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degeneracy of the states, and we can define a function Ui : S ! R, which we call the
intersection seam.
The sets S and R3N are not completely independent. The Neumann–Wigner theo-rem3
(the noncrossing rule) states that two conditions have to be imposed on the Hamil-tonian
in order for two states of the same symmetry to be degenerate. In diatomic
molecules with only one internal degree of freedom, PES of the same symmetry may not
intersect (hence “noncrossing rule”). In larger molecules the rule limits the dimension-ality
of the intersection hyperline to M2 where M is the number of internal degrees of
freedom. For states of different symmetry or spin, there is only one condition (degener-acy),
and therefore such crossings are possible even in diatomic molecules. Section 5.2
presents more details on the theory of PES intersections.
PES crossings occur often in real systems4. Because they allow the system to start
on one state’s PES and continue on another’s, they facilitate radiationless transitions
between electronic states. In Chapter 5 we present an implementation of algorithms for
locating and optimizing intersection seams and demonstrate their work with examples.
1.1.1 Methods for the ground electronic state
The ground state is of particular interest in electronic structure theory because chemical
reactions mostly occur on the lowest-energy PES. One of the conventional approaches to
approximately solve for the ground state energy is to use Hartree–Fock method, which
employs variational principle and is based on the mean-field description of electron–
electron interactions. Using a set of one-electron basis set functions, one solves a system
of Roothaan equations self-consistently to obtain molecular orbitals and their energies.
Hartree–Fock method can be roughly described as taking the following steps. The
reader is encouraged to consult electronic structure texts5, 6 for more details.
4
Object Description
| Title | Development of predictive electronic structure methods and their application to atmospheric chemistry, combustion, and biologically relevant systems |
| Author | Epifanovskiy, Evgeny |
| Author email | epifanov@usc.edu; epifanov@usc.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Chemistry |
| School | College of Letters, Arts and Sciences |
| Date defended/completed | 2011-03-21 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-04-28 |
| Advisor (committee chair) | Krylov, Anna I. |
| Advisor (committee member) |
Wittig, Curt Johnson, Clifford |
| Abstract | This work demonstrates electronic structure techniques that enable predictive modeling of the properties of biologically relevant species. Chapters 2 and 3 present studies of the electronically excited and detached states of the chromophore of the green fluorescent protein, the mechanism of its cis-trans isomerization, and the effect of oxidation. The bright excited ππ∗ state of the chromophore in the gas phase located at 2.6 eV is found to have an autoionizing resonance nature as it lies above the electron detachment level at 2.4 eV. The calculation of the barrier for the ground-state cis-trans isomerization of the chromophore yields 14.8 kcal/mol, which agrees with an experimental value of 15.4 kcal/mol; the electronic correlation and solvent stabilization are shown to have an important effect. In Chapter 3, a one-photon two-electron mechanism is proposed to explain the experimentally observed oxidative reddening of the chromophore. Chapter 4 considers the excited states of uracil. It demonstrates the role of the one-electron basis set and triples excitations in obtaining the converged values of the excitation energies of the nπ∗ and ππ∗ states. The effects of the solvent and protein environment are included in some of the models.; Chapter 5 describes an implementation of the algorithm for locating and exploring intersection seams between potential energy surfaces. The theory is illustrated with examples from atmospheric and combustion chemistry. |
| Keyword | electronic structure theory; coupled clusters theory; equation of motion theory; organic chromophore; green fluorescent protein; uracil |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3801 |
| Contributing entity | University of Southern California |
| Rights | Epifanovskiy, Evgeny |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Epifanovskiy-4557 |
| Archival file | uscthesesreloadpub_Volume14/etd-Epifanovskiy-4557.pdf |
Description
| Title | Page 14 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | degeneracy of the states, and we can define a function Ui : S ! R, which we call the intersection seam. The sets S and R3N are not completely independent. The Neumann–Wigner theo-rem3 (the noncrossing rule) states that two conditions have to be imposed on the Hamil-tonian in order for two states of the same symmetry to be degenerate. In diatomic molecules with only one internal degree of freedom, PES of the same symmetry may not intersect (hence “noncrossing rule”). In larger molecules the rule limits the dimension-ality of the intersection hyperline to M2 where M is the number of internal degrees of freedom. For states of different symmetry or spin, there is only one condition (degener-acy), and therefore such crossings are possible even in diatomic molecules. Section 5.2 presents more details on the theory of PES intersections. PES crossings occur often in real systems4. Because they allow the system to start on one state’s PES and continue on another’s, they facilitate radiationless transitions between electronic states. In Chapter 5 we present an implementation of algorithms for locating and optimizing intersection seams and demonstrate their work with examples. 1.1.1 Methods for the ground electronic state The ground state is of particular interest in electronic structure theory because chemical reactions mostly occur on the lowest-energy PES. One of the conventional approaches to approximately solve for the ground state energy is to use Hartree–Fock method, which employs variational principle and is based on the mean-field description of electron– electron interactions. Using a set of one-electron basis set functions, one solves a system of Roothaan equations self-consistently to obtain molecular orbitals and their energies. Hartree–Fock method can be roughly described as taking the following steps. The reader is encouraged to consult electronic structure texts5, 6 for more details. 4 |
