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Multi-reference configuration interaction
In MRCI methods, the wave function is expanded as:
YMRCI
=
NCSF
å
L=1
cL jyLi : (1.22)
The basis functions of the expansion fjyLig are configuration state functions (CSFs).
The CSFs, which are linear combinations of Slater determinants, are eigenfunctions of
spin operators and have a correct spatial symmetry77. The MRCI energies and wave
functions are obtained by diagonalizing the Hamiltonian in the basis of the CSFs.
MRCI calculations begin by determining zero-order wave functions and MOs in a
CASSCF calculation. The CASSCF wave function includes configurations created by
all possible excitations within an active orbital space. The coefficients of the expan-sion
(1.22), cL, and the MOs are variationally optimized. Dynamical correlation is
then described by MRCI by including single and double excitations from the refer-ence
CASSCF configurations. The MRCI method is very accurate, provided that all the
important configurations are included in the expansion. This requirement is easily satis-fied
for small molecules, but as the size of the system increases, the expansion becomes
prohibitively large, and truncations are necessary. The Davidson correction78 provides
a simple formula for evaluating the contribution of the missing quadruple excitations to
the energy computed with configuration interaction with up to double excitations.
Scaled opposite-spin CIS(D)
In the same manner as SOS-MP2 is introduced for correcting the ground state energy,
SOS-CIS(D) is designed for excitation energies79. The computational scaling of SOS-CIS(
D) is only O(N4), which is a significant improvement over the O(N5) scaling of
17
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 27 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | Multi-reference configuration interaction In MRCI methods, the wave function is expanded as: YMRCI = NCSF å L=1 cL jyLi : (1.22) The basis functions of the expansion fjyLig are configuration state functions (CSFs). The CSFs, which are linear combinations of Slater determinants, are eigenfunctions of spin operators and have a correct spatial symmetry77. The MRCI energies and wave functions are obtained by diagonalizing the Hamiltonian in the basis of the CSFs. MRCI calculations begin by determining zero-order wave functions and MOs in a CASSCF calculation. The CASSCF wave function includes configurations created by all possible excitations within an active orbital space. The coefficients of the expan-sion (1.22), cL, and the MOs are variationally optimized. Dynamical correlation is then described by MRCI by including single and double excitations from the refer-ence CASSCF configurations. The MRCI method is very accurate, provided that all the important configurations are included in the expansion. This requirement is easily satis-fied for small molecules, but as the size of the system increases, the expansion becomes prohibitively large, and truncations are necessary. The Davidson correction78 provides a simple formula for evaluating the contribution of the missing quadruple excitations to the energy computed with configuration interaction with up to double excitations. Scaled opposite-spin CIS(D) In the same manner as SOS-MP2 is introduced for correcting the ground state energy, SOS-CIS(D) is designed for excitation energies79. The computational scaling of SOS-CIS( D) is only O(N4), which is a significant improvement over the O(N5) scaling of 17 |
