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which suggests that the coupling between two electronic states becomes large when they
are nearly degenerate. In such situations, the adiabatic approximation breaks down, and
transitions between different electronic states become possible.
5.2.2 Crossing location and minimization
Although the set of equations (5.6) is infinite, the energy denominator in (5.10) suggests
that the coupling between only two electronic states needs to be taken into account in the
regions of proximity of their PESs, and the couplings with other states can be neglected.
The description of conical intersections and the algorithms for locating MECPs are
based on a first order perturbative treatment of the electronic Schr¨odinger equation in
the vicinity of the intersection8, 23. Recently, second-order treatment that accounts for
the curvature of the seam, in addition to the first-order linear terms, has been reported24.
At the intersection point R, the electronic Hamiltonian has the following matrix
form in the so-called “crude adiabatic basis” ffi(r;R0)g, eigenstates of the electronic
Hamiltonian at a nearby point R0:
He(R) =
0
BB@
H11 H12
H12 H22
1
CCA
; (5.11)
where Hi j(R) =
fi(r;R0) jHe(R)jfj(r;R0)
r.
After finding the eigenvalues of the Hamiltonian (5.11), one can readily write the
conditions on the matrix elements that ensure that the states are degenerate:
8>><
>>:
H11H22 = 0;
H12 = 0:
(5.12)
140
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 150 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | which suggests that the coupling between two electronic states becomes large when they are nearly degenerate. In such situations, the adiabatic approximation breaks down, and transitions between different electronic states become possible. 5.2.2 Crossing location and minimization Although the set of equations (5.6) is infinite, the energy denominator in (5.10) suggests that the coupling between only two electronic states needs to be taken into account in the regions of proximity of their PESs, and the couplings with other states can be neglected. The description of conical intersections and the algorithms for locating MECPs are based on a first order perturbative treatment of the electronic Schr¨odinger equation in the vicinity of the intersection8, 23. Recently, second-order treatment that accounts for the curvature of the seam, in addition to the first-order linear terms, has been reported24. At the intersection point R, the electronic Hamiltonian has the following matrix form in the so-called “crude adiabatic basis” ffi(r;R0)g, eigenstates of the electronic Hamiltonian at a nearby point R0: He(R) = 0 BB@ H11 H12 H12 H22 1 CCA ; (5.11) where Hi j(R) = fi(r;R0) jHe(R)jfj(r;R0) r. After finding the eigenvalues of the Hamiltonian (5.11), one can readily write the conditions on the matrix elements that ensure that the states are degenerate: 8>>< >>: H11H22 = 0; H12 = 0: (5.12) 140 |
