Density functional theory: an advanced course
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Heidelberg [u.a.]
Springer
2011
|
| Schriftenreihe: | Theoretical and mathematical physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XV, 531 S. graph. Darst. |
| ISBN: | 9783642140891 |
Internformat
MARC
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| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2011 | |
| 300 | |a XV, 531 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1805095143394508800 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
INTRODUCTION 1
FOUNDATIONS OF DENSITY FUNCTIONAL THEORY: EXISTENCE THEOREMS 11 2.1
HOHENBERG-KOHN THEOREM 11
2.2 DEGENERATE GROUND STATES 18
2.3 VARIATIONAL EQUATION, INTERACTING V-REPRESENTABILITY, FUNCTIONAL
DIFFERENTIABILITY 21
2.4 FRACTIONAL PARTICLE NUMBERS, DERIVATIVE DISCONTINUITY 37 2.5
SPIN-POLARIZED SYSTEMS 40
2.6 CURRENT DENSITY FUNCTIONAL THEORY 46
2.7 EXCITED STATES: PART 1 55
EFFECTIVE SINGLE-PARTICLE EQUATIONS 57
3.1 KOHN-SHAM EQUATIONS 57
3.2 NONINTERACTING V-REPRESENTABILITY 70
3.3 DEGENERATE KOHN-SHAM GROUND STATES 73
3.4 JANAK'S THEOREM, FRACTIONAL PARTICLE NUMBERS 76
3.5 KOHN-SHAM EQUATIONS FOR SPIN-POLARIZED SYSTEMS 80
3.6 INTERPRETATION OF KOHN-SHAM EIGENVALUES: RELATION TO IONIZATION
POTENTIAL, FERMI SURFACE AND BAND GAP 84 3.6.1 IONIZATION POTENTIAL 84
3.6.2 FERMI SURFACE 88
3.6.3 BAND GAP 99
3.7 KOHN-SHAM EQUATIONS OF CURRENT DENSITY FUNCTIONAL THEORY 101
EXCHANGE-CORRELATION ENERGY FUNCTIONAL 109
4.1 DEFINITION OF EXACT EXCHANGE WITHIN DFT 109
4.2 EXACT REPRESENTATIONS OF E XC [N] 115
4.2.1 VARIANT (A): KOHN-SHAM PERTURBATION THEORY 115 4.2.2 VARIANT (B):
ADIABATIC CONNECTION 126
4.3 LOCAL DENSITY APPROXIMATION (LDA) 129
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1002961629
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
4.3.1 EXCHANGE 131
4.3.2 CORRELATION: HIGH-DENSITY LIMIT 132
4.3.3 CORRELATION: LOW-DENSITY LIMIT 135
4.3.4 CORRELATION: INTERPOLATION BETWEEN HIGH- AND LOW-DENSITY REGIME
135
4.3.5 DENSITY FUNCTIONAL: LOCAL DENSITY APPROXIMATION (LDA) . 137 4.3.6
SPIN-POLARIZED ELECTRON GAS: LOCAL SPIN-DENSITY APPROXIMATION (LSDA) 142
4.4 NONLOCAL CORRECTIONS TO THE LDA 145
4.4.1 WEAKLY INHOMOGENEOUS ELECTRON GAS 145
4.4.2 COMPLETE LINEAR RESPONSE 152
4.4.3 GRADIENT EXPANSION 153
4.5 GENERALIZED GRADIENT APPROXIMATION (GGA) 169
4.5.1 MOMENTUM SPACE VARIANT 170
4.5.2 REAL SPACE VARIANT 175
4.5.3 COMBINATION OF MOMENTUM AND REAL SPACE VARIANTS 179 4.5.4
SEMI-EMPIRICAL CONSTRUCTION OF GGAS 182
4.5.5 MERITS AND LIMITATIONS OF GGAS 185
4.6 WEIGHTED DENSITY APPROXIMATION (WDA) 201
4.7 SELF-INTERACTION CORRECTIONS (SIC) 202
4.8 META-GGA (MGGA) 204
4.9 LDA+LF 211
VIRIAL THEOREMS 219
5.1 SCALING BEHAVIOR OF ENERGY CONTRIBUTIONS 219
5.2 CONVENTIONAL VIRIAL THEOREM 221
5.3 DFT VIRIAL THEOREM 222
5.4 HELLMANN-FEYNMAN THEOREM 224
ORBITAL FUNCTIONAL: OPTIMIZED POTENTIAL METHOD 227
6.1 MOTIVATION 227
6.1.1 ATOMIC NEGATIVE IONS 227
6.1.2 DISPERSION FORCES 228
6.1.3 STRONGLY CORRELATED SYSTEMS 230
6.1.4 THIRD GENERATION OF DFT 232
6.2 DERIVATION OF OPM INTEGRAL EQUATION 233
6.2.1 COMPACT NOTATION 233
6.2.2 DIRECT FUNCTIONAL DERIVATIVE 234
6.2.3 TOTAL ENERGY MINIMIZATION 239
6.2.4 INVARIANCE OF DENSITY 241
6.2.5 EXACT RELATIONS BASED ON OPM INTEGRAL EQUATION 244 6.2.6
KRIEGER-LI-IAFRATE APPROXIMATION (KLI) 248
6.2.7 OPM IN CASE OF DEGENERACY 250
6.3 EXCHANGE-ONLY RESULTS 254
6.4 FIRST-PRINCIPLES IMPLICIT CORRELATION FUNCTIONALS 271
IMAGE 3
CONTENTS XI
6.4.1 KOHN-SHAM PERTURBATION THEORY 272
6.4.2 KOHN-SHAM-BASED RANDOM PHASE APPROXIMATION 276 6.4.3 INTERACTION
STRENGTH INTERPOLATION (ISI) 278
6.5 MODEL-BASED ORBITAL-DEPENDENT EXCHANGE-CORRELATION FUNCTIONALS 279
6.5.1 SELF-INTERACTION CORRECTED LDA 280
6.5.2 COLLE-SALVETTI FUNCTIONAL 280
6.5.3 META-GGA 281
6.5.4 GLOBAL, SCREENED AND LOCAL HYBRID FUNCTIONALS 281 6.6 ANALYSIS OF
ORBITAL-DEPENDENT CORRELATION FUNCTIONALS 288 6.6.1 DISPERSION FORCE 288
6.6.2 CORRELATION ENERGY 294
6.6.3 CORRELATION POTENTIAL 298
6.7 ORBITAL-DEPENDENT REPRESENTATION OF 2-PARTICLE DENSITY 304
7 TIME-DEPENDENT DENSITY FUNCTIONAL THEORY 307
7.1 RUNGE-GROSS THEOREM 307
7.2 TIME-DEPENDENT KOHN-SHAM EQUATIONS 325
7.3 EXCHANGE-CORRELATION ACTION: ADIABATIC LOCAL DENSITY APPROXIMATION
AND BEYOND 329
7.4 TIME-DEPENDENT LINEAR RESPONSE 331
7.5 SPIN-POLARIZED TIME-DEPENDENT DENSITY FUNCTIONAL THEORY 335 7.6
EXCITED STATES: PART II 336
8 RELATIVISTIC DENSITY FUNCTIONAL THEORY 35 1
8.1 NOTATION 352
8.2 FIELD THEORETICAL BACKGROUND 353
8.3 EXISTENCE THEOREM 361
8.4 RELATIVISTIC KOHN-SHAM EQUATIONS 367
8.5 TOWARDS A WORKABLE RDFT SCHEME: NO-PAIR APPROXIMATION 371 8.6
NO-PAIR RDFT 373
8.7 VARIANTS OF RDFT 376
8.8 RELATIVISTIC EXCHANGE-CORRELATION FUNCTIONAL: CONCEPTS AND
ILLUSTRATIVE RESULTS 384
8.8.1 RELATIVISTIC IMPLICIT FUNCTIONALS: OPTIMIZED POTENTIAL METHOD 384
8.8.2 ROLE OF RELATIVISTIC CORRECTIONS IN E XC : I. PROTOTYPE RESULTS
FOR ATOMS 388
8.8.3 RELATIVISTIC LOCAL DENSITY APPROXIMATION 393
8.8.4 RELATIVISTIC GENERALIZED GRADIENT APPROXIMATION 397 8.8.5 ROLE OF
RELATIVISTIC CORRECTIONS IN XC : II. PROTOTYPE RESULTS FOR MOLECULES
AND SOLIDS 398
9 FURTHER READING 401
IMAGE 4
XUE CONTENTS
A FUNCTIONALS AND THE FUNCTIONAL DERIVATIVE 403
A. 1 DEFINITION OF THE FUNCTIONAL 403
A.2 FUNCTIONAL DERIVATIVE 405
A.3 CALCULATIONAL RULES 409
A.4 VARIATIONAL PRINCIPLE 411
B SECOND QUANTIZATION IN MANY-BODY THEORY 413
B.I AF-PARTICLE HUBERT SPACE 413
B.I.I REALIZATION IN FIRST QUANTIZED FORM 413
B. 1.2 FORMAL REPRESENTATION 417
B.2 FOCK SPACE 421
B.2.1 CREATION AND ANNIHILATION OPERATORS 421
B.2.2 1-PARTICLE OPERATORS 425
B.2.3 2-PARTICLE OPERATORS 428
C SCALING BEHAVIOR OF MANY-BODY METHODS 433
D EXPLICIT DENSITY FUNCTIONALS FOR THE KINETIC ENERGY: THOMAS-FERMI
MODELS AND BEYOND 437
E ASYMPTOTIC BEHAVIOR OF QUASI-PARTICLE AMPLITUDES 445
F QUANTIZATION OF NONINTERACTING FERMIONS IN RELATIVISTIC QUANTUM
FIELD THEORY 449
G RENORMALIZATION SCHEME OF VACUUM QED 457
H RELATIVISTIC HOMOGENEOUS ELECTRON GAS 467
H.I BASIC PROPAGATORS 467
H.2 RESPONSE FUNCTIONS 468
H.3 GROUND STATE ENERGY 473
H.4 GROUND STATE FOUR CURRENT 478
I RENORMALIZATION OF INHOMOGENEOUS ELECTRON GAS 481
J GRADIENT CORRECTIONS TO THE RELATIVISTIC LDA 485
K GORDON DECOMPOSITION 489
L SOME USEFUL FORMULAE 493
REFERENCES 499
INDEX 517 |
| any_adam_object | 1 |
| author | Engel, Eberhard 1959- Dreizler, Reiner M. 1936- |
| author_GND | (DE-588)132987880 (DE-588)112869785 |
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| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Chemie / Pharmazie Physik |
| format | Book |
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| id | DE-604.BV036886471 |
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| indexdate | 2024-07-20T10:54:36Z |
| institution | BVB |
| isbn | 9783642140891 |
| language | English |
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| series2 | Theoretical and mathematical physics |
| spelling | Engel, Eberhard 1959- Verfasser (DE-588)132987880 aut Density functional theory an advanced course Eberhard Engel ; Reiner M. Dreizler Heidelberg [u.a.] Springer 2011 XV, 531 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Theoretical and mathematical physics Dichtefunktionalformalismus (DE-588)4258514-4 gnd rswk-swf Dichtefunktionalformalismus (DE-588)4258514-4 s DE-604 Dreizler, Reiner M. 1936- Verfasser (DE-588)112869785 aut Erscheint auch als Online-Ausgabe 978-3-642-14090-7 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3484427&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=020801741&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Engel, Eberhard 1959- Dreizler, Reiner M. 1936- Density functional theory an advanced course Dichtefunktionalformalismus (DE-588)4258514-4 gnd |
| subject_GND | (DE-588)4258514-4 |
| title | Density functional theory an advanced course |
| title_auth | Density functional theory an advanced course |
| title_exact_search | Density functional theory an advanced course |
| title_full | Density functional theory an advanced course Eberhard Engel ; Reiner M. Dreizler |
| title_fullStr | Density functional theory an advanced course Eberhard Engel ; Reiner M. Dreizler |
| title_full_unstemmed | Density functional theory an advanced course Eberhard Engel ; Reiner M. Dreizler |
| title_short | Density functional theory |
| title_sort | density functional theory an advanced course |
| title_sub | an advanced course |
| topic | Dichtefunktionalformalismus (DE-588)4258514-4 gnd |
| topic_facet | Dichtefunktionalformalismus |
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