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1021/j100412a098
The theory for unimolecular reactions described in part 1 is applied to the recombination of methyl radicals in the high-pressure limit. The model potential energy surface and the methodology are briefly described. Results are presented for the recombination rate constant k_ ∞ at T = 300, 500, 1000, and 2000 K. Canonical and Boltzmann averaged microcanonical values of k_ ∞ are compared, and the influence of a potential energy interpolation parameter and a separation-dependent symmetry correction on k_ ∞ are examined. Earlier theoretical models and extensive experimental results are compared with the present results which are found to have a negative temperature dependence. The present results agree well with some of the available but presently incomplete experimental determinations of the high-pressure recombination rate constant for this reaction over the 300-2000 K temperature range. There is also agreement with a decomposition rate constant for a vibrationally excited ethane molecule produced by chemical activation.https://authors.library.caltech.edu/records/czxg4-r5k86Product quantum state distributions in unimolecular reactions involving highly flexible transition states
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp86
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.451693
An expression for the distribution of quantum states of the reaction products of unimolecular dissociations is obtained, based on statistical theory. A recently formulated RRKM-type treatment of unimolecular reactions with highly flexible transition states is used to obtain a distribution of quantum states of the products, by introducing an adiabatic approximation for motion from transition state to products. Any impulsive (nonadiabatic) exit channel effects are neglected thereby. Both the final yields of the quantum states of the products and the time evolution of these states are considered. The time evolution of the yield of the products can permit a direct test of non-RRKM effects and, additionally via the long-time component, of other aspects of RRKM theory. The long-time component of the yield of individual quantum states of the products then provides a test of the additional (here, adiabatic) approximation. Such tests are the more definitive the narrower the distribution of initial E's and J's of the dissociating molecule.https://authors.library.caltech.edu/records/z2zx0-8nm28Iteratively determined effective Hamiltonians for the adiabatically reduced coupled equations approach to intramolecular dynamics calculations
https://resolver.caltech.edu/CaltechAUTHORS:KLIjcp86b
Authors: {'items': [{'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Voth-G-A', 'name': {'family': 'Voth', 'given': 'Gregory A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1986
DOI: 10.1063/1.451691
An iterative procedure is proposed for determining increasingly accurate effective Hamiltonians for use in the adiabatically reduced coupled equations approach to intramolecular dynamics calculations [J. Chem. Phys. 84, 2254 (1986)]. The relationships between this iterative determination of the effective Hamiltonian, which is based on an adiabatic approximation, and some other partitioning methods for determining an effective Hamiltonian are discussed. The present iterative procedure provides accurate agreement with the exact dynamics for the two specific model systems studied.https://authors.library.caltech.edu/records/n481e-qy977Recent Developments in Electron Transfer Reactions
https://resolver.caltech.edu/CaltechAUTHORS:20150702-121009995
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1987
Earlier results and more recent developments in electron transfer reactions are reviewed. The more recent results include inverted behavior, electronic orientation effects on reaction rates, solvent dynamics, early steps in photosynthesis, and light emission from metal electrodes.https://authors.library.caltech.edu/records/hghkq-92v92Superexchange versus an intermediate BChl− mechanism in reaction centers of photosynthetic bacteria
https://resolver.caltech.edu/CaltechAUTHORS:20150617-100539459
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1987
DOI: 10.1016/0009-2614(87)80061-1
Kinetic and singlet-triplet data are used to treat the mechanism of electron transfer for BChl*_2-BChl-BPh in bacterial photosynthetic reaction centers. The data favor a two-step transfer rather than a superexchange single step.https://authors.library.caltech.edu/records/vfbpn-hs295Dynamical effects in electron transfer reactions. II. Numerical solution
https://resolver.caltech.edu/CaltechAUTHORS:20120626-123353890
Authors: {'items': [{'id': 'Nadler-W', 'name': {'family': 'Nadler', 'given': 'Walter'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1987
DOI: 10.1063/1.451951
In part I a reaction–diffusion equation was introduced for the description of electron transfer reactions which are induced by fluctuations in both the solvent polarization and in the intramolecular vibrational coordinates. We analyze the model employing a generalized moment expansion for the time behavior of the survival probability Q(t), i.e., for the fraction of molecules that have not transferred their electron at time t. Numerical and, in the narrow reaction window limit, analytical solutions are given for the average survival times τ. When the contribution of the intramolecular coordinates is appreciable an approximate power‐law behavior τ∝τ^α_L, with 0<α≤1, is found for the dependence of τ on the solvent dielectric relaxation time τ_L, in the large τ_L regime. Within the framework of the generalized moment description Q(t) is approximated as a superposition of several optimized exponential functions. In the small and intermediate τ_L regimes it is found that a single‐ or bi‐exponential description, respectively, is sufficient. Simple formulas for such approximations in terms of the average survival times are given. Furthermore it is demonstrated that in the large τ_L regime a truly multiexponential time behavior for the survival probability is encountered which, over a certain range of time, can appear to be algebraic, i.e., Q(t) ∝t^(−γ). The relation of these results to experimental data is discussed.https://authors.library.caltech.edu/records/bt8mq-cyr32Low-frequency expansion for probability amplitudes: An alternative approach to certain intramolecular dynamics problems
https://resolver.caltech.edu/CaltechAUTHORS:20120626-093523453
Authors: {'items': [{'id': 'Nadler-W', 'name': {'family': 'Nadler', 'given': 'Walter'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1987
DOI: 10.1063/1.452346
We present an algorithm to determine the averaged time evolution of the probability amplitude for a nonstationary state in a quantum mechanical system. The algorithm is based on a low‐frequency expansion of the probability amplitude and is related to the generalized moment expansion method which has been applied successfully to the description of dynamic correlation functions in stochastic systems. It is shown that the proposed algorithm gives excellent results for the description of quantum beats in the time evolution of the occupation probability for a nonstationary state in model systems. The relation of the algorithm to other theoretical approaches and the relevance for the description of intramolecular energy transfer processes is discussed.https://authors.library.caltech.edu/records/8vy5k-xcx46High pressure rate constants for unimolecular dissociation/free radical recombination: Determination of the quantum correction via quantum Monte Carlo path integration
https://resolver.caltech.edu/CaltechAUTHORS:KLIjcp87
Authors: {'items': [{'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1987
DOI: 10.1063/1.452985
The determination of a quantum correction factor for the transitional modes of a unimolecular dissociation/free radical recombination reaction having a transition state of varying looseness is described. The quantum correction factor for the high pressure canonical rate constant is calculated via Monte Carlo path integral evaluation of partition function ratios, and is applied to the recombination reaction 2CH3-->C2H6.https://authors.library.caltech.edu/records/rpeyz-7wv04Mechanisms of the Early Steps in Bacterial Photosynthesis and Their Implications for Experiment
https://resolver.caltech.edu/CaltechAUTHORS:20150629-142629044
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1002/ijch.198800031
The current situation on experiment and theory as regards the early electron transfer steps in bacterial photosynthesis is discussed. Recent experiments have limited the mechanistic possibilities, while an internal consistency test has limited the values of some parameters in the superexchange mechanism. The partitioning method has provided a useful and unified way of treating superexchange and other properties in these systems. The alternative reaction mechanisms have a number of consequences, and various experimental tests are considered or suggested.https://authors.library.caltech.edu/records/gs52y-83k64Non-exponential time behavior of electron transfer in an inhomogeneous polar medium
https://resolver.caltech.edu/CaltechAUTHORS:20150629-121821767
Authors: {'items': [{'id': 'Nadler-W', 'name': {'family': 'Nadler', 'given': 'W.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1016/0009-2614(88)87083-0
An analysis is made of electron transfer (ET) in a polar medium described by a distribution of dielectric relaxation times, for the case that intramolecular contributions to the ET are negligible. The generalized moment expansion is used for an approximate multi-exponential description of the non-exponential time behavior of the ET. As an example, ET in glycerol-like solvents is considered, treated by the spatially inhomogeneous model for dielectric relaxation. For this model the ET rate at long times is found to vary as τ_0^(−1), τ_0 being a dielectric relaxation time parameter, in contrast with a fractional dependence at short times.https://authors.library.caltech.edu/records/6h3fh-j4829On the theory of the state distribution of the reaction products and rates of unimolecular dissociations
https://resolver.caltech.edu/CaltechAUTHORS:20150617-104047821
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1016/0009-2614(88)87119-7
A recent variational implementation of RRKM theory, plus an additional dynamical assumption, is used to calculate the distribution of quantum states of reaction products of unimolecular dissociations. It is assumed that the "conserved" modes of the molecule are vibrationally adiabatic after passage through the transition state region, but that the "transitional modes" are non-adiabatic until the "loose transition state" region is reached. The rate constants k_(EJ) themselves are those of RRKM theory, but, for energies below those needed to yield vibrationally excited products, the phase space theory expression (PST) is obtained for the distribution of rotational states of the products. The product state distribution differs from that of PST when the energy is sufficient to permit product vibrational excitation. The unimolecular reactions considered are those for which there is no potential energy barrier for the reverse reaction (recombination).https://authors.library.caltech.edu/records/jz291-9be15Intramolecular Dynamics and Unimolecular Reactions
https://resolver.caltech.edu/CaltechAUTHORS:20150629-152216407
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1002/bbpc.198800052
In this article we describe recent research of our group on the rate constants and the distribution of quantum states of the reaction products of unimolecular dissociations and on methods to treat intramolecular dynamics. Connections among various transition state type theories are also discussed.https://authors.library.caltech.edu/records/qg1j4-vgw64Application of artificial intelligence methods to intramolecular dynamics calculations
https://resolver.caltech.edu/CaltechAUTHORS:20150617-125717488
Authors: {'items': [{'id': 'Lederman-S-M', 'name': {'family': 'Lederman', 'given': 'Steven M.'}}, {'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1016/0009-2614(88)85040-1
The application of artificial intelligence (AI) methods to the determination of intramolecular quantum dynamics for multidimensional systems is described. An AI method based on a physically motivated search algorithm and evaluation function is considered. In both the cases of quantum beats and energy "dissipation" the results for the intramolecular vibrational energy redistribution within an eleven-coordinate model system are shown to be accurate with a considerably reduced number of basis states.https://authors.library.caltech.edu/records/g309r-ska21An internal consistency test and its implications for the initial steps in bacterial photosynthesis
https://resolver.caltech.edu/CaltechAUTHORS:20150617-131950593
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1016/0009-2614(88)85041-3
Comparison of theoretical expressions for superexchange and chemical intermediate mechanisms for electron transfer from the bacteriochlorophyll dimer to a pheophytin reveals a common factor influencing their rates. If the former mechanism is to dominate the latter an internal consistency test becomes possible and is derived. Consequences are investigated for matrix elements, singlet-triplet splitting of the BChl_2+BPh - radical pair and other properties. Two possible alternative mechanisms are also considered. To discriminate among some of the possibilities the study of the effect of an applied electric field on BChl depletion and on the initial rates is suggested.https://authors.library.caltech.edu/records/adzwf-dwf32Mean relaxation time description of quasi-dissipative behavior in finite-state quantum systems
https://resolver.caltech.edu/CaltechAUTHORS:20150629-095319961
Authors: {'items': [{'id': 'Nadler-W', 'name': {'family': 'Nadler', 'given': 'W.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1016/0009-2614(88)87305-6
An approximately single-exponential decay of an initially prepared non-stationary state can occur in quantum systems even if there are only a finite number of states. The time scale τ of the decay is then much shorter than the recurrence time T of the system. We describe here a method for calculating the probability amplitude of the non-stationary state, observed on a time scale γ^(−1), by a mean relaxation time approximation. In many cases the resulting decay constant Γ(γ) is almost independent of γ for τ⪡γ^(−1)⪡T, and the value found for it in this regime constitutes the actually observed decay constant.https://authors.library.caltech.edu/records/m9vdm-t6r89The use of artificial intelligence methods in studying quantum intramolecular vibrational dynamics
https://resolver.caltech.edu/CaltechAUTHORS:LEDjcp88
Authors: {'items': [{'id': 'Lederman-S-M', 'name': {'family': 'Lederman', 'given': 'Steven M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1063/1.454469
Artificial intelligence methods are used to treat the time evolution in intramolecular quantum dynamics. Comparison is made of several AI search algorithms and evaluation functions in an application to the study of quantum intramolecular vibrational redistribution. A combination of a beam search and a best-first search is used, in conjunction with an accumulated evaluation function which encourages both searching and ultimately satisfying the uncertainty principle. The methods developed are applied to an 11-coordinate heavy central mass problem and used to treat both quantum beats and "dissipative" intramolecular energy transfer. Good agreement is obtained with the "exact" quantum dynamics.https://authors.library.caltech.edu/records/hqjra-tvp70Unimolecular reaction rate theory for highly flexible transition states: use of conventional coordinates
https://resolver.caltech.edu/CaltechAUTHORS:20150623-150755674
Authors: {'items': [{'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1021/j100322a020
An alternative method for implementing RRKM theory for unimolecular reactions with highly flexible transition states is
described using conventional coordinates. The number of available states for motion in the transition state state N_(EJ) is determined
via an appropriate average over the absolute space orientations and body-fixed momenta of the two fragments. The results
of calculations of N_(EJ) for the C_2H_6 → 2CH_3 reaction (or alternatively for the corresponding recombination reaction) obtained
from the present expression are shown to be equivalent numerically to those obtained previously by Wardlaw and Marcus.https://authors.library.caltech.edu/records/p1cc0-a6r59Potential-energy surfaces, unimolecular processes and spectroscopy
https://resolver.caltech.edu/CaltechAUTHORS:20120605-142011640
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1039/f29888401237
The present symposium brings together research in a number of fields: the quantum-chemical calculation of molecular potential-energy surfaces, rotational–vibrational spectroscopy, methods of calculating rotational–vibrational energy levels, unimolecular reactions and intramolecular dynamics. Several aspects of the work are discussed including some recent developments on rates and products' quantum state distributions for unimolecular dissociations having highly flexible transition states. The usefulness of having improved potential-energy surfaces, particularly the bonding and hindered rotational potentials in the dissociations, is noted. In various other studies in this symposium a better knowledge of the surfaces would be particularly helpful. New results on a semiclassical quantization method are also described.https://authors.library.caltech.edu/records/zps0x-fs582Unimolecular reaction rate theory for highly flexible transition states. 2. Conventional coordinate formulas for the various possible fragment combinations: miscellaneous topics
https://resolver.caltech.edu/CaltechAUTHORS:20150624-084938500
Authors: {'items': [{'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1021/j100330a018
A method for using conventional coordinates in the implementation of RRKM theory for unimolecular dissociations was
described in part 1 of this series, for the case where both fragment molecules are nonlinear. The corresponding formalism
for all possible types of fragments, atomic, linear, and nonlinear fragments and their combinations, is presented here. Also
discussed analytically is the tendency, in a unimolecular dissociation, for the position of the transition state to move to shorter
fragment-fragment separation distances with increasing total energy E. This tendency has marked consequences, including
increasing deviation of rate constants from those of phase space theory with increasing E and, in the case of fragment-fragment
recombination, a corresponding tendency for high-pressure rate constants to decrease with increasing temperature. Two
other topics considered in this paper are the case of two minima in the variational calculation and the role of the repulsive
potential energy curves in the unimolecular dissociations under consideration.https://authors.library.caltech.edu/records/g5bvs-1fb08Application of unimolecular reaction rate theory for highly flexible transition states to the dissociation of NCNO into NC and NO
https://resolver.caltech.edu/CaltechAUTHORS:KLIjcp88
Authors: {'items': [{'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'S. J.'}}, {'id': 'Khundkar-L-R', 'name': {'family': 'Khundkar', 'given': 'L. R.'}}, {'id': 'Zewail-A-H', 'name': {'family': 'Zewail', 'given': 'A. H.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1063/1.455670
A recently described method for implementing RRKM theory for unimolecular reactions with highly flexible transition states is applied to the calculation of energy and angular momentum resolved rate constants and rotational–vibrational energy distributions for the reaction NCNO--><sub></sub><sup>h nu </sup> NCNO*-->NCNO(vib. hot)-->NC+NO. The dissociation rate results are compared to the recent experimental results of Khundkar et al., and the vibrational and rotational distribution results are compared to the experimental values of Nadler et al. Comparison is also made with phase space theory calculations. The calculated rotational distributions at energies below the vibrational threshold of the products are the same as those of PST. At energies (2348, 2875 cm^−1) above this threshold energy the rovibrational distribution is in better agreement with the data than is that of PST. The need for obtaining more accurate ab initio potential energy surfaces is noted, particularly for treating reactions at still higher energies.https://authors.library.caltech.edu/records/6j422-3jn19Semiclassical wave packets in the angle representation and their role in molecular dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20150629-100242890
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1988
DOI: 10.1016/0009-2614(88)87320-2
Molecular wave packets generated by Gaussian optical pulses are discussed in the present paper. The systems treated either have pulses which are narrow relative to the width of the spectral absorption band or have molecules whose absorption band can be approximated by a Gaussian. One convenient approximate description is given, it is shown, by a semiclassical angle variable representation, which we used earlier in the treatment of inelastic molecular collisions. The results offer a relatively simple description of the motion of the packet, including its periods of oscillation, the time spent in various regions, and its extension in space at various times. The results are applied elsewhere to experimental data and to quantum mechanical calculations. The wave packet description is multidimensional.https://authors.library.caltech.edu/records/vp8zf-mb732Molecular state evolution after excitation with an ultra-short laser pulse: A quantum analysis of NaI and NaBr dissociation
https://resolver.caltech.edu/CaltechAUTHORS:20150617-144807338
Authors: {'items': [{'id': 'Engel-V', 'name': {'family': 'Engel', 'given': 'Volker'}}, {'id': 'Metiu-H', 'name': {'family': 'Metiu', 'given': 'Horia'}}, {'id': 'Almeida-R', 'name': {'family': 'Almeida', 'given': 'Raphael'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Zewail-A-H', 'name': {'family': 'Zewail', 'given': 'Ahmed H.'}}]}
Year: 1988
DOI: 10.1016/0009-2614(88)87319-6
In recent experiments Rose, Rosker and Zewail have used a femtosecond pulse to dissociate NaI and NaBr, and a second pulse to probe the "transition state" by LIF. Here we show that quantum calculations, on a model system with no adjustable parameters, reproduce the principal observed features.https://authors.library.caltech.edu/records/mh319-0a153Relation between charge transfer absorption and fluorescence spectra and the inverted region
https://resolver.caltech.edu/CaltechAUTHORS:20150629-115003405
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1989
DOI: 10.1021/j100345a040
The theoretical expression for the plot of a charge transfer (CT) band intensity vs frequency is known to parallel that for the plot of electron-transfer rate constant k^(ET) vs –ΔG^0. We use this parallelism to explore a recent model in the literature on the possible role, if any, of partial dielectric saturation of the solvent on the "inverted region" of electron-transfer reactions. A simple approximate expression is obtained for the full width at half-maximum for the k^(ET) and spectral plots and is tested using recent numerical results for calculated k^(ET) vs –ΔG^0 curves. Studies of experimental widths of CT bands are used, thereby, to test ideas on the possible presence and effects of partial dielectric saturation and on the observation of the inverted region. Further uses of charge-transfer spectra, when both the absorption and fluorescence data are available, are also described, including the determination of the "0 → 0 transition energy" ΔE_( 0 → 0) for systems displaying little or no vibrational structure.https://authors.library.caltech.edu/records/k1xew-k8736Application of unimolecular reaction rate theory for highly flexible transition states to the dissociation of CH2CO into CH2 and CO
https://resolver.caltech.edu/CaltechAUTHORS:KLIjcp89
Authors: {'items': [{'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1989
DOI: 10.1063/1.457035
A previously described implementation of Rice–Ramsberger–Kassel–Marcus (RRKM) theory for unimolecular dissociation processes involving a highly flexible transition state is applied to the dissociation of CH2CO into CH2 and CO. Results of theoretical calculations for the energy and angular momentum resolved rate constants are presented. Using an added dynamical approximation, the product vibrational–rotational distributions are also calculated. The calculated rate constants are compared with the corresponding experimentally determined quantities where possible. Comparison is also made with phase space theory (PST). The RRKM-based calculations are in good agreement with both the experimentally determined rate constants of Zewail and co-workers and the experimentally determined photofragment excitation spectra of Moore and co-workers. The results on rates are in contrast to the corresponding results from PST calculations. The RRKM-based theory for the product vibrational–rotational distributions predicts a moderately greater probability for vibrational excitations than does PST (particularly for excess energies just above the threshold for excitation of a particular vibrational mode of the products). In other respects the RRKM-based predictions of the ro-vibrational product state distributions are quite similar to those of PST.https://authors.library.caltech.edu/records/qdxvy-ts571Vibrational energy redistribution across a heavy atom
https://resolver.caltech.edu/CaltechAUTHORS:20150629-090950200
Authors: {'items': [{'id': 'Lederman-S-M', 'name': {'family': 'Lederman', 'given': 'Steven M.'}}, {'id': 'López-V', 'name': {'family': 'López', 'given': 'Vicente'}}, {'id': 'Fairén-V', 'name': {'family': 'Fairén', 'given': 'Victor'}}, {'id': 'Voth-G-A', 'name': {'family': 'Voth', 'given': 'Gregory A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1989
DOI: 10.1016/0301-0104(89)90010-4
Vibrational energy relaxation is studied for a model system with two different ligands separated by a heavy atom, there being initially an excess energy in one metal-ligand subsystem. The model has eleven coordinates to achieve a high density of states (two coordinates for one metal-ligand subsystem and nine for the other). The behavior was studied using classical and quantum mechanical methods, and the results compared. Artificial intelligence searching was used in the quantum treatment, because of the large number of potentially contributing quantum states. For the present system the adiabatic separation of motion of the local group modes, previously characterized for a C-C-Sn ligand in a smaller system, still holds when the other ligand has this high density of states. Further, the agreement between the classical and quantum results is much improved over that obtained earlier for a four-coordinate symmetric system. In the latter case isolated intrinsic resonances were responsible for the "energy transfer" which was facilitated sometimes by tunneling. The present agreement of the classical and quantum calculations is generally quantitative at shorter times and at least qualitative for longer times for most states studied. This agreement is encouraging since the former can be less computationally intensive.https://authors.library.caltech.edu/records/szmck-pba51Electron Transfer in a Dynamically Disordered Polar Medium
https://resolver.caltech.edu/CaltechAUTHORS:20150610-105049032
Authors: {'items': [{'id': 'Nadler-W', 'name': {'family': 'Nadler', 'given': 'Walter'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
DOI: 10.1002/ijch.199000008
Intramolecular electron transfer (ET) processes with the main energetic
contributions coming from the solvent reorganization are investigated for a polar
medium that exhibits dynamic disorder. Dynamic disorder provides a description
of the anomalous relaxational behavior of correlation functions in complex glass-like
systems, alternative to static disorder. In particular, the questions addressed are
whether time-resolved observation of nonexponential ET in such a medium can
readily distinguish experimentally between static and dynamic disorder and whether
a contribution of intramolecular degrees of freedom to the ET can be identified by it.https://authors.library.caltech.edu/records/4f853-8rf70Reorganization free energy for electron transfers at liquid-liquid and dielectric semiconductor-liquid interfaces
https://resolver.caltech.edu/CaltechAUTHORS:20150318-111039114
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
DOI: 10.1021/j100366a005
The reorganization free energy is calculated for a reaction (i) between two reactants, each in its own dielectric medium,
separated by an interface, and (ii) between a reactant and some semiconductors. An expression is also given for the rate
constant of an electron-transfer reaction at an interface between reactants in two immiscible phases. Under certain conditions
it is shown that the reorganization energy for the two immiscible-liquid system is the sum of the electrochemical reorganization
energies of the two reactants, each in its own respective solvent. The reorganization energy for a semiconductor-liquid system
can differ considerably from the corresponding metal-liquid value, even a factor of 2.https://authors.library.caltech.edu/records/0n047-b6x51Comparison of Experimental and Theoretical Electronic Matrix Elements for Long-Range Electron Transfer
https://resolver.caltech.edu/CaltechAUTHORS:20150520-100601063
Authors: {'items': [{'id': 'Siddharth-P', 'name': {'family': 'Siddharth', 'given': 'Prabha'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
DOI: 10.1021/j100370a046
The dependence of electron-transfer rates on the number of intervening groups is treated by using a single calculational method for four separate series of compounds: a biphenylyl donor and a 2-naphthyl acceptor, separated by various rigid saturated hydrocarbon bridges, a dimethoxynaphthyl donor and a dicyanovinyl acceptor, separated by norbornyl groups, a Ru(NH_3)_5^II donor and a Ru(NH_3)_5^III acceptor, separated by different numbers of dithiaspiro rings, and an OS(NH_3)_5^II donor and an
Ru(NH_3)_5^III acceptor separated by an isonicotinyl plus a variable number of proline groups, which again provide a rigid spacer. The results for the electron-transfer matrix element obtained both with direct diagonalization and with the partitioning method are compared with each other, with the experimental results and, where available, with previously calculated results.https://authors.library.caltech.edu/records/fettd-aeh74Dynamics of electron transfer for a nonsuperexchange coherent mechanism. 2. Numerical calculations
https://resolver.caltech.edu/CaltechAUTHORS:20150514-152741359
Authors: {'items': [{'id': 'Almeida-R', 'name': {'family': 'Almeida', 'given': 'R.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
DOI: 10.1021/j100370a045
The expressions in part 1 are used to treat the dynamics of electron transfer in the donor-acceptor system D*BA via a molecular bridge B. By use of a fast Fourier transform method, results are obtained for the maximum "population" of B^- and for other properties for this coherent but nonsuperexchange model. Several approximate ideas on rate populations and energy distributions are tested by using various values for the numerical parameters.https://authors.library.caltech.edu/records/527k0-16p28Dynamics of electron transfer for a nonsuperexchange coherent mechanism. 1
https://resolver.caltech.edu/CaltechAUTHORS:20150422-135108860
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Almeida-R', 'name': {'family': 'Almeida', 'given': 'R.'}}]}
Year: 1990
DOI: 10.1021/j100370a044
In addition to mechanisms such as superexchange and a chemical intermediate mechanism for electron transfer from a donor
D* to an acceptor A via a molecular bridge B, a third possibility occurs when the BA electronic coupling is very strong and
the D*B and D+B- states have energies moderately close to each other. This mechanism is discussed here. Like superexchange,
it is a coherent one, in contrast to the chemical intermediate mechanism, where the transfer is sequential and incoherent.
The dynamics of the mechanism are discussed, particularly the maximum population of "B-" and the question of whether
an effective rate constant for its disappearance can be considerably larger than the maximum adiabatic rate constant. There
are, as yet, no experimental data on the mechanism, though the synthesis of suitable D*BA's may permit its observation.
In the treatment three collective nuclear coordinates are introduced, permitting independent reorganization energies for each
reactive center. With certain approximations, namely, equal vibration frequencies and a nonadiabatic first step, the problem
is reduced analytically to a one-coordinate one, which can be readily treated numerically. One rough but simple analytical
result for the latter is also given.https://authors.library.caltech.edu/records/khq5k-54r14Theory of electron-transfer rates across liquid-liquid interfaces
https://resolver.caltech.edu/CaltechAUTHORS:20150514-111330363
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
DOI: 10.1021/j100373a051
The theory developed in a previous paper for the geometry of the encounter complex, the reorganization energy, and the
electron-transfer rate constant at a liquid-liquid interface is applied to existing data on the rate constant. To treat cyclic
voltammetric (CV) studies of electron transfer across the interface, the nature of the encounters is examined and a bimolecular-type rate treatment is used. When one redox pair is in large excess, it has been pointed out that a single-phase CV
analysis for diffusion/reaction can be utilized. In the present paper we avoid in this analysis the assumption that the second
("concentrated") phase is metallike. The experimental result deduced in this way for the true exchange current electron-transfer
rate constant at the interface is compared with that estimated from the present theory of the rate constant, using metal-liquid
electrochemical exchange rate constants. The type of agreement found is encouraging, considering the various approximations
involved, and further experimental studies and tests would be of interest.https://authors.library.caltech.edu/records/6jdqm-43v84Theory of charge-transfer spectra in frozen media
https://resolver.caltech.edu/CaltechAUTHORS:20150519-090711379
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
DOI: 10.1021/j100375a038
Absorption and fluorescence maxima of charge-transfer spectra in frozen media are treated, noting that only some of the
nuclear motions for liquid medium are frozen in corresponding solid or glassy phase. Account is taken of the fact that the
conditions under which the static dielectric constant of the frozen phase is measured do not usually correspond to those in
which the initial state of the solute system is prepared. Expressions for the maxima are obtained in terms of the optical
and static dielectric constants of the liquid and frozen (solid or glassy) phases. Comparison of Stokes shifts hv_a-hv_f at conventional
fluorescence times in frozen media with Stokes shifts at picosecond or subpicosecond times in liquid media would be of interest.https://authors.library.caltech.edu/records/4vaaa-k5v61Unimolecular Reactions, Rates and Quantum State Distribution of Products
https://resolver.caltech.edu/CaltechAUTHORS:20150107-103454609
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
Microcanonical rates and products rovibrational quantum state distributions of
several unimolecular dissociations, and canonical rates of some bimolecular
associations, are discussed from the viewpoint of variational Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The results are compared with the experimental
data and with the very useful benchmark theory, phase space theory. A two-transition-state description is discussed for the threshold regions for the products
vibrational excitations.https://authors.library.caltech.edu/records/atce3-6ts16Application of unimolecular reaction rate theory for highly flexible transition states to the dissociation of CH2CO into CH2 and CO. II. Photofragment excitation spectra for vibrationally-excited fragments
https://resolver.caltech.edu/CaltechAUTHORS:KLIjcp90
Authors: {'items': [{'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
DOI: 10.1063/1.459023
Results on vibrationally-excited ketene photofragment excitation (PHOFEX) spectra of Moore and co-workers are interpreted in terms of a previously described variational implementation of Rice–Ramsberger–Kassel–Marcus (RRKM) theory. At subvibrational excitations, the predictions of this theory reduce to those of phase space theory (PST). However, for excess energies just above the threshold of excitation of a particular vibrational mode of the products, the present theory predicts a significantly greater probability for vibrational excitation, compared with PST, in closer agreement with the experimental results, and predicts an energy dependence of the PHOFEX spectrum that is closer to the observed one. A key feature, to which the present calculations lead, is a two-transition state (TS) description for each vibrational excitation of the products, the PST TS region dominating at the threshold for that excitation and an inner TS region dominating at somewhat higher (~200 cm^−1) energies. The behavior contrasts partly with that of the unimolecular dissociation rate constant kEJ (except at the threshold for kEJ), because of the different focus of the two types of measurements. The theory provides a consistent interpretation of both properties.https://authors.library.caltech.edu/records/r399c-sse73Electron-transfer reactions in proteins: a calculation of electronic coupling
https://resolver.caltech.edu/CaltechAUTHORS:20150513-151932588
Authors: {'items': [{'id': 'Siddarth-P', 'name': {'family': 'Siddarth', 'given': 'Prabha'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1990
DOI: 10.1021/j100385a015
The distance and medium dependences of the electronic coupling for electron-transfer reactions in proteins (particularly
the ruthenated myoglobins studied by Gray et al.) are calculated. An extended-Hückel method is used to treat individually
the donor, the acceptor, and the intervening protein. A search method is used to select a subset (~15-20) of the approximately
150 amino acid residues as being the most relevant for the electron transfer. Approximate agreement is found between ratios
of experimental matrix elements (approximated as ratios of square roots of rate constants) and of calculated electronic matrix
elements. No adjustable parameters were introduced in the diagonalization. Only parameters available in the literature
from other (non-electron-transfer) sources were employed.https://authors.library.caltech.edu/records/paazm-2mh61Summarizing Remarks
https://resolver.caltech.edu/CaltechAUTHORS:20120419-131156389
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1991
DOI: 10.1039/dc9919100479
[None].https://authors.library.caltech.edu/records/swcef-1bj31Structure and Dynamics of Reactive Transition-States – Summarizing Remarks
https://resolver.caltech.edu/CaltechAUTHORS:20150610-151853619
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1991
DOI: 10.1039/dc9919100479
This Discussion has been exciting and broad in scope. We are particularly indebted to
Professor John Simons and his organizing committee for having arranged this interestingly
varied meeting.https://authors.library.caltech.edu/records/z44s0-rb981Theory of electron-transfer rates across liquid-liquid interfaces. 2. Relationships and application
https://resolver.caltech.edu/CaltechAUTHORS:20150610-145333343
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1991
DOI: 10.1021/j100158a023
In part 1 an expression was obtained for the exchange current rate constant k^(ii)_(12) for an electron transfer between a reactant
in one liquid and a second reactant in a second immiscible liquid, across an (assumed) sharp interfacial boundary. This
expression is used to obtain a relation between k^(ii)_(12) and the self-exchange rate constants k_(11) and k_(22) for electron transfer in
homogeneous solutions, each redox species being in its respective liquid phase. The relation provides an extension of the
"cross-relation" for one-phase electron transfer to this two-phase case. An expression is also given relating k^(ii)_(12) to the usual
metal-liquid electrochemical exchange current rate constants k^(el)_1 and k^(el)_2 these k^(el)'s referring to each reactant in its respective
solvent phase. An alternative limiting model for the interfacial region is also considered, in which that region is now broad,
instead of sharp. The results of both models are compared with the limited available kinetic data, and the desirability of
further experimental studies is noted.https://authors.library.caltech.edu/records/cpcts-11b46Intramolecular dynamics. I. Curvilinear normal modes, local modes, molecular anharmonic Hamiltonian, and application to benzene
https://resolver.caltech.edu/CaltechAUTHORS:ZHAjcp91
Authors: {'items': [{'id': 'Zhang-Yongfeng', 'name': {'family': 'Zhang', 'given': 'Yongfeng'}}, {'id': 'Klippenstein-S-J', 'name': {'family': 'Klippenstein', 'given': 'Stephen J.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1991
DOI: 10.1063/1.460216
The Hamiltonian based on curvilinear normal modes and local modes (CNLM) is discussed using Wilson's exact vibrational Hamiltonian as basis, the CNLM representation diagonalizing only the normal mode block of FG matrix in curvilinear internal coordinates. Using CNLM the kinetic and potential energy operators for benzene are given, including cubic and quartic anharmonicity in the potential energy and cubic and quartic terms in the kinetic energy expansion in curvilinear coordinates. Using symmetrized coordinates and cubic and higher force constants the number and identity of the independent symmetry allowed (A1g) such force constants are obtained. The relation to conventional anharmonic force constants is then given and the allowed contributions of the latter are obtained. The results are applied to CH overtone spectra and intramolecular vibrational dynamics in Part III of this series.https://authors.library.caltech.edu/records/pxy26-5hx63Theory of anharmonically modified Coriolis coupling in the S1 state of benzene and relation to experiment
https://resolver.caltech.edu/CaltechAUTHORS:HELjcp91
Authors: {'items': [{'id': 'Helman-A', 'name': {'family': 'Helman', 'given': 'Adam'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1991
DOI: 10.1063/1.461095
Avoided crossings between quasidegenerate rovibrational states in the Doppler-free two-photon excitation of the 141 mode in the S1 excited state of benzene are treated theoretically. Two sets of avoided crossings in plots of spectral line frequency vs J at a given K and DeltaK have been reported experimentally between an initially prepared "light" state (141 in zeroth order) and dark states, namely, one which in zeroth order is a 51101161 state, the other being in zeroth order a 62111 and/or possibly a 31161 state, implicated earlier by Neusser et al. The identification of these states makes the phenomenon an excellent candidate for treatment of the avoided crossing via a Van Vleck transformation, no other basis set states being needed for the diagonalization in order to extract the important features. Two successive transformations are used for handling direct coupling and coupling via virtual states. The dominant calculated contribution to the coupling is, jointly, Coriolis plus cubic–cubic anharmonic interactions between vibrational modes.Playing less of a role are Coriolis terms in which the inverse moment of inertia tensor is expanded up to quadratic terms in the coordinates. There results a 5×5 (for coupling to 51101161 ) and a 3×3 (for coupling to 62111 or 31161 ) matrix of the transformed Hamiltonian, each of which can also be described, if desired, to a very good approximation by a 2×2 matrix. The coupling element V0 and the difference of the rotational constants for the light and dark states (DeltaB) are obtained from the plots of line position vs J(J+1) obtained. For the 141 to 51101161 and for the 141 to 62111 couplings the theoretical results are in reasonable agreement with the experimental results, no adjustable parameters being employed. For a coupling of 141 to 31161 the calculated V0 would be much too high compared with experiment (a factor of 10), the coupling involving the exchange of only three instead of four vibrational quanta. A situation in which the 141 state is coupled to the 62111 state to yield an avoided crossing and off-resonantly coupled to the 31161 state would be consistent with some experimental results and not affect the reasonable agreement of the slope difference and splitting for the avoided crossing plots.https://authors.library.caltech.edu/records/afpex-8t768Global Potential Energy Contour Plots for Chemical Reactions. Muttiple Reaction Paths, Bifurcations, and Applicability of Transition-State Theory
https://resolver.caltech.edu/CaltechAUTHORS:20150617-150657971
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1991
DOI: 10.1021/j100174a042
A global reduced-dimensional potential energy contour plot is described for the simultaneous representation of reactions X-3Y ⇌ X_2 + XY, X_3Y ⇌ X + X_2Y, and X_2 + YX ⇌ X_2Y + X, where the X's may be different. The analysis provides some insight into the nature of the transition states, the role of bifurcations, and the applicability of transition-state theory (TST). Recent results of a quantum chemistry calculation for the X = H, Y = 0 system are discussed in these terms. More generally, some Topographical conditions for the inapplicability of TST are suggested. This limitation of TST arises from a preempting of the transition state for one reaction by another and appears to be relatively rare.https://authors.library.caltech.edu/records/rpcjz-pg466Schrödinger equation for strongly interacting electron-transfer systems
https://resolver.caltech.edu/CaltechAUTHORS:20150514-110110841
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1992
DOI: 10.1021/j100183a048
The Schrödinger equation for strongly interacting electron-transfer systems is described, the eigenvalues depending on a
dielectric polarization function P(r) for the medium, on the internal coordinates q, and, when the electron transfer is coupled
to a dissociation, on a generalized coordinate Q. A choice of the reaction coordinate for the variation of P(r), q, and Q,
so as to reach the saddle-point, and the calculation of the free energy of activation are described. The question of suitable
data on the solvent dependence of strong-overlap systems is also considered.https://authors.library.caltech.edu/records/jvd8t-eth71Intramolecular dynamics. II. Artificial intelligence search evaluation function and treatment of resonance centers for large systems
https://resolver.caltech.edu/CaltechAUTHORS:ZHAjcp92a
Authors: {'items': [{'id': 'Zhang-Yongfang', 'name': {'family': 'Zhang', 'given': 'Yongfang'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1992
DOI: 10.1063/1.462648
The role of resonance centers in obtaining large size matrices via an artificial intelligence (AI) search is discussed. The results are used to develop for an AI search an evaluation function which takes cognizance of isolated internal resonances in these many-state systems. The effect of later-accepted states on resonance centers is included. This evaluation function and one without a resonance factor are used in Part III of this series. A search is made there to select zeroth-order vibrational states of benzene that are used in a diagonalization treatment of CH overtone spectra. When there are many overlapping resonances, as in that case, a comparison of results obtained with those two types of evaluation function is of particular interest.https://authors.library.caltech.edu/records/372kj-v6f98Calculation of electron-transfer matrix elements of bridged systems using a molecular fragment approach
https://resolver.caltech.edu/CaltechAUTHORS:20150514-155515321
Authors: {'items': [{'id': 'Siddarth-P', 'name': {'family': 'Siddarth', 'given': 'Prabha'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1992
DOI: 10.1021/j100187a008
A perturbation method for calculating the electronic coupling for electron-transfer reactions between a donor and an acceptor separated by large or small bridges is developed. In this approach the intervening bridge is subdivided into smaller molecular fragments, thereby enabling calculations on larger systems. This method of molecular fragments is tested for a series of polyproline bridged systems. The results obtained for the electron transfer matrix element are compared with those obtained from direct diagonalization of the full bridge and with experimental results. Previously, the result for the direct diagonalization of the bridge had been shown to agree with that obtained from diagonalization of the entire donor bridge-acceptor system. The vertical donor-bridge orbital energy difference is estimated with the aid of a donor bridge charge-transfer spectrum.https://authors.library.caltech.edu/records/czws7-vwp93Skiing the Reaction Rate Slopes
https://resolver.caltech.edu/CaltechAUTHORS:20150126-094754947
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1992
DOI: 10.1126/science.256.5063.1523
On the way from reactants to products, a chemical reaction passes through what chemists term the transition state-for a brief moment, the participants in the reaction may look like one large molecule ready to fall apart. The nature of this elusive state is the subject of a number of exciting recent developments that involve theory and experiment
in the study of chemical reaction rates. They include time-resolved studies of molecules in the transition state region, spectrcopic observations of that region, reactive scattering state-to-state cross sections for
reactions such as H + H_2 → H_2 + H, and experimental/theoretical studies of electron transfer processes in the condensed phase. The experiments of
Lovejoy et al. described in this issue of Science involve the fundamental question of the quantization of vibrational energy levels of the transition state and its
implications for unimolecular reaction rate theory.https://authors.library.caltech.edu/records/yfw2j-c0y31Intramolecular dynamics. III. Theoretical studies of the CH overtone spectra for benzene
https://resolver.caltech.edu/CaltechAUTHORS:ZHAjcp92b
Authors: {'items': [{'id': 'Zhang-Yongfeng', 'name': {'family': 'Zhang', 'given': 'Yongfeng'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1992
DOI: 10.1063/1.463789
The electronic states of the ionic excimer Ar<sup> + + </sup><sub>2</sub> are calculated using ab initio multireference configuration interaction and effective core pseudopotentials. Among states dissociating into Ar+(2P)+Ar+(2P), all are found to be repulsive, except the ground state, which occurs to be quasibound near Re=4.1a0 with a well depth of >=230 cm^−1. All states originating from Ar++(3P,1D,1S)+Ar are bound with dissociation energies in the range 3200–4500 cm^−1 and equilibrium distances between 5.6a0 and 6a0. Simulation emission spectra from bound excited states are derived from the calculated potentials and the possible contribution of the Ar<sup> + + </sup><sub>2</sub> ion to the third continuum fluorescence is discussed.https://authors.library.caltech.edu/records/r1v8t-wfd78Electron-transfer reactions in proteins: an artificial intelligence approach to electronic coupling
https://resolver.caltech.edu/CaltechAUTHORS:20150608-144656403
Authors: {'items': [{'id': 'Siddarth-P', 'name': {'family': 'Siddarth', 'given': 'Prabha'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1021/j100112a047
The electronic interactions which are responsible for electron transfer in proteins are treated using an artificial
intelligence (AI) approach and a quantum mechanical formulation of superexchange. An AI search procedure
is devised to select the most important amino acid residues which mediate long-range electron transfer. All
the valence orbitals of these amino acid residues are used in a diagonalization of the "bridge" orbitals. The
electronic coupling matrix element is then calculated by using second-order perturbation theory to couple the
bridge orbitals to the donor and acceptor orbitals. The relative values of the electronic coupling elements
obtained with this model are shown to be in good agreement with experimental results for cytochrome c derivatives,
without use of adjustable parameters. Further, an optimum path calculation in which the path consists of
several amino acids is also presented and compared with the many amino acid calculation. The various results
show that not merely the separation distance but also the nature of the protein medium separating the redox
centers is an important factor in controlling the rate of these electron-transfer reactions.https://authors.library.caltech.edu/records/c6ar2-7fy76Tight-binding approximation for semi-infinite solids. Application of a transform method and of delta function normalization
https://resolver.caltech.edu/CaltechAUTHORS:20120308-102140211
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1063/1.464905
A transform method for treating semi‐infinite solids in the tight‐binding (TB) approximation is introduced. The difference equations for the TB orbital coefficients are converted, thereby, to convenient algebraic equations. For this purpose, a Dirac delta function normalization for the wave function is also introduced, instead of the usual box one. Single and coupled bands are treated, and the methods are applied elsewhere to electron transfer problems at interfaces.https://authors.library.caltech.edu/records/9y9qn-xxq57Theoretical study of intramolecular vibrational relaxation of acetylenic CH vibration for v=1 and 2 in large polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si
https://resolver.caltech.edu/CaltechAUTHORS:STUjcp93a
Authors: {'items': [{'id': 'Stuchebrukhov-A-A', 'name': {'family': 'Stuchebrukhov', 'given': 'A. A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1063/1.464843
Quantum calculations are reported for the intramolecular vibrational energy redistribution and absorption spectra of the first two excited states of the acetylenic CH stretch vibration in the polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si. Using approximate potential energy surfaces, comparison is made with the corresponding recent experimental spectra. It is found that a model of intramolecular vibrational relaxation based on the assumption of sequential off-resonance transitions via third and fourth order vibrational couplings (as opposed to direct high order couplings) is in agreement with experimental results on spectral linewidths. In a semiclassical limit this type of relaxation corresponds to a dynamic tunneling in phase space. It is shown that the local density of resonances of third and fourth order, rather than the total density of states, plays a central role for the relaxation. It is found that in the Si molecule an accidental absence of appropriate resonances results in a bottleneck in the initial stages of relaxation. As a result, an almost complete localization of the initially prepared excitation occurs. It is shown that an increase of the mass alone of the central atom from C to Si cannot explain the observed difference in the C and Si molecules. The spectral linewidths were calculated with the Golden Rule formula after prediagonalization of the relevant vibrational states which are coupled in the molecule to the CH vibration, directly or indirectly. For the spectral calculations, in addition to the direct diagonalization, a modified recursive residue generation method was used, allowing one to avoid diagonalization of the transformed Lanczos Hamiltonian. With this method up to 30 000 coupled states could be analyzed on a computer with relatively small memory. The efficiency of C programming language for the problem is discussed.https://authors.library.caltech.edu/records/2fp04-8nc44Surface properties of solids using a semi-infinite approach and the tight-binding approximation
https://resolver.caltech.edu/CaltechAUTHORS:OUYjcp93a
Authors: {'items': [{'id': 'Ou-Yang-H', 'name': {'family': 'Ou-Yang', 'given': 'Hui'}}, {'id': 'Källebring-B', 'name': {'family': 'Källebring', 'given': 'Bruno'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1063/1.465096
A semi-infinite approach (rather than a slab method or finite number of layers) is used to treat surface properties such as wave functions, energy levels, and Fermi surfaces of semi-infinite solids within the tight-binding (TB) approximation. Previous single-band results for the face-centered cubic lattice with a (111) surface and for the simple cubic lattice with a (001) surface are extended to semi-infinite layers, while the extension to calculations of other surfaces is straightforward. Treatment of more complicated systems is illustrated in the calculation of the graphite (0001) surface. Four interacting bands are considered in the determination of the wave functions, energies, and Fermi surface of the graphite (0001) surface. For the TB model used, the matrix elements in the secular determinants for the semi-infinite solid and for the infinite bulk solid obey the same expressions, and the wave functions are closely related. Accordingly, the results for the bulk system can then be directly applied to the semi-infinite one. The main purpose of the present paper is to provide wave functions and other properties used elsewhere to treat phenomena such as scanning tunneling microscopy and electron transfer rates at electrodes.https://authors.library.caltech.edu/records/9rb4e-bk789A theoretical model of scanning tunneling microscopy: Application to the graphite (0001) and Au(111) surfaces
https://resolver.caltech.edu/CaltechAUTHORS:OUYjcp93b
Authors: {'items': [{'id': 'Ou-Yang-H', 'name': {'family': 'Ou-Yang', 'given': 'Hui'}}, {'id': 'Källebring-B', 'name': {'family': 'Källebring', 'given': 'Bruno'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1063/1.464696
An expression for the scanning tunneling microscopy (STM) current between the tip and sample is presented using first-order perturbation theory for a two-Hamiltonian formalism ("reactants" and "products"). The calculated STM current depends on the square of the sample-tip matrix elements, averaged over a selection of random points in wave vector space. In the limit of low voltage and temperature, this averaging is over the Fermi surface of the sample. The model is applied to the graphite (0001) and Au(111) surfaces using a simple model (chain) of a tungsten tip and the tight-binding approximation. Comparisons with experiments and with the result for graphite obtained by Tersoff and Lang using a molybdenum tip are given. The theory is applied elsewhere to STM of adsorbates.https://authors.library.caltech.edu/records/4zkxm-y5x69Perturbation theory approach to dynamical tunneling splitting of local mode vibrational states in ABA molecules
https://resolver.caltech.edu/CaltechAUTHORS:STUjcp93b
Authors: {'items': [{'id': 'Stuchebrukhov-A-A', 'name': {'family': 'Stuchebrukhov', 'given': 'A. A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1063/1.464502
We introduce a point of view for treating the dynamical tunneling splitting of symmetric local mode vibrational states in ABA molecules (A=H typically) which is the one we have employed in treating the vibrational spectroscopy of CH overtones in molecules such as (CX3)3YCCH. Namely, the vibrational coupling corresponding to the dynamical tunneling in semiclassical mechanics via many intermediate off-resonance weak transitions between initial and final states can be treated by a standard high-order perturbation theory. We apply that method to the present simpler problem of tunneling splittings in ABA molecules, and compare the results with those of exact diagonalization, the semiclassical method, and the periodic orbit quantization. Of all the approximate methods, the perturbation theory was found to provide the best approximation to the results of exact diagonalization for the system treated. The relationship between these three methods and application to the problem of vibrational relaxation in polyatomic molecules with tunneling mechanism of intramolecular vibrational relaxation is discussed.https://authors.library.caltech.edu/records/zax90-d5467Electron-transfer reactions in proteins: electronic coupling in myoglobin
https://resolver.caltech.edu/CaltechAUTHORS:20150421-133036781
Authors: {'items': [{'id': 'Siddarth-P', 'name': {'family': 'Siddarth', 'given': 'Prabha'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1021/j100125a004
Recent measurements of electron-transfer (ET) rates in Ru(NH_3)_5 His myoglobin derivatives have shown the
need for improved theories for treating the "path" of long-range ET. We have investigated these systems
theoretically using a combined artificial intelligence (AI)-superexchange method. As in our previous articles,
this model first employs an AI search technique that yields the important amino acid residues for the mediation
of electrons between the donor and the acceptor. A quantum mechanical method is then used to diagonalize
the orbitals of the selected protein subset and to calculate the electronic coupling. Encouraging agreement with
experimental data is found, no adjustable parameters having been introduced. The results yield the relevant
amino acid paths.https://authors.library.caltech.edu/records/7kzfq-8s081Electron transfer reactions in chemistry. Theory and experiment
https://resolver.caltech.edu/CaltechAUTHORS:20150414-104906889
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1103/RevModPhys.65.599
Since the late 1940s, the field of electron transfer processes
has grown enormously, both in chemistry and biology.
The development of the field, experimentally and
theoretically, as well as its relation to the study of other
kinds of chemical reactions, represents to us an intriguing
history, one in which many threads have been
brought together. In this lecture, some history, recent
trends, and my own involvement in this research are described.https://authors.library.caltech.edu/records/ta6z9-5ac64Electron Transfer Reactions in Chemistry: Theory and Experiment (Nobel Lecture)
https://resolver.caltech.edu/CaltechAUTHORS:20150318-132728406
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1002/anie.199311113
Since the late 1940s, the field of electron transfer processes has grown enormously, both in chemistry and biology. The development of the field, experimentally and theoretically, as well as its relation to the study of other kinds of chemical reactions, presents to us an intriguing history, one in which many threads have been brought together. In this lecture, some history, recent trends, and my own involvement in this research are described.https://authors.library.caltech.edu/records/ys99j-5t633Theory of fluorescence excitation spectra using anharmonic-coriolis coupling in S1 and internal conversion to S0. I. General formalism
https://resolver.caltech.edu/CaltechAUTHORS:HELjcp93a
Authors: {'items': [{'id': 'Helman-A', 'name': {'family': 'Helman', 'given': 'Adam'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1063/1.466002
A treatment of one- or two-photon fluorescence excitation spectra is described using the vibration–rotation coupling of zeroth order states in the excited electronic state and nonadiabatic coupling to the ground state. Using perturbation theory, experimental harmonic frequencies, an anharmonic force field, and various theoretical Coriolis coupling constants, a quasistationary molecular eigenstate in an excited electronic state S1 is first calculated. The S1 eigenstate is then coupled via the nonadiabatic nuclear kinetic energy operator (internal conversion) to rovibronic states in the ground state manifold, the latter states approximated in a simple manner. A search algorithm is used to select the S1 dark states and the S0 states. Both the perturbation theory coefficient and the Franck–Condon factors are employed in the evaluation function used in the search. The results are applied in part II to the channel three problem in benzene.https://authors.library.caltech.edu/records/yay0j-q7053Theory of fluorescence excitation spectra using anharmonic-Coriolis coupling in S1 and internal conversion to S0. II. Application to the channel three problem in benzene for the 14112 band
https://resolver.caltech.edu/CaltechAUTHORS:HELjcp93b
Authors: {'items': [{'id': 'Helman-A', 'name': {'family': 'Helman', 'given': 'Adam'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1063/1.466003
Rotational lines in the fluorescence excitation spectra of the 14112 band of the first excited singlet state (S1) of benzene are calculated for various J and K. For this purpose, perturbation theory is used to obtain an "eigenstate" in S1. Internal conversion to S0 via Franck–Condon (FC) factors is then calculated. A search procedure is used to obtain the important contributors to this S1 state and to this internal conversion process S1-->S0 using the perturbation theory coefficients and the FC factors in the evaluation function. At low J, the calculated lines with K=0 are sharp, other lines being broadened and diminished in intensity. The calculated K=0 lines have a linewidth proportional to J(J+1). For high J, the lines with K=J remain sharp, the other lines being broadened and diminished in intensity. These various results are in general agreement with the experimental findings. The onset of channel three in benzene occurs in the present mechanism via anharmonic-Coriolis coupling in the S1 state plus internal conversion to S0. The calculations suggest that, at low J, parallel Coriolis coupling causes mixing of the in-plane mode-excited ``light state'' with in-plane modes that are anharmonically coupled to out-of-plane modes.Dark states with certain excited out-of-plane mode contributions possess large FC factors for the internal conversion to S0. At high J, on the other hand, the in-plane modes are coupled directly to these out-of-plane modes by perpendicular Coriolis coupling. Paths involving two perpendicular Coriolis operators are important at high J in the present calculation—their matrix elements are larger at high J and so they become more competitive relative to purely anharmonic coupling operators. Such two-Coriolis paths at high J are expected to yield multiple excitation in the out-of-plane modes and further enhance the internal conversion. The perpendicular Coriolis coupling is least at J=K and so these lines survive at high J. Two-Coriolis operator paths are calculated to be relatively unimportant at low J. The present calculations, using the same electronic matrix element, account for both the low JK = 0 and high JK = J sets of lines being the dominant ones. Aspects regarding further study are discussed.https://authors.library.caltech.edu/records/asa5q-v8813Quantum correction for electron transfer rates. Comparison of polarizable versus nonpolarizable descriptions of solvent
https://resolver.caltech.edu/CaltechAUTHORS:SONjcp93
Authors: {'items': [{'id': 'Song-X', 'name': {'family': 'Song', 'given': 'Xueyu'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1063/1.465654
The electron transfer rate constant is treated using the spin-boson Hamiltonian model. The spectral density is related to the experimentally accessible data on the dielectric dispersion of the solvent, using a dielectric continuum approximation. On this basis the quantum correction for the ferrous–ferric electron transfer rate is found to be a factor 9.6. This value is smaller than the corresponding result (36) of Chandler and co-workers in their pioneering quantum simulation using a molecular model of the system [J. S. Bader, R. A. Kuharski, and D. Chandler, J. Chem. Phys. 93, 230 (1990)]. The likely reason for the difference lies in use of a rigid water molecular model in the simulation, since we find that other models for water in the literature which neglect the electronic and vibrational polarizability also give a large quantum effect. Such models are shown to overestimate the dielectric dispersion in one part of the quantum mechanically important region and to underestimate it in another part. It will be useful to explore a polarizable molecular model which reproduces the experimental dielectric response over the relevant part of the frequency spectrum.https://authors.library.caltech.edu/records/5fv66-jn626Vibrational Superexchange Mechanism of Intramolecular Vibrational Relaxation in (CH_3)_3CCCH Molecules
https://resolver.caltech.edu/CaltechAUTHORS:20150610-133027887
Authors: {'items': [{'id': 'Stuchebrukhov-A-A', 'name': {'family': 'Stuchebrukhov', 'given': 'A. A.'}}, {'id': 'Mehta-A', 'name': {'family': 'Mehta', 'given': 'A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1021/j100150a008
Quantum calculations are reported for the dynamics of intramolecular vibrational energy redistribution of the
acetylenic CH stretch in (CH_3)_3CCCH molecules. This paper is an extension of our previous publication (J.
Chem. Phys. 1993, 98, 6044) where the line widths of the CH overtone transitions were calculated in several
molecules of a general class (CX_3)_3YCCH, and it was found that the relaxation is due to a sequence of many
weak off-resonance vibrational transitions between tiers of directly coupled states. The coupling of the CH
stretch to a manifold of quasi-resonant states resembles the superexchange mechanism of coupling between
donor and acceptor states in long-distance electron-transfer reactions. An analysis based on total population
in each tier is introduced. The very rapid decrease of this population in the intermediate tiers with tier index
provides evidence that the relaxation dynamics occurs via tunneling (vibrational superexchange) under a dynamic
barrier in the tier space of the system. Details of the time evolution of the population under the dynamic barrier
in the course of relaxation are described. "Dead end" states, their effect on the time-evolution and on spectra,
their removal via inclusion of additional anharmonicities, and, thereby, their probable artificial nature in the
present case are discussed.https://authors.library.caltech.edu/records/gj09e-94s43Correlation between theory and experiment in electron-transfer reactions in proteins: electronic couplings in modified cytochrome c and myoglobin derivatives
https://resolver.caltech.edu/CaltechAUTHORS:20150608-143120329
Authors: {'items': [{'id': 'Siddarth-P', 'name': {'family': 'Siddarth', 'given': 'Prabha'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1993
DOI: 10.1021/j100152a008
The artificial intelligence-superexchange method of estimating the long-range electronic coupling in proteins
that we have developed previously is used to study electron-transfer reactions in Ru-modified cytochrome c and
myoglobin derivatives. Good correlations between theoretical and experimental rate constants are obtained
using the present method. Amino acid paths for electron transfer are analyzed.https://authors.library.caltech.edu/records/8dxg2-94p71Decay and Recurrences of Wave Packets in Nonlinear Quantum Systems
https://resolver.caltech.edu/CaltechAUTHORS:20150609-085711487
Authors: {'items': [{'id': 'Stuchebrukbov-A-A', 'name': {'family': 'Stuchebrukbov', 'given': 'A. A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1994
DOI: 10.1021/j100064a007
A simple and analytical model of quantum recurrences in wave packet dynamics of nonlinear vibrational systems
is presented. It is shown that in addition to "normal" rephasing time τR the width of the packet experiences
very strong recurrences at τR/2. In a quasiclassical limit, which can be studied explicitly in this model, the
recurrences disappear and the decay becomes irreversible. Recent femtosecond experimental results of Zewail
and co-workers are discussed in the framework of this analytical model.https://authors.library.caltech.edu/records/6ezz1-ycg98Scanning tunneling microscopy theory for an adsorbate: Application to adenine adsorbed on a graphite surface
https://resolver.caltech.edu/CaltechAUTHORS:OUYjcp94
Authors: {'items': [{'id': 'Ou-Yang-H', 'name': {'family': 'Ou-Yang', 'given': 'Hui'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Källebring-B', 'name': {'family': 'Källebring', 'given': 'Bruno'}}]}
Year: 1994
DOI: 10.1063/1.466824
An expression is obtained for the current in scanning tunneling microscopy (STM) for a single adsorbate molecule. For this purpose the ``Newns–Anderson'' treatment (a ``discrete state in a continuum'' treatment) is used to obtain wave functions and other properties of the adsorbate/substrate system. The current is expressed in terms of the adsorbate–tip matrix elements, and an effective local density of states of the adsorbate/substrate system, at the adsorbate. As an example, the treatment is applied to the STM image of adenine adsorbed on a graphite surface, and the results are compared with experiment. The dependence of the image on the position of adenine with respect to the underlying graphite is considered. A discussion is given of the type of experimental STM data needed for suitable comparison of theory and experiment. In an analysis of the calculations, the role of each atom, its neighbors, next nearest neighbors, etc., in an adsorbed molecule is considered. The need for using in the present calculation more orbitals than only the HOMO and the LUMO of the adsorbate is also noted.https://authors.library.caltech.edu/records/m34qj-32r02Free Energy of Nonequilibrium Polarization Systems. 4. A Formalism Based on the Nonequilibrium Dielectric Displacement
https://resolver.caltech.edu/CaltechAUTHORS:20150608-150915281
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1994
DOI: 10.1021/j100080a012
An expression for the free energy of nonequilibrium polarization systems, valid in the presence or absence of
dielectric images, is derived using the nonequilibrium dielectric displacement and electric field vectors. The
results are compared with those based on the nonequilibrium polarization vector (Part I). For the case of
longitudinal polarization they are equivalent. However, the present expression is simpler and more compact.
The results are compared with others in the literature.https://authors.library.caltech.edu/records/sh5h2-3t261Reflections on early days in electron transfer
https://resolver.caltech.edu/CaltechAUTHORS:20150408-065556787
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1994
DOI: 10.1016/1010-6030(94)02019-1
As an introduction to this NATO workshop, some of the early electron transfer days, beginning with the late 1940s, are recounted.https://authors.library.caltech.edu/records/hd8q4-8s861IVR in Overtones of the Acetylenic C-H Stretch in Propyne
https://resolver.caltech.edu/CaltechAUTHORS:20150610-135730980
Authors: {'items': [{'id': 'Mehta-A', 'name': {'family': 'Mehta', 'given': 'Aseem'}}, {'id': 'Stuchebrukhov-A-A', 'name': {'family': 'Stuchebrukhov', 'given': 'A. A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1995
DOI: 10.1021/j100009a026
Quantum calculations are reported for the high-resolution spectra and dynamics of the first and second overtone
of the acetylenic C-H stretch (ν_1) in propyne. The calculational method used is similar to that we have used
earlier for lower energy states. Lack of low-order Fenni resonances lead to a vibrational superexchange
mechanism of decay of the initially populated bright state. The importance of the total density of states and
quartic couplings between zeroth-order states is investigated. Comparison with recent experimental results
is discussed.https://authors.library.caltech.edu/records/qvd5z-jpj02Global Potential Energy Contour Plots for Chemical Reactions. Stepwise vs Concerted 2 + 2 Cycloaddition
https://resolver.caltech.edu/CaltechAUTHORS:20150318-131128407
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1995
DOI: 10.1021/ja00121a024
A global contour plot is described for reactions involving stepwise or concerted addition of two ethylenes
to form cyclobutane. The relevant isomers of the various species and of the reaction paths, with plains or valleys,
minima, saddle points, and domes or conical intersections, are described. Two collective asymmetric coordinates
are introduced as axes for the plot, which presents an overview of the system and which complements the usual
2-dimensional cuts of the many-dimensional potential energy surface. Other global coordinates are also introduced.
The plot involves a pointwise minimization of the potential energy with respect to the coordinates not used as axes.
A permutation symmetry can be used to derive the various coordinates. Free energy and entropy (or number of
states) curves versus a reaction coordinate are discussed.https://authors.library.caltech.edu/records/hq0ww-e9b08Theoretical Study of Electron Transfer in Ferrocytochromes
https://resolver.caltech.edu/CaltechAUTHORS:20150318-105106794
Authors: {'items': [{'id': 'Stuchebrukhov-A-A', 'name': {'family': 'Stuchebrukhov', 'given': 'A. A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1995
DOI: 10.1021/j100019a044
A series of calculations is reported of the superexchange electronic matrix element between donor and acceptor
states in photoinduced long-distance electron-transfer reactions in seven Ru-modified proteins: Ru(bpy)_2im-(HisX)-cyt c, where X = 33, 39, 58, 62, 66, 72, 79. Calculated results are compared with experimental data.
The model used for the calculation includes a detailed description of the donor and acceptor wave functions
in terms of ligand field theory. The intervening protein medium is treated within the extended Hiickel theory.
It is found that the symmetry and spatial properties of the donor/acceptor wave functions impose certain
selection rules on the pathways used in electron transfer. Some paths through σ bonds are not allowed due
to the symmetry requirement, for example. Also, the influence of the spatial mutual orientation of the donor
and acceptor orbitals in the protein on the rates of electron transfer is analyzed. It is found that there is a
strong stereochemical effect in this type of reaction. The mutual orientation of the orbitals is an important
factor which determines the reaction rate, in addition to such factors as distance between donor and acceptor
and concrete chemical structure of the protein matrix discussed before in the literature. In the calculations,
a new method of transition amplitudes is applied. The method can be used for proteins and other large
systems involving several thousand atoms. Numerically, the new method reduces the calculation of the
electronic coupling between donor and acceptor to the problem of finding iteratively the minimum of a
multidimensional parabola, and avoids the diagonalization of the Hamiltonian matrix.https://authors.library.caltech.edu/records/vyshj-qbw80Solvent dynamics-modified RRKM theory in clusters
https://resolver.caltech.edu/CaltechAUTHORS:20150408-065026591
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1995
DOI: 10.1016/0009-2614(95)00899-F
Kramers and RRKM theories are used to formulate a solvent dynamics-modified treatment of unimolecular reaction rates in clusters. The canonical Kramers' description is modified so as to apply to microcanonical systems. An entropic gradient, arising from all coordinates but the reaction coordinate q, and a q-dependent microcanonical vibrational temperature are introduced. A simple expression is obtained relating the rate constant to its RRKM value and permitting comparison with recent experiments. An application is also made to the Kramers' turnover region.https://authors.library.caltech.edu/records/0zp77-3mz55Symmetry or asymmetry of k_(ET) and i_(STM) vs. potential curves
https://resolver.caltech.edu/CaltechAUTHORS:20120208-115452548
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1996
DOI: 10.1039/FT9969203905
The symmetry or asymmetry of STM current vs. bias potential and of electron transfer (ET) rate vs. overpotential curves is discussed for ET and for STM patterns across ordered monolayers. The superexchange expression for the electronic coupling matrix element, the Fermi–Dirac distribution and, for the ET reaction, the reorganization, are included. A mean potential approximation is assumed for the effect of bias or overpotential on the electronic orbitals or the ordered monolayer. Consequences for the symmetry vs. asymmetry of the ln(k_(ET))vs. overpotential and for the ln(i_(STM)) and pattern vs. bias are described. Examples of some relevant experiments are considered.https://authors.library.caltech.edu/records/f06sj-y6d41Tunneling matrix element in Ru-modified blue copper proteins: Pruning the protein in search of electron transfer pathways
https://resolver.caltech.edu/CaltechAUTHORS:20150407-142735239
Authors: {'items': [{'id': 'Gehlen-J-N', 'name': {'family': 'Gehlen', 'given': 'John N.'}}, {'id': 'Daizadeh-I', 'name': {'family': 'Daizadeh', 'given': 'Iraj'}}, {'id': 'Stuchebrukhov-A-A', 'name': {'family': 'Stuchebrukhov', 'given': 'A. A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1996
DOI: 10.1016/0020-1693(95)04917-7
We investigate with semi-empirical extended Hückel theory calculations the tunneling matrix element for electron transfer in three ruthenium-modified blue copper azurin molecules from the bacterium Pseudomonas aeruginosa which have been recently synthesized and studied experimentally by Gray and co-workers. All of the atoms in the protein can be included in the calculations with the method of transition amplitudes that has been developed recently. Our particular focus here, however, is to develop procedures that create a truncated protein much smaller than the initial 2000 atom one, the aim being to retain only those amino acids that are important to the electron tunneling mechanism. Such a procedure, which we refer to as 'pruning', is useful, first because it reduces the size of the problem, perhaps allowing for more accurate techniques to be used on the truncated protein, and second because it allows for the identification of the regions in the protein in which the tunneling electron is localized. The pruning procedures enable us to reduce the number of atoms required in an extended Hückel theory analysis of the tunneling mechanism by approximately a factor of 10 over that in the original protein.https://authors.library.caltech.edu/records/q31sp-4k190Gaussian field model of dielectric solvation dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20150513-153506257
Authors: {'items': [{'id': 'Song-Xueyu', 'name': {'family': 'Song', 'given': 'Xueyu'}}, {'id': 'Chandler-D', 'name': {'family': 'Chandler', 'given': 'David'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1996
DOI: 10.1021/jp960887e
Extending the Gaussian model of solvation (Chandler, D. Phys. Rev. E 1993, 48, 2898) to dynamics, we focus specifically on the problem of dielectric relaxation. In the Gaussian model, the solvent is described in terms of a linear responding field that is expelled from the volume occupied by the solute. The excluded volume affects the normal modes of the system, thereby playing a significant role in solvation dynamics. Even in the context of dielectric continuum theory, the excluded volume affects the polarization response outside that volume. We show that this effect can be analyzed generally and analytically.https://authors.library.caltech.edu/records/gdcxv-8dd92Solvent dynamics: Modified Rice–Ramsperger–Kassel–Marcus theory. II. Vibrationally assisted case
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp96
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1996
DOI: 10.1063/1.472385
Expressions are given for a solvent dynamics-modified Rice–Ramsperger–Kassel–Marcus (RRKM) theory for clusters. The role of vibrational assistance across the transition state region is included. The usual differential equation for motion along the slow coordinate X in constant temperature systems is modified so as to apply to microcanonical systems. A negative entropy term, –Sv(X), replaces the (1/T)∂U/∂X or (1/T)∂G/∂X which appears in canonical systems. Expressions are obtained for the RRKM-type rate constant k(X) and for the Sv(X) which appear in the differential equation. An approximate solution for steady-state conditions is given for the case that the "reaction window" is narrow. The solution then takes on a simple functional form. The validity of the assumption can be checked a posteriori. Recrossings of the transition state are included and the condition under which the treatment approaches that in Part I is described.https://authors.library.caltech.edu/records/9amf2-t3f56Electron transfer reactions in chemistry. Theory and experiment
https://resolver.caltech.edu/CaltechAUTHORS:20150415-110624300
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1997
DOI: 10.1351/pac199769010013
Since the late 1940s, the field of electron transfer processes has grown enonnously, both in chemistry and
biology. The development of the field, experimentally and theoretically, as well as its relation to the study
of other kinds of chemical reactions, represents to us an intriguing history, one in which many threads have
been brought together. In this lecture, some history, recent trends, and my own involvement in this research
are described.https://authors.library.caltech.edu/records/dwnew-42q75A sequential formula for electronic coupling in long range bridge-assisted electron transfer: Formulation of theory and application to alkanethiol monolayers
https://resolver.caltech.edu/CaltechAUTHORS:HSUjcp97
Authors: {'items': [{'id': 'Hsu-C-P', 'name': {'family': 'Hsu', 'given': 'Chao-Ping'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1997
DOI: 10.1063/1.473398
A recursion relation is formulated for the Green's function for calculating the effective electron coupling in bridge-assisted electronic transfer systems, within the framework of the tight-binding Hamiltonian. The recursion expression relates the Green's function of a chain bridge to that of the bridge that is one unit less. It is applicable regardless of the number of orbitals per unit. This method is applied to the system of a ferrocenylcarboxy-terminated alkanethiol on the Au(111) surface. At larger numbers of bridge units, the effective coupling strength shows an exponential decay as the number of methylene(–CH2–) units increases. This sequential formalism shows numerical stability even for a very long chain bridge and, since it uses only small matrices, requires much less computer time for the calculation. Identical bridge units are not a requirement, and so the method can be applied to more complicated systems.https://authors.library.caltech.edu/records/q5fbb-4es42Time-Dependent Stokes Shift and Its Calculation from Solvent Dielectric Dispersion Data
https://resolver.caltech.edu/CaltechAUTHORS:20150421-135525609
Authors: {'items': [{'id': 'Hsu-Chao-Ping', 'name': {'family': 'Hsu', 'given': 'Chao-Ping'}}, {'id': 'Song-Xueyu', 'name': {'family': 'Song', 'given': 'Xueyu'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1997
DOI: 10.1021/jp9630885
The time-dependent solvation correlation function (the Stokes shift response function), which describes the solvent response to a sudden change in the charge distribution of a solute molecule, is calculated here directly from experimentally measured dielectric dispersion data, ε(ω), of the solvent. In the calculation a reaction field with the dielectric continuum assumption is used. This simple model is applied to the experimental results of Jimenez et al. for photoexcited coumarin and water as a solvent, and encouraging agreement is obtained using the experimental data on ε(ω).https://authors.library.caltech.edu/records/2xmyp-22261Theory of Rates of S_N2 Reactions and Relation to Those of Outer Sphere Bond Rupture Electron Transfers
https://resolver.caltech.edu/CaltechAUTHORS:20150519-085740363
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1997
DOI: 10.1021/jp963722e
A model is considered for S_N2 reactions, based on two interacting states. Relevant bond energies, standard electrode potentials, solvent contributions (nonequilibrium polarization), and steric effects are included. A unified approach is introduced in which there can be a flux density for crossing the transition state, which is either bimodal, one part leading to S_N2 and the other to ET products, or unimodal with a less marked energy-dependent separation of the rates of formation of these products. In a unified description an expression is given for the reorganization energy, which reduces in the appropriate limits to the pure S_N2 and ET/bond rupture cases. Expressions are obtained for the S_N2 rate constant and for its relation to that of the concerted electron transfer/bond rupture reaction. Applications of the theory are made to the cross-relation between rate constants of cross and identity reactions, experimental entropies and energies of activation, the relative rates of S_N2 and ET reactions, and the possible expediting of an outer sphere ET reaction by an incipient S_N2-type interaction. Results on the photoelectron emission threshold energies of ions in solution provide some information on a solvation term, and another quantity can be estimated using data from gas phase S_N2 reactions or from quantum chemistry calculations. Also introduced for comparison is an adiabatic model that is an extension of a bond energy−bond order formulation for gas phase reactions.https://authors.library.caltech.edu/records/gpx56-4et84Electron Transfer Model for the Electric Field Effect on Quantum Yield of Charge Separation in Bacterial Photosynthetic Reaction Centers
https://resolver.caltech.edu/CaltechAUTHORS:20150513-153233889
Authors: {'items': [{'id': 'Tanaka-Shigenori', 'name': {'family': 'Tanaka', 'given': 'Shigenori'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1997
DOI: 10.1021/jp9632854
The effect of an electric field on a photoinduced charge separation process is treated theoretically. The system considered is a reaction center (RC) of photosynthetic bacteria, involving an electron transfer (ET) from the electronically excited singlet state of the bacteriochlorophyll dimer (P) to the bacteriopheophytin (H) and quinone (Q). In contrast to formulations which focus only on the forward steps and do not explain the major effect on the quantum yield of P^+Q^- or, in Q-depleted samples, of P^+H^-, the present study includes the effect on the back reactions, an effect which we find to be large. The low-frequency medium and high-frequency intramolecular vibrational modes are included in the calculation of the various ET rates. Recent experimental results on the ET energetics, including the estimated effect of static heterogeneity in RCs, are incorporated. The rate equations for the population densities of distinct states are solved for both oriented and randomly oriented (isotropic) RC samples, and the results are compared with experimental data for the field-induced reduction of the quantum yield of formation of charge-separated state P^+Q^-. A simple (quasi-equilibrium) model calculation illustrates the essential features of this analysis of the electric field effect and compares reasonably well with these numerical results of the more detailed model. The question of the electric field effect on the fluorescence quantum yield is also addressed, and a suggestion is made for consistency with the data on the formation of P^+Q^-.https://authors.library.caltech.edu/records/f6vv1-n2q43Source of Image Contrast in STM Images of Functionalized Alkanes on Graphite: A Systematic Functional Group Approach
https://resolver.caltech.edu/CaltechAUTHORS:20150422-091143996
Authors: {'items': [{'id': 'Claypool-C-L', 'name': {'family': 'Claypool', 'given': 'Christopher L.'}}, {'id': 'Faglioni-F', 'name': {'family': 'Faglioni', 'given': 'Francesco'}, 'orcid': '0000-0002-3327-8848'}, {'id': 'Goddard-W-A-III', 'name': {'family': 'Goddard', 'given': 'William A., III'}, 'orcid': '0000-0003-0097-5716'}, {'id': 'Gray-H-B', 'name': {'family': 'Gray', 'given': 'Harry B.'}, 'orcid': '0000-0002-7937-7876'}, {'id': 'Lewis-N-S', 'name': {'family': 'Lewis', 'given': 'Nathan S.'}, 'orcid': '0000-0001-5245-0538'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1997
DOI: 10.1021/jp9701799
A series of functionalized alkanes and/or alkyl alcohols have been prepared and imaged by scanning tunneling microscopy (STM) methods on graphite surfaces. The stability of these ordered overlayers has facilitated reproducible collection of STM images at room temperature with submolecular resolution, in most cases allowing identification of individual hydrogen atoms in the alkane chains, but in all cases allowing identification of molecular length features and other aspects of the image that can be unequivocally related to the presence of functional groups in the various molecules of concern. Functional groups imaged in this study include halides (X = F, Cl, Br, I), amines, alcohols, nitriles, alkenes, alkynes, ethers, thioethers, and disulfides. Except for −Cl and −OH, all of the other functional groups could be distinguished from each other and from −Cl or −OH through an analysis of their STM metrics and image contrast behavior. The dominance of molecular topography in producing the STM images of alkanes and alkanols was established experimentally and also was consistent with quantum chemistry calculations. Unlike the contrast of the methylene regions of the alkyl chains, the STM contrast produced by the various functional groups was not dominated by topographic effects, indicating that variations in local electronic coupling were important in producing the observed STM images of these regions of the molecules. For molecules in which electronic effects overwhelmed topographic effects in determining the image contrast, a simple model is presented to explain the variation in the electronic coupling component that produces the contrast between the various functional groups observed in the STM images. Additionally, the bias dependence of these STM images has been investigated and the contrast vs bias behavior is related to factors involving electron transfer and hole transfer that have been identified as potentially being important in dominating the electronic coupling in molecular electron transfer processes.https://authors.library.caltech.edu/records/6vfct-4mr44Electron transfer reactions in chemistry - Theory and experiment
https://resolver.caltech.edu/CaltechAUTHORS:20150408-070409394
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1997
DOI: 10.1016/S0022-0728(97)00091-0
Since the late 1940s, the field of electron transfer processes has grown enormously in chemistry, electrochemistry, and biology. The development of the field, experimentally and theoretically, as well as its relation to the study of the other kinds of chemical reactions, presents an intriguing history in which many threads have been brought together. In this article, some history, recent trends, and my own involvement are described.https://authors.library.caltech.edu/records/vshy0-2sn42Time-dependent fluorescence spectra of large molecules in polar solvents
https://resolver.caltech.edu/CaltechAUTHORS:20150609-082842994
Authors: {'items': [{'id': 'Hsu-Chao-Ping', 'name': {'family': 'Hsu', 'given': 'Chao-Ping'}}, {'id': 'Georgievskii-Y', 'name': {'family': 'Georgievskii', 'given': 'Yuri'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1998
DOI: 10.1021/jp980255n
A method is described for incorporating the vibronic transitions of a solute molecule in the calculation of the time evolution of its fluorescence spectrum in a polar solvent. In this initial article, systems are treated in which the intramolecular vibrational relaxation is much faster than the observed delay time. The overall fluorescence spectrum is then shown to be a convolution of the steady-state absorption and emission spectra of the solute in a nonpolar solvent and the time-dependent emission line shape arising only from polar interactions. Calculations are made for coumarin 153 in acetonitrile, using the dielectric dispersion data of the solvent available from experimental measurements. The results are in encouraging agreement with experimental spectra. Results are also given for the dynamic Stokes shift in methanol.https://authors.library.caltech.edu/records/asnm4-chc46Dynamic Stokes shift in solution: Effect of finite pump pulse duration
https://resolver.caltech.edu/CaltechAUTHORS:20090918-104720373
Authors: {'items': [{'id': 'Georgievskii-Y', 'name': {'family': 'Georgievskii', 'given': 'Yuri'}}, {'id': 'Hsu-C-P', 'name': {'family': 'Hsu', 'given': 'Chao-Ping'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1998
DOI: 10.1063/1.476155
The time-evolution of the fluorescence spectrum of a dissolved chromophore excited by an ultrafast pump pulse is considered. The average value of the energy difference of the solute in its excited and ground states is used to describe the relaxation of the maximum of the transient fluorescence spectrum to its equilibrium value (dynamic Stokes shift, DSS). A simple formula for the normalized DSS is obtained which generalizes an earlier standard classical expression and includes the effect of a pump pulse of finite duration. As an example, dielectric dispersion data are used for a dipolar solute in water to estimate the quantum correction to the standard DSS expression. The correction is negligible when the frequency of the pump pulse is close to the maximum in the absorption spectrum, but a deviation from the standard formula can be expected for the pump pulse tuned to a far wing of the absorption band of the chromophore. An expression is given for this deviation.https://authors.library.caltech.edu/records/wbp4k-vm254Remarks on dissociative anion potential energy curves for organic electron transfers
https://resolver.caltech.edu/CaltechAUTHORS:20150318-103054448
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1998
DOI: 10.3891/acta.chem.scand.52-0858
Data on electron-molecule collisions in the gas phase have been used to obtain
information on the potential energy curve for the dissociation of a transient
anion RX' - , where R is frequently an organic group and X often a halide. The
data include thermal dissociative attachment energies and vertical attachment
energies of RX. The data also consist of collision cross-sections (elastic. inelastic
and dissociative) which vary with the energy of the incident electron and with
the vibrational state or temperature of the molecule. Relevant expressions are
discussed. An approximate temperature-dependent expression is given for the
thermal dissociative attachment cross-section. The potential energy curve of the
transient anion appears in the theory of electron transfer reactions of RX that
are accompanied by the bond rupture of R-X.https://authors.library.caltech.edu/records/vv3h6-5yj40Ion Pairing and Electron Transfer
https://resolver.caltech.edu/CaltechAUTHORS:20150513-165258796
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1998
DOI: 10.1021/jp9834457
Several scenarios are considered for the effect of electrolytes, specifically for ion pairing, on the rates of electron transfer reactions: (i) electron transfer followed by ion transfer, (ii) ion-pair dissociation followed by electron transfer, or (iii) ion transfer accompanying the electron transfer. The latter may involve fast or slow (diffusive) ionic motion. A distinction is made between ion reorganization (case (iii)) and the formation of real chemical intermediates. The ion pairs themselves may be tight (contact) or loose (solvent separated). The discussion is illustrated with an example in the literature. Differences in degree in behavior of intramolecular and intermolecular electron transfer, due to differences in extent of ionic motion, are noted.https://authors.library.caltech.edu/records/8n7gq-4sn48Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model
https://resolver.caltech.edu/CaltechAUTHORS:GEOjcp99
Authors: {'items': [{'id': 'Georgievskii-Y', 'name': {'family': 'Georgievskii', 'given': 'Yuri'}}, {'id': 'Hsu-C-P', 'name': {'family': 'Hsu', 'given': 'Chao-Ping'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1999
DOI: 10.1063/1.478425
The effect of solvent fluctuations on the rate of electron transfer reactions is considered using linear response theory and a second-order cumulant expansion. An expression is obtained for the rate constant in terms of the dielectric response function of the solvent. It is shown thereby that this expression, which is usually derived using a molecular harmonic oscillator ("spin-boson") model, is valid not only for approximately harmonic systems such as solids but also for strongly molecularly anharmonic systems such as polar solvents. The derivation is a relatively simple alternative to one based on quantum field theoretic techniques. The effect of system inhomogeneity due to the presence of the solute molecule is also now included. An expression is given generalizing to frequency space and quantum mechanically the analogue of an electrostatic result relating the reorganization free energy to the free energy difference of two hypothetical systems [J. Chem. Phys. 39, 1734 (1963)]. The latter expression has been useful in adapting specific electrostatic models in the literature to electron transfer problems, and the present extension can be expected to have a similar utility.https://authors.library.caltech.edu/records/ka056-vwk28Science Over Politics
https://resolver.caltech.edu/CaltechAUTHORS:20141125-084907203
Authors: {'items': [{'id': 'Lanza-R-P', 'name': {'family': 'Lanza', 'given': 'Robert P.'}}, {'name': {'family': 'Baltimore', 'given': 'David'}, 'orcid': '0000-0001-8723-8190'}, {'id': 'Dulbecco-R', 'name': {'family': 'Dulbecco', 'given': 'Renato'}}, {'id': 'Gell-Mann-M', 'name': {'family': 'Gell-Mann', 'given': 'Murray'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1999
DOI: 10.1126/science.283.5409.1849b
Last month, 70 members of the U.S. Congress, including Henry Hyde, Chairman of the House Judiciary Committee, and J. C. Watts Jr. Republican Conference Chairman, signed a letter urging the federal government to ban all research on stem cells obtained from human embryos and fetuses. The letter calls upon the U.S. Department of Health and Human Services (DHHS) to reverse National Institutes of Health (NIH) Director Harold Varmus's decision to allow funding of pluripotent stem cell research. The lawmakers object "in the strongest possible terms" to Varmus's decision, as well as to the memorandum issued in January by DHHS General Counsel Harriet Rabb, which served as the legal basis for Varmus's position. In their letter, the members of Congress state, "Any NIH action to initiate funding of such research would violate both the letter and spirit of the federal law banning federal support for research in which human embryos are harmed or destroyed." Federal laws and regulations, they claim, have protected human embryos and fetuses "from harmful experimentation at the hands of the Federal government" for more than two decades. "This area of law has provided a bulwark against government's misuse and exploitation of human beings in the name of medical progress. It would he a travesty for this Administration to attempt to unravel this accepted ethical standard."https://authors.library.caltech.edu/records/2r59m-8yf44An intramolecular theory of the mass-independent isotope effect for ozone. I
https://resolver.caltech.edu/CaltechAUTHORS:HATjcp99
Authors: {'items': [{'id': 'Hathorn-B-C', 'name': {'family': 'Hathorn', 'given': 'B. C.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 1999
DOI: 10.1063/1.480267
An intramolecular theory of the unusual mass-independent isotope effect for ozone formation and dissociation is described. The experiments include the enrichment factor, its dependence on the ambient pressure, the ratio of the formation rates of symmetric and asymmetric ozone isotopomers, the enrichment of ozone formed from heavily enriched oxygen isotopes, the comparison of that enrichment to that when the heavy isotopes are present in trace amounts, the isotopic exchange rate constant, and the large mass-dependent effect when individual rate constants are measured, in contrast with the mass-independent effect observed for scrambled mixtures. To explain the results it is suggested that apart from the usual symmetry number ratio of a factor of 2, the asymmetric ozone isotopomers have a larger density of reactive (coupled) quantum states, compared with that for the symmetric isotopomers (about 10%), due to being more "RRKM-like" (Rice–Ramsperger–Kessel–Marcus): Symmetry restricts the number of intramolecular resonances and coupling terms in the Hamiltonian which are responsible for making the motion increasingly chaotic and, thereby, increasingly statistical. As a result the behavior occurs regardless of whether the nuclei are bosons (16O, 18O) or fermions (17O). Two alternative mechanisms are also considered, one invoking excited electronic states and the other invoking symmetry control in the entrance channel. Arguments against each are given. An expression is given relating the mass-independent rates of the scrambled systems to the mass-dependent rates of the unscrambled ones, and the role played by a partitioning term in the latter is described. Different definitions for the enrichment factor for heavily enriched isotopic systems are also considered. In the present paper attention is focused on setting up theoretical expressions and discussing relationships. They provide a basis for future detailed calculations.https://authors.library.caltech.edu/records/0rya1-bxr25On the theory of electron transfer reactions at semiconductor electrode/liquid interfaces
https://resolver.caltech.edu/CaltechAUTHORS:GAOjcp00a
Authors: {'items': [{'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Georgievskii-Y', 'name': {'family': 'Georgievskii', 'given': 'Yuri'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2000
DOI: 10.1063/1.480918
Electron transfer reaction rate constants at semiconductor/liquid interfaces are calculated using the Fermi Golden Rule and a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the electronic structures of semiconductors with surfaces and are compared. The maximum electron transfer rate constants at Si/viologen2+/+ and InP/Me2Fc+/0 interfaces are computed using the tight-binding type calculations for the solid and the extended-Hückel for the coupling to the redox agent at the interface. These results for the bulk states are compared with the experimentally measured values of Lewis and co-workers, and are in reasonable agreement, without adjusting parameters. In the case of InP/liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states.https://authors.library.caltech.edu/records/8j7w5-wmq11Nonadiabatic Electron Transfer at Metal Surfaces
https://resolver.caltech.edu/CaltechAUTHORS:20150316-132413291
Authors: {'items': [{'id': 'Gosavi-S', 'name': {'family': 'Gosavi', 'given': 'Shachi'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2000
DOI: 10.1021/jp9933673
The present article treats the role of the density of electronic states ρ_F at the Fermi level of a metal in affecting the rate of nonadiabatic electron transfer. The rate constant k_(ET) is calculated for the electron transfer across an alkanethiol monolayer on platinum and on gold. The ρ_F of platinum is about 7.5 times that of gold, the difference being mainly due to the d band of Pt. In spite of this difference, the electron transfer rate constant k_(ET) calculated in the present paper increases only by a factor of about 1.8, instead of the factor of about 7.5 expected using ρ_F alone. Implications of these results for present and past experiments are described. Bands which are weakly coupled (e.g., the d-band of Pt in the present case) contribute much less to the rate constant than is suggested by their density of states ρ_F. Thereby, k_(ET) is approximately independent of ρ_F in two cases: (1) adiabatic electron transfer and (2) nonadiabatic electron transfer when the extra ρ_F is due to the d electrons. Experiments which can test the latter are discussed.https://authors.library.caltech.edu/records/7x211-9ee94Tutorial on rate constants and reorganization energies
https://resolver.caltech.edu/CaltechAUTHORS:20150317-093530066
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2000
DOI: 10.1016/S0022-0728(00)00011-5
These lecture notes, presented as a tutorial at the Euroconference on Modern Trends in Electrochemistry of Molecular Interfaces, consist of the following sections: (i) elementary transition state theory of reaction rates; (ii) elementary ion solvation theory; (iii) elementary solvent reorganization theory; (iv) generalizations; (v) extension to the metal | liquid interface; (vi) extension to the liquid | liquid interface, and (vii) examples of references.https://authors.library.caltech.edu/records/xjg2d-4ye54On the theory of ion transfer rates across the interface of two immiscible liquids
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp00
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2000
DOI: 10.1063/1.481950
Ion transfer across the interface of two immiscible liquids involves a mechanism for initiating desolvation from the first liquid, A, and concerted solvation by the second, B. In the present article a mechanism is considered in which this initiation is facilitated by the ion attaching itself to the tip of a solvent protrusion of B into A. (Protrusions have been observed in computer simulations and termed "fingers" or "cones.") It is presumed that the most effective protrusion represents a balance between two opposing effects: the more convex the protrusion the less probable the ion/protrusion formation but also the less the resistance to extrusion of the intervening liquid between the ion and the surface. An analogy of the latter to hydrodynamics is noted, namely, the more convex the surface the less the frictional force it exerts on the approaching ion. After diffusion in coordinate and solvation space across the interfacial region, the final detachment of the ion from solvent A is assumed to occur from a protrusion of A into B. Existing data on ion transfer rates are discussed, including the question of diffusion vs kinetic control. Computer simulations that correspond to the experimental conditions in realistic liquids for measurement of the electrochemical exchange current rate constant k0 are suggested. They can be used to test specific theoretical features. With a suitable choice of systems the need (and a major barrier to the simulations) for having a base electrolyte in such simulations can be bypassed. An experiment for the real-time observation of an ion leaving the interface is also suggested.https://authors.library.caltech.edu/records/jwc5e-7r070On the theory of electron transfer reactions at semiconductor/liquid interfaces. II. A free electron model
https://resolver.caltech.edu/CaltechAUTHORS:GAOjcp00b
Authors: {'items': [{'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2000
DOI: 10.1063/1.1309528
Electron transfer reactions at semiconductor/liquid interfaces are studied using the Fermi Golden rule and a free electron model for the semiconductor and the redox molecule. Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states where the effective electron mass in the semiconductor need not equal the actual electron mass. The calculated maximum electron transfer rate constants are compared with the experimental results as well as with the theoretical results obtained in Part I using tight-binding calculations. The results, which are analytic for an s-electron in the redox agent and reduced to a quadrature for pz- and dz2-electrons, add to the insight of the earlier calculations.https://authors.library.caltech.edu/records/2dy2y-km687An intramolecular theory of the mass-independent isotope effect for ozone. II. Numerical implementation at low pressures using a loose transition state
https://resolver.caltech.edu/CaltechAUTHORS:HATjcp00
Authors: {'items': [{'id': 'Hathorn-B-C', 'name': {'family': 'Hathorn', 'given': 'B. C.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2000
DOI: 10.1063/1.1321045
A theory is described for the variation in the rate constants for formation of different ozone isotopomers from oxygen atoms and molecules at low pressures. The theory is implemented using a simplified description which treats the transition state as loose. The two principal features of the theory are a phase space partitioning of the transition states of the two exit channels after formation of the energetic molecule and a small (ca. 15%) decrease in the effective density of states, rho [a "non-Rice–Ramsperger–Kassel–Marcus (RRKM) effect"], for the symmetric ozone isotopomers [B. C. Hathorn and R. A. Marcus, J. Chem. Phys. 111, 4087 (1999)]. This decrease is in addition to the usual statistical factor of 2 for symmetric molecules. Experimentally, the scrambled systems show a "mass-independent" effect for the enrichments delta (for trace) and E (for heavily) enriched systems, but the ratios of the individual isotopomeric rate constants for unscrambled systems show a strongly mass-dependent behavior. The contrasting behavior of scrambled and unscrambled systems is described theoretically using a "phase space" partitioning factor. In scrambled systems an energetic asymmetric ozone isotopomer is accessed from both entrance channels and, as shown in paper I, the partitioning factor becomes unity throughout. In unscrambled systems, access to an asymmetric ozone is only from one entrance channel, and differences in zero-point energies and other properties, such as the centrifugal potential, determine the relative contributions (the partitioning factors) of the two exit channels to the lifetime of the resulting energetic ozone molecule. They are responsible for the large differences in individual recombination rate constants at low pressures. While the decrease in rho for symmetric systems is attributed to a small non-RRKM effect eta, these calculated results are independent of the exact origin of the decrease. The calculated "mass-independent" enrichments, delta and E, in scrambled systems are relatively insensitive to the transition state (TS), because of the absence of the partitioning factor in their case (for a fixed non-RRKM eta). They are compared with the data at room temperature. Calculated results for the ratios of individual isotopomeric rate constants for the strongly mass-independent behavior for unscrambled systems are quite sensitive to the nature of the TS because of the partitioning effect. The current data are available only at room temperature but the loose TS is valid only at low temperatures. Accordingly, the results calculated for the latter at 140 K represent a prediction, for any given eta. At present, a comparison of the 140 K results can be made only with room temperature data. They show the same trends as, and are in fortuitous agreement, with the data. Work is in progress on a description appropriate for room temperature.https://authors.library.caltech.edu/records/q1eem-edv13Temperature dependence of the electronic factor in the nonadiabatic electron transfer at metal and semiconductor electrodes
https://resolver.caltech.edu/CaltechAUTHORS:20150317-094130275
Authors: {'items': [{'id': 'Gosavi-S', 'name': {'family': 'Gosavi', 'given': 'Shachi'}}, {'id': 'Gao-Yi-Qin', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2001
DOI: 10.1016/S0022-0728(00)00452-6
The temperature dependence of the electronic contribution to the nonadiabatic electron transfer rate constant (k_(ET)) at metal electrodes is discussed. It is found in these calculations that this contribution is proportional to the absolute temperature T. A simple interpretation is given. We also consider the nonadiabatic rate constant for electron transfer at a semiconductor electrode. Under conditions for the maximum rate constant, the electronic contribution is also estimated to be proportional to T, but for different reasons than in the case of metals (Boltzmann statistics and transfer at the conduction band edge for the semiconductor versus Fermi–Dirac statistics and transfer at the Fermi level, which is far from the band edge, of the metal).https://authors.library.caltech.edu/records/nfks9-11168Possible mechanism of OH frequency shift dynamics in water
https://resolver.caltech.edu/CaltechAUTHORS:20150316-133842258
Authors: {'items': [{'id': 'Georgievskii-Y', 'name': {'family': 'Georgievskii', 'given': 'Yuri'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2001
DOI: 10.1021/jp0036700
The results of the recent infrared pump−probe experiment are analyzed, in which the time evolution of the spectrum of the OH-stretching vibration excited by an ultrashort laser pulse in the dilute solution HDO/D_2O was measured. To interpret the results of the experiment, a formalism developed earlier for a different application, optical transitions of the chromophoric molecules in polar solvent, is used. A mechanism of the IR shift dynamics in water is suggested, involving α-relaxation (structural relaxation), which may also be related to the dielectric behavior of water. A suggestion is made for computer simulations as well as for an experimental test of the proposed mechanism.https://authors.library.caltech.edu/records/05w0v-gh982Brief comments on perturbation theory of a nonsymmetric matrix: The GF matrix
https://resolver.caltech.edu/CaltechAUTHORS:20150316-145509289
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2001
DOI: 10.1021/jp004164d
Perturbation theory for nonsymmetric matrices is discussed for the GF matrix for molecular vibrations. As a simple extension of early results, two approaches are given: one a direct diagonalization of the nonsymmetric matrix, the other a presymmetrization. Presymmetrization of the GF matrix, well known for ΔF, is also described here for ΔG. It permits the use of standard perturbation theory for symmetric matrices. Application of the second-order expression for the ΔG case to the determination of the frequencies of many ozone isotopomers is given elsewhere.https://authors.library.caltech.edu/records/v71qp-m4w84Pressure effects on bimolecular recombination and unimolecular dissociation reactions
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp01
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}]}
Year: 2001
DOI: 10.1063/1.1370552
The treatment of pressure effects on bimolecular recombinations and unimolecular dissociations is discussed. The analysis of recombination and dissociation reactions is made by showing how the nonequilibrium energy (E) and angular momentum (J)-dependent steady-state population distribution functions for the two reactions are related to each other and to the equilibrium population distribution function at the given E and J. As a special case a strong collision model is then used for the collisional rotational angular momentum transfer, and a ladder model for the collisional energy transfer. An analytical result is obtained for states below the dissociation threshold. The extension to recombinations with two exit channels is described, for application to ozone formation and isotopic effects.https://authors.library.caltech.edu/records/spkfq-7ez73Estimation of vibrational frequencies and vibrational densities of states in isotopically substituted nonlinear triatomic molecules
https://resolver.caltech.edu/CaltechAUTHORS:20150316-135714897
Authors: {'items': [{'id': 'Hathorn-B-C', 'name': {'family': 'Hathorn', 'given': 'B. C.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2001
DOI: 10.1021/jp003849a
For use in unimolecular reactions, a simple method is introduced for obtaining the unknown vibration frequencies of the many asymmetric isotopomers of a molecule from those of the symmetric ones. The method is illustrated for a triatomic molecule XYZ, ozone. It is based on the neglect of a single G matrix element in the GF expression for XYZ, yielding for it a block-factored expression of the XYX type for the frequencies of all the isotopomers XYZ. It agrees with available data to the accuracy needed, a few cm^(-1). The first-order perturbation vanishes. (The zeroth-order case is not a symmetric molecule since it contains all three masses.) A simple second-order perturbation result for the GF matrix using data for one asymmetric isotopomer then provides agreement to about 1 cm^(-1). The virtues of the method are its simplicity, transparency, and novelty, though normally one would use much more general methods such as ASYM 20 or 40. The method itself is not restricted to triatomic molecules.https://authors.library.caltech.edu/records/74jjp-8vk64Strange and Unconventional Isotope Effects in Ozone Formation
https://resolver.caltech.edu/CaltechAUTHORS:20141112-111645976
Authors: {'items': [{'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2001
DOI: 10.1126/science.1058528
The puzzling mass-independent isotopic enrichment in ozone formation contrasts markedly with the more recently observed large unconventional mass-dependent ratios of the individual ozone formation rate constants in certain systems. An RRKM (Rice, Ramsperger, Kassel, Marcus)-based theory is used to treat both effects. Restrictions of symmetry on how energy is shared among the rotational/vibrational states of the ozone isotopomer, together with an analysis of the competition between the transition states of its two exit channels, permit the calculation of isotope effects consistent with a wide array of experimental results.https://authors.library.caltech.edu/records/mbx8y-5t147Does Symmetry Drive Isotopic Anomalies in Ozone Isotopomer Formation? - Response
https://resolver.caltech.edu/CaltechAUTHORS:20141112-132905878
Authors: {'items': [{'id': 'Janssen-C', 'name': {'family': 'Janssen', 'given': 'Christof'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2001
DOI: 10.1126/science.294.5544.951a
Gao and Marcus presented a modified Rice, Ramsperger, Kassel, Marcus (RRKM)–based theory to explain the strange and unconventional ozone isotope effect that has puzzled scientists for years. In earlier studies, mass spectrometric and diode laser measurements of ozone isotopomers in "scrambled" oxygen mixtures pointed toward a symmetry origin for isotope fractionation. Kinetic studies, however, contradicted the dominant role of symmetry, and later experiments revealed an unconventional mass dependency, in which isotopomer formation correlates with the enthalpy of the competing isotopic exchange. Marcus and co-workers have offered a solution to this puzzle by imposing two different fractionation factors. The first was incorporated into the theory as an ad hoc factor to describe possible nonstatistical effects, which affect asymmetric and symmetric molecule formation differently. The second, which can be called zero-point energy fractionation (ZPEF), can be treated within the RRKM theory and relates to competing properties of the exit channel transition states.https://authors.library.caltech.edu/records/e7n8s-wr761Application of the z-transform to composite materials
https://resolver.caltech.edu/CaltechAUTHORS:GAOjcp01
Authors: {'items': [{'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2001
DOI: 10.1063/1.1416127
Applications of the z-transform were made earlier to interfacial electron transfer involving semi-infinite solids, e.g., semiconductor/liquid and metal/liquid interfaces and scanning tunneling microscopy. It is shown how the method is readily adapted to treat composite materials, such as solid/solid interfaces or "molecular wire"/solid interfaces.https://authors.library.caltech.edu/records/20dgf-vtv21On the theory of the strange and unconventional isotopic effects in ozone formation
https://resolver.caltech.edu/CaltechAUTHORS:GAOjcp02a
Authors: {'items': [{'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2002
DOI: 10.1063/1.1415448
The strange mass-independent isotope effect for the enrichment of ozone and the contrastingly unconventional strong mass-dependent effect of individual reaction rate constants are studied using statistical (RRKM)-based theory with a hindered-rotor transition state. Individual rate constant ratios of recombination reactions and enrichments are calculated. The theory assumes (1) an "eta-effect," which can be interpreted as a small deviation from the statistical density of states for symmetric isotopomers, compared with the asymmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. A partitioning effect controls the recombination rate constant ratios. It arises from small differences in zero-point energies of the two exit channels of dissociation of an asymmetric ozone isotopomer, which are magnified into large differences in numbers of states in the two competing exit channel transition states. In enrichment experiments, in contrast, this partitioning factor disappears exactly [Hathorn and Marcus, J. Chem. Phys. 112, 9497 (2000)], and what remains is the eta-effect. Both aspects can be regarded as "symmetry driven" isotopic effects. The two experiments, enrichments and rate constant ratios, thus reveal markedly different theoretical aspects of the phenomena. The calculated low-pressure ozone enrichments, the low-pressure recombination rate constant ratios, the effects of pressure on the enrichment, on the individual recombination rate constant ratios, and on the recombination rate constant are consistent with the experimental data. The temperature dependence of the enrichment and of the recombination rate constant ratios is discussed and a variety of experimental tests are proposed. The negative temperature dependence of the isotopic exchange rate constant for the reaction 16O + 18O18O-->16O18O + 18O at 130 K and 300 K is used for testing or providing information on the nature of a variationally determined hindered-rotor transition state. The theory is not limited to ozone formation but is intended to apply to other reactions where a symmetrical stable or unstable gas phase molecule may be formed.https://authors.library.caltech.edu/records/4ewmr-syr27Photophysical Properties of PS-2 Reaction Centers and a Discrepancy in Exciton Relaxation Times
https://resolver.caltech.edu/CaltechAUTHORS:20150316-142918406
Authors: {'items': [{'id': 'Renger-T', 'name': {'family': 'Renger', 'given': 'Thomas'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2002
DOI: 10.1021/jp013342f
Exciton relaxation in the PS-2 reaction center of green plants is studied to explain a discrepancy of 2 orders of magnitude in certain relaxation times. Structural information from an earlier computer model and a recent low resolution structural study are combined with circular dichroism (CD) at 77 K, fluorescence line narrowing spectra at 1.6 K, and pump−probe spectra at 77 K to make predictions on the linear absorption spectrum at 77 K, fluorescence spectrum at 5 K, and absorption difference spectrum for modified pheophytin of the D_2 branch at 5 K. A width of the inhomogeneous distribution function of pigment energies of Δ_(inh) = 300 cm^(-1) and a mean vertical pigment transition energy corresponding to 669 nm are assumed for all pigments, based on the CD data, and a correlation radius of 5 Å for the protein vibrations is deduced from the pump−probe data. The two peripheral chlorophylls resolved in a recent structure are calculated to give rise to optical dephasing times larger than 10 ps at wavelengths shorter than 670 nm, in agreement with dephasing times obtained in hole burning experiments. It is proposed, thereby, that the 2 orders of magnitude discrepancy between the fastest transfer times observed in hole burning and these in pump−probe experiments is due to the peripheral chlorophylls. Non-Markovian effects in the exciton-vibrational coupling are found to contribute significantly to optical line shape functions in the form of vibrational sidebands but to have minor influence on the relaxation dynamics of the excitons.https://authors.library.caltech.edu/records/afz5r-vp542Theoretical investigation of the directional electron transfer in 4-aminonaphthalimide compounds
https://resolver.caltech.edu/CaltechAUTHORS:20150316-140735254
Authors: {'items': [{'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2002
DOI: 10.1021/jp011980s
Photoinduced electron-transfer reactions in small supramolecular systems, such as the 4-aminonaphthalimide compounds, are interesting in that there are two alternative directions for the electron transfer to occur. Nevertheless, the electron transfer occurs only along one path, as deduced from pH-dependent fluorescence quenching studies of selected compounds. The role of the electronic coupling matrix element and the effect of the charges accompanying protonation are considered so as to explain the directionality of the electron transfer and other results. A related mechanism is suggested for interpreting the behavior of similar molecules, which serve as fluorescent sensors of metal ions.https://authors.library.caltech.edu/records/xt5qs-24097On the relation of protein dynamics and exciton relaxation in pigment–protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra
https://resolver.caltech.edu/CaltechAUTHORS:RENjcp02
Authors: {'items': [{'id': 'Renger-T', 'name': {'family': 'Renger', 'given': 'Thomas'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2002
DOI: 10.1063/1.1470200
A theory for calculating time– and frequency–domain optical spectra of pigment–protein complexes is presented using a density matrix approach. Non-Markovian effects in the exciton–vibrational coupling are included. A correlation function is deduced from the simulation of 1.6 K fluorescence line narrowing spectra of a monomer pigment–protein complex (B777), and then used to calculate fluorescence line narrowing spectra of a dimer complex (B820). A vibrational sideband of an excitonic transition is obtained, a distinct non-Markovian feature, and agrees well with experiment on B820 complexes. The theory and the above correlation function are used elsewhere to make predictions and compare with data on time–domain pump–probe spectra and frequency–domain linear absorption, circular dichroism and fluorescence spectra of Photosystem II reaction centers.https://authors.library.caltech.edu/records/6hrb3-v8078A theoretical study of ozone isotopic effects using a modified ab initio potential energy surface
https://resolver.caltech.edu/CaltechAUTHORS:GAOjcp02b
Authors: {'items': [{'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Chen-W-C', 'name': {'family': 'Chen', 'given': 'Wei-Chen'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2002
DOI: 10.1063/1.1488577
A modified ab initio potential energy surface (PES) is used for calculations of ozone recombination and isotopic exchange rate constants. The calculated low-pressure isotopic effects on the ozone formation reaction are consistent with the experimental results and with the theoretical results obtained earlier [J. Chem. Phys. 116, 137 (2002)]. They are thereby relatively insensitive to the properties of these PES. The topics discussed include the dependence of the calculated low-pressure recombination rate constant on the hindered-rotor PES, the role of the asymmetry of the potential for a general X + YZ reaction (Y[not-equal]Z), and the partitioning to form each of the two recombination products: XYZ and XZY.https://authors.library.caltech.edu/records/vr00n-7dd42Charge Transfer on the Nanoscale: Current Status
https://resolver.caltech.edu/CaltechAUTHORS:20150331-135208356
Authors: {'items': [{'id': 'Adams-D-M', 'name': {'family': 'Adams', 'given': 'David M.'}}, {'id': 'Brus-L', 'name': {'family': 'Brus', 'given': 'Louis'}}, {'id': 'Chidsey-C-E-D', 'name': {'family': 'Chidsey', 'given': 'Christopher E. D.'}}, {'id': 'Creager-S', 'name': {'family': 'Creager', 'given': 'Stephen'}}, {'id': 'Creutz-C', 'name': {'family': 'Creutz', 'given': 'Carol'}}, {'id': 'Kagan-C-R', 'name': {'family': 'Kagan', 'given': 'Cherie R.'}}, {'id': 'Kamat-P-V', 'name': {'family': 'Kamat', 'given': 'Prashant V.'}}, {'id': 'Lieberman-M', 'name': {'family': 'Lieberman', 'given': 'Marya'}}, {'id': 'Lindsay-S', 'name': {'family': 'Lindsay', 'given': 'Stuart'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Metzger-R-M', 'name': {'family': 'Metzger', 'given': 'Robert M.'}}, {'id': 'Michel-Beyerle-M-E', 'name': {'family': 'Michel-Beyerle', 'given': 'M. E.'}}, {'id': 'Miller-J-R', 'name': {'family': 'Miller', 'given': 'John R.'}}, {'id': 'Newton-M-D', 'name': {'family': 'Newton', 'given': 'Marshall D.'}}, {'id': 'Rolison-D-R', 'name': {'family': 'Rolison', 'given': 'Debra R.'}}, {'id': 'Sankey-O', 'name': {'family': 'Sankey', 'given': 'Otto'}}, {'id': 'Schanze-K-S', 'name': {'family': 'Schanze', 'given': 'Kirk S.'}}, {'id': 'Yardley-J', 'name': {'family': 'Yardley', 'given': 'James'}}, {'id': 'Zhu-Xiaoyang', 'name': {'family': 'Zhu', 'given': 'Xiaoyang'}}]}
Year: 2003
DOI: 10.1021/jp0268462
This is the report of a DOE-sponsored workshop organized to discuss the status of our understanding of charge-transfer processes on the nanoscale and to identify research and other needs for progress in nanoscience and nanotechnology. The current status of basic electron-transfer research, both theoretical and experimental, is addressed, with emphasis on the distance-dependent measurements, and we have attempted to integrate terminology and notation of solution electron-transfer kinetics with that of conductance analysis. The interface between molecules or nanoparticles and bulk metals is examined, and new research tools that advance description and understanding of the interface are presented. The present state-of-the-art in molecular electronics efforts is summarized along with future research needs. Finally, novel strategies that exploit nanoscale architectures are presented for enhancing the efficiences of energy conversion based on photochemistry, catalysis, and electrocatalysis principles.https://authors.library.caltech.edu/records/7rrv5-24g35A model for the cooperative free energy transduction and kinetics of ATP hydrolysis by F-1-ATPase
https://resolver.caltech.edu/CaltechAUTHORS:GAOpnas03
Authors: {'items': [{'id': 'Gao-Yi-Qin', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Yang-Wei', 'name': {'family': 'Yang', 'given': 'Wei'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Karplus-M', 'name': {'family': 'Karplus', 'given': 'Martin'}}]}
Year: 2003
DOI: 10.1073/pnas.1334188100
PMCID: PMC208758
Although the binding change mechanism of rotary catalysis by which F1-ATPase hydrolyzes ATP has been supported by equilibrium, kinetic, and structural observations, many questions concerning the function remain unanswered. Because of the importance of this enzyme, the search for a full understanding of its mechanism is a key problem in structural biology. Making use of the results of free energy simulation and experimental binding constant measurements, a model is developed for the free energy change during the hydrolysis cycle. This model makes possible the development of a kinetic scheme for ATP hydrolysis by F-1-ATPase, in which the rate constants are associated with specific configurations of the beta subunits. An essential new element is that the strong binding site for ADP,Pi is shown to be the beta(DP) site, in contrast to the strong binding site for ATP, which is beta(TP). This result provides a rationale for the rotation of the y subunit, which induces the cooperativity required for a tri-site binding change mechanism. The model explains a series of experimental data, including the ATP concentration dependence of the rate of hydrolysis and catalytic site occupation for both the Escherichia coli F1-ATPase (EcF(1)) and Thermophilic Bacillus PS3 F-1-ATPase (TF1), which have different behavior.https://authors.library.caltech.edu/records/2hg8m-09w20Variable-range hopping electron transfer through disordered bridge states: Application to DNA
https://resolver.caltech.edu/CaltechAUTHORS:20150316-143858263
Authors: {'items': [{'id': 'Renger-T', 'name': {'family': 'Renger', 'given': 'Thomas'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2003
DOI: 10.1021/jp026789c
A theory for electron transfer through a donor−bridge−acceptor system is described that involves tunneling and hopping-like transfers and an intermediate regime. The theory considers how a delocalization of electronic states and static and dynamic disorder in electronic energies influence the charge transfer rate and is used to study experiments on hole transfer through DNA. While an exponential distance dependence of the yield of hole trapping is observed experimentally for small bridges, the yield for long bridges is reported to be almost distance-independent. For long bridge lengths, for which thermally activating hopping dominates over tunneling, the model considers two competing channels, a hopping via localized states and a transfer through partly delocalized states. The variable-range hopping mechanism and the delocalized states aspect of the theory are used to interpret the flat rather than a slow decrease of yield with increasing distance reported in experiments with long bridges.https://authors.library.caltech.edu/records/ctwf6-sr615A model for charge transfer inverse photoemission
https://resolver.caltech.edu/CaltechAUTHORS:20150317-091835898
Authors: {'items': [{'id': 'Gosavi-S', 'name': {'family': 'Gosavi', 'given': 'Shachi'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2003
DOI: 10.1016/j.electacta.2003.07.007
Charge transfer inverse photoemission spectroscopy (CTRIPS), the phenomenon of inverse photoemission at a metal–solution interface, has been the subject of a variety of experiments. An approximate theoretical model is presented which includes (1) the electronic structure of the metal; (2) the principal features of the emission spectra, such as the high and low frequency thresholds at a given injection energy of the electron or hole, and the intensity of the light emission versus electrode potential; (3) the role of surface states; and (4) the question of direct versus indirect radiative transitions. A broad array of experiments from different groups is surveyed and treated. There is a considerable need for experiments to fill many missing "gaps" in the data, and various experiments are suggested.https://authors.library.caltech.edu/records/155c1-xre26Mass-independent isotope effect in the earliest processed solids in the solar system: A possible chemical mechanism
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp04
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2004
DOI: 10.1063/1.1803507
A major constraint is described for a possible chemical origin for the "mass-independent" oxygen isotope phenomenon in calcium-aluminum rich inclusions (CAIs) in meteorites at high temperatures (similar to1500-2000 K). A symmetry-based dynamical eta effect is postulated for O atom-monoxide recombination on the surface of growing CAIs. It is the surface analog of the volume-based eta effect occurring in a similar phenomenon for ozone in the gas phase [Y. Q. Gao, W. C. Chen, and R. A. Marcus, J. Chem. Phys. 117, 1536 (2002), and references cited therein]: In the growth of CAI grains an equilibrium is postulated between adsorbed species XO (ads)+O (ads)--> <--XO2* (ads), where XO2* (ads) is a vibrationally excited adsorbed dioxide molecule and X can be Si, Al, Ti, or other metals and can be C for minerals less refractory than the CAIs. The surface of a growing grain has an entropic effect of many order of magnitude on the position of this monoxide-dioxide equilibrium relative to its volume-based position by acting as a concentrator. The volume-based eta effect for ozone in the earlier study is not applicable to gas phase precursors of CAIs, due to the rarity of three-body recombination collisions at very low pressures and because of the high H-2 and H concentration in solar gas, which reduces gaseous O and gaseous dioxides and prevents the latter from acting as storage reservoirs for the two heavier oxygen isotopes. A surface eta effect yields XO2* (ads) that is mass-independently rich in O-17 and O-18, and yields XO (ads)+O (ads) that is mass-independently poor in the two heavier oxygen isotopes. When the XO2* (ads) is deactivated by vibrational energy loss to the grain, it has only one subsequent fate, evaporation, and so undergoes no further isotopic fractionation. After evaporation the XO2 again has only one fate, which is to react rapidly with H and ultimately form O-16-poor H2O. The other species, O (ads)+XO (ads), are O-16 rich and react with Ca (ads) and other adsorbed metal atoms or metallic monoxides to form CAIs. The latter are thereby mass-independently poor in O-17 and O-18. Some O (ads) used to form the minerals are necessarily in excess of the XO (ads), because of the stoichiometry of the mineral, and modify the fractionation pattern. This effect is incorporated into the mechanistic and mathematical scheme. A merit of this chemical mechanism for the oxygen isotope anomaly is that only one oxygen reservoir is required in the solar nebula. It also does not require a sequestering of intermediate products which could undergo isotopic exchange, hence undoing the original isotopic fractionations. The gas phase source of adsorbed O atoms in this environment is either O or H2O. As inferred from data on the evaporation of Mg2SiO4 taken as an example, the source of O (ads) is primarily H2O rather than O and is accompanied by the evolution of H-2. Nonisotopic kinetic experiments can determine more sharply the mechanism of condensed phase growth of these minerals. Laboratory tests are proposed to test the existence of a surface eta effect on the growing CAI surfaces at these high temperatures.https://authors.library.caltech.edu/records/txp28-deb77Mechanisms of fluorescence blinking in semiconductor nanocrystal quantum dots
https://resolver.caltech.edu/CaltechAUTHORS:TANjcp05a
Authors: {'items': [{'id': 'Tang-J', 'name': {'family': 'Tang', 'given': 'Jau'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2005
DOI: 10.1063/1.1993567
The light-induced spectral diffusion and fluorescence intermittency (blinking) of semiconductor nanocrystal quantum dots are investigated theoretically using a diffusion-controlled electron-transfer (DCET) model, where a light-induced one-dimensional diffusion process in energy space is considered. Unlike the conventional electron-transfer reactions with simple exponential kinetics, the model naturally leads to a power-law statistics for the intermittency. We formulate a possible explanation for the spectral broadening and its proportionality to the light energy density, the –3/2 power law for the blinking statistics of the fluorescence intermittency, the breakdown of the power-law behavior with a bending tail for the "light" periods, a lack of bending tail for the "dark" periods (but would eventually appear at later times), and the dependence of the bending tail on light intensity and temperature. This DCET model predicts a critical time tc (a function of the electronic coupling strength and other quantities), such that for times shorter than tc the exponent for the power law is –1/2 instead of –3/2. Quantitative analyses are made of the experimental data on spectral diffusion and on the asymmetric blinking statistics for the "on" and "off" events. Causes for deviation of the exponent from the ideal value of –3/2 are also discussed. Several fundamental properties are determined from the present experimental data, the diffusion correlation time, the Stokes shift, and a combination of other molecular-based quantities. Specific experiments are suggested to test the model further, extract other molecular properties, and elucidate more details of the light-induced charge-transfer dynamics in quantum dots.https://authors.library.caltech.edu/records/gze1a-8kx97On the theory of the CO+OH reaction, including H and C kinetic isotope effects
https://resolver.caltech.edu/CaltechAUTHORS:CHEjcp05
Authors: {'items': [{'id': 'Chen-W-C', 'name': {'family': 'Chen', 'given': 'Wei-Chen'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2005
DOI: 10.1063/1.2031208
The effect of pressure, temperature, H/D isotopes, and C isotopes on the kinetics of the OH+CO reaction are investigated using Rice-Ramsperger-Kassel-Marcus theory. Pressure effects are treated with a step-ladder plus steady-state model and tunneling effects are included. New features include a treatment of the C isotope effect and a proposed nonstatistical effect in the reaction. The latter was prompted by existing kinetic results and molecular-beam data of Simons and co-workers [J. Phys. Chem. A 102, 9559 (1998); J. Chem. Phys. 112, 4557 (2000); 113, 3173 (2000)] on incomplete intramolecular energy transfer to the highest vibrational frequency mode in HOCO*. In treating the many kinetic properties two small customary vertical adjustments of the barriers of the two transition states were made. The resulting calculations show reasonable agreement with the experimental data on (1) the pressure and temperature dependence of the H/D effect, (2) the pressure-dependent 12C/13C isotope effect, (3) the strong non-Arrhenius behavior observed at low temperatures, (4) the high-temperature data, and (5) the pressure dependence of rate constants in various bath gases. The kinetic carbon isotopic effect is usually less than 10 per mil. A striking consequence of the nonstatistical assumption is the removal of a major discrepancy in a plot of the kOH+CO/kOD+CO ratio versus pressure. A prediction is made for the temperature dependence of the OD+CO reaction in the low-pressure limit at low temperatures.https://authors.library.caltech.edu/records/3360y-ka816Diffusion-Controlled Electron Transfer Processes and Power-Law Statistics of Fluorescence Intermittency of Nanoparticles
https://resolver.caltech.edu/CaltechAUTHORS:TANprl05
Authors: {'items': [{'id': 'Tang-J', 'name': {'family': 'Tang', 'given': 'Jau'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2005
DOI: 10.1103/PhysRevLett.95.107401
A mechanism involving diffusion-controlled electron transfer processes in Debye and non-Debye dielectric media is proposed to elucidate the power-law distribution for the lifetime of a blinking quantum dot. This model leads to two complementary regimes of power law with a sum of the exponents equal to 2, and to a specific value for the exponent in terms of a distribution of the diffusion correlation times. It also links the exponential bending tail with energetic and kinetic parameters.https://authors.library.caltech.edu/records/fv50p-hwv17Explanation of quantum dot blinking without the long-lived trap hypothesis
https://resolver.caltech.edu/CaltechAUTHORS:FRAprb05
Authors: {'items': [{'id': 'Frantsuzov-P-A', 'name': {'family': 'Frantsuzov', 'given': 'Pavel A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2005
DOI: 10.1103/PhysRevB.72.155321
A simple model explaining the experimental data on QDs luminescence blinking is suggested. The model does not assume the presence of the long-lived electron traps. The bleaching of the QD luminescence is a result of the Auger assisted radiationless relaxation of the excitation through the deep surface states. Possible ways of the experimental verification of the model are discussed.https://authors.library.caltech.edu/records/0nvvw-6wd67Three-isotope plot of fractionation in photolysis: A perturbation theoretical expression
https://resolver.caltech.edu/CaltechAUTHORS:PRAjcp05
Authors: {'items': [{'id': 'Prakash-M-K', 'name': {'family': 'Prakash', 'given': 'M. K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2005
DOI: 10.1063/1.2102908
The slope of the three-isotope plot for the isotopomer fractionation by direct or nearly direct photodissociation is obtained using a perturbation theoretical analysis. This result, correct to first order in the mass difference, is the same as that for equilibrium chemical exchange reactions, a similarity unexpected a priori. A comparison is made with computational results for N2O photodissociation. This theoretical slope for mass-dependent photolytic fractionation can be used to analyze the data for isotopic anomalies in spin-allowed photodissociation reactions. Earlier work on chemical equilibria is extended by avoiding a high-temperature approximation.https://authors.library.caltech.edu/records/8ytf7-v2x84Isotopomer fractionation in the UV photolysis of N_2O: Comparison of theory and experiment
https://resolver.caltech.edu/CaltechAUTHORS:20150316-150216501
Authors: {'items': [{'id': 'Prakash-M-K', 'name': {'family': 'Prakash', 'given': 'Meher K.'}}, {'id': 'Weibel-J-D', 'name': {'family': 'Weibel', 'given': 'Jason D.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2005
DOI: 10.1029/2005JD006127
In the photodissociation of N_2O, absorption cross sections differ with isotopic substitution, leading to a wavelength-dependent fractionation of the various isotopomers. Several models ranging from shifts by zero-point energy differences to propagation of wave packets on the excited electronic state potential energy surface have been proposed to explain the observed fractionations. We present time-independent fractionation calculations for the isotopomers 447, 448, 456, 546, and 556. Besides largely agreeing with the experimental data, these calculations have the advantage of not being computationally intensive, as well as satisfying the physical facts that the asymmetric stretch and the doubly degenerate bending vibration are the principal Franck-Condon active modes in the photodissociation. The latter is reflected in the actual dissociation and in the high rotational excitation and lack of vibrational excitation of the N_2 product. The calculations are based on a multidimensional reflection principle using an ab initio potential energy surface. The theory for the absorption cross section and isotopomer fractionation accompanying photodissociation is described. The absolute value of the theoretically calculated absorption cross section is very close (90%) to the experimentally observed value. The present computations also provide data for the slope of a three-isotope plot of the fractionation of 447/446 relative to 448/446, using the fractionations at different wavelengths. The resulting slope is compared with a perturbation theoretical expression for direct photodissociation given elsewhere.https://authors.library.caltech.edu/records/rnhjc-w9f97Micelle-enhanced dissociation of a Ru cation/DNA complex
https://resolver.caltech.edu/CaltechAUTHORS:20150316-131449116
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2005
DOI: 10.1021/jp051988s
Anionic surfactant monomers have a large catalytic effect on the dissociation rate constant of a Ru_2^(4+)−DNA complex, an effect further enhanced upon exceeding the critical micelle concentration. Electrostatic estimates are made of this effect, the effect of salt and temperature on the binding constant, and of the binding constant itself. The effects are compared with the experiment, and the calculated salt effect on the binding constant is compared with condensation theory. The results indicate that the catalytic effect is primarily nonelectrostatic (hydrophobic) in nature.https://authors.library.caltech.edu/records/k8vwe-h7f77Single particle versus ensemble average: From power-law intermittency of a single quantum dot to quasistretched exponential fluorescence decay of an ensemble
https://resolver.caltech.edu/CaltechAUTHORS:TANjcp05b
Authors: {'items': [{'id': 'Tang-J', 'name': {'family': 'Tang', 'given': 'Jau'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2005
DOI: 10.1063/1.2128409
Light-induced diffusion-controlled electron transfer is proposed as an underlying mechanism for the intermittency (power law and breakdown) of a single quantum dot and ensemble-averaged fluorescence decay. The intensity decay can be approximated to a stretched exponential expression. The physical links to the free energy gap, reorganization energy, electronic coupling, and diffusion correlation times are discussed. A procedure is described for extracting these molecular-based parameters from experiments and is demonstrated with examples using existing data.https://authors.library.caltech.edu/records/4bbvt-k7061On the theory of the reaction rate of vibrationally excited CO molecules with OH radicals
https://resolver.caltech.edu/CaltechAUTHORS:CHEjcp06
Authors: {'items': [{'id': 'Chen-W-C', 'name': {'family': 'Chen', 'given': 'Wei-Chen'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2006
DOI: 10.1063/1.2148408
The dependence of the rate of the reaction CO+OH-->H+CO2 on the CO-vibrational excitation is treated here theoretically. Both the Rice-Ramsperger-Kassel-Marcus (RRKM) rate constant kRRKM and a nonstatistical modification knon [W.-C. Chen and R. A. Marcus, J. Chem. Phys. 123, 094307 (2005).] are used in the analysis. The experimentally measured rate constant shows an apparent (large error bars) decrease with increasing CO-vibrational temperature Tv over the range of Tv's studied, 298–1800 K. Both kRRKM(Tv) and knon(Tv) show the same trend over the Tv-range studied, but the knon(Tv) vs Tv plot shows a larger effect. The various trends can be understood in simple terms. The calculated rate constant kv decreases with increasing CO vibrational quantum number v, on going from v=0 to v=1, by factors of 1.5 and 3 in the RRKM and nonstatistical calculations, respectively. It then increases when v is increased further. These results can be regarded as a prediction when v state-selected rate constants become available.https://authors.library.caltech.edu/records/60781-19v14R. A. Marcus on R. A. Marcus
https://resolver.caltech.edu/CaltechAUTHORS:20110808-143338638
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2006
It is a pleasure to address you, young scientists on this special occasion. Almost sixty-two
years ago, I received my Ph.D. from McGill University in Montreal, Canada. Like you, I loved
learning new subjects, and looked forward to the life ahead.https://authors.library.caltech.edu/records/ema2g-4ct15Photoinduced Spectral Diffusion and Diffusion-Controlled Electron Transfer Reactions in Fluorescence Intermittency of Quantum Dots
https://resolver.caltech.edu/CaltechAUTHORS:20150330-071612890
Authors: {'items': [{'id': 'Tang-Jau', 'name': {'family': 'Tang', 'given': 'Jau'}, 'orcid': '0000-0003-2078-1513'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2006
DOI: 10.1002/jccs.200600001
An overview is given for the experimental and theoretical development on fluorescence intermittency (blinking) in semiconductor crystalline nanoparticles. We consider a model with photoinduced spectral diffusion and diffusion-controlled electron transfer processes as the underlying mechanism for intermittency in quantum dots. Depending on the frequency response of a dielectric medium, anomalous/normal diffusion in energy space leads to power-law intermittency for single quantum dots and quasi-stretched exponential decay in ensemble-averaged fluorescence intensity. Intricate relationship between single particle and ensemble behavior is discussed. Some kinetic and energetic parameters are linked to the temporal behavior of blinking statistics and ensemble fluorescence decay.https://authors.library.caltech.edu/records/0acbn-e2y88Chain dynamics and power-law distance fluctuations of single-molecule systems
https://resolver.caltech.edu/CaltechAUTHORS:TANpre06
Authors: {'items': [{'id': 'Tang-J', 'name': {'family': 'Tang', 'given': 'Jau'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2006
DOI: 10.1103/PhysRevE.73.022102
Chain-dynamics-induced distance fluctuations between any two points in a finite chain with or without cross links are investigated. This model leads to three regimes of temporal behavior for distance autocorrelation: (i) initial flat time dependence, (ii) t–alpha power law, and (iii) long-time exponential decay. For an ideal Rouse chain with frequency-independent friction, alpha=(1/2). The span of the characteristic power-law behavior of a long chain could be reduced significantly with the presence of cross links.https://authors.library.caltech.edu/records/nyzyh-ge463Determination of energetics and kinetics from single-particle intermittency and ensemble-averaged fluorescence intensity decay of quantum dots
https://resolver.caltech.edu/CaltechAUTHORS:TANjcp06
Authors: {'items': [{'id': 'Tang-J', 'name': {'family': 'Tang', 'given': 'Jau'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2006
DOI: 10.1063/1.2227394
Quantification of energetics and kinetics for the band-edge exciton states of quantum dots and the long-lived dark state is important for better understanding of the underlying mechanism for single-particle intermittency and ensemble fluorescence intensity decay. Based on a multistate diffusion-reaction model by extending our previous studies, we analyze experimental data from ensemble measurements and fluorescence intermittency of single quantum dots and determine important molecular-based quantities such as Stokes shift, free energy gap, activation energy, reorganization energy, and other kinetic parameters.https://authors.library.caltech.edu/records/xwjbd-t1698Summarizing lecture: factors influencing enzymatic H-transfers, analysis of nuclear tunnelling isotope effects and thermodynamic versus specific effects
https://resolver.caltech.edu/CaltechAUTHORS:20110714-092204898
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2006
DOI: 10.1098/rstb.2006.1873
PMCID: PMC1647317
In the articles in this Discussion, a wide variety of topics are treated, including reorganization energy,
initially introduced for electron transfers ('environmentally assisted tunnelling'), nuclear tunnelling,
H/D and ^(12)C/^(13)C kinetic isotope effects (KIEs), the effect of changes of distal and nearby amino acid
residues using site-directed mutagenesis, and dynamics versus statistical effects. A coordinate-free
form of semi-classical theory is used to examine topics on data such as tunnelling versus 'over-thebarrier'
paths and temperature and pressure effects on KIEs. The multidimensional semi-classical
theory includes classically allowed and classically forbidden transitions. More generally, we address
the question of relating kinetic to thermodynamic factors, as in the electron transfer field, so learning
about specific versus thermodynamic effects in enzyme catalysis and KIEs.https://authors.library.caltech.edu/records/v3vw8-h0j11Enzymatic catalysis and transfers in solution. I. Theory and computations, a unified view
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp06b
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2006
DOI: 10.1063/1.2372496
The transfer of hydride, proton, or H atom between substrate and cofactor in enzymes has been extensively studied for many systems, both experimentally and computationally. A simple equation for the reaction rate, an analog of an equation obtained earlier for electron transfer rates, is obtained, but now containing an approximate analytic expression for the bond rupture-bond forming feature of these H transfers. A "symmetrization," of the potential energy surfaces is again introduced [R. A. Marcus, J. Chem. Phys. 43, 679 (1965); J. Phys. Chem. 72, 891 (1968)], together with Gaussian fluctuations of the remaining coordinates of the enzyme and solution needed for reaching the transition state. Combining the two expressions for the changes in the difference of the two bond lengths of the substrate-cofactor subsystem and in the fluctuation coordinates of the protein leading to the transition state, an expression is obtained for the free energy barrier. To this end a two-dimensional reaction space (m,n) is used that contains the relative coordinates of the H in the reactants, the heavy atoms to which it is bonded, and the protein/solution reorganization coordinate, all leading to the transition state. The resulting expression may serve to characterize in terms of specific parameters (two "reorganization" terms, thermodynamics, and work terms), experimental and computational data for different enzymes, and different cofactor-substrate systems. A related characterization was used for electron transfers. To isolate these factors from nuclear tunneling, when the H-tunneling effect is large, use of deuterium and tritium transfers is of course helpful, although tunneling has frequently and understandably dominated the discussions. A functional form is suggested for the dependence of the deuterium kinetic isotope effect (KIE) on DeltaG° and a different form for the 13C KIE. Pressure effects on deuterium and 13C KIEs are also discussed. Although formulated for a one-step transfer of a light particle in an enzyme, the results would also apply to single-step transfers of other atoms and groups in enzymes and in solution.https://authors.library.caltech.edu/records/q506h-r5k45On the theory of organic catalysis "on water"
https://resolver.caltech.edu/CaltechAUTHORS:20150317-095444811
Authors: {'items': [{'id': 'Jung-Yousung', 'name': {'family': 'Jung', 'given': 'Yousung'}, 'orcid': '0000-0003-2615-8394'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2007
DOI: 10.1021/ja068120f
A molecular origin of the striking rate increase observed in a reaction on water is studied theoretically. A key aspect of the on-water rate phenomenon is the chemistry between water and reactants that occurs at an oil−water phase boundary. In particular, the structure of water at the oil−water interface of an oil emulsion, in which approximately one in every four interfacial water molecules has a free ("dangling") OH group that protrudes into the organic phase, plays a key role in catalyzing reactions via the formation of hydrogen bonds. Catalysis is expected when these OH's form stronger hydrogen bonds with the transition state than with the reactants. In experiments more than a 5 orders of magnitude enhancement in rate constant was found in a chosen reaction. The structural arrangement at the "oil−water" interface is in contrast to the structure of water molecules around a small hydrophobic solute in homogeneous solution, where the water molecules are tangentially oriented. The latter implies that a breaking of an existing hydrogen-bond network in homogeneous solution is needed in order to permit a catalytic effect of hydrogen bonds, but not for the on-water reaction. Thereby, the reaction in homogeneous aqueous solution is intrinsically slower than the surface reaction, as observed experimentally. The proposed mechanism of rate acceleration is discussed in light of other on-water reactions that showed smaller accelerations in rates. To interpret the results in different media, a method is given for comparing the rate constants of different rate processes, homogeneous, neat and on-water, all of which have different units, by introducing models that reduce them to the same units. The observed deuterium kinetic isotope effect is discussed briefly, and some experiments are suggested that can test the present interpretation and increase our understanding of the on-water catalysis.https://authors.library.caltech.edu/records/va9pg-3jc17Norman Sutin: A personal tribute
https://resolver.caltech.edu/CaltechAUTHORS:20150316-151423614
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2007
DOI: 10.1021/jp079514b
It is a pleasure to participate in this issue honoring a longtime
friend and colleague, Norman Sutin. In the early days of
electron transfer almost 50 years ago, Norman pioneered the
application of fast stopped-flow techniques to the study of
electron-transfer reactions, determining the effect of the driving
force, -ΔG°, and reorganization energies on the rates of
electron-transfer reactions, and extending Henry Taube's innersphere
atom-transfer mechanism to fast reactions. Later, Norman
initiated the use of "Rubpy", tris(2,2'-bipyridine)ruthenium(II),
to studies of photoinduced electron transfer by showing that its
excited state can be quenched by electron transfer. Today,
"Rubpy" is a central player in the quest to construct solar
conversion devices to split water, and a Google search on tris-
(2,2'-bipyridine)ruthenium(II) returns almost 100,000 hits!https://authors.library.caltech.edu/records/fr0s4-jp618H and other transfers in enzymes and in solution: Theory and computations, a unified view. 2. Applications to experiment and computations
https://resolver.caltech.edu/CaltechAUTHORS:20150317-104923432
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2007
DOI: 10.1021/jp071589s
Equations obtained in part I for the free-energy barrier to one-step enzymatic reactions between bound reactants are discussed. The rate is expressed in terms of λ_o (protein reorganization energy), ΔG° (standard free energy of reaction of the H-transfer step), bond breaking/bond forming term, w (work terms), and H-transmission property. Two alternative approximations for the coupling of the bond breaking/bond forming and protein are distinguished experimentally in favorable cases by the ΔG° where the maximum deuterium kinetic isotope effect occurs. Plots of log rate versus ΔG° and properties such as ΔS* and ΔS° are discussed. The weak or zero T-dependence of the kinetic isotope effect for wild-type enzymes operating under physiological conditions is interpreted in terms of vanishing (or isotopically insensitive) w plus transfer from the lowest H-state. Static and dynamic protein flexibility is discussed. While the many correlations accessible for electron transfers are not available for H-transfers in enzymes, a combination of experiment, computation, and analytical approaches can assist in evaluating the utility of the present equations and in suggesting further experiments and computations. A protein reorganization energy λ_o is obtained in the literature from the extended valence bond formalism where diabatic electronic states are used. A method is suggested for extracting it when instead a bond distance difference coordinate is used. The results may provide a bridge between the two approaches.https://authors.library.caltech.edu/records/va2x8-gkj10Evidence for a diffusion-controlled mechanism for fluorescence blinking of colloidal quantum dots
https://resolver.caltech.edu/CaltechAUTHORS:PELpnas07
Authors: {'items': [{'id': 'Pelton-M', 'name': {'family': 'Pelton', 'given': 'Matthew'}}, {'id': 'Smith-Glenna', 'name': {'family': 'Smith', 'given': 'Glenna'}}, {'id': 'Scherer-N-F', 'name': {'family': 'Scherer', 'given': 'Norbert F.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2007
DOI: 10.1073/pnas.0706164104
PMCID: PMC1964845
Fluorescence blinking in nanocrystal quantum dots is known to exhibit power-law dynamics, and several different mechanisms have been proposed to explain this behavior. We have extended the measurement of quantum-dot blinking by characterizing fluctuations in the fluorescence of single dots over time scales from microseconds to seconds. The power spectral density of these fluctuations indicates a change in the power-law statistics that occurs at a time scale of several milliseconds, providing an important constraint on possible mechanisms for the blinking. In particular, the observations are consistent with the predictions of models wherein blinking is controlled by diffusion of the energies of electron or hole trap states.https://authors.library.caltech.edu/records/5v16n-13q43An interpretation of fluctuations in enzyme catalysis rate, spectral diffusion, and radiative component of lifetimes in terms of electric field fluctuations
https://resolver.caltech.edu/CaltechAUTHORS:PRApnas07
Authors: {'items': [{'id': 'Prakash-M-K', 'name': {'family': 'Prakash', 'given': 'Meher K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2007
DOI: 10.1073/pnas.0707859104
Time-dependent fluctuations in the catalysis rate ({delta}k(t)) observed in single-enzyme experiments were found in a particular study to have an autocorrelation function decaying on the same time scale as that of spectral diffusion {delta}{omega}0(t). To interpret this similarity, the present analysis focuses on a factor in enzyme catalysis, the local electrostatic interaction energy (E) at the active site and its effect on the activation free energy barrier. We consider the slow fluctuations of the electrostatic interaction energy ({delta}E(t)) as a contributor to {delta}k(t) and relate the latter to {delta}{omega}0(t). The resulting relation between {delta}k(t) and {delta}{omega}0(t) is a dynamic analog of the solvatochromism used in interpreting solvent effects on organic reaction rates. The effect of the postulated {delta}E(t) on fluctuations in the radiative component ({delta}{gamma}Formula(t)) of the fluorescence decay of chromophores in proteins also is examined, and a relation between {delta}{gamma}Formula(t) and {delta}{omega}0(t) is obtained. Experimental tests will determine whether the correlation functions for {delta}k(t), {delta}{omega}0(t), and {delta}{gamma}Formula are indeed similar for any enzyme. Measurements of dielectric dispersion, {varepsilon}({omega}), for the enzyme discussed elsewhere will provide further insight into the correlation function for {delta}E(t). They also will determine whether fluctuations in the nonradiative component {gamma}Formula of the lifetime decay has a different origin, fluctuations in distance for example.https://authors.library.caltech.edu/records/6p14b-eqs12An approximate theory of the ozone isotopic effects: Rate constant ratios and pressure dependence
https://resolver.caltech.edu/CaltechAUTHORS:GAOjcp07
Authors: {'items': [{'id': 'Gao-Y-Q', 'name': {'family': 'Gao', 'given': 'Yi Qin'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2007
DOI: 10.1063/1.2806189
The isotopic effects in ozone recombination reactions at low pressures are studied using an approximate theory which yields simple analytic expressions for the individual rate constant ratios, observed under "unscrambled" conditions. It is shown that the rate constant ratio between the two competing channels XYZ-->X+YZ and XYZ-->XY+Z is mainly determined by the difference of the zero-point energies of diatomic molecules YZ and XY and by the efficiency of the deactivation of the newly formed excited ozone molecules, whereas the mass-independent fractionation depends on a "nonstatistical" symmetry factor eta and the collisional deactivation efficiency. Formulas for the pressure effects on the enrichment and on the rate constant ratios are obtained, and the calculated results are compared with experiments and more exact calculations. In all cases, ratios of isotope rates and the pressure dependence of enrichments, the agreement is good. While the initial focus was on isotope effects in the formation of O3, predictions are made for isotope effects on ratios of rate constants in other reactions such as O+CO-->CO2, O+NO-->NO2, and O+SO-->SO2.https://authors.library.caltech.edu/records/2066k-00536Dielectric dispersion interpretation of single enzyme dynamic disorder, spectral diffusion, and radiative fluorescence lifetime
https://resolver.caltech.edu/CaltechAUTHORS:20150316-153424442
Authors: {'items': [{'id': 'Prakash-M-K', 'name': {'family': 'Prakash', 'given': 'Meher K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2008
DOI: 10.1021/jp0758869
A formulation based on measurable dielectric dispersion of enzymes is developed to estimate fluctuations in electrostatic interaction energy on time scales as long as milliseconds to seconds at a local site in enzymes. Several single molecule experimental observations occur on this time scale, currently unreachable by real time computational trajectory simulations. We compare the experimental results on the autocorrelation function of the fluctuations of catalysis rate with the calculations using the dielectric dispersion formulation. We also discuss the autocorrelation functions of the fluorescence lifetime and of spectral diffusion. We use a previously derived relation between the observables and the electric field fluctuations and calculate the latter using dielectric dispersion data for the proteins and the Onsager regression hypothesis.https://authors.library.caltech.edu/records/bkr1p-wmg83Isotopomer fractionation in the UV photolysis of N_2O: 2. Further comparison of theory and experiment
https://resolver.caltech.edu/CaltechAUTHORS:20150316-141630410
Authors: {'items': [{'id': 'Chen-Wei-Chen', 'name': {'family': 'Chen', 'given': 'Wei-Chen'}}, {'id': 'Prakash-M-K', 'name': {'family': 'Prakash', 'given': 'Meher K.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2008
DOI: 10.1029/2007JD009180
Wavelength-dependent fractionation of various isotopomers in the photodissociation of N_2O is studied. The absorption cross sections are calculated by a time-independent reflection principle, related to the Prakash et al. (2005) treatment but now with an inclusion of the NN stretching coordinate and both the 2A′ and 1A″ electronic excited states. The added 1A″ state is found to have little effect on both the absorption cross section and the fractionation. The improvements include more physical details in the photodissociation of N_2O, while maintaining an advantage of a treatment in the work by Prakash et al. (2005) that was not computationally intensive. The present calculated fractionation, without a significant adjustable parameter, gives good agreement with experiments in the absorption cross section in the low-energy region, the important region for the experimentally observed isotopic fractionation.https://authors.library.caltech.edu/records/haa02-1wp25Universal emission intermittency in quantum dots, nanorods and nanowires
https://resolver.caltech.edu/CaltechAUTHORS:20150316-162909140
Authors: {'items': [{'id': 'Frantsuzov-P-A', 'name': {'family': 'Frantsuzov', 'given': 'Pavel'}}, {'id': 'Kuno-M', 'name': {'family': 'Kuno', 'given': 'Masaru'}}, {'id': 'Jankó-B', 'name': {'family': 'Jankó', 'given': 'Boldizsár'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2008
DOI: 10.1038/nphys1001
Virtually all known fluorophores exhibit mysterious episodes of emission intermittency. A remarkable feature of the phenomenon is a power-law distribution of on- and off-times observed in colloidal semiconductor quantum dots, nanorods, nanowires and some organic dyes. For nanoparticles, the resulting power law extends over an extraordinarily wide dynamic range: nine orders of magnitude in probability density and five to six orders of magnitude in time. Exponents hover about the ubiquitous value of -3/2. Dark states routinely last for tens of seconds—practically forever on quantum mechanical timescales. Despite such infinite states of darkness, the dots miraculously recover and start emitting again. Although the underlying mechanism responsible for this phenomenon remains a mystery and many questions persist, we argue that substantial theoretical progress has been made.https://authors.library.caltech.edu/records/pjzvp-vv724The mercury photosensitized reaction of dimethyl ether
https://resolver.caltech.edu/CaltechAUTHORS:MARjcp48
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Darwent-B-deB', 'name': {'family': 'Darwent', 'given': 'B. deB.'}}, {'id': 'Steacie-E-W-R', 'name': {'family': 'Steacie', 'given': 'E. W. R.'}}]}
Year: 2008
DOI: 10.1063/1.1746701
The mercury photosensitized reaction of dimethyl ether has been investigated at pressures between 28 and 500 mm and at temperatures between 25°C and 292°C. At 25°C the products consist almost entirely of hydrogen and 1,2-dimethoxyethane, and the initial step has been shown to be the abstraction of a hydrogen atom.At higher temperatures CH2O, CH4, C2H6 and probably CH3OC2H5 become important products. They are derived from the decomposition of the methoxy methyl radical followed by subsequent radical recombination reactions. Carbon monoxide is produced in the later stages from the decomposition of formaldehyde.By varying the light intensity and pressure it has been shown that ethane and dimethoxyethane are produced by second order recombination of methyl and methoxy methyl radicals respectively. The activation energies of the following reactions have been estimated: CH3+CH3OCH3→CH4+CH3OCH2 E=9.0 kcal. CH3OCH2→CH3+CH2O E=19 kcal., the only assumption being that methyl and methoxy methyl radicals recombine with zero activation energy.https://authors.library.caltech.edu/records/7c73g-h2e12On collisional energy transfer in recombination and dissociation reactions: A Wiener–Hopf problem and the effect of a near elastic peak
https://resolver.caltech.edu/CaltechAUTHORS:ZHUjcp08
Authors: {'items': [{'id': 'Zhu-Z', 'name': {'family': 'Zhu', 'given': 'Zhaoyan'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2008
DOI: 10.1063/1.3026605
The effect of the large impact parameter near-elastic peak of collisional energy transfer for unimolecular dissociation/bimolecular recombination reactions is studied. To this end, the conventional single exponential model, a biexponential model that fits the literature classical trajectory data better, a model with a singularity at zero energy transfer, and the most realistic model, a model with a near-singularity, are fitted to the trajectory data in the literature. The typical effect of the energy transfer on the recombination rate constant is maximal at low pressures and this region is the one studied here. The distribution function for the limiting dissociation rate constant k0 at low pressures is shown to obey a Wiener–Hopf integral equation and is solved analytically for the first two models and perturbatively for the other two. For the single exponential model, this method yields the trial solution of Troe. The results are applied to the dissociation of O3 in the presence of argon, for which classical mechanical trajectory data are available. The k0's for various models are calculated and compared, the value for the near-singularity model being about ten times larger than that for the first two models. This trend reflects the contribution to the cross section from collisions with larger impact parameter. In the present study of the near-singularity model, it is found that k0 is not sensitive to reasonable values for the lower bound. Energy transfer values <ΔE>'s are also calculated and compared and can be similarly understood. However, unlike the k0 values, they are sensitive to the lower bound, and so any comparison of a classical trajectory analysis for <ΔE>'s with the kinetic experimental data needs particular care.https://authors.library.caltech.edu/records/zb0j1-9k554Interaction between Experiments, Analytical Theories, and Computation
https://resolver.caltech.edu/CaltechAUTHORS:20090828-231034880
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2009
DOI: 10.1021/jp811456b
This article is a summary of a talk given at the ACS Centennial Symposium in Physical Chemistry in Philadelphia in 2008, updated with more recent studies. In keeping with the spirit of the symposium, the article is in part historical and in part a review of the newer research. The talk was divided into two parts, the first on different isotopic effects in chemistry, including the mass-independent fractionation phenomenon in gases and H/D isotope effects in enzymes, and the second on two different surface phenomena, "The Bad and the Good". The "Bad" is the fluorescence intermittency of semiconductor nanoparticles, (quantum dots, QD) being an unwanted feature in sensor applications. The "Good" is the "on water" catalysis of organic reactions, a mode of green chemistry. The possible role of Auger-type mechanisms in trapping and detrapping in the QD and hence in the formation of dark and light periods is explored. Some suggestions are made on the novel "breakpoint" phenomenon discovered for H transfer in a thermophilic enzyme.https://authors.library.caltech.edu/records/d52qn-jst26Spiers Memorial Lecture: Interplay of theory and computation in chemistry—examples from on-water organic catalysis, enzyme catalysis, and single-molecule fluctuations
https://resolver.caltech.edu/CaltechAUTHORS:20100216-095943407
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2010
DOI: 10.1039/b920917b
In this lecture, several examples are considered that illustrate the interplay of experiment, theory, and computations. The examples include on-water catalysis of organic reactions, enzymatic catalysis, single molecule fluctuations, and some much earlier work on electron transfer and atom or group transfer reactions. Computations have made a major impact on our understanding and in the comparisons with experiments. There are also major advantages of analytical theories that may capture in a single equation an entire field and relate experiments of one type to those of another. Such a theory has a generic quality. These topics are explored in the present lecture.https://authors.library.caltech.edu/records/v1rr0-5g875Interaction of theory and experiment: examples from single molecule studies of nanoparticles
https://resolver.caltech.edu/CaltechAUTHORS:20100303-142653450
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2010
DOI: 10.1098/rsta.2009.0261
PMCID: PMC3263810
This article is in part the author's perspective on the revolution that has occurred in theoretical chemistry during the past half-century. In this period much of theoretical chemistry has moved from its initial emphasis on analytic treatments, resulting in equations for physical chemical and chemical phenomena, to the detailed computation of many different systems and processes. In the best sense the old and the new are complementary and their coexistence can benefit both. Experiment too has seen major developments. One of the newer types of experiment is that of single molecule studies. They range from those on small inorganic and organic nanoparticles to large biological species. We illustrate some of the issues that arise, using the topic of 'quantum dots' (QDs), and choosing a particular inorganic nanoparticle, CdSe, the most studied of these systems. Its study reflects the problems that arise in experiment and in theories in this field. The complementary nature of the conventional ensemble experiments and the new single molecule experiments is described and is illustrated by trajectories for the two types of experiments. The research in the QD field is both experimentally and theoretically a currently ongoing process, for which the answers are not fully known in spite of the large body of research. The detailed role of surface states is part of the problem. The field continues to yield new and unexpected results. In a sense this part of the article is an interim report that illustrates one analytic approach to the topic and where computer calculations and simulations can be expected to provide added insight.https://authors.library.caltech.edu/records/jm4sj-1ma56Coriolis coupling as a source of non-RRKM effects in triatomic near-symmetric top molecules: Diffusive intramolecular energy exchange between rotational and vibrational degrees of freedom
https://resolver.caltech.edu/CaltechAUTHORS:20100714-151352457
Authors: {'items': [{'id': 'Kryvohuz-M', 'name': {'family': 'Kryvohuz', 'given': 'M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2010
DOI: 10.1063/1.3430508
A classical theory is proposed to describe the non-RRKM effects in activated asymmetric top
triatomic molecules observed numerically in classical molecular dynamics simulations of ozone.
The Coriolis coupling is shown to result in an effective diffusive energy exchange between the
rotational and vibrational degrees of freedom. A stochastic differential equation is obtained for the
K-component of the rotational angular momentum that governs the diffusion.https://authors.library.caltech.edu/records/0dtee-44c52Coriolis coupling as a source of non-RRKM effects in ozone molecule: Lifetime statistics of vibrationally excited ozone molecules
https://resolver.caltech.edu/CaltechAUTHORS:20121129-095751831
Authors: {'items': [{'id': 'Kryvohuz-M', 'name': {'family': 'Kryvohuz', 'given': 'M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2010
DOI: 10.1063/1.3430514
A theory that describes the non-RRKM (non-Rice-Ramsperger-Kassel-Marcus) effects in the lifetime statistics of activated ozone molecules is derived. The non-RRKM effects are shown to originate due to the diffusive energy exchange between vibrational and rotational degrees of freedom in ozone molecule. The lifetime statistics is found to be intramolecular diffusion controlled at long times. The theoretical results are in good agreement with the direct MD simulations of lifetime statistics.https://authors.library.caltech.edu/records/bpqhx-ffn16Protruding interfacial OH groups and 'on-water' heterogeneous catalysis
https://resolver.caltech.edu/CaltechAUTHORS:20100720-084322628
Authors: {'items': [{'id': 'Jung-Yousung', 'name': {'family': 'Jung', 'given': 'Yousung'}, 'orcid': '0000-0003-2615-8394'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2010
DOI: 10.1088/0953-8984/22/28/284117
The key aspect of the remarkable organic catalysis that is observed to occur at the organic/water phase boundary, the so-called 'on-water' catalysis (Narayan et al 2005 Angew. Chem. 44 3275), was recently proposed to be the protruding OH groups of water molecules at the interface that interact with the transition state (TS) via hydrogen bonding and lower activation barriers (Jung and Marcus 2007 J. Am. Chem. Soc. 129 5492). In particular, the cycloaddition reaction of quadricyclane (Q) with dimethyl azodicarboxylate (DMAD) on-water was calculated to be more than 100 000 times more efficient in terms of rate constant than the neat reaction. In this paper, we review and consider a related reaction of Q with dimethyl acetylenedicarboxylate, where nitrogen, a good H-bond acceptor, in DMAD is replaced by carbon, a poor H-bond acceptor. A very low rate acceleration of acetylenedicarboxylate on-water relative to the neat reaction is obtained theoretically, as compared to DMAD on-water, due to the relatively low H-bonding ability of acetylenedicarboxylate with water at the TS relative to the reactants. We suggest that there may also be an 'intrinsic steric effect' or orientational advantage in the on-water catalysis in general, and both electronic and steric effects may be in operation for the smaller on-water catalysis for the cycloaddition reaction of quadricyclane and acetylenedicarboxylate. A preliminary quantum mechanical/molecular mechanical (QM/MM) simulation including 1264 water molecules for the on-water reaction of DMAD + Q also suggests that there are indeed approximately two–four more H-bonds between the TS and the dangling OH groups than between the reactants and the surface.https://authors.library.caltech.edu/records/0tfcn-f0c43Isotopomer Fractionation in the UV Photolysis of N_2O: 3. 3D Ab Initio Surfaces and Anharmonic Effects
https://resolver.caltech.edu/CaltechAUTHORS:20100928-111337712
Authors: {'items': [{'id': 'Chen-W-C', 'name': {'family': 'Chen', 'given': 'Wei-Chen'}}, {'id': 'Nanbu-S', 'name': {'family': 'Nanbu', 'given': 'Shinkoh'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2010
DOI: 10.1021/jp101691r
The wavelength-dependent isotopic fractionation of N_2O is calculated, extending our previous work, Parts 1 and 2, in several aspects: (1) the fully three-dimensional ab initio electronic potential and transition dipole moment surfaces of S. Nanbu and M. S. Johnson (J. Chem. Phys. A 2004, 108, 8905) are used to calculate the absorption cross sections, instead of a 2D surface and (2) the vibrational frequencies and wave functions with anharmonicity correction are used for the ground electronic state. The results for the absorption spectrum and for the isotopic fractionation of the different isotopomers are discussed. One difference between experiments measuring the absorption coefficient (von Hessberg et al. Atmos. Chem. Phys. 2004, 4, 1237) and the others that measure instead the photodissociation is also discussed. Experiments on the quantum yield for wavelengths longer than 200 nm (>50000 cm^(−1)) would be helpful in treating the observed difference.https://authors.library.caltech.edu/records/pg6mp-efj28Microscopic structure and dynamics of air/water interface by computer simulations-comparison with sum-frequency generation experiments
https://resolver.caltech.edu/CaltechAUTHORS:20110330-082835207
Authors: {'items': [{'id': 'Wang-Yanting', 'name': {'family': 'Wang', 'given': 'Yanting'}}, {'id': 'Hodas-N-O', 'name': {'family': 'Hodas', 'given': 'Nathan O.'}}, {'id': 'Jung-Yousung', 'name': {'family': 'Jung', 'given': 'Yousung'}, 'orcid': '0000-0003-2615-8394'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2011
DOI: 10.1039/c0cp02745f
The air/water interface was simulated and the mode amplitudes and their ratios of the effective nonlinear sum-frequency generation (SFG) susceptibilities (A_(eff)'s) were calculated for the ssp, ppp, and sps polarization combinations and compared with experiments. By designating "surface-sensitive" free OH bonds on the water surface, many aspects of the SFG measurements were calculated and compared with those inferred from experiment. We calculate an average tilt angle close to the SFG observed value of 35, an average surface density of free OH bonds close to the experimental value of about 2.8 × 10^(18) m^(−2), computed ratios of A_(eff)'s that are very similar to those from the SFG experiment, and their absolute values that are in reasonable agreement with experiment. A one-parameter model was used to calculate these properties. The method utilizes results available from independent IR and Raman experiments to obtain some of the needed quantities, rather than calculating them ab initio. The present results provide microscopic information on water structure useful to applications such as in our recent theory of on-water heterogeneous catalysis.https://authors.library.caltech.edu/records/0d6mh-7ak67Bimolecular Recombination Reactions: Low Pressure Rates in Terms of Time-Dependent Survival Probabilities, Total J Phase Space Sampling of Trajectories, and Comparison with RRKM Theory
https://resolver.caltech.edu/CaltechAUTHORS:20110525-140218220
Authors: {'items': [{'id': 'Ghaderi-N', 'name': {'family': 'Ghaderi', 'given': 'N.'}, 'orcid': '0000-0002-6257-1373'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2011
DOI: 10.1021/jp111833m
We consider the bimolecular formation and redissociation of complexes using classical trajectories and the survival probability distribution function P(E,J,t) of the intermediate complexes at time t as a function of the energy E and total angular momentum quantum number J. The P(E,J,t) and its deviation from single exponential behavior is a main focus of the present set of studies. Together with weak deactivating collisions, the P(E,J,t) and a cumulative reaction probability at the given E and J can also be used to obtain the recombination rate constant k at low pressures of third bodies. Both classical and quantum expressions are given for k in terms of P(E,J,t). The initial conditions for the classical trajectories are sampled for atom−diatom reactions for various (E,J)'s using action-angle variables. A canonical transformation to a total J representation reduces the sampling space by permitting analytic integration over several of the variables. A similar remark applies for the calculation of the density of states of the intermediate complex ρ and for the number of states N* of the transition state as a function of E and J. The present approach complements the usual approach based on the rate of the reverse reaction, unimolecular dissociation, and the equilibrium constant. It provides results not necessarily accessible from the unimolecular studies. The formalism is applied elsewhere to the study of nonstatistical aspects of the recombination and redissociation of the resulting ozone molecules and comparison with RRKM theory.https://authors.library.caltech.edu/records/416x1-8vz83At the birth of modern semiclassical theory
https://resolver.caltech.edu/CaltechAUTHORS:20120702-094840540
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2012
DOI: 10.1080/00268976.2012.672772
The rapid development of the semiclassical theory of Miller and Marcus and its applications in the 1970s was an exciting experience. Some of these developments and the issues involved are described in the present overview.https://authors.library.caltech.edu/records/z74zn-04f17A Maximum Likelihood Method for Power Law Distributions That
Does Not Break Down When the Slope Is Close to Unity
https://resolver.caltech.edu/CaltechAUTHORS:20120807-084455644
Authors: {'items': [{'id': 'Zhu-Z', 'name': {'family': 'Zhu', 'given': 'Zhaoyan'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2012
DOI: 10.1021/jp303697j
A general maximum likelihood estimation (MLE) method is given to analyze experimental data with a power law form with any power exponent which does not break down for a power close to −1. It contrasts thereby with a standard procedure that does. It can be extended to a power law with an exponential tail and more generally to other distribution forms. Inasmuch as the theoretical value of the power for dye-sensitized charge recombination in semiconductors systems, and for certain charge injection, is −1 (Chen, W.; Marcus, R. A., J. Phys. Chem. C, accepted), the present correction to the current MLE method has immediate application to the data in these systems, but it is equally applicable to other systems, regardless of whether the power is −1.https://authors.library.caltech.edu/records/z7rwe-daf41Theory of a Single Dye Molecule Blinking with a Diffusion-Based Power Law Distribution
https://resolver.caltech.edu/CaltechAUTHORS:20120824-135906485
Authors: {'items': [{'id': 'Chen-W-C', 'name': {'family': 'Chen', 'given': 'Wei-Chen'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2012
DOI: 10.1021/jp303837g
In single molecule studies of injection of an electron from a photoexcited dye into a semiconductor nanoparticle or into a film of such nanoparticles, the injection may be into the conduction band or into the band gap, depending on the system. The theory of the process and its return are discussed, in particular when a power law for the waiting time distribution may be expected and what that power might be. To this end a reaction–diffusion equation is set up and solved. When the injection is into the conduction band, a power law is predicted for the return of the electron to the dye cation but not for the injection. After a short time, the law for the waiting time distribution has a power of −1. At short times, before the slower return due to an increasing radius is recognized, the power law is −1/2. When the injection is into the band gap, a −1 power law is predicted for both the injection and the return. Available data are discussed in terms of the theory. A corollary is that single molecule studies for the injection can determine whether the injection is into the band gap or into the conduction band. The theory is tested by single molecule studies of various systems, such as comparing different dye–TiO_2, dye–Al_2O_3, and dye–ZrO_2 systems and comparing specific dye–TiO_2 systems as a function of pH, and dye hole injection into p-type NiO.https://authors.library.caltech.edu/records/04hdc-3gw52Electron transfer theory and its inception
https://resolver.caltech.edu/CaltechAUTHORS:20121107-085534949
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2012
DOI: 10.1039/c2cp90116a
It is a pleasure to introduce this issue on electron transfer processes. The field has
developed greatly and in many different directions not envisioned in the late
1940s. The modern electron transfer era began at that time in the form of studies
on the simplest class of reactions in all of chemistry, isotopic exchange reactions
of the electron transfer type. In their simplest form no chemical bonds are
broken or formed, only an electron is transferred from one reactant to the
other. I remember how surprised and excited I was reading in 1955 a paper
by Bill Libby (W. F. Libby, J. Phys. Chem., 1952, 56, 893), written several
years earlier, explaining why some of these reactions were slow and others fast.
In his explanation he used the Franck–Condon principle to interpret
the results: he noted that when an electron "jumped" from one reactant to the
other the slow moving nuclei changed neither their positions nor their momenta
during the jump, and what the consequences were. I was especially excited, since
that principle had originally been introduced to explain molecular spectra rather
than chemical reaction rates. But perhaps at this point I should say a few words on
how I came into theoretical chemistry as a practitioner just a few years earlier.https://authors.library.caltech.edu/records/wtfyz-7h398Semiclassical evaluation of kinetic isotope effects in 13-atomic system
https://resolver.caltech.edu/CaltechAUTHORS:20121127-083321198
Authors: {'items': [{'id': 'Kryvohuz-M', 'name': {'family': 'Kryvohuz', 'given': 'M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2012
DOI: 10.1063/1.4754660
The semiclassical instanton approach discussed by Kryvohuz [J. Chem. Phys. 134, 114103 (2011)10.1063/1.3565425] is applied to calculate kinetic H/D isotope effect (KIE) of intramolecular hydrogen transfer in cis-1,3-pentadiene. All 33 vibrational degrees of freedom are treated quantum mechanically with semiclassical approximation. Nuclear quantum effects such as tunneling under the barrier and zero-point energy are automatically incorporated in the theory, and are shown to be responsible for the observed appreciable kinetic isotope effect in cis-1,3-pentadiene. Over the barrier passage is also automatically included. Numerical calculations are performed on an empirical valence bond potential energy surface and compared with the previous experimental and theoretical studies. An estimation of heavy-atom ^(12)C/^(13)C KIE in the same system is also provided and the factors contributing to it are discussed.https://authors.library.caltech.edu/records/vr4hc-yy551Theory of vibrational equilibria and pooling at solid-diatom interfaces
https://resolver.caltech.edu/CaltechAUTHORS:20131101-074844947
Authors: {'items': [{'id': 'Boney-E-T-D', 'name': {'family': 'Boney', 'given': 'E. T. D.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2013
DOI: 10.1063/1.4821991
In the present paper we provide a statistical theory for the vibrational pooling and fluorescence time dependence observed in infrared laser excitation of CO on an NaCl surface. The pooling is seen in experiment and in computer simulations. In the theory, we assume a rapid equilibration of the quanta in the substrate and minimize the free energy subject to the constraint at any time t of a fixed number of vibrational quanta N(t). At low incident intensity, the distribution is limited to one-quantum exchanges with the solid and the Debye frequency of the solid plays a key role in limiting the range of this one-quantum domain. The resulting inverted vibrational equilibrium population depends only on fundamental parameters of the oscillator (ω_e and ω_eχ_e ) and the surface (ω_D and T). The relation to the Treanor gas phase treatment is discussed. Unlike the solid phase system, the gas phase system has no Debye-constraining maximum.https://authors.library.caltech.edu/records/jmhbj-46c74Theory of mass-independent fractionation of isotopes, phase space accessibility, and a role of isotopic symmetry
https://resolver.caltech.edu/CaltechAUTHORS:20131210-091708864
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2013
DOI: 10.1073/pnas.1213080110
PMCID: PMC3816477
Key experimental and theoretical features of mass-independent fractionation (MIF) of isotopes, also known as the η-effect, are summarized, including its difference from the exit channel zero-point energy difference effect. The latter exactly cancels in the MIF. One key experimental result is that the MIF for O_3 formation is a low-pressure phenomenon and, moreover, that it decreases with increasing pressure of third bodies at pressures far below the "Lindemann fall-off" pressures for three-body recombination of O and O_2. A possible origin of the MIF is discussed in terms of a role for isotopologue symmetry in intramolecular energy sharing. An explanation is suggested for the large difference in the fall-off pressure for recombination and the pressure for a large decrease in MIF, in terms of a difference between deactivating collisions and what we term here "symmetry-changing collisions". It is noted that the theory of the MIF involves four recombination rate constants and an equilibrium constant, for each trace isotope, seven rate constants in all and two equilibrium constants. A conceptual shortcut is noted. Experimental and computational information that may provide added insight into the MIF mechanism and tests is described.https://authors.library.caltech.edu/records/9prn6-sm582On the infrared fluorescence of monolayer ^(13)CO:NaCl(100)
https://resolver.caltech.edu/CaltechAUTHORS:20131203-151324950
Authors: {'items': [{'id': 'Boney-E-T-D', 'name': {'family': 'Boney', 'given': 'E. T. D.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2013
DOI: 10.1063/1.4827823
Computations are presented to describe and analyze the high levels of infrared laser induced vibrational excitation of a monolayer of absorbed ^(13)CO on a NaCl(100) surface. Extending the vibrational site-to-site surface hopping technique of Corcelli and Tully, kinetic Monte Carlo computations are used to incorporate single-quantum vibrational pooling and depooling of the ^(13)CO by phonon excitation to allow up to the n = 45 vibrational state under different lasing conditions. Previously unpredicted pooling peaks at n > 16 are calculated and, under the highest fluence conditions, pooling up to the n = 32 state is found in the calculation. These results lead to the prediction of a secondary local maximum in the dispersed fluorescence of monolayer CO:NaCl(100) under sufficiently high fluence excitation conditions. At times on the order of ms, we recover similar behavior for both high and low fluence results. The calculations confirm that, for situations where the Debye frequency limited n domain restriction approximately holds, the vibrational state population deviates from a Boltzmann population linearly in n, a result that we have derived earlier theoretically for a domain of n restricted to one-phonon transfers. This theoretically understood term, linear in n, dominates the Boltzmann term and is responsible for the inversion of the population of vibrational states, P_n.https://authors.library.caltech.edu/records/e7tkp-7mv62Reprint of: RRKM reaction rate theory for transition states of any looseness
https://resolver.caltech.edu/CaltechAUTHORS:20140102-111251066
Authors: {'items': [{'id': 'Wardlaw-D-M', 'name': {'family': 'Wardlaw', 'given': 'David M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2013
DOI: 10.1016/j.cplett.2013.08.061
Unimolecular rate theory for various types of reactions is implemented for any looseness of transition state. Quantum states are counted for all but the "transitional" modes, their phase space being counted via Monte Carlo sampling. The rate constant k_(EJ) is then weighted with the initial E and J distributions.https://authors.library.caltech.edu/records/d1kp4-g7e63Historical perspective on: RRKM reaction rate theory for transition states of any looseness [Volume 110, Issue 3, 28 September 1984, Pages 230–234]
https://resolver.caltech.edu/CaltechAUTHORS:20140102-140326103
Authors: {'items': [{'id': 'Wardlaw-D-M', 'name': {'family': 'Wardlaw', 'given': 'David M.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2013
DOI: 10.1016/j.cplett.2013.08.041
The field of unimolecular reactions and bimolecular recombination processes [1], [2], [3], [4], [5], [6], [7] and [8] has undergone a number of changes during the past 90 or so years. In the middle 1920s, the theories of Hinshelwood, Rice/Ramsperger, and Kassel were developed at a time when little was known about potential energy surfaces. So the theory was phrased in terms of the sharing of energy in a dissociating or isomerizing molecule among 'squared terms', meaning the kinetic energies and potential energies of harmonic molecular vibrations. In fact, in those early days, before the development of gas phase free radical mechanisms for unimolecular reactions, the latter were assumed to be non-free radical dissociations. They were realized, in the 1930s, to be, largely, dissociations, followed by subsequent free radical reactions. (Hinshelwood received the Nobel Prize for this free radical work.) On the theoretical side, transition state theory emerged in the mid 1930s, and in 1951–1952 I was involved in blending it and RRK theory together [9] and [10], resulting in what later became known as RRKM theory.https://authors.library.caltech.edu/records/anhc4-q6h15On the mechanism of photoinduced dimer dissociation in the plant UVR8 photoreceptor
https://resolver.caltech.edu/CaltechAUTHORS:20140505-073007993
Authors: {'items': [{'id': 'Voityuk-A-A', 'name': {'family': 'Voityuk', 'given': 'Alexander A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Michele-Beyerle-M-E', 'name': {'family': 'Michele-Beyerle', 'given': 'Maria-Elisabeth'}}]}
Year: 2014
DOI: 10.1073/pnas.1402025111
PMCID: PMC3986182
UV-B absorption by the photoreceptor UV resistance locus 8 (UVR8) consisting of two identical protein units triggers a signal chain used by plants in connection with protection and repair of UV-B induced damage. X-ray structural analysis of the purified protein [Christie JM, et al. (2012) Science 335(6075):1492–1496] [Wu D, et al. (2012) Nature 484(7393): 214–220] has revealed that the dimer is held together by arginine–aspartate salt bridges. In this paper we address the initial processes in the signal chain. On the basis of high-level quantum-chemical calculations, we propose a mechanism for the photodissociation of UVR8 that consists of three steps: (i) In each monomer, multiple tryptophans form an extended light-harvesting system in which the L_a excited state of Trp233 experiences strong electrostatic stabilization by the protein environment. The strong stabilization singles out this tryptophan to be an efficient exciton acceptor that accumulates the excitation energy from the entire protein subunit. (ii) A fast decay of the locally excited state by charge separation generates the radical ion pair Trp285(+)-Trp233(−) with a dipole moment of ∼18 D. (iii) Key to the proposed mechanism is that this large dipole moment drives the breaking of the salt bridges between the two monomer subunits. The suggested mechanism for the UV-B–driven dissociation of the dimer that rests on the prominent players Trp233 and Trp285 explains the experimental results obtained from mutagenesis of UVR8.https://authors.library.caltech.edu/records/ksx22-62z52Computed and Experimental Absorption Spectra of the Perovskite CH_3NH_3PbI_3
https://resolver.caltech.edu/CaltechAUTHORS:20141007-153655799
Authors: {'items': [{'id': 'Zhu-Xi', 'name': {'family': 'Zhu', 'given': 'Xi'}}, {'id': 'Su-Haibin', 'name': {'family': 'Su', 'given': 'Haibin'}, 'orcid': '0000-0001-9760-6567'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Michel-Beyerle-Maria-E', 'name': {'family': 'Michel-Beyerle', 'given': 'Maria E.'}}]}
Year: 2014
DOI: 10.1021/jz501174e
Electronic structure and light absorption properties of the perovskite CH_3NH_3PbI_3 are investigated by relativistic density functional theory with quasiparticle GW corrections and many-body interactions. The nature of the Wannier exciton is studied by solving the Bethe–Salpeter equation augmented with the analysis of a conceptual hydrogen-like model. The computed absorption spectrum unravels a remarkable absorption "gap" between the first two absorption peaks. This discontinuity is maintained in the calculated tetragonal structure that, however, is not stable at low temperature. Most importantly, the discontinuity is also observed in the experimental absorption spectrum of the orthorhombic single crystal at low temperature (4 K). However, in contrast to the single crystal, in a polycrystalline perovskite film at 5 K the "gap" is filled by a monotonously increasing absorption throughout the visible range. This feature of thin films points to the potential significance of defect absorption for the excellent light harvesting properties of perovskite-based solar cells.https://authors.library.caltech.edu/records/zy03q-x4q08Bimolecular Recombination Reactions: K‑Adiabatic and K‑Active Forms of RRKM Theory, Nonstatistical Aspects, Low-Pressure Rates, and Time-Dependent Survival Probabilities with Application to Ozone. 2
https://resolver.caltech.edu/CaltechAUTHORS:20141027-134216967
Authors: {'items': [{'id': 'Ghaderi-N', 'name': {'family': 'Ghaderi', 'given': 'Nima'}, 'orcid': '0000-0002-6257-1373'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2014
DOI: 10.1021/jp506788z
We consider for bimolecular recombination reactions the K-adiabatic versus the K-active forms of RRKM theory, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. When that product is approximately a prolate symmetric top, with two moments of inertia of the product substantially larger than the third, K becomes a dynamically slowly varying quantity and the K-adiabatic form of RRKM theory is the appropriate version to use. Using classical trajectory results for the rate constant for ozone formation in the low-pressure region as an example, excellent agreement for the recombination rate constant k_(rec) with the K-adiabatic RRKM theory is observed. Use of a two transition state (inner, outer TS) formalism also obviates any need for assessing recrossings in the exit channel. In contrast, the K-active form of RRKM theory for this system disagrees with the trajectory results by a factor of about 2.5. In this study we also consider the distribution of the (E, J) resolved time-dependent survival probabilities P(E, J, t) of the intermediate O_3^* formed from O + O_2. It is calculated using classical trajectories. The initial conditions for classical trajectories were selected using action-angle variables and a total J representation for (E, J) resolved systems, as described in Part I.1 The difference between K-active and K-adiabatic treatments is reflected also in a difference of the K-active RRKM survival probability P(E, J, t) from its trajectory-based value and from its often non-single-exponential decay. It is shown analytically that k_(rec) (K-active) ≥ k_(rec) (K-adiabatic), independent of the details of the TS (e.g., variational or fixed RRKM theory, 1-TS or 2-TS). Nonstatistical effects for O_3^* formation include a small initial recrossing of the transition state, a slow (several picoseconds) equipartitioning of energy among the two O–O bonds of the newly formed O_3^*, and a small nondissociation (a quasi-periodicity) of some trajectories originating in O_3^* (∼10%) and so, by microscopic reversibility, are not accessible from O + O_2. An apparently new feature of the present results is the comparison of classical trajectories with K-adiabatic and K-active theories for rate constants of bimolecular recombinations. The quantum mechanical counterpart of classical K-adiabatic RRKM theory is also given, and its comparison with the experimental k_(rec) for O_3 is given elsewhere.https://authors.library.caltech.edu/records/1heyt-krx38Extension of the diffusion controlled electron transfer theory for intermittent fluorescence of quantum dots: inclusion of biexcitons and the difference of "on" and "off" time distributions
https://resolver.caltech.edu/CaltechAUTHORS:20140508-095956304
Authors: {'items': [{'id': 'Zhu-Z', 'name': {'family': 'Zhu', 'given': 'Zhaoyan'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'R. A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2014
DOI: 10.1039/c4cp01274g
The equations for the diffusion controlled electron transfer (DCET) theory of quantum dot blinking are
extended to include biexcitons. In contrast to excitons, which under go resonant light to dark transitions,
the biexcitons, having a much larger total energy, undergo a Fermi's Golden rule type transfer (many
acceptance states). The latter immediately gives rise to an exponential tail for the light state, and it is
explained why the dark state power law behavior is unaffected. Results are given for both continuous
and pulsed excitation. The typical -3/2 power law for the light state at low light intensities, and for the
dark state at all intensities, as well as dependence of the exponential tail on the square of the light
intensity, and a decrease of the power in the power law for the light state from -3/2 to less negative
values with increasing light intensity are all consistent with the theory. The desirability of measuring the
dependence of the spectral diffusion coefficient on light intensity at room temperature as a test of
several aspects of the theory is noted.https://authors.library.caltech.edu/records/kr6te-1jm21Elucidating the role of disorder and free-carrier recombination kinetics in CH₃NH₃PbI₃ perovskite films
https://resolver.caltech.edu/CaltechAUTHORS:20150821-154456315
Authors: {'items': [{'id': 'La-o-vorakiat-Chan', 'name': {'family': 'La-o-vorakiat', 'given': 'Chan'}, 'orcid': '0000-0002-0231-8499'}, {'id': 'Salim-Teddy', 'name': {'family': 'Salim', 'given': 'Teddy'}}, {'id': 'Kadro-Jeannette', 'name': {'family': 'Kadro', 'given': 'Jeannette'}}, {'id': 'Khuc-Mai-Thu', 'name': {'family': 'Khuc', 'given': 'Mai-Thu'}}, {'id': 'Haselsberger-Reinhard', 'name': {'family': 'Haselsberger', 'given': 'Reinhard'}}, {'id': 'Cheng-Liang', 'name': {'family': 'Cheng', 'given': 'Liang'}}, {'id': 'Xia-Huanxin', 'name': {'family': 'Xia', 'given': 'Huanxin'}}, {'id': 'Gurzadyan-Gagik-G', 'name': {'family': 'Gurzadyan', 'given': 'Gagik G.'}}, {'id': 'Su-Haibin', 'name': {'family': 'Su', 'given': 'Haibin'}, 'orcid': '0000-0001-9760-6567'}, {'id': 'Lam-Yeng-Ming', 'name': {'family': 'Lam', 'given': 'Yeng Ming'}, 'orcid': '0000-0001-9390-8074'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Michel-Beyerle-Maria-Elisabeth', 'name': {'family': 'Michel-Beyerle', 'given': 'Maria-Elisabeth'}}, {'id': 'Chia-Elbert-E-M', 'name': {'family': 'Chia', 'given': 'Elbert E. M.'}, 'orcid': '0000-0003-2066-0834'}]}
Year: 2015
DOI: 10.1038/ncomms8903
PMCID: PMC4532878
Apart from broadband absorption of solar radiation, the performance of photovoltaic devices is governed by the density and mobility of photogenerated charge carriers. The latter parameters indicate how many free carriers move away from their origin, and how fast, before loss mechanisms such as carrier recombination occur. However, only lower bounds of these parameters are usually obtained. Here we independently determine both density and mobility of charge carriers in a perovskite film by the use of time-resolved terahertz spectroscopy. Our data reveal the modification of the free carrier response by strong backscattering expected from these heavily disordered perovskite films. The results for different phases and different temperatures show a change of kinetics from two-body recombination at room temperature to three-body recombination at low temperatures. Our results suggest that perovskite-based solar cells can perform well even at low temperatures as long as the three-body recombination has not become predominant.https://authors.library.caltech.edu/records/f8hnw-xex49Theory for rates, equilibrium constants, and Brønsted slopes in F₁-ATPase single molecule imaging experiments
https://resolver.caltech.edu/CaltechAUTHORS:20151021-130628918
Authors: {'items': [{'id': 'Volkán-Kacsó-Sándor', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}, 'orcid': '0000-0003-3327-2865'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2015
DOI: 10.1073/pnas.1518489112
PMCID: PMC4655567
A theoretical model of elastically coupled reactions is proposed for single molecule imaging and rotor manipulation experiments on F₁-ATPase. Stalling experiments are considered in which rates of individual ligand binding, ligand release, and chemical reaction steps have an exponential dependence on rotor angle. These data are treated in terms of the effect of thermodynamic driving forces on reaction rates, and lead to equations relating rate constants and free energies to the stalling angle. These relations, in turn, are modeled using a formalism originally developed to treat electron and other transfer reactions. During stalling the free energy profile of the enzymatic steps is altered by a work term due to elastic structural twisting. Using biochemical and single molecule data, the dependence of the rate constant and equilibrium constant on the stall angle, as well as the Brønsted slope are predicted and compared with experiment. Reasonable agreement is found with stalling experiments for ATP and GTP binding. The model can be applied to other torque-generating steps of reversible ligand binding, such as ADP and Pi release, when sufficient data become available.https://authors.library.caltech.edu/records/7d9pn-4cj17Phonon Mode Transformation Across the Orthohombic-Tetragonal Phase Transition in a Lead Iodide Perovskite CH_3NH_3PbI_3: A Terahertz Time-Domain Spectroscopy Approach
https://resolver.caltech.edu/CaltechAUTHORS:20160111-111349964
Authors: {'items': [{'id': 'La-o-vorakiat-Chan', 'name': {'family': 'La-o-vorakiat', 'given': 'Chan'}, 'orcid': '0000-0002-0231-8499'}, {'id': 'Xia-Huanxin', 'name': {'family': 'Xia', 'given': 'Huanxin'}}, {'id': 'Kadro-J', 'name': {'family': 'Kadro', 'given': 'Jeannette'}}, {'id': 'Salim-T', 'name': {'family': 'Salim', 'given': 'Teddy'}}, {'id': 'Zhao-Daming', 'name': {'family': 'Zhao', 'given': 'Daming'}, 'orcid': '0000-0001-5046-2199'}, {'id': 'Ahmed-T', 'name': {'family': 'Ahmed', 'given': 'Towfiq'}}, {'id': 'Lam-Yeng-Ming', 'name': {'family': 'Lam', 'given': 'Yeng Ming'}, 'orcid': '0000-0001-9390-8074'}, {'id': 'Zhu-Jian-Xin', 'name': {'family': 'Zhu', 'given': 'Jian-Xin'}, 'orcid': '0000-0001-7991-3918'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Michel-Beyerle-M-E', 'name': {'family': 'Michel-Beyerle', 'given': 'Maria-Elisabeth'}}, {'id': 'Chia-E-E-M', 'name': {'family': 'Chia', 'given': 'Elbert E. M.'}, 'orcid': '0000-0003-2066-0834'}]}
Year: 2016
DOI: 10.1021/acs.jpclett.5b02223
We study the temperature-dependent phonon modes of the organometallic lead iodide perovskite CH_3NH_3PbI_3 thin film across the terahertz (0.5–3 THz) and temperature (20–300 K) ranges. These modes are related to the vibration of the Pb–I bonds. We found that two phonon modes in the tetragonal phase at room temperature split into four modes in the low-temperature orthorhombic phase. By use of the Lorentz model fitting, we analyze the critical behavior of this phase transition. The carrier mobility values calculated from the low-temperature phonon mode frequencies, via two theoretical approaches, are found to agree reasonably with the experimental value (∼2000 cm^2 V^(–1) s^(–1)) from a previous time-resolved THz spectroscopy work. Thus, we have established a possible link between terahertz phonon modes and the transport properties of perovskite-based solar cells.https://authors.library.caltech.edu/records/4bv54-cf992Theory of single-molecule controlled rotation experiments, predictions, tests, and comparison with stalling experiments in F₁-ATPase
https://resolver.caltech.edu/CaltechAUTHORS:20161013-110352184
Authors: {'items': [{'id': 'Volkán-Kacsó-Sándor', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}, 'orcid': '0000-0003-3327-2865'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2016
DOI: 10.1073/pnas.1611601113
PMCID: PMC5087055
A recently proposed chemomechanical group transfer theory of rotary biomolecular motors is applied to treat single-molecule controlled rotation experiments. In these experiments, single-molecule fluorescence is used to measure the binding and release rate constants of nucleotides by monitoring the occupancy of binding sites. It is shown how missed events of nucleotide binding and release in these experiments can be corrected using theory, with F1-ATP synthase as an example. The missed events are significant when the reverse rate is very fast. Using the theory the actual rate constants in the controlled rotation experiments and the corrections are predicted from independent data, including other single-molecule rotation and ensemble biochemical experiments. The effective torsional elastic constant is found to depend on the binding/releasing nucleotide, and it is smaller for ADP than for ATP. There is a good agreement, with no adjustable parameters, between the theoretical and experimental results of controlled rotation experiments and stalling experiments, for the range of angles where the data overlap. This agreement is perhaps all the more surprising because it occurs even though the binding and release of fluorescent nucleotides is monitored at single-site occupancy concentrations, whereas the stalling and free rotation experiments have multiple-site occupancy.https://authors.library.caltech.edu/records/ebh8v-2b283Phonon features in terahertz photoconductivity spectra due to data analysis artifact: A case study on organometallic halide perovskites
https://resolver.caltech.edu/CaltechAUTHORS:20170324-094431788
Authors: {'items': [{'id': 'La-o-vorakiat-Chan', 'name': {'family': 'La-o-vorakiat', 'given': 'Chan'}, 'orcid': '0000-0002-0231-8499'}, {'id': 'Cheng-Liang', 'name': {'family': 'Cheng', 'given': 'Liang'}}, {'id': 'Salim-T', 'name': {'family': 'Salim', 'given': 'Teddy'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Michel-Beyerle-M-E', 'name': {'family': 'Michel-Beyerle', 'given': 'Maria-Elisabeth'}}, {'id': 'Lam-Yeng-Ming', 'name': {'family': 'Lam', 'given': 'Yeng Ming'}, 'orcid': '0000-0001-9390-8074'}, {'id': 'Chia-E-E-M', 'name': {'family': 'Chia', 'given': 'Elbert E. M.'}, 'orcid': '0000-0003-2066-0834'}]}
Year: 2017
DOI: 10.1063/1.4978688
We propose a simple scenario where the superimposed phonon modes on the photoconductive spectra are experimental artifacts due to the invalid formula used in data analysis. By use of experimental and simulated data of CH_3NH_3PbI_3 perovskites as a case study, we demonstrate that a correction term must be included in the approximated thin-film formula used in the literature; otherwise, parts of the spectra with high background permittivity near the phonon-mode resonances might interfere with the transient photoconductivity. The implication of this work is not limited to perovskites but other materials with strong vibrational modes within the THz spectral range.https://authors.library.caltech.edu/records/x10vd-hv385Theory of long binding events in single-molecule–controlled rotation experiments on F_1-ATPase
https://resolver.caltech.edu/CaltechAUTHORS:20170628-102612597
Authors: {'items': [{'id': 'Volkán-Kacsó-Sándor', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}, 'orcid': '0000-0003-3327-2865'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2017
DOI: 10.1073/pnas.1705960114
PMCID: PMC5514755
The theory of elastic group transfer for the binding and release rate constants for nucleotides in F_1-ATPase as a function of the rotor angle is further extended in several respects. (i) A method is described for predicting the experimentally observed lifetime distribution of long binding events in the controlled rotation experiments by taking into account the hydrolysis and synthesis reactions occurring during these events. (ii) A method is also given for treating the long binding events in the experiments and obtaining the rate constants for the hydrolysis and synthesis reactions occurring during these events. (iii) The theory in the previous paper is given in a symmetric form, an extension that simplifies the application of the theory to experiments. It also includes a theory-based correction of the reported "on" and "off" rates by calculating the missed events. A near symmetry of the data about the angle of −40° and a "turnover" in the binding rate data vs. rotor angle for angles greater than ∼∼40° is also discussed.https://authors.library.caltech.edu/records/n8rkn-g6z02Low-frequency optical phonon modes and carrier mobility in the halide perovskite CH_3NH_3PbBr_3 using terahertz time-domain spectroscopy
https://resolver.caltech.edu/CaltechAUTHORS:20171122-075047461
Authors: {'items': [{'id': 'Zhao-Daming', 'name': {'family': 'Zhao', 'given': 'Daming'}, 'orcid': '0000-0001-5046-2199'}, {'id': 'Skelton-J-M', 'name': {'family': 'Skelton', 'given': 'Jonathan M.'}}, {'id': 'Hu-Hongwei', 'name': {'family': 'Hu', 'given': 'Hongwei'}}, {'id': 'La-o-vorakiat-Chan', 'name': {'family': 'La-o-vorakiat', 'given': 'Chan'}, 'orcid': '0000-0002-0231-8499'}, {'id': 'Zhu-Jian-Xin', 'name': {'family': 'Zhu', 'given': 'Jian-Xin'}, 'orcid': '0000-0001-7991-3918'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Michel-Beyerle-M-E', 'name': {'family': 'Michel-Beyerle', 'given': 'Maria-Elisabeth'}}, {'id': 'Lam-Yeng-Ming', 'name': {'family': 'Lam', 'given': 'Yeng Ming'}, 'orcid': '0000-0001-9390-8074'}, {'id': 'Walsh-A', 'name': {'family': 'Walsh', 'given': 'Aron'}, 'orcid': '0000-0001-5460-7033'}, {'id': 'Chia-E-E-M', 'name': {'family': 'Chia', 'given': 'Elbert E. M.'}, 'orcid': '0000-0003-2066-0834'}]}
Year: 2017
DOI: 10.1063/1.4993524
As a light absorber in photovoltaic applications, hybrid organic-inorganic halide perovskites should have long and balanced diffusion lengths for both the separated electrons and holes before recombination, which necessitates high carrier mobility. In polar semiconductors, the room-temperature carrier mobility is often limited by the scattering between carriers and the lowest-frequency optical phonon modes. Using terahertz time-domain spectroscopy, we examine the temperature evolution of these phonon modes in CH_3NH_3PbBr_3 and obtained high carrier mobility values using Feynman's polaron theory. This method allows us to estimate the upper limit of carrier mobilities without the need to create photogenerated free carriers, and can be applied to other heteropolar semiconductor systems with large polarons.https://authors.library.caltech.edu/records/7ct02-deh75What can be learned about the enzyme ATPase from single-molecule studies of its subunit F₁?
https://resolver.caltech.edu/CaltechAUTHORS:20200416-143316039
Authors: {'items': [{'id': 'Volkán-Kacsó-S', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2017
DOI: 10.1017/s0033583517000129
We summarize the different types of single molecule experiments on the F₁ component of F₀F₁-ATP Synthase and what has been learned from them. We also describe results from our recent studies on interpreting the experiments using a chemical-mechanical theory for these biological motors.https://authors.library.caltech.edu/records/2b8m7-g1j85A Theory for Rate Constants in Rotation Trajectories of F_1-ATPase
https://resolver.caltech.edu/CaltechAUTHORS:20180510-132615402
Authors: {'items': [{'id': 'Volkán-Kacsó-S', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2018
DOI: 10.1016/j.bpj.2017.11.2838
I present an elastic chemo-mechanical theory to treat single molecule imaging and "stalling" experiments in the F1-ATPase enzyme. Using a molecular group transfer approach the theory couples chemical reactions in the stator and the physics of torsional elasticity in the rotor. In the theory we predicted and compared with experiment the rate and equilibrium constant dependence of steps such as ATP binding as a function of the rotor angle.[PNAS, 112, 14230 (2015)] Using independent experimental data from biochemical ensemble and single-molecule imaging experiments, the model correctly predicts the controlled rotation data on fluorescent ATP without any adjustable parameters. We took into account the biasing effect of finite experimental time resolution in the single fluorescence trajectories and treated these data by developing computational statistical methods.[PNAS, 113 (48), 12029 (2016)] A theory-based method for the extraction of rate constants for hydrolysis and synthesis from controlled rotation data was also provided for angular range where no such data is currently available [PNAS, 114, 7272 (2016)] The framework is generic and we plan to apply it to other biomolecular motors.https://authors.library.caltech.edu/records/93j14-3np67Model for Concerted Power Stroke Generation in Single Myosin V and F_1-ATPase Imaging Trajectories
https://resolver.caltech.edu/CaltechAUTHORS:20190219-110814625
Authors: {'items': [{'id': 'Volkán-Kacsó-S', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2019
DOI: 10.1016/j.bpj.2018.11.1498
The idea of a concerted mechanism of molecular group transfer and large conformational change in power stroke generation serves as the basis for an elasto-chemical theory of the rate constants that dictate the stepping kinetics in single F1-ATPase motors. The theory was employed to calculate the rate and equilibrium constant dependence on the rotor angle in experiments with magnetic tweezers. Using independent biochemical and single-molecule imaging data, the model was used to correctly predict the rates of binding and release of fluorescently labeled ATP without any adjustable parameters. This initial success of the model prompted its further development to other systems and experiments. In particular, the idea of group transfer elastically coupled to conformational change monitored by the probe is applied and extended to (1) calculate power stroke rate constants in two different force-spectroscopy experiments on single and double-headed myosin V; to (2) extract rate constants for hydrolysis and synthesis from controlled rotation data on F1-ATPase; and to (3) account for "dynamical effects" due to the internal and probe-related friction in the single-molecule imaging experiments.
An important aspect of the analysis is the statistical modeling of biasing effects of finite time resolution in the photon-counting trajectories and the finite response time of the imaging probes.https://authors.library.caltech.edu/records/0ktma-2da55Monitoring Electron–Phonon Interactions in Lead-Halide Perovskites Using Time-Resolved THz Spectroscopy
https://resolver.caltech.edu/CaltechAUTHORS:20190729-101612764
Authors: {'items': [{'id': 'Zhao-Daming', 'name': {'family': 'Zhao', 'given': 'Daming'}, 'orcid': '0000-0001-5046-2199'}, {'id': 'Hu-Hongwei', 'name': {'family': 'Hu', 'given': 'Hongwei'}}, {'id': 'Haselsberger-R', 'name': {'family': 'Haselsberger', 'given': 'Reinhard'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}, {'id': 'Michel-Beyerle-M-E', 'name': {'family': 'Michel-Beyerle', 'given': 'Maria-Elisabeth'}}, {'id': 'Lam-Yeng-Ming', 'name': {'family': 'Lam', 'given': 'Yeng Ming'}, 'orcid': '0000-0001-9390-8074'}, {'id': 'Zhu-Jian-Xin', 'name': {'family': 'Zhu', 'given': 'Jian-Xin'}, 'orcid': '0000-0001-7991-3918'}, {'id': 'La-o-vorakiat-Chan', 'name': {'family': 'La-o-vorakiat', 'given': 'Chan'}, 'orcid': '0000-0002-0231-8499'}, {'id': 'Beard-M-C', 'name': {'family': 'Beard', 'given': 'Matthew C.'}, 'orcid': '0000-0002-2711-1355'}, {'id': 'Chia-E-E-M', 'name': {'family': 'Chia', 'given': 'Elbert E. M.'}, 'orcid': '0000-0003-2066-0834'}]}
Year: 2019
DOI: 10.1021/acsnano.9b02049
Lead halide perovskite semiconductors have low-frequency phonon modes within the lead halide sublattice and thus are considered to be soft. The soft lattice is considered to be important in defining their interesting optoelectronic properties. Electron–phonon coupling governs hot-carrier relaxation, carrier mobilities, carrier lifetimes, among other important electronic characteristics. Directly observing the interplay between free charge carriers and phonons can provide details on how phonons impact these properties (e.g., exciton populations and other collective modes). Here, we observe a delicate interplay among carriers, phonons, and excitons in mixed-cation and mixed-halide perovskite films by simultaneously resolving the contribution of charge carriers and phonons in time-resolved terahertz photoconductivity spectra. We are able to observe directly the increase in phonon population during carrier cooling and discuss how thermal equilibrium populations of carriers and phonons modulate the carrier transport properties, as well as reduce the population of carriers within band tails. We are also able to observe directly the formation of free charge carriers when excitons interact with phonons and dissociate and to describe how free carriers and exciton populations exchange through phonon interactions. Finally, we also time-resolve how the carriers are screened via the Coulomb interaction at low and room temperatures. Our studies shed light on how charge carriers interact with the low-energy phonons and discuss implications.https://authors.library.caltech.edu/records/423nk-rcg72Method to extract multiple states in F₁-ATPase rotation experiments from jump distributions
https://resolver.caltech.edu/CaltechAUTHORS:20191127-111513039
Authors: {'items': [{'id': 'Volkán-Kacsó-S', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}}, {'id': 'Le-Luan-Q', 'name': {'family': 'Le', 'given': 'Luan Q.'}}, {'id': 'Zhu-Kaicheng', 'name': {'family': 'Zhu', 'given': 'Kaicheng'}, 'orcid': '0000-0003-0218-4985'}, {'id': 'Su-Haibin', 'name': {'family': 'Su', 'given': 'Haibin'}, 'orcid': '0000-0001-9760-6567'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2019
DOI: 10.1073/pnas.1915314116
PMCID: PMC6926002
A method is proposed for analyzing fast (10 μs) single-molecule rotation trajectories in F₁ adenosinetriphosphatase (F₁-ATPase). This method is based on the distribution of jumps in the rotation angle that occur in the transitions during the steps between subsequent catalytic dwells. The method is complementary to the "stalling" technique devised by H. Noji et al. [Biophys. Rev. 9, 103–118, 2017], and can reveal multiple states not directly detectable as steps. A bimodal distribution of jumps is observed at certain angles, due to the system being in either of 2 states at the same rotation angle. In this method, a multistate theory is used that takes into account a viscoelastic fluctuation of the imaging probe. Using an established sequence of 3 specific states, a theoretical profile of angular jumps is predicted, without adjustable parameters, that agrees with experiment for most of the angular range. Agreement can be achieved at all angles by assuming a fourth state with an ∼10 μs lifetime and a dwell angle about 40° after the adenosine 5′-triphosphate (ATP) binding dwell. The latter result suggests that the ATP binding in one β subunit and the adenosine 5′-diphosphate (ADP) release from another β subunit occur via a transient whose lifetime is ∼10 μs and is about 6 orders of magnitude smaller than the lifetime for ADP release from a singly occupied F₁-ATPase. An internal consistency test is given by comparing 2 independent ways of obtaining the relaxation time of the probe. They agree and are ∼15 μs.https://authors.library.caltech.edu/records/ve67g-jet16Fast States Revealed by Theory of Jumps in F1-ATPase Rotation Experiments
https://resolver.caltech.edu/CaltechAUTHORS:20200210-084544277
Authors: {'items': [{'id': 'Volkán-Kacsó-S', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}}, {'id': 'Le-Luan-Q', 'name': {'family': 'Le', 'given': 'Luan Q.'}}, {'id': 'Su-Haibin', 'name': {'family': 'Su', 'given': 'Haibin'}, 'orcid': '0000-0001-9760-6567'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2020
DOI: 10.1016/j.bpj.2019.11.1120
Single-molecule spectroscopies revealed the stepping rotation of an F1-ATPase enzyme in which a substep can have microsecond transition dynamics. Here we describe a method for analyzing fast single molecule rotation trajectories in F1-ATPase monitored by a 40 nanometer probe. This method focuses on the rotation jumps that occur in the transitions during the steps between dwells in single molecule trajectories. These jumps are related to the "instantaneous" rotation velocity and they exhibit a bimodal distribution at certain angles, indicating that the system produces both forward and a backward torques at the same angle, due to being in either of two states. Two states at the same angle is a key assumption used to extracts rate constants in stalling experiments, so by observing the bimodal distributions we provide support for this assumption. To calculate the distribution of jumps, we use a multi-state theory to describe the visco-elastic fluctuation of the imaging probe. The predicted jump distribution in the transitions yields a relaxation time which agrees with its value of 14 microseconds in the dwell fluctuations. Using a sequence of three states, the theoretical profile of angular jumps agrees with experiment for most of the angular range, but full agreement between theory and experiment is reached if a fourth, 10 microsecond lifetime state is assumed with an effective dwell half way through the 80 degree substep. It suggests that the ATP binding in one subunit and the ADP release from another subunit occurs via this transient. The ability to detect a state that is comparable or shorter than the instrumental relaxation time indicates that this jump distribution based method can be used to effectively increase the time resolution of the imaging apparatus.https://authors.library.caltech.edu/records/x470m-m1c58Exploring the State of the F₁-ATPase after ATP Binding and before ADP Release: Effects of Conformational Changes on Phosphate Displacement
https://resolver.caltech.edu/CaltechAUTHORS:20200210-112257799
Authors: {'items': [{'id': 'Matute-R-A', 'name': {'family': 'Matute', 'given': 'Ricardo A.'}, 'orcid': '0000-0002-0644-3799'}, {'id': 'Volkán-Kacsó-S', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2020
DOI: 10.1016/j.bpj.2019.11.2044
Single-molecule imaging experiments provide information that is not available from ensemble experiments. We are interested in the interpretation of dynamical studies imaging and manipulation in F₁-ATPase single-molecules. One key question that has arisen in single molecule stalling experiments is the erratic behavior a rotor angle of 55° between the binding and hydrolysis dwell angles of 0 and 80°, respectively. In our previous theoretical work, we used the elastic property of the rotor-stator structure to treat the experiments on controlled rotation. Our modeling suggests that there has to be a change in the bonding network, for example, of hydrogen bonds, as the system transitions between the two dwell points, perhaps at 55°, as indicated by an unusual stalling behavior around that angle. Therefore, in order to get further insights on these events, we have performed full-atomistic molecular dynamics (MD) simulations on the F₁-ATPase to explore the relationship between the conformational changes and the phosphate displacement. The pK_a values for phosphoric acid are 2.2, 7.2, and 12.3; although the effective pK_a for H₂PO₄⁻ within the binding site could be different. Hence, both protonation states (i.e., H₂PO₄⁻ and HPO₄²⁻) were assessed, performing molecular dynamics for 650 ns at 298.15K (Nose-Hoover thermostat) using the CHARMM36 force field. After the analysis of five MD trajectories, we found that the displacement of the phosphate was, to some extent, correlated with the dynamics of the protein. Moreover, one of the MD trajectories led to the complete release of the diprotic phosphate.https://authors.library.caltech.edu/records/v83mx-6y770Sum frequency generation, calculation of absolute intensities, comparison with experiments, and two-field relaxation-based derivation
https://resolver.caltech.edu/CaltechAUTHORS:20200129-135825343
Authors: {'items': [{'id': 'Niu-Kai', 'name': {'family': 'Niu', 'given': 'Kai'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2020
DOI: 10.1073/pnas.1906243117
PMCID: PMC7022212
The experimental sum frequency generation (SFG) spectrum is the response to an infrared pulse and a visible pulse and is a highly surface-sensitive technique. We treat the surface dangling OH bonds at the air/water interface and focus on the absolute SFG intensities for the resonant terms, a focus that permits insight into the consequences of some approximations. For the polarization combinations, the calculated linewidths for the water interface dangling OH SFG band at 3,700 cm⁻¹ are, as usual, too large, because of the customary neglect of motional narrowing. The integrated spectrum is used to circumvent this problem and justified here using a Kubo-like formalism and theoretical integrated band intensities rather than peak intensities. Only relative SFG intensities are usually reported. The absolute integrated SFG intensities for three polarization combinations for sum frequency, visible, and infrared beams are computed. We use molecular dynamics and the dipole and the polarizability matrix elements obtained from infrared and Raman studies of H₂O vapor. The theoretical expressions for two of the absolute susceptibilities contain only a single term and agree with experiment to about a factor of 1.3, with no adjustable parameters. The Fresnel factors are included in that comparison. One of the susceptibilities contains instead four positive and negative terms and agrees less well. The expression for the SFG correlation function is normally derived from a statistical mechanical formulation using a time-evolving density matrix. We show how a derivation based on a two-field relaxation leads to the same final result.https://authors.library.caltech.edu/records/pz2ae-pr332Reflections on electron transfer theory
https://resolver.caltech.edu/CaltechAUTHORS:20201207-153231500
Authors: {'items': [{'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2020
DOI: 10.1063/5.0035434
Some of the early history leading to the 1956 The Journal of Chemical Physics article on a theory of electron transfer reactions is described.
In the development of electron transfer theory in 1956, the simplicity of the final equation for the free energy barrier, after a lengthy and complex derivation, came to me as a surprise. It was indeed a "Eureka" moment, and I give some of its history here.
The theory developed via a rather circuitous route, beginning with a question from a graduate student in a class on statistical mechanics that I taught at Brooklyn Poly. The question was whether a certain model (the Ising model) involving nearest neighbor interactions could be applied to shielded charges along a polymeric chain, a polyelectrolyte. His interest was in applying the theory to experimental data he was obtaining in the laboratory. The answer was yes, and I became interested more generally in the electrostatic properties of polyelectrolytes and in the several seemingly different ways of calculating their electrostatic free energy.
To extend my background in electrostatics and treat this topic in a more fundamental way I researched every book on electrostatics/electromagnetic theory in the Brooklyn Poly library and found one that provided physical insight into the various concepts. After writing a pair of articles on polyelectrolytes, I then wondered what to do next. I had long decided that applying a theory I derived in 1952, later known as Rice–Ramsperger–Kassel–Marcus (RRKM) theory, was not a desirable option. There were almost no relevant experimental data on unimolecular reactions or bimolecular recombination reactions at the time. Extensive data, laboratory and computational, for testing the theory were to come later in the 1960s and subsequent decades.https://authors.library.caltech.edu/records/9dscn-3mn35On the theory of charge transport and entropic effects in solvated molecular junctions
https://resolver.caltech.edu/CaltechAUTHORS:20210127-125542902
Authors: {'items': [{'id': 'Sowa-Jakub-K', 'name': {'family': 'Sowa', 'given': 'Jakub K.'}, 'orcid': '0000-0003-4104-2664'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2021
DOI: 10.1063/5.0034782
Experimental studies on single-molecule junctions are typically in need of a simple theoretical approach that can reproduce or be fitted to experimentally measured transport data. In this context, the single-level variant of the Landauer approach is most commonly used, but methods based on Marcus theory are also gaining popularity. Recently, a generalized theory unifying these two approaches has also been developed. In the present work, we extend this theory so that it includes entropic effects (which can be important when polar solvents are involved but are likely minor for solid-state systems). We investigate the temperature-dependence of the electric current and compare it to the behavior predicted by the Landauer and the conventional Marcus theory. We argue that this generalized theory provides a simple yet effective framework for understanding charge transport through molecular junctions. Furthermore, we explore the role of the entropic effects in different transport regimes and suggest experimental criteria for detecting them in solvated molecular junctions. Finally, in order to account for nuclear tunneling effects, we also demonstrate how lifetime broadening can be introduced into the Marcus–Levich–Dogonadze–Jortner-type description of electron transport.https://authors.library.caltech.edu/records/wkmd8-56h59The Drude-Smith Equation and Related Equations for the Frequency-Dependent Electrical Conductivity of Materials: Insight from a Memory Function Formalism
https://resolver.caltech.edu/CaltechAUTHORS:20210628-191053480
Authors: {'items': [{'id': 'Chen-Wei-Chen', 'name': {'family': 'Chen', 'given': 'Wei-Chen'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2021
DOI: 10.1002/cphc.202100299
PMCID: PMC8456847
The Drude-Smith equation is widely used for treating the frequency-dependent electrical conductivity of materials in the terahertz region. An attractive feature is its sparsity of adjustable parameters. A significant improvement over Drude theory for these materials, the theory includes backscattering of the charge carriers. It has nevertheless been criticized, including by Smith himself, because of the arbitrariness of a step in the derivation. We recall a somewhat similar behavior of back scattering in fluids observed in molecular dynamics computations and discussed in terms of memory functions. We show how theories such as Drude-Smith and Cocker et al. are examples of a broader class of theories by showing how they also arise as particular cases of a memory function formalism that divides the interactions into short and long range.https://authors.library.caltech.edu/records/je0t9-w4224Utilizing correlation functions to develop a multistate model of P. denitrificans F₁-ATPase and enhance single-molecule imaging resolution
https://resolver.caltech.edu/CaltechAUTHORS:20220422-224453523
Authors: {'items': [{'id': 'Suiter-Nathan-M', 'name': {'family': 'Suiter', 'given': 'Nathan'}}, {'id': 'Volkán-Kacsó-Sándor', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}, 'orcid': '0000-0003-3327-2865'}, {'id': 'Matute-Ricardo-A', 'name': {'family': 'Matute', 'given': 'Ricardo A.'}}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2022
DOI: 10.1016/j.bpj.2021.11.2819
F₁-ATPase enzyme is a biological motor which hydrolyzes ATP. The enzyme has been observed via single-molecule imaging experiments wherein the enzyme is allowed to rotate freely while being recorded using a gold nanoparticle. During hydrolysis, the enzyme causes Brownian noise when rotating to new chemical states because of a size difference between the 4 nm enzyme and 40 nm probe. The unconvoluted rotary movement has been revealed using techniques including rotational correction, correlation functions, and comparison of average rotational jumps which contribute to developing a multistate model. Within P. denitrificans F₁, the timestep used in experimentation is limited to 100 μs. After correction for tilting, a method for evaluating all three subunits uniformly was implemented in further evaluations. Using corrected data, the torsional spring constant of the rotary shaft was found to be near 25 pN nM for most subunits with a few subunits at much higher values. Implementation of the time correlation function which was proven to be stationary yielded a viscoelastic relaxation time around unity. The relaxation time provides a method for calculating a diffusion coefficient to develop a multistate model and elucidate hidden kinetic states of the functioning enzyme.https://authors.library.caltech.edu/records/vnsc2-ckw47F₁-ATPase Rotary Mechanism: Interpreting Results of Diverse Experimental Modes With an Elastic Coupling Theory
https://resolver.caltech.edu/CaltechAUTHORS:20220520-231783000
Authors: {'items': [{'id': 'Volkán-Kacsó-Sándor', 'name': {'family': 'Volkán-Kacsó', 'given': 'Sándor'}, 'orcid': '0000-0003-3327-2865'}, {'id': 'Marcus-R-A', 'name': {'family': 'Marcus', 'given': 'Rudolph A.'}, 'orcid': '0000-0001-6547-1469'}]}
Year: 2022
DOI: 10.3389/fmicb.2022.861855
PMCID: PMC9072658
In this chapter, we review single-molecule observations of rotary motors, focusing on the general theme that their mechanical motion proceeds in substeps with each substep described by an angle-dependent rate constant. In the molecular machine F₁-ATPase, the stepping rotation is described for individual steps by forward and back reaction rate constants, some of which depend strongly on the rotation angle. The rotation of a central shaft is typically monitored by an optical probe. We review our recent work on the theory for the angle-dependent rate constants built to treat a variety of single-molecule and ensemble experiments on the F₁-ATPase, and relating the free energy of activation of a step to the standard free energy of reaction for that step. This theory, an elastic molecular transfer theory, provides a framework for a multistate model and includes the probe used in single-molecule imaging and magnetic manipulation experiments. Several examples of its application are the following: (a) treatment of the angle-dependent rate constants in stalling experiments, (b) use of the model to enhance the time resolution of the single-molecule imaging apparatus and to detect short-lived states with a microsecond lifetime, states hidden by the fluctuations of the imaging probe, (c) treatment of out-of-equilibrium "controlled rotation" experiments, (d) use of the model to predict, without adjustable parameters, the angle-dependent rate constants of nucleotide binding and release, using data from other experiments, and (e) insights obtained from correlation of kinetic and cryo-EM structural data. It is also noted that in the case where the release of ADP would be a bottleneck process, the binding of ATP to another site acts to accelerate the release by 5–6 orders of magnitude. The relation of the present set of studies to previous and current theoretical work in the field is described. An overall goal is to gain mechanistic insight into the biological function in relation to structure.https://authors.library.caltech.edu/records/2emz2-jtc81