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(i) RI decomposed integrals; (ii) Cholesky decomposed integrals; (iii) using localized
MOs; (iv) using frozen natural orbitals (FNO)23.
HOSVD decomposition. There are multiple ways to define SVD for more than two
dimensions. In this study we use the Tucker decomposition as high-order SVD
A =
Rå
t1=1
Rå
t2=1
Rå
t3=1
Rå
t4=1
g(t1; t2; t3; t4)a(w; t1)a(x; t2)a(y; t3)a(z; t4) (6.5)
This form assumes a multidimensional core which is expanded by matrices a(x; t).
R is the rank of Tucker decomposition. Because the core has the same dimensionality
as the original tensor, the number of parameters in this decomposition does not have a
reduced scaling. In the equation above, even after the reduction of the rank, the number
of parameters grows as O(n4). Therefore, an improvement is required to use Tucker
decomposition for reduced-scaling methods.
TT decomposition. In the TT decomposition, a target tensor A(w;x;y; z) is represented
as
A = å
a1a2a3a4
awa
1ax
a1a2ay
a2a3az
a3 (6.6)
TT decomposition involves three-index tensors at most, thereby enabling reduced-scaling
representation of higher-order tensors with appropriate rank reduction. In addi-tion,
the decomposition algorithm is based on partial SVD of unfolding matrices, which
is better positioned to solve the rank reduction problem than the iterative algorithms
used in CP decomposition.
* * *
166
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 176 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | (i) RI decomposed integrals; (ii) Cholesky decomposed integrals; (iii) using localized MOs; (iv) using frozen natural orbitals (FNO)23. HOSVD decomposition. There are multiple ways to define SVD for more than two dimensions. In this study we use the Tucker decomposition as high-order SVD A = Rå t1=1 Rå t2=1 Rå t3=1 Rå t4=1 g(t1; t2; t3; t4)a(w; t1)a(x; t2)a(y; t3)a(z; t4) (6.5) This form assumes a multidimensional core which is expanded by matrices a(x; t). R is the rank of Tucker decomposition. Because the core has the same dimensionality as the original tensor, the number of parameters in this decomposition does not have a reduced scaling. In the equation above, even after the reduction of the rank, the number of parameters grows as O(n4). Therefore, an improvement is required to use Tucker decomposition for reduced-scaling methods. TT decomposition. In the TT decomposition, a target tensor A(w;x;y; z) is represented as A = å a1a2a3a4 awa 1ax a1a2ay a2a3az a3 (6.6) TT decomposition involves three-index tensors at most, thereby enabling reduced-scaling representation of higher-order tensors with appropriate rank reduction. In addi-tion, the decomposition algorithm is based on partial SVD of unfolding matrices, which is better positioned to solve the rank reduction problem than the iterative algorithms used in CP decomposition. * * * 166 |
