Phd records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:03:48 +0000The excitation operator method and the valence excited states of ethylene
https://resolver.caltech.edu/CaltechTHESIS:09272010-083324433
Authors: {'items': [{'id': 'Dunning-T-H', 'name': {'family': 'Dunning', 'given': 'Thomas Harold'}, 'show_email': 'NO'}]}
Year: 1970
DOI: 10.7907/RJ3Z-DE73
The problem of describing the electronic excited states of an atomic or molecular system can be reduced to one of finding a form for an operator A^+(E) such that it satisfies the following equation:
[Ĥ, A^+(E)] | 0> = ΔE A^+(E) | 0>.
Four approximations to the excitation operator, A^+(E), have been considered: (a) the single transition approximation, corresponding to excitation into virtual orbitals, (b) the improved single transition approximation which allows for the self-consistent field adjustment of the virtual orbital, (c) the Tamm-Dancoff approximation, corresponding to selective configuration interaction in the excited state and (d) the random-phase approximation which attempts to take into account correlation in both ground and excited states.
Analyzing the excitation operator method in terms of the approximations to the excitation operator listed above, we found that the correlation does not always enter in the ground and excited states in a particularly balanced manner and that self-consistent field changes in the core are neglected. In addition, the strong "mixing" of certain doubly excited configurations into the ground state wavefunction, such as (π*απ*β) in ethylene, is shown to lead to a number of problems in the random-phase approximation, e.g., an instability in the triplet equations.
The excitation operator approach is illustrated by ab initio calculations on a number of valence excited states of the ethylene molecule. These calculations indicate that the lowest singlet π→π* state of ethylene is not a valence state as previously assumed, but that it is significantly more diffuse, e.g., in the improved single transition approximation the <z^2> for the π*-orbital in the singlet state is 26.3 a.u. compared to 2.8 a.u. in the corresponding triplet state. This behavior is a consequence of the ionic nature of the wavefunction of the singlet state and, thus, is expected to be characteristic of such states in general. We find that σ-π correlation, as included in the above approximations to the excitation operator, does not play an essential role in the description of the excited states, although its effect on the charge distribution of the singlet π→π*state is substantial.https://thesis.library.caltech.edu/id/eprint/6056