Optimised projections for the ab initio simulation of large and strongly correlated systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Springer Theses
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVI, 215 S. graph. Darst. |
| ISBN: | 9783642232374 364223237X |
Internformat
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| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a XVI, 215 S. |b graph. Darst. | ||
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
1 AN INTRODUCTION TO LINEAR-SCALING AB INITIO CALCULATIONS 1 1.1 THE
CHALLENGES OF SPATIAL AND ELECTRONIC COMPLEXITY 1 1.2 OUTLINE OF
DISSERTATION 2
1.3 THE BORN-OPPENHEIMER APPROXIMATION 5
1.4 DENSITY FUNCTIONAL THEORY 7
1.5 THE KOHN-SHAM EQUATIONS 10
1.6 EXCHANGE, CORRELATION AND THE LOCAL DENSITY APPROXIMATION. . . 13
1.7 SPIN-DENSITY FUNCTIONAL THEORY 15
1.8 THE PSEUDOPOTENTIAL APPROXIMATION 16
1.9 PERIODICITY AND BRILLOUIN ZONE SAMPLING 20
1.10 THE PLANE-WAVE AND PSINC BASIS SETS 22
1.11 DENSITY-MATRIX FORMULATION OF DFT 25
1.12 WANNIER FUNCTION AND DENSITY-MATRIX LOCALISATION 27 1.13 THE ONETEP
METHOD 29
REFERENCES 32
2 LINEAR-SCALING DFT + U FOR LARGE STRONGLY-CORRELATED SYSTEMS . . 37 2.
1 STRONGLY-CORRELATED SYSTEMS 37
2.2 THE DFT + U METHOD 40
2.3 FRAMEWORK FOR LINEAR-SCALING DFT + U 45
2.4 VARIATIONS WITH RESPECT TO THE DENSITY KERNEL 48
2.5 VARIATIONS WITH RESPECT TO THE NGWFS 52
2.6 VARIATIONS WITH RESPECT TO IONIC POSITIONS 54
2.7 SCALING TESTS ON NICKEL OXIDE NANO-CLUSTERS 56
2.7.1 COMPUTATIONAL METHODOLOGY 56
2.7.2 SCALING OF COMPUTATIONAL EFFORT FOR DFT + U 57
2.8 CONCLUDING REMARKS 60
REFERENCES 61
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1013511581
DIGITALISIERT DURCH
IMAGE 2
XIV CONTENTS
3 PROJECTOR SELF-CONSISTENT DFT + U USING NONORTHOGONAL GENERALISED
WANNIER FUNCTIONS 65
3.1 LOCALISED STRONGLY-CORRELATED SUBSPACES 65
3.2 METHODOLOGICAL FRAMEWORK 67
3.3 THE SPATIAL FORM OF HYDROGENIC SUBSPACES 68
3.4 WANNIER FUNCTIONS FOR LOCALISED SUBSPACES 70
3.5 THE SELF-CONSISTENT PROJECTOR METHOD 72
3.6 APPLICATION TO LIGATED IRON PORPHYRINS 74
3.6.1 IRON PORPHYRIN DERIVATIVES 75
3.6.2 COMPUTATIONAL METHODOLOGY 76
3.6.3 U AND Z-DEPENDENCE OF MAGNETIC DIPOLE MOMENTS AND INTERACTION
ENERGIES 76
3.6.4 Z-DEPENDENCE OF SUBSPACE OCCUPANCY IN FEP AND FEP(CO) 78
3.6.5 Z-DEPENDENT KOHN-SHAM BANDGAP OF FEP AND FEP(CO) 78
3.6.6 Z-DEPENDENT ELECTRIC DIPOLE MOMENTS OF FEP AND FEP(CO) 79
3.6.7 DEPENDENCE ON THE INTERACTION PARAMETER U 80
3.7 CONVERGENCE OF THE PROJECTOR SELF-CONSISTENCY ALGORITHM . . . 83
3.8 COMPUTATIONAL COST OF PROJECTOR SELF-CONSISTENCY 84
3.9 FORCES IN PROJECTOR SELF-CONSISTENT DFT + U 85
3.10 CONCLUDING REMARKS 86
REFERENCES 86
4 SUBSPACE REPRESENTATIONS IN AB INITIO METHODS FOR STRONGLY CORRELATED
SYSTEMS 89
4.1 MOTIVATION 89
4.2 NONORTHOGONAL REPRESENTATIONS OF THE OCCUPANCY MATRIX 90 4.2.1 THE
"FULL" AND "ON-SITE" REPRESENTATIONS 91
4.2.2 THE "DUAL" REPRESENTATION 93
4.2.3 REQUIREMENT FOR A SUBSPACE-LOCALISED HERMITIAN PROJECTION OPERATOR
94
4.2.4 THE "TENSORIAL" REPRESENTATION 96
4.3 APPLICATION TO THE DFT + U METHOD 97
4.3.1 THE TENSORIALLY INVARIANT DFT + U FUNCTIONAL 98 4.3.2 DFT + U
POTENTIAL AND IONIC FORCES 99
4.3.3 THE CASE OF ORTHONORMAL HUBBARD PROJECTORS 100 4.3.4 INVARIANCE
UNDER GENERALISED LOEWDIN TRANSFORMS 102 4.4 STRONGLY-CORRELATED
INSULATOR: BULK NICKEL OXIDE 103
4.4.1 COMPUTATIONAL METHODOLOGY 103
4.4.2 OCCUPANCIES AND MAGNETIC DIPOLE MOMENTS 106 4.4.3 KOHN-SHAM
EIGENSPECTRA 110
IMAGE 3
CONTENTS XV
4.5 MAGNETIC MOLECULE: THE COPPER PHTHALOCYANINE DIMER 113 4.5.1
COMPUTATIONAL METHODOLOGY 115
4.5.2 MAGNETIC DIPOLE MOMENTS 116
4.5.3 KOHN-SHAM EIGENSTATES 118
4.6 CONCLUDING REMARKS 120
REFERENCES 121
5 GEOMETRIC ASPECTS OF REPRESENTATION OPTIMISATION 125 5.1 MOTIVATION
125
5.2 TENSOR CALCULUS APPLIED TO ELECTRONIC STRUCTURE THEORY 128 5.2.1
TENSORIAL INVARIANCE 129
5.3 PARTIAL DIFFERENTIATION OF TENSORS 131
5.4 A METRIC CONNECTION ON THE SUPPORT MANIFOLD 133
5.5 VARIATION OF THE DENSITY KERNEL AND HAMILTONIAN 135
5.5.1 UNCORRECTED MATRIX UPDATES 135
5.5.2 GEOMETRICALLY CORRECTED MATRIX UPDATES 137
5.6 TENSORIAL CONSISTENCY IN ENERGY GRADIENTS 140
5.7 FIRST-ORDER DENSITY-MATRIX PRESERVATION 144
5.8 CONCLUDING REMARKS 148
REFERENCES 149
6 A NUMERICAL STUDY OF GEOMETRIC CORRECTIONS FOR REPRESENTATION
OPTIMISATION 151
6.1 COMPUTATIONAL METHODOLOGY FOR NAPHTHALENE 151
6.2 GEOMETRIC DENSITY KERNEL CORRECTIONS IN NAPHTHALENE 153 6.3
COMMUTATOR AND GRADIENT CONJUGACY IN NAPHTHALENE 155 6.4 TOTAL-ENERGY
CONVERGENCE IN NAPHTHALENE 159
6.5 COMPUTATIONAL METHODOLOGY FOR OLIGOACENE POLYMERS 160 6.6 GEOMETRIC
DENSITY KERNEL CORRECTIONS IN OLIGOACENES 164 6.7 COMMUTATOR AND
CONJUGACY CONDITION IN OLIGOACENES 164 6.8 COMPUTATIONAL PERFORMANCE IN
OLIGOACENES 166
6.9 CONCLUDING REMARKS 168
REFERENCES 168
7 TENSORIAL ASPECTS OF CALCULATING HUBBARD U INTERACTION PARAMETERS. .
171
7.1 THE LINEAR DENSITY-RESPONSE METHOD 172
.1 TOWARDS A PROJECTOR-DECOMPOSED METHOD 173
.2 THE NON-LOCALLY RESOLVED FOUR-INDEX U TENSOR 175 .3 THE SCALAR
INTERACTION U 176
.4 THE LOCALLY RESOLVED TWO-INDEX U TENSOR 176
.5 GENERALISATION OF THE DFT + U POTENTIAL AND IONIC FORCES TO THE
TENSORIAL FORMALISM 177
7.1.6 PROSPECTS FOR A LINEAR-SCALING IMPLEMENTATION 178
IMAGE 4
XVI CONTENTS
7.2 THE CONSTRAINED RANDOM PHASE APPROXIMATION 179
7.2.1 THE INDEPENDENT-PARTICLE GREEN'S FUNCTION AND IRREDUCIBLE
POLARISABILITY OPERATOR 180
7.2.2 SPECTRAL FUNCTIONS 181
7.2.3 THE LOW-ENERGY HUBBARD MODEL OF CRPA 182
7.2.4 DIELECTRIC FUNCTION, SCREENED COULOMB INTERACTION AND HUBBARD U
TENSOR 183
7.2.5 MAKING USE OF A FREQUENCY-DEPENDENT U 185
7.3 INTERACTION TENSOR UPDATE WITH HUBBARD PROJECTORS 186 7.3.1 GEOMETRY
OF THE HUBBARD SUPPORT MANIFOLDS 187 7.3.2 FIRST ORDER CHANGES TO THE
HUBBARD U TENSOR 188 7.3.3 INVARIANCE OF THE INTERACTION ANISOTROPY 190
7.3.4 APPLICABILITY OF THE METHOD 192
7.3.5 CHANGES IN NON-INVARIANT SCALARS 193
7.4 CONCLUDING REMARKS 195
REFERENCES 196
8 DISCUSSION AND CONCLUSION 199
8.1 SYNOPSIS 199
8.2 FUTURE WORK 201
APPENDIX: GEOMETRIC OBSERVATIONS 203
CURRICULUM VITAE 211 |
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| spelling | O'Regan, David D. Verfasser aut Optimised projections for the ab initio simulation of large and strongly correlated systems David D. O'Regan 1. ed. Berlin [u.a.] Springer 2012 XVI, 215 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer Theses Dichtefunktionalformalismus (DE-588)4258514-4 gnd rswk-swf Elektronenkorrelation (DE-588)4210527-4 gnd rswk-swf Ab-initio-Rechnung (DE-588)4141062-2 gnd rswk-swf Starke Kopplung (DE-588)4382353-1 gnd rswk-swf Elektronenkorrelation (DE-588)4210527-4 s Starke Kopplung (DE-588)4382353-1 s Ab-initio-Rechnung (DE-588)4141062-2 s Dichtefunktionalformalismus (DE-588)4258514-4 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3853569&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024409602&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Regan, David D. Optimised projections for the ab initio simulation of large and strongly correlated systems Dichtefunktionalformalismus (DE-588)4258514-4 gnd Elektronenkorrelation (DE-588)4210527-4 gnd Ab-initio-Rechnung (DE-588)4141062-2 gnd Starke Kopplung (DE-588)4382353-1 gnd |
| subject_GND | (DE-588)4258514-4 (DE-588)4210527-4 (DE-588)4141062-2 (DE-588)4382353-1 |
| title | Optimised projections for the ab initio simulation of large and strongly correlated systems |
| title_auth | Optimised projections for the ab initio simulation of large and strongly correlated systems |
| title_exact_search | Optimised projections for the ab initio simulation of large and strongly correlated systems |
| title_full | Optimised projections for the ab initio simulation of large and strongly correlated systems David D. O'Regan |
| title_fullStr | Optimised projections for the ab initio simulation of large and strongly correlated systems David D. O'Regan |
| title_full_unstemmed | Optimised projections for the ab initio simulation of large and strongly correlated systems David D. O'Regan |
| title_short | Optimised projections for the ab initio simulation of large and strongly correlated systems |
| title_sort | optimised projections for the ab initio simulation of large and strongly correlated systems |
| topic | Dichtefunktionalformalismus (DE-588)4258514-4 gnd Elektronenkorrelation (DE-588)4210527-4 gnd Ab-initio-Rechnung (DE-588)4141062-2 gnd Starke Kopplung (DE-588)4382353-1 gnd |
| topic_facet | Dichtefunktionalformalismus Elektronenkorrelation Ab-initio-Rechnung Starke Kopplung |
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