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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 15:36:47 +0000The Iterative Schwinger Variational Method Applied to Electron-Molecule Continuum Processes
https://resolver.caltech.edu/CaltechTHESIS:06062011-113312144
Authors: {'items': [{'id': 'Lucchese-Robert-Ross', 'name': {'family': 'Lucchese', 'given': 'Robert Ross'}, 'show_email': 'NO'}]}
Year: 1982
DOI: 10.7907/JS31-4A21
<p>We have developed the iterative Schwinger variational method to study electron-molecule scattering problems within the Hartree-Fock approximation. The method is based on the iterative use of the Schwinger variational principle and can obtain exact static-exchange scattering solutions. This approach has been implemented using standard single-center expansion techniques. We present results using the Schwinger variational expression for e-He and e-He<sup>+</sup> collisions and find very rapid convergence of the phase shifts with increasing basis set size. We then discuss the iterative use of the Schwinger variational expression and give results for e-H<sub>2</sub> and e-H<sup>+</sup><sub>2</sub> scattering which show very rapid convergence of the iterative method. We have applied this method to low energy 3-CO<sub>2</sub> scattering and obtained differential and integral elastic scattering cross sections. We determined that the <sup>2</sup>π<sub>u</sub> shape resonance in this system occurs at an energy of 5.39 eV with a width of 0.64 eV in contrast to previously published static-exchange results.</p>
<p>We have also used the iterative Schwinger variational method to study the valence shell photoionization of N<sub>2</sub> and CO<sub>2</sub> as well as the K-shell photoionization of CO<sub>2</sub>. These results agree well with available experimental data. The vibrational branching ratios for photoionization of 3σ<sub>g</sub> level of N<sub>2</sub> were found to agree quantitatively with experimental measurements when an adequate number of internuclear spacings were considered. The effects of vibrational averaging on 4σ<sub>g</sub> photoionization of CO<sub>2</sub> were also studied. A detailed comparison of the results obtained using the Schwinger method and other theoretical methods for studying photoionization has been made.</p>
<p>The iterative Schwinger variational method has proven to be an accurate and efficient method for obtaining Hartree-Fock level scattering solutions, and it has allowed us to study electron-molecule continuum processes in more detail and for larger systems than previously possible.</p>https://thesis.library.caltech.edu/id/eprint/6501Investigation of coriolis mixing in benzene
https://resolver.caltech.edu/CaltechTHESIS:03292010-084636927
Authors: {'items': [{'id': 'Runnels-J-H', 'name': {'family': 'Runnels', 'given': 'John Hulett'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/yxqj-6804
An explanation for some recent observations in the
electronic absorption spectrum of benzene by Schlag and
coworkers is proposed. Several vibrational lines of the
S_0 to S_1 transition have been studied by these authors with the Doppler—free, two—photon technique developed earlier. The resolution of this technique is so high that individual Δ J=0, Δ K=0 rotational lines in the Q—branch of a given vibrational transition may be seen in the electronic absorption spectrum. A major progression in the two—photon spectrum is the 14^1_0 1^n_0 progression. It was found that the 14^1_0 1^0_0 and 14^1_0 1^1_0 transitions had well—resolved rotationalstructure, but the 14^1_0 1^2_0 transition had reduced, not well
resolved rotational structure--except for the prominent K=0
lines for small to medium values of J. This suggested to
us Coriolis mixing. The model presented here utilizes a
suggestion of Riedle et al.The Coriolis coupling to
neighboring vibrational states is followed by a rapid
radiationless depletion of these states, consistent with
the decreased fluorescence yield observed by Wunsch et al.
Estimates are made of the density of states of the various
symmetries; these estimates are then used to estimate the
extent of the relevant Coriolis mixing. The model results
in a large decrease in intensity of non—zero K lines
relative to the K=0 lines for the 14^1_0 1^2_0 transition, but not for the 14^1_0 1^0_0 and 14^1_0 1^1_0 transitions, in agreement with the experimental observations, making a few assumptions discussed below, but without the use of adjustable parameters. Predictions are then made for the rotational structure of other strong transitions in the two—photon spectrum of benzene.
https://thesis.library.caltech.edu/id/eprint/5640Studies of the Energetics and Mechanisms of Organometallic Reactions in the Gas Phase
https://resolver.caltech.edu/CaltechTHESIS:11012019-144753562
Authors: {'items': [{'id': 'Halle-Linda-F', 'name': {'family': 'Halle', 'given': 'Linda F.'}, 'show_email': 'NO'}]}
Year: 1983
DOI: 10.7907/29x4-wk61
<p>An ion beam apparatus is used to study reactions of the three first row group 8 atomic metal ions, Fe<sup>+</sup>, C<sup>o+</sup>, and Ni<sup>+</sup>, as well as the diatomic FeH<sup>+</sup> species, with small organic molecules. The kinetic energy dependence of these processes is examined. Analysis of the thresholds for endothermic reactions yields bond strengths of the metal ion to various substituent groups. The thermochemical information derived in this manner and from more qualitative observations is used to assess the mechanisms by which these ions react with small organic molecules.</p>
<p>Chapter I provides a brief summary of some of the organometallic systems previously studied using the ion beam apparatus. Chapter II presents the culmination of our studies of reactions of the first row group 8 metal ions with alkanes in which the extensive use of deuterium and <sup>13</sup>C-labeled compounds provides further elaboration of the mechanisms by which these ions activate carbon-carbon and carbon-hydrogen bonds.</p>
<p>Chapter III examines the consequences of incorporating a carbonyl group into the hydrocarbon from investigations of the reactions of Co<sup>+</sup> with aldehydes and ketones. Analysis of products formed at high relative kinetic energies are used in conjunction with thermochemical estimates to infer mechanistic details and construct qualitative reaction coordinate diagrams for the interactions of Co<sup>+</sup> with carbonyl compounds.</p>
<p>Chapter IV represents an extension of our determinations of metal-carbon bond strengths to include fluorinated substituents. In particular, measurements of the Ni<sup>+</sup>-CH<sub>2</sub> and N<sup>+</sup>-CF<sub>2</sub> bond energies are reported. The implication of these carbene bond strengths for the metathesis of fluorinated olefins is discussed.</p>
<p>Chapter V reports the first ion beam experiment of an organometallic fragment, the FeH<sup>+</sup> species. Thermochemical information is obtained from reactions involving proton transfer from, and hydride transfer to, FeH<sup>+</sup>. We find that oxidative addition of FeH<sup>+</sup> to D<sub>2</sub> or hydrocarbons via Fe(IV) or four-centered intermediates is not a facile process, while reversible insertion of olefins into Fe<sup>+</sup>-H occurs with moderate cross section at low energies. Preliminary results for the reactions of FeH<sup>+</sup> with alcohols, aldehydes, and ethers are also discussed.</p>https://thesis.library.caltech.edu/id/eprint/11881Nature and Energy Redistribution of Highly Vibrationally Excited Polyatomic Molecules
https://resolver.caltech.edu/CaltechETD:etd-04032008-111559
Authors: {'items': [{'email': 'joe.perry@gatech.edu', 'id': 'Perry-Joseph-Walter', 'name': {'family': 'Perry', 'given': 'Joseph Walter'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/YDWZ-Z639
<p>This thesis is a primarily experimental study of the spectroscopy and dynamics of highly vibrationally excited molecules in the ground and excited electronic states. Linear spectroscopic studies have been performed on CH-stretching overtones of medium and large sized molecules in the gas and solid phases. Also new time-resolved methods based on nonlinear uultiphoton ionization spectroscopy have been applied on the picosecond time-scale to the study of ultrafast intramolecular vibrational-energy redistribution (IVR) in isolated molecules.</p>
<p>The first observation of high-energy CH stretching overtones of molecules in low-temperature solids is reported. Spectra of the <sup>ν</sup>CH = 5 transitions of many aromatic molecules at ~2K reveal homogeneously broadened bands which are assigned to inequivalent local modes by studies of same isotopically substituted molecules. Typical linewidths give population lifetimes of ~50 fs for aromatic compared to 100-200 fs for methyl CHs in these large molecules. The polarization ratios of durene CH overtones are in good agreement with those predicted with the localized bond-mode transition moments.</p>
<p>Overtone spectra of some gas-phase deuterated methanes and tetramethyl compounds have been studied. Spectra of CHD<sub>3</sub> have shown severe vibrational mixing at <sup>ν</sup>CH = 6 and 7 with an apparent tuning of the Fermi-resonance between |<sup>ν</sup>CH> and discrete stretch-bend combination states, e.g., |<sup>(ν-1)</sup>CH, <sup>2</sup>bend>. Nonetheless, the lifetime of the CHD<sub>3</sub> overtones must be long (≥5 ps) as evidenced by the narrow resolution limited linewidths. The splitting of the |6,0>± states of CH<sub>2</sub>D<sub>2</sub> is inferred to be <10 cm<sup>-1</sup> and shows that the coupling of the CH oscillators is relatively weak in agreement with theoretical prediction. In general, the results on the CH overtones indicate a significant role of CH stretch-normal mode coupling in the spectra and dynamics.</p>
<p>Picosecond pump and probe multiphoton ionization is developed for the study of IVR in isolated molecules. Experimental evidence for IVR is presented. Nonexponential decay of vibronic states of S<sub>1</sub> trans-stilbene is analyzed in terms of a population rate equation and time-dependent Franck-Condon factor description of IVR. The thermally-averaged IVR time constant is about 2 ps. Also, the excess vibrational energy dependence of the S<sub>1</sub> trans-stilbene isomerization rate is determined for total vibrational energy of 2000 to 4500 cm<sup>-1</sup> and good agreement is found with calculated thermally averaged rates based on independent results on jet-cooled molecules.</p>https://thesis.library.caltech.edu/id/eprint/1259Catalysis of the Electroreduction of Dioxygen by Monomeric and Dimeric Cobalt Porphyrins
https://resolver.caltech.edu/CaltechTHESIS:10072016-152635305
Authors: {'items': [{'id': 'Durand-Richard-Raymond-Jr', 'name': {'family': 'Durand', 'given': 'Richard Raymond, Jr.'}, 'show_email': 'NO'}]}
Year: 1984
DOI: 10.7907/h738-ft41
<p>Mechanistic aspects of the catalytic electroreduction of dioxygen by monomeric and dimeric cobalt porphyrins were investigated. The catalysts were examined while either adsorbed to graphite electrodes or dissolved in concentrated acids.</p>
<p>Monomeric cobalt(II) porphyrins adsorbed to graphite electrodes were found to reduce dioxygen to hydrogen peroxide. Cyclic and rotating disk voltammetry were used to examine the kinetics and mechanism of the catalyzed reactions. These monomeric catalysts exhibited behavior atypical of simple redox catalysis.</p>
<p>The mechanisms by which the reduction of dioxygen at graphite electrodes is catalyzed by cofacial dicobalt and related porphyrins has been investigated. The products of the reductions, the electrode potential where the reduction proceeds and the mechanistic role of protons were among the topics examined. A comparison of the behavior of several new cofacial metalloporphyrins has led to a more detailed proposal for the mechanisms by which they operate.</p>
<p>Monomeric and dimeric cobalt porphyrins have been dissolved in trifluoromethanesulfonic acid (5.6 M) and concentrated phosphoric acid without demetalation. The electrocatalytic reduction of dioxygen by solutions of the catalysts was examined by rotating disk and ring-disk voltammetry. The dissolved metalloporphyrins provide improved stability to the catalysts.</p>
<p>The reaction of a cobalt(II) complex with superoxide was examined electrochemically in a non-aqueous electrolyte. The affinity of superoxide for cobalt(II) has been demonstrated by cyclic voltammetry. The results of this study were related to mechanisms of dioxygen reduction in aqueous media.</p>https://thesis.library.caltech.edu/id/eprint/9937Picosecond Dynamics of Intramolecular Vibrational-Energy Redistribution (IVR) in Jet-Cooled Molecules
https://resolver.caltech.edu/CaltechETD:etd-04072008-152253
Authors: {'items': [{'id': 'Felker-Peter-Mark', 'name': {'family': 'Felker', 'given': 'Peter Mark'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/x48p-n096
<p>Theoretical and experimental results concerning the dynamical manifestations of intramolecular vibrational-energy redistribution (IVR) in the temporally resolved fluorescence of jet-cooled molecules are presented. A first concern is with the derivation of the characteristics of the beat-modulated fluorescence decays which arise from multilevel vibrational coupling within a molecule. Relations connecting quantum beat frequencies, phases, and modulation depths to coupling parameters are presented. Likely sources of deviations of experimental results from theoretical predictions are considered. And, the direct link between IVR and time-resolved fluorescence experiments is discussed with emphasis placed on the physical interpretation of vibrational quantum beats and the nature of IVR as a function of vibrational energy in a molecule. Secondly, the results of picosecond time-resolved measurements of IVR on jet-cooled anthracene at different excess energies are reported and analyzed. The nature of IVR as a function of vibrational energy, the relevant timescales for the process, and the details of pertinent vibrational couplings are determined. Thirdly, experimental and theoretical results pertaining to the role of molecular rotations in IVR are presented. Finally, experimental results on jet-cooled t-stilbene are reported and analyzed with the aim of assessing the generality of our theoretical treatment and the anthracene results.</p>https://thesis.library.caltech.edu/id/eprint/1297The Schwinger Variational Principle Applied to Molecular Photoionization
https://resolver.caltech.edu/CaltechTHESIS:01232019-115959754
Authors: {'items': [{'id': 'Smith-Maile-Elizabeth', 'name': {'family': 'Smith', 'given': 'Maile Elizabeth'}, 'show_email': 'NO'}]}
Year: 1985
DOI: 10.7907/4m95-c614
<p>We have developed a method based upon the Schwinger Variational Principle to study molecular photoionization and electron molecule scattering. We obtain exact static-exchange solutions to the equations for the continuum orbitals within the Hartree-Fock approximation, and from these we derive cross sections and angular distributions for both of the above processes. We have applied this method to photoionization of the valence levels of three different systems.</p>
<p>The first application of this method is in a study of the photoionization of the valence levels of NO. For photoionization of the 5σ level we find that the magnitudes of the cross sections for the resulting b<sup>3</sup>Π and A<sup>1</sup>Π states of NO<sup>+</sup> are not in the statistical 3:1 ratio and that the position of the peaks in the shape resonances appear at significantly different photoelectron kinetic energies. The differences are a reflection of the sensitivity of the shape resonances to small changes in the exchange component of the molecular ion potential. We also examined photoionization of the 2π and 4σ levels of NO and found that these levels, along with the 5σ, exhibit shape resonances in the σ continuum.</p>
<p>Vibrationally resolved branching ratios and vibrational state-specific asymmetry parameters for photoionization of the 5σ level of CO are presented. The agreement between these results and the measured data was obscured by autoionization peaks superimposed upon the region of the spectrum in which the experiment was performed. The limited experimental data which are not obscured by autoionization, agree quite well with our results.</p>
<p>Finally, a study of the photoionization of the 5σ level of CO adsorbed on a nickel surface is reported. Approximating this system by the linear triatomic molecule NiCO leads to cross sections and angular distributions which are in good agreement with experimental data. The use of polarized, highly tunable synchrotron radiation along with detection at various angles yields far more information than can be obtained from the photoionization of the same molecule in the gas phase. With this technique it is possible to determine the adsorbate geometry, resolve partial channels, and resolve the photoemisison from two degenerate orbitals of different symmetries, simply by making appropriate choice of the polarization and collection angles. Examples of these techniques are discussed.</p>https://thesis.library.caltech.edu/id/eprint/11360The Theory of Long Distance Electron Transfer Reactions
https://resolver.caltech.edu/CaltechTHESIS:04012014-082222627
Authors: {'items': [{'id': 'Beratan-David-Nathan', 'name': {'family': 'Beratan', 'given': 'David Nathan'}, 'orcid': '0000-0003-4758-8676', 'show_email': 'NO'}]}
Year: 1986
DOI: 10.7907/FF39-DP24
<p>The rate of electron transport between distant sites was studied. The rate depends crucially on the chemical details of the donor, acceptor, and surrounding medium. These reactions involve electron tunneling through the intervening medium and are, therefore, profoundly influenced by the geometry and energetics of the intervening molecules. The dependence of rate on distance was considered for several rigid donor-acceptor "linkers" of experimental importance. Interpretation of existing experiments and predictions for new experiments were made.</p>
<p>The electronic and nuclear motion in molecules is correlated. A Born-Oppenheimer separation is usually employed in quantum chemistry to separate this motion. Long distance electron transfer rate calculations require the total donor wave function when the electron is very far from its binding nuclei. The Born-Oppenheimer wave functions at large electronic distance are shown to be qualitatively wrong. A model which correctly treats the coupling was proposed. The distance and energy dependence of the electron transfer rate was determined for such a model.</p>
https://thesis.library.caltech.edu/id/eprint/8175Theoretical Studies of Intramolecular Dynamics and Energy Redistribution
https://resolver.caltech.edu/CaltechETD:etd-11292006-135710
Authors: {'items': [{'id': 'Voth-Gregory-Alan', 'name': {'family': 'Voth', 'given': 'Gregory Alan'}, 'show_email': 'NO'}]}
Year: 1987
DOI: 10.7907/MD4H-AZ79
<p>By virtue of various theoretical techniques, the fundamental mechanisms responsible for intramolecular vibrational energy redistribution (IVR) in isolated molecules are studied in this thesis. One such mechanism, the nonlinear resonance, is examined in some detail for several systems. In particular, nonlinear stretch-bend resonances in a series of isotopically substituted methanes are predicted to have a large effect on the spectral properties of those molecules. By using a semiclassical analysis, the general properties of stretch-bend interactions are further examined, and the quantum mechanical manifestations of classical resonances are characterized in detail. A related problem, the role of classical resonances in the multiphoton absorption process by an anharmonic oscillator, is also analyzed.</p>
<p>In addition, it is demonstrated that the quantum mechanical coupled equations which describe the fundamental IVR process may be simplified. This simplification is achieved by virtue of an "adiabatic" approximation for those state amplitudes which are sufficiently off-resonant with (i.e., different in energy from) the experimentally prepared quantum state. The approximate coupled equations are based on an effective Hamiltonian which contains renormalized self-energies and interactions between the zeroth-order quantum states. This formalism may be applied to describe the quasidissipative flow of probability out of an initially prepared vibrational state in a large molecule, and it may also be adapted to treat multiphoton absorption processes in polyatomic molecules when one or more lasers are present.</p>https://thesis.library.caltech.edu/id/eprint/4686Theoretical Studies of Chemical Reaction Dynamics
https://resolver.caltech.edu/CaltechTHESIS:03062013-161416978
Authors: {'items': [{'id': 'Klippenstein-Stephen-Jacob', 'name': {'family': 'Klippenstein', 'given': 'Stephen Jacob'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/dbrd-wj15
<p>In this thesis theoretical models a.re developed and/or applied to the study of the dynamics of a variety of chemical reactions. First, a semiclassical model is developed to describe the effect of mutual orientation of the donor and acceptor on the rate of electron transfer between two large aromatic groups. The next reaction considered is that of gas phase H-atom transfer reactions. In this case a comparison is made of two previously developed approximations for the treatment of the particular case of H-atom transfer between two heavy particles.</p>
<p>The next topic involves the study of the rate of intramolecular vibrational redistribution of energy. First, an iterative procedure is developed for determining more and more accurate effective Hamiltonians for the description of the dynamics. The foundation of this method is the separation of the basis states into resonant and nonresonant sets followed by an adiabatic approximation for the dynamics of the off-resonant set. A second study involves the application of artificial intelligence techniques to the choice of a small set of basis states which are the states of greatest importance to the redistribution dynamics.</p>
<p>The remainder of the thesis is devoted to the study of those unimolecular dissociation/free radical recombination reactions which contain highly flexible transition states. For these reactions, a method for determining the quantum partition function for the transition state in terms of path integral ratios is developed and applied to the study of the thermally activated methyl radical recombination. Subsequently, a method is developed for determining the number of states, for the transition state, at a given energy and angular momentum. The basis of the method is the use of conventional Euler angle coordinates in the Monte Carlo evaluation of phase space integrals. This method is applied to the NCNO, CH₂CO, and H₂O₂ photodissociation processes. Also presented is a discussion of both the trend of the location of the transition state with increasing energy and the possible influence of excited potential energy surfaces.</p>
https://thesis.library.caltech.edu/id/eprint/7501Artificial Intelligence in Quantum Intramolecular Dynamics with Application to a Heavy Central Mass Problem
https://resolver.caltech.edu/CaltechTHESIS:03082013-103249804
Authors: {'items': [{'email': 'huss@beloit.edu', 'id': 'Lederman-Steven-Mark', 'name': {'family': 'Lederman', 'given': 'Steven Mark'}, 'show_email': 'NO'}]}
Year: 1988
DOI: 10.7907/8333-3M02
<p>This dissertation consists in effect, of three parts, each involving some aspect of intramolecular vibrational relaxation. The first section contains simple approximate statistical formulas for the density of vibrational and rovibrational states by symmetry type for non-linear molecules. A modified Whitten-Rabinovitch estimate of the density of states by symmetry type for linear molecules is also derived. Sample calculations are given, which serve to demonstrate the accuracy of all formulas given. In the second section, a 4-coordinate model is presented and is used to treat the vibrational energy redistribution in a molecule with a heavy central metal atom. Local group modes are identified using perturbation theory, and their dynamical separation and importance in analyzing energy redistribution is noted. A comparison of classical and quantum calculations on the model system is also given. In the third section, artificial intelligence methods are used to treat the time-evolution of intramolecular quantum dynamics. Comparison is made of several AI search algorithms and of evaluation functions, proposed here, in an application to the study of quantum intramolecular vibrational relaxation. The methods developed are applied to an 11-coordinate heavy central mass problem and are used to treat both vibrational quantum beats and "dissipative" intramolecular energy transfer.</p>https://thesis.library.caltech.edu/id/eprint/7505Studies in dynamics
https://resolver.caltech.edu/CaltechETD:etd-10292007-104923
Authors: {'items': [{'id': 'Wang-Neng-E', 'name': {'family': 'Wang', 'given': 'Neng E.'}, 'show_email': 'NO'}]}
Year: 1995
DOI: 10.7907/j1ch-3v41
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In this thesis, three parts of my work are reported. The first part of the work was done with Prof. Rudy Marcus, the second and third parts of the work were done with Prof. Bill Goddard. Here I would like to summarize the results from each part briefly.
In the first part, we propose doing Scanning Tunneling Microscopy(STM) current calculations with a new model in the spheroidal coordinate system. The tip is modeled as a hyperboloid. The electrostatic potential part of this model is solved exactly. The free electron model of the whole system is also solved exactly.
In the second part, we found that the Nose Canonical Molecular Dynamics, the most commonly used CMD method, leads to the wrong heat capacity for the system and hence is inconsistent with the thermodynamics. To solve this problem, we propose Two Nose variable Dynamics by changing the dimensionality of the Nose variable s and its conjugate [...] from one- to two-dimension.
In the third part, The exact expression for the quantum statistical partition function in the canonical ensemble is given. The physical interpretation of each term for N-particle system is discussed. The new formula is applied to the weakly degenerate quantum ideal case. By analyzing each term in the expansion, it is possible that this canonical partition function can be applied to cases where both quantum correlation effects and particle interactions are important.
https://thesis.library.caltech.edu/id/eprint/4305Quantum Effects in Electron Transfer Reactions and Solvation Dynamics
https://resolver.caltech.edu/CaltechTHESIS:02172022-225929135
Authors: {'items': [{'email': 'xsong@iastate.edu', 'id': 'Song-Xueyu', 'name': {'family': 'Song', 'given': 'Xueyu'}, 'orcid': '0000-0001-5142-4223', 'show_email': 'NO'}]}
Year: 1996
DOI: 10.7907/ejw2-cy95
This thesis focuses on the quantum effects of electron transfer reactions in solutions and solvation dynamics of pure solvent. A prototypical model system, the
Fe⁺² + Fe⁺³ ⇌ Fe⁺³ + Fe⁺² reaction in water, 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 of 9.6, which is significantly smaller than the corresponding values calculated from molecular models which neglect the electronic and vibrational polarization of the solvent. Using an imaginary free energy method, a general formula for the rate valid in all orders of perturbation in electronic coupling is derived for a renormalized classical bath. It is found that the quantum degrees of freedom can be effectively eliminated from the model by renormalizing the electronic coupling matrix element to the first order approximation for the quantum modes. Furthermore, a similar result is obtained for the quantum bath with a better approximation scheme. In application it has been shown that the rate has a nonmonotonic behavior as a function of the coupling matrix element in the inverted region. In the solvent dynamics controlled regime a one-particle Green function method is used to calculate the electron transfer reaction rate with a spin-boson Hamiltonian. A quantum version of Zusman’s result on solvent dynamical effect in electron transfer reactions is obtained for the symmetric case. It is shown that the quantum effect for most of the realistic systems is not significant at room temperature and it would become important for some fast dielectric relaxation solvents like water. In solvation dynamics studies a Gaussian field model is used to obtain the charge density correlation function of the solution in terms of charge density correlation function of the solvent. It then becomes possible to calculate the time-dependent solvation free energy without using the "uniform dielectric approximation." It is found that the nonuniformity in the vicinity of the solute indeed retards the solvation relaxation.https://thesis.library.caltech.edu/id/eprint/14502New Methods for the Study of Intramolecular and Solvent Dynamics
https://resolver.caltech.edu/CaltechTHESIS:02172022-233103988
Authors: {'items': [{'id': 'Mehta-Aseem', 'name': {'family': 'Mehta', 'given': 'Aseem'}, 'show_email': 'NO'}]}
Year: 1997
DOI: 10.7907/75xn-rr09
<p>Some of the fastest processes of relevance to chemical physicists occur on pico to femtosecond timescales. In the following chapters two of such fast processes axe investigated with novel theoretical methods to obtain insight into experimental observations at the molecular level.</p>
<p>One of the major topics of interest in chemical physics has been about energy localization in polyatomic molecules. The "golden rule" formula states that the rate for the intramolecular relaxation of energy (IVR) that is initially localized in one part of the molecule is proportional to the density of states at that energy. Here, a general mechanism of the energy redistribution out of an initially populated "light" or "bright" state is elucidated. It is shown that, for a family of acetylenic molecules, the relaxation is due to a sequence of weak off-resonant directly coupled states rather than all the available states. This mechanism shows how the rates of IVR can be significantly slower than those predicted by a naive application of the "golden rule," since mainly only the initial weak off-resonant couplings govern the rate of IVR.</p>
<p>Another topic that has attracted substantial interest in the chemical physics community is that of solvation. Various heavily applied theories of reaction rates, such as the electron transfer theory, have viewed the solvent as a dielectric continuum. Recent experiments and simulations have shown that the very fast solvation response provides interesting information on the molecular nature of the solvent. Here, a new method for doing molecular dynamics (MD) calculations for solvation is developed. This method uses the reaction field method to obtain the long range potential for a small cluster of molecules rather than using the usual Ewald sum technique with periodic boundary conditions (PBC). It is shown, here, that this method may be used successfully for solvent dynamics simulations. This method may prove superior for such calculations as compared to the PBC approach, since it does not impose an artificial isotropy on the problem as is the case with the PBC calculations.</p>https://thesis.library.caltech.edu/id/eprint/14503On the Theory of Electron Transfer Reactions: Superexchange Coupling and Polar Solvation Dynamics
https://resolver.caltech.edu/CaltechTHESIS:02162022-191638374
Authors: {'items': [{'email': 'cherri@sinica.edu.tw', 'id': 'Hsu-Chao-Ping', 'name': {'family': 'Hsu', 'given': 'Chao-Ping'}, 'orcid': '0000-0002-7187-427X', 'show_email': 'NO'}]}
Year: 1998
DOI: 10.7907/k5yt-g844
<p>A recursion relation is formulated for the Green's function for calculating the effective electron coupling in bridge-assisted electron transfer systems, within the framework of the tight-binding Hamiltonian. The non-perturbative recursion expression relates the Green’s function of a chain bridge to that of a bridge which is one unit less. The method is used to calculate the electronic coupling between a gold electrode and each of the molecules. (η⁵-C₅H₅)Fe(η⁵-C₅H₄)CO₂(CH₂)ₙSH and (η⁵-C₅H₅)Fe(η⁵-C₅H₄)(CH₂)ₙSH (n = 3 to 50). At larger numbers of bridge units, the effective coupling strength shows an exponential decay as the number of methylene 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, such as proteins. Most of the calculated coupling strengths, if converted to rate constants according to a nonadiabatic expression, agree well with the experimental results.</p>
<p>The time-dependent dynamic Stokes shift function, which describes the solvent response to a sudden change in the charge distribution of a solute molecule, is expressed in terms of experimentally measured dielectric dispersion data of the solvent, using a simple dielectric continuum model. The result is applied to photoexcited coumarin 343 in water, and encouraging agreement with the experimental data is obtained. A simple formula is also derived which includes the effect of a pump pulse of finite duration. Such an effect is negligible when the frequency of a 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. To calculate further the time-dependent fluorescence spectral lineshapes, a method is described for incorporating the vibronic transitions of a solute molecule. The intramolecular vibrational relaxation is assumed to be much faster
than the observation delay time. Calculations are made for coumarin 153 in acetonitrile. The results are again in encouraging agreement with experimental spectra. Results are also given for the dynamic Stokes shift in methanol.</p>https://thesis.library.caltech.edu/id/eprint/14500Why molecules look the way they do in STM : a systematic functional group approach
https://resolver.caltech.edu/CaltechTHESIS:10192009-081325550
Authors: {'items': [{'id': 'Claypool-C-L', 'name': {'family': 'Claypool', 'given': 'Christopher L.'}, 'show_email': 'NO'}]}
Year: 1999
DOI: 10.7907/AAWF-HM84
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 sub-molecular 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, allenes, and disulfides. 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. 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, a theoretical model based on perturbation theory has been developed to predict the scanning tunneling microscopy (STM) images of molecules adsorbed on graphite. The model is applicable to a variety of different molecules with reasonable computational effort and provides images that are in qualitative agreement with experimental results. The computations correlate well with the STM data of functionalized alkanes and allow assessment of the structure and orientation of most of the functionalized alkanes that have been studied experimentally. In addition, the computations suggest that the highly diffuse virtual orbitals of the adsorbed molecules, despite being much farther in energy from the Fermi level of the graphite than the occupied orbitals, may play an important role in determining e STM image contrast of such systems.
https://thesis.library.caltech.edu/id/eprint/5304Theory of Ozone Isotopic Effects and Various Electron Transfer Reaction
https://resolver.caltech.edu/CaltechTHESIS:03192014-125137237
Authors: {'items': [{'id': 'Gao-Yi-Qin', 'name': {'family': 'Gao', 'given': 'Yi Qin'}, 'show_email': 'NO'}]}
Year: 2001
DOI: 10.7907/fj7v-ht75
<p>Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.</p>
<p> The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O→+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.</p>
<p>Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform
method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, 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.</p>
<p>Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle,
two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.</p>
https://thesis.library.caltech.edu/id/eprint/8146Electron Transfer at Metal Surfaces
https://resolver.caltech.edu/CaltechETD:etd-03192003-095722
Authors: {'items': [{'email': 'shachi@ncbs.res. in', 'id': 'Gosavi-Shachi-Sharadchandra', 'name': {'family': 'Gosavi', 'given': 'Shachi Sharadchandra'}, 'orcid': '0000-0001-7219-8333', 'show_email': 'NO'}]}
Year: 2003
DOI: 10.7907/KK8A-ZF26
<p>In recent years there has been considerable interest in electrode processes at metal surfaces with alkanethiol monolayers attached to them. One effect of the monolayer is that the electron transfer rate from the redox reagent in solution to the metal (gold or platinum are commonly used) becomes clearly nonadiabatic and the effect of the density of states of the metal on such a rate can be investigated.</p>
<p>We develop a way of writing the wave function of a semi-infinite metal using tight-binding matrix elements and the 'Z-transform', a discrete Laplace transform. Using these k-dependent metal wave functions we calculate the coupling matrix element between the metal and the redox reagent and thus the electron transfer rate constant. We then study the effect of changing the density of electronic states at the Fermi level (DOS) of a metal on the rate of nonadiabatic electron transfer by changing the metal.</p>
<p>The DOS of platinum is about 7.5 times that of gold, the difference being mainly due to the d-band of Pt. Inspite of this difference, the calculated electron transfer rate constant increases only by a factor of about 1.8. 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. Thereby, the rate constant is approximately independent of the density of states in two cases: adiabatic electron transfer and nonadiabatic electron transfer when the extra density of states is due to weakly coupled bands. Our results are in agreement with experiments performed with systems similar to those used in our calculations.</p>
<p>We next employ our method to calculate the temperature dependence of the electronic contribution to the nonadiabatic electron transfer rate constant at metal and semiconductor electrodes. We find that the electronic contribution in metals is proportional to T, and under conditions for the maximum rate constant, that at semiconductor electrodes is also 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 vs. Fermi-Dirac statistics and transfer at the Fermi level, which is far from the band edge, of the metal).</p>
<p>On a different topic, we study the inverse photoemission spectra at metal electrode-liquid interfaces. In such experiments, an electron transfer redox agent was used to inject electrons or holes into a metal and create excited electronic states of the metal. Emission thus occurs in competition with energy loss and radiationless transitions. Some of the excited states decay radiatively and gave a frequency-dependent spectrum. The spectrum may be analysed to probe the electronic structure of the metal above and below its Fermi level. The experimental technique, known in the literature as charge transfer inverse photoemission spectroscopy (CTRIPS), is treated theoretically here.</p>
<p>We give a possible explanation of the data using a model, experimental band structures (from vacuum inverse photemission) and surface states from solution electroreflectance (ER) experiments and propose experiments that could be performed to further clarify the mechanism of electron transfer.</p>https://thesis.library.caltech.edu/id/eprint/1004Theoretical Studies of Single Molecule Biophysical Systems and Photochemical Ensembles
https://resolver.caltech.edu/CaltechETD:etd-09062007-233423
Authors: {'items': [{'email': 'meher@caltech.edu', 'id': 'Ayalasomayajula-Meher-Kiran-Prakash', 'name': {'family': 'Ayalasomayajula', 'given': 'Meher Kiran Prakash'}, 'show_email': 'NO'}]}
Year: 2008
DOI: 10.7907/5D2K-7H81
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
The focus of the present thesis is on theoretical analysis to understand the experimental results from three quite different systems - enzymes, RNA hairpins and nitrous oxide (N2O). Some experiments on single enzymes showed very unusual data: in separate experiments the fluctuations in catalysis rate ([...]) and fluorescence lifetime ([...]) of chromophore in single enzymes showed long-lasting autocorrelations, represented by a stretched exponential and power-law, respectively. With the aim of interpreting the origin of these fluctuations, we proposed a formulation based on fluctuations in electrostatic interaction energy ([...]) at the active site in the enzyme leading to the fluctuations in the various observables. We developed relations between the autocorrelation functions of [...], [...], spectral diffusion ([...]) and the radiative component of fluorescence lifetime ([...]). It was pointed out that the relation between [...] and [...], seen experimentally and modeled theoretically by using the relation noted above, is a dynamic analog of the solvatochromism concept used in the catalysis of organic reactions by solvent. The estimation of fluctuations in electrostatic interactions on the milliseconds to seconds time scale by computational methods is not possible, which are typically limited to tens of nanoseconds. To calculate the autocorrelation of electrostatic interactions and to compare them with experiments, we used the frequency dependent dielectric response of proteins and related it to the autocorrelation of [...]. Based on this formulation, we find a good agreement between the single molecule data on the enzyme candida antarctica lipase B and the calculation using dielectric response data on the enzyme. In single molecule data from other enzymes for which [...] is not yet available, we have predictions based on a commonly observed functional form of [...] for other proteins.
Single molecule experiments on RNA hairpins were used to test a nonequilibrium statistical physics result - Crooks' theorem. Crooks' theorem is about an exact equality relating the probability distributions of work done (W) on a system by varying an external parameter in the forward and reverse directions in a predetermined way. Usually in the single molecule experiments this predetermined variation is a constant rate ([...]) of increase or decrease of the external force for all runs of the experiment. Our study focuses on the relevance of the RNA hairpin unfolding experiments to the theorem. The unfolding of the molecule leads to a drop in the externally controlled force on the molecule, a condition which is not suited to the existing derivations of Crooks' theorem. An alternative interpretation of the experimental unfolding and refolding data using a phenomenological force-dependent distortion of activation barriers is provided to gain insight into the data on the probability distribution of work done during unfolding, refolding corresponding to different rates of change of force. This interpretation shows that the crossing of the unfolding and refolding work distributions which happens at the same value of W for all [... is a necessary but not sufficient condition to verify the theorem.
The experimental data on UV photodissociation of the greenhouse gas N2O and the associated isotope effects are important from the perspective of atmospheric interest. The calculations in the literature to model the photodissociation observations are of two kinds - some are computationally intensive quantum mechanical methods using wave packet propagation and the others are based on empirical calculations. The two different calculations we present, based on two different variants of the 'multidimensional reflection principle' maintain the simplicity of computation, while using the available ab initio data on the molecule for the potential energy surfaces and the transition dipole moments. In one of the calculations, the absorption cross section was broadened empirically to get agreement with the absorption data and the results were then used to make calculations of isotopologue fractionation. This broadening was also needed in a wave packet propagation calculation. In a later calculation, without introducing the broadening factor, the results were compared only on one side of the absorption cross section, where the isotopic fractionation measurements are available. Using these two methods, the fractionation of heavier isotopologues of N2O with respect to the most abundant isotopologue [...] were calculated and compared with the experiments. A simple relation between the fractionations of [...] and [...] was observed in the results from our calculations. A perturbation theoretical result was used to derive this relationship, which is independent of the detailed calculations required for each of the isotopologues individually.https://thesis.library.caltech.edu/id/eprint/3367Isotope Effects in Chemical Processes of Atmospheric Interest
https://resolver.caltech.edu/CaltechETD:etd-01222009-173227
Authors: {'items': [{'email': 'cwc@caltech.edu', 'id': 'Chen-Wei-Chen', 'name': {'family': 'Chen', 'given': 'Wei-Chen'}, 'show_email': 'YES'}]}
Year: 2009
DOI: 10.7907/WCH2-W090
<p>The thesis is focused on the theoretical study of the isotope effects in three atmospheric reactions, the CO+OH reaction, the photolysis of N₂O, and the ozone formation. The CO+OH reaction is investigated by using both Rice-Ramsperger-Kassel-Marcus theory and its nonstatistical modification, which was prompted by existing molecular-beam data on incomplete intramolecular energy transfer in the HOCO* intermediate. The resulting calculations show reasonable agreement with most experimental data, except the O isotope effect. Two predictions are made: the temperature dependence of the OD+CO reaction; and the rate constant k<sub>v</sub> decreasing with increasing CO vibrational quantum number v from v = 0 to v = 1. In both experiments and our calculation, the kinetic oxygen isotope effect is different from the expected value (i.e. the mass-dependent slope), which may be due to the H-tunneling. An experiment that avoids a possible role of vibrationally excited OH radicals as reactants in the O isotope effect is also suggested to remove the discrepancy in the O isotope effect between the experiments and calculations.</p>
<p>The UV photolysis of the greenhouse gas N₂O and its isotope effects are important in atmospheric chemistry. Based on the multidimensional reflection principle using the available ab initio data on the molecule for the potential energy surfaces and the transition dipole moments, we provide an accurate but not computationally intensive method in obtaining the absorption cross section. The present calculated fractionation gives good agreement with the experimental absorption cross section in the low-energy region, where the experimentally observed isotopic fractionation occurs. We also suggest a single effective mass, a linear combination of two main coordinates for the photolysis, to determine the slope of a multi-element isotope plot and to yield approximate agreement between the experimental data and a "mass-dependent" fractionation, which range from 0.47 to 3.28.</p>
<p>A modified ab initio potential energy surface 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)]. This result showed that they are relatively insensitive to the properties of the PES.</p>
https://thesis.library.caltech.edu/id/eprint/285Nonlinear Dynamics of Nanoscale Systems
https://resolver.caltech.edu/CaltechTHESIS:05202011-154531397
Authors: {'items': [{'email': 'nhodas@gmail.com', 'id': 'Hodas-Nathan-Oken', 'name': {'family': 'Hodas', 'given': 'Nathan Oken'}, 'show_email': 'NO'}]}
Year: 2011
DOI: 10.7907/8CK3-8F45
This work builds theoretical tools to better understand nanoscale systems, and it ex- plores experimental techniques to probe nanoscale dynamics using nonlinear optical microscopy. In both the theory and experiment, this work harnesses nonlinearity to explore new boundaries in the ongoing attempts to understand the amazing world that is much smaller than we can see. In particular, the first part of this work proves the upper-bounds on the number and quality of oscillations when the sys- tem in question is homogeneously driven and has discrete states, a common way of describing nanoscale motors and chemical systems, although it has application to networked systems in general. The consequences of this limit are explored in the context of chemical clocks and limit cycles. This leads to the analysis of sponta- neous oscillations in GFPmut2, where we postulate that the oscillations must be due to coordinated rearrangement of the beta-barrel. Next, we utilize nonlinear optics to probe the constituent structures of zebrafish muscle. By comparing experimental observations with computational models, we show how second harmonic generation differs from fluorescence for confocal imaging. We use the wavelength dependence of the second harmonic generation conversion efficiency to extract information about the microscopic organization of muscle fibers, using the coherent nature of second ix harmonic generation as an analytical probe. Finally, existing experiments have used a related technique, sum-frequency generation, to directly probe the dynamics of free OH bonds at the water-vapor boundary. Using molecular dynamic simulations of the water surface and by designating surface-sensitive free OH bonds on the water surface, many aspects of the sum-frequency generation measurements were calcu- lated and compared with those inferred from experiment. 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 results provide insight into the microscopic dynamics at the air-water interface and have useful application in the field of on-water catalysis.https://thesis.library.caltech.edu/id/eprint/6413Studies in Recombination and Dissociation Reactions for Collisional Energy Transfer and Electron Transfer of Nanocrystals and Dye Molecules
https://resolver.caltech.edu/CaltechTHESIS:04132012-142451725
Authors: {'items': [{'email': 'zhu.zhaoyan@gmail.com', 'id': 'Zhu-Zhaoyan', 'name': {'family': 'Zhu', 'given': 'Zhaoyan'}, 'show_email': 'NO'}]}
Year: 2012
DOI: 10.7907/C23D-SR83
This dissertation consists of three parts. In the first part, the effect of the large impact parameter near-elastic peak of collisional energy transfer for unimolecular dissociation/bimolecular recombination reactions and deviation from equilibrium case is studied. To this end the conventional single exponential model, a bi-exponential 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. A theory is developed for the population distribution as a function of the energy E of a dissociating model, and used to calculate the three-body low pressure recombination rate constant. In the second part, the electron transfer process in the single quantum dot fluorescence blinking phenomenon is studied. The DCET (diffusion controlled electron transfer) model has been modified to explain the exponential cutoff of the power law time distribution of the bright state and the quadratic dependence of the exponential tail on the excitation intensity. Based on ensemble measurements it is proposed that an exponential tail for the dark state time distribution for long time experiments exists for single trajectory experiments. In the last part, we develop a general MLE (maximum likelihood estimation) method to analyze experimental data with a potential distribution of power law form which can be extended to a power law with an exponential tail and more generally, many other distribution forms.https://thesis.library.caltech.edu/id/eprint/6933Vibrational Pooling and Constrained Equilibration on Surfaces
https://resolver.caltech.edu/CaltechTHESIS:09302013-141151012
Authors: {'items': [{'email': 'boneye@gmail.com', 'id': 'Boney-Evans-T-D', 'name': {'family': 'Boney', 'given': 'Evans T. D.'}, 'show_email': 'YES'}]}
Year: 2014
DOI: 10.7907/JM2J-XX84
<p>In this thesis, 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 so 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<sub>e</sub> and ω<sub>e</sub>χ<sub>e</sub>) and the surface (ω<sub>D</sub> and T). Possible applications and relation to the Treanor gas phase treatment are discussed. Unlike the solid phase system, the gas phase system has no Debye-constraining maximum. We discuss the possible distributions for arbitrary N-conserving diatom-surface pairs, and include application to H:Si(111) as an example.</p>
<p>Computations are presented to describe and analyze the high levels of infrared laser-induced vibrational excitation of a monolayer of absorbed <sup>13</sup>CO on a NaCl(100) surface. 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. Nonetheless, the full kinetic calculation is necessary to capture the result in detail.</p>
<p>We discuss the one-to-one relationship between N and γ and the examine the state space of the new distribution function for varied γ. We derive the Free Energy, F = NγkT − kTln(∑P<sub>n</sub>), and effective chemical potential, μn ≈ γkT, for the vibrational pool. We also find the anti correlation of neighbor vibrations leads to an emergent correlation that appears to extend further than nearest neighbor.</p>
https://thesis.library.caltech.edu/id/eprint/7967Theory of Dynamical Processes in Semiconductor Quantum Dots
https://resolver.caltech.edu/CaltechTHESIS:08102016-154641607
Authors: {'items': [{'email': 'donaldhong@gmail.com', 'id': 'Hong-Yun-Hua', 'name': {'family': 'Hong', 'given': 'Yun-Hua'}, 'orcid': '0000-0002-5868-8827', 'show_email': 'NO'}]}
Year: 2017
DOI: 10.7907/Z99G5JT3
The focus of this dissertation is on the theory of the electronic dynamical processes in semiconductor quantum dots (QDs). The first part of the dissertation introduces the calculation method of electronic eigenstates used through the dissertation, the sp<sup>3</sup>s<sup>*</sup> tight-binding (TB) method, and the application of the symmetry-adapted linear combination (SALC) of atomic orbitals to the TB method. The combination of the SALC and TB method reduces the computational load, and generates reliable electronic eigenstates and eigenvalues of Wurtzite CdSe QDs. The second part of the dissertation uses the calculated eigenstates and eigenvalues of CdSe QDs, whose band gap states are removed by a passivation layer, to calculate various kinds of physical properties, such as the structure, the permanent dipole moment, the band gap, the molecular orbitals, the density of states (DOS), and the absorption spectrum. These calculated results are compared with the respective experimental measurements in further discussions. The last part of the dissertation focuses on the studies of the size-dependent trend of the Auger electron-hole recombination process that causes the semiconductor QDs to remain in the dark state, including the cases of a negative trion, a positive trion, and a biexciton, in semiconductor QDs. The rates of these Auger processes are expressed in the form of Fermi’s golden rule, where the Coulombic interaction between the two electrons is the operator. Although the calculated results shows larger size dependence than that of the experimental findings, the literature of recent experiments and theories points out potential remedies to the discrepancy by modifying the current computational setting and theory in the dissertation.https://thesis.library.caltech.edu/id/eprint/9899