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The trivial CP decomposition is obtained as follows: the first representing vector
codes the index of the first dimension as a unit vector, the second one does the same
for the second dimension, and the last representing vector contains the values corre-sponding
to such multi-index. Obviously, the rank of such decomposition is n3 (for the
two-electron integrals), and the storage requirements (R = n3 sets of four n-dimensional
vectors need to be stored) are increased relative to the full four-index tensor (n4 ele-ments).
However, if the rank can be significantly reduced, then the storage requirements
(4 n R) of the decomposed tensor can become much smaller and linear scaling can, in
principle, be achieved.
Recently, an efficient (and easily parallelizable) rank-reduction algorithm (based on
the accelerated gradient method) have been developed by Hackbusch and coworkers12
and applied to two-electron integrals and MP2 amplitudes. They demonstrated that
ranks of these basic quantities can be significantly reduced by this algorithm giving rise
to n1:2n2:5 depending on the thresholds used. The scaling of their algorithm depends
on the ratio of the initial and final ranks. Thus, the cost of the rank reduction step
can be decreased if one starts with a representation which is more compact than the
trivial decomposition. The authors12 suggested that using RI or Cholesky decomposed
integrals as a starting point of the rank reduction procedure can considerably increase
the efficiency of this most time-consuming step.
Once the integrals are represented in the CP format, the contractions with any two-index
tensors (MO coefficients C or T1 amplitudes) can be trivially performed at the
163
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 173 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | The trivial CP decomposition is obtained as follows: the first representing vector codes the index of the first dimension as a unit vector, the second one does the same for the second dimension, and the last representing vector contains the values corre-sponding to such multi-index. Obviously, the rank of such decomposition is n3 (for the two-electron integrals), and the storage requirements (R = n3 sets of four n-dimensional vectors need to be stored) are increased relative to the full four-index tensor (n4 ele-ments). However, if the rank can be significantly reduced, then the storage requirements (4 n R) of the decomposed tensor can become much smaller and linear scaling can, in principle, be achieved. Recently, an efficient (and easily parallelizable) rank-reduction algorithm (based on the accelerated gradient method) have been developed by Hackbusch and coworkers12 and applied to two-electron integrals and MP2 amplitudes. They demonstrated that ranks of these basic quantities can be significantly reduced by this algorithm giving rise to n1:2n2:5 depending on the thresholds used. The scaling of their algorithm depends on the ratio of the initial and final ranks. Thus, the cost of the rank reduction step can be decreased if one starts with a representation which is more compact than the trivial decomposition. The authors12 suggested that using RI or Cholesky decomposed integrals as a starting point of the rank reduction procedure can considerably increase the efficiency of this most time-consuming step. Once the integrals are represented in the CP format, the contractions with any two-index tensors (MO coefficients C or T1 amplitudes) can be trivially performed at the 163 |
