Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2012
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| Schlagworte: | |
| Online-Zugang: | kostenfrei https://nbn-resolving.org/urn:nbn:de:bvb:19-152656 Inhaltsverzeichnis |
| Beschreibung: | X, 133 S. |
Internformat
MARC
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| 100 | 1 | |a Clin, Lucien Cyril |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory |c von Lucien Cyril Clin |
| 264 | 1 | |c 2012 | |
| 300 | |a X, 133 S. | ||
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| 502 | |a München, Univ., Diss., 2012 | ||
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| 912 | |a ebook | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025715285 | ||
Datensatz im Suchindex
| _version_ | 1804150053400477696 |
|---|---|
| adam_text | IMAGE 1
C O N T E N T S
1 I N T R O D U C T I O N 1
2 FUNDAMENTALS 5
2.1 T H E SCHRODINGER EQUATION 6
2.2 THE BORN-OPPENHEIMER APPROXIMATION 6
2.3 T H E HARTREE-FOCK METHOD 7
2.3.1 HARTREE-FOCK THEORY 8
2.3.2 LCAO AND THE ROOTHAAN-HALL EQUATION 10
2.3.3 SYMMETRIC ORTHONORMALIZATION 11
2.3.4 THE FOCK MATRIX AND THE HARTREE-FOCK ENERGY 12
2.3.5 THE SELF-CONSISTENT FIELD METHOD 13
2.4 T H E DENSITY OPERATOR AND MATRIX 14
2.5 LINEAR SCALING HARTREE-FOCK 16
2.5.1 INTEGRAL SCREENING AND DIRECT SCF 17
2.5.2 DENSITY-MATRIX BASED HARTREE-FOCK 17
2.5.3 LINEAR SCALING FOCK MATRIX CONSTRUCTION 18
3 E L E C T R O N CORRELATION 2 1
3.1 CONFIGURATION INTERACTION AND COUPLED CLUSTER 22
3.2 T H E RANDOM PHASE APPROXIMATION 23
3.3 MANY-BODY PERTURBATION THEORY 24
3.3.1 MTFLLER-PLESSET PERTURBATION THEORY 25
3.3.2 SECOND ORDER M0LLER-PLESSET THEORY (MP2) 26
3.3.3 PARAMETRIZED MP2 27
3.4 LOCAL CORRELATION METHODS 27
3.4.1 ORBITAL LOCALIZATION METHODS 28
3.4.2 LOCAL MP2 30
3.5 EXPLICITLY CORRELATED METHODS 31
VII
HTTP://D-NB.INFO/103245122X
IMAGE 2
4 LAPLACE-TRANSFORM M0LLER-PLESSET PERTURBATION T H E O R Y 3 3
4.1 LAPLACE-TRANSFORM MP2 33
4.1.1 ORBITAL INVARIANCE AND RELATION T O LOCAL MP2 36
4.1.2 RELATION T O LYAPUNOV EQUATIONS 37
4.2 ATOMIC-ORBITAL M P THEORY (AO-MP) 38
4.2.1 PSEUDO-DENSITY MATRICES AND OPERATORS 39
4.2.2 THE M P N ENERGY AS A FUNCTIONAL OF THE DENSITY MATRIX 40
5 CHOLESKY D E C O M P O S E D D E N S I T I E S IN M P 2 4 1
5.1 CHOLESKY-DECOMPOSED PSEUDO-DENSITY MATRICES (CDD-MP2) 41
5.1.1 CHOLESKY DECOMPOSITION 43
5.1.2 CDD AS LOCALIZED PSEUDO-MO 43
5.1.3 INTEGRAL SCREENING 44
5.2 IMPLEMENTATION OF CDD-MP2 47
5.2.1 THE CHOLESKY DECOMPOSITION ALGORITHM 48
5.2.2 SCREENING PREREQUISITES 50
5.2.3 EXTERNAL SCREENING FOR F T I 51
5.2.4 INTERNAL SCREENING FOR HTI 52
5.2.5 FORMATION OF THE HTI 54
5.2.6 LAST TRANSFORMATIONS T O F T I 54
5.2.7 CONTRACTION T O MP2 ENERGY 56
5.3 RESULTS AND DISCUSSION 56
5.3.1 MATRIX SPARSITIES 57
5.3.2 INTEGRAL NUMBERS AND ACCURACY 58
5.3.3 TIMINGS 61
5.3.4 CONCLUSION 65
6 R E S O L U T I O N O F T H E IDENTITY C D D - M P 2 8 1
6.1 RESOLUTION OF THE IDENTITY AND DENSITY FITTING 81
6.2 THE RI-CDD-MP2 ALGORITHM 83
6.3 OMP PARALLELIZATION 84
6.4 RESULTS AND DISCUSSION 85
6.4.1 TIMINGS 85
6.4.2 ACCURACY 86
6.4.3 PARALLEL RI-CDD-MP2 88
6.4.4 CONCLUSION 90
VIII
IMAGE 3
CONTENTS
7 M E T H O D SPECIFIC CHOLESKY D E C O M P O S I T I O N 1 0 3
7.1 DECOMPOSITIONS OF THE ERI MATRIX 103
7.1.1 RESOLUTION OF THE IDENTITY 104
7.1.2 CHOLESKY DECOMPOSITION 104
7.1.3 TENSOR APPROXIMATION 105
7.2 METHOD SPECIFIC CHOLESKY DECOMPOSITION (MSCD) 106
7.2.1 TECHNICAL DETAILS 108
7.2.2 RESULTS AND DISCUSSION 108
8 CONCLUSION A N D O U T L O O K 1 1 1
A E X P O N E N T I A L L Y W E I G H T E D E N E R G Y DIFFERENCES IN M
P 2 1 1 7
B KRONECKER P R O D U C T A P P R O X I M A T I O N O F E R I 1 2 1
C LIST O F ABBREVIATIONS 1 2 3
D LIST O F A C A D E M I C TEACHERS 1 3 3
I X
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| spelling | Clin, Lucien Cyril Verfasser aut Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory von Lucien Cyril Clin 2012 X, 133 S. txt rdacontent n rdamedia nc rdacarrier München, Univ., Diss., 2012 (DE-588)4113937-9 Hochschulschrift gnd-content Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:19-152656 http://edoc.ub.uni-muenchen.de/15265/ Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:19-152656 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025715285&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Clin, Lucien Cyril Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory |
| subject_GND | (DE-588)4113937-9 |
| title | Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory |
| title_auth | Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory |
| title_exact_search | Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory |
| title_full | Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory von Lucien Cyril Clin |
| title_fullStr | Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory von Lucien Cyril Clin |
| title_full_unstemmed | Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory von Lucien Cyril Clin |
| title_short | Cholesky decomposed density matrices in laplace transform Møller-Plesset perturbation theory |
| title_sort | cholesky decomposed density matrices in laplace transform moller plesset perturbation theory |
| topic_facet | Hochschulschrift |
| url | http://edoc.ub.uni-muenchen.de/15265/ https://nbn-resolving.org/urn:nbn:de:bvb:19-152656 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025715285&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT clinluciencyril choleskydecomposeddensitymatricesinlaplacetransformmøllerplessetperturbationtheory |