Fundamentals of time-dependent density functional theory:
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| Format: | Book |
| Language: | English |
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Berlin [u.a.]
Springer
2012
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| Series: | Lecture notes in physics
837 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XXXII, 559 S. graph. Darst. |
| ISBN: | 3642235174 9783642235177 |
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MARC
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| 245 | 1 | 0 | |a Fundamentals of time-dependent density functional theory |c Miguel A. L. Marques ... eds. |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
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| 490 | 1 | |a Lecture notes in physics |v 837 | |
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IMAGE 1
CONTENTS
PART I THEORY AND EXPERIMENT: WHY W E NEED TDDFT 1 SHORT-PULSE PHYSICS 3
1.1 INTRODUCTION 3
1.2 SPECTROSCOPIC TOOLS 4
1.3 PHYSICS WITH INTENSE SHORT LASER PULSES 5
1.3.1 ABOVE THRESHOLD IONIZATION 6
1.3.2 HIGH HARMONIC GENERATION 7
1.4 FEMTOSECOND SCIENCE 8
1.5 ATTOSECOND SCIENCE 9
1.5.1 ELECTRON SPECTROSCOPY: RABBIT AND STREAKING . . . 10
1.5.2 ATTOSECOND TRANSIENT ABSORPTION 12
1.5.3 ION SPECTROSCOPY: ELECTRON LOCALIZATION ON THE ATTOSECOND
TIMESCALE 12
1.5.4 CONTROL OF DISSOCIATIVE IONIZATION 13
1.6 CONCLUSIONS 13
2 SPECTROSCOPY IN THE FREQUENCY DOMAIN 15
2.1 INTRODUCTION 15
2.2 PROBE-ELECTRON INTERACTION 16
2.2.1 PHOTON PROBE 16
2.2.2 ELECTRON-ELECTRON SCATTERING 18
2.2.3 FINITE MOMENTUM TRANSFERS 18
2.3 PROPERTIES TO STUDY 19
2.3.1 RESPONSE FUNCTIONS 19
2.3.2 TYPICAL EXCITATIONS 20
2.4 TECHNIQUES 21
2.4.1 ELLIPSOMETRY 21
2.4.2 PHOTOEMISSION SPECTROSCOPIES 22
2.4.3 PHOTON ABSORPTION 24
XIII
HTTP://D-NB.INFO/1013868625
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X I V C O N T E N T S
2.4.4 INELASTIC SCATTERING 26
2.4.5 NON-LINEAR OPTICS 28
2.5 SUMMARY 28
3 THE MICROSCOPIC DESCRIPTION O F A MACROSCOPIC EXPERIMENT 29
3.1 INTRODUCTION 29
3.2 THEORETICAL SPECTROSCOPY 30
3.3 PHOTOEMISSION SPECTRA AND SPECTRAL FUNCTIONS 32
3.4 MICROSCOPIC DESCRIPTION OF NEUTRAL EXCITATIONS 37
3.5 MICROSCOPIC RESPONSE BEYOND THE INDEPENDENT-PARTICLE PICTURE 41
3.6 MICROSCOPIC-MACROSCOPIC CONNECTION 45
3.7 CONCLUSIONS 50
PART II BASIC THEORY
4 INTRODUCTION TO TDDFT 53
4.1 INTRODUCTION 53
4.2 ONE-TO-ONE DENSITY-POTENTIAL MAPPING 57
4.3 TIME-DEPENDENT KOHN-SHAM EQUATIONS 61
4.4 MORE DETAILS AND EXTENSIONS 63
4.4.1 THE SURFACE CONDITION 64
4.4.2 INTERACTING AND NON-INTERACTING V-REPRESENTABILITY 65
4.4.3 A VARIATIONAL PRINCIPLE 66
4.4.4 THE TIME-DEPENDENT CURRENT 67
4.4.5 BEYOND THE TAYLOR-EXPANSION 68
4.4.6 EXACT TDKS SCHEME AND ITS PREDICTIVITY 69
4.4.7 TDDFT IN OTHER REALMS 71
4.5 FREQUENCY-DEPENDENT LINEAR RESPONSE 72
4.5.1 THE DENSITY-DENSITY RESPONSE FUNCTION 72
4.5.2 EXCITATION ENERGIES AND OSCILLATOR STRENGTHS FROM A MATRIX
EQUATION 75
4.5.3 THE XC KERNEL 79
4.5.4 SPIN-DECOMPOSED EQUATIONS 81
4.5.5 A CASE STUDY: THE HE ATOM 82
4.6 HIGHER-ORDER RESPONSE 86
4.7 APPROXIMATE FUNCTIONALS 88
4.7.1 ADIABATIC APPROXIMATIONS: ALDA, AGGA, AB3LYP, ETC 89
4.7.2 ORBITAL FUNCTIONALS 90
4.7.3 HYDRODYNAMICALLY BASED KERNELS 91
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CONTENTS X V
4.8 GENERAL PERFORMANCE AND CHALLENGES 92
4.8.1 EXTENDED SYSTEMS 92
4.8.2 FINITE SYSTEMS 95
4.8.3 NON-PERTURBATIVE ELECTRON DYNAMICS 97
5 EXACT CONDITIONS AND THEIR RELEVANCE IN TDDFT 101
5.1 INTRODUCTION 101
5.2 REVIEW OF THE GROUND STATE 102
5.2.1 BASIC DEFINITIONS 102
5.2.2 STANDARD APPROXIMATIONS 104
5.2.3 FINITE SYSTEMS 104
5.2.4 EXTENDED SYSTEMS 106
5.3 OVERVIEW FOR TDDFT 107
5.3.1 DEFINITIONS 108
5.3.2 APPROXIMATIONS 109
5.4 GENERAL CONDITIONS I L L
5.4.1 ADIABATIC LIMIT I L L
5.4.2 EQUATIONS OF MOTION I L L
5.4.3 SELF-INTERACTION 113
5.4.4 INITIAL-STATE DEPENDENCE 113
5.4.5 COUPLING-CONSTANT DEPENDENCE 113
5.4.6 TRANSLATIONAL INVARIANCE 114
5.5 LINEAR RESPONSE 115
5.5.1 CONSEQUENCES O F GENERAL CONDITIONS 115
5.5.2 PROPERTIES O F THE KERNEL 116
5.5.3 EXCITED STATES 118
5.6 EXTENDED SYSTEMS AND CURRENTS 121
5.6.1 GRADIENT EXPANSION IN THE CURRENT 121
5.6.2 POLARIZATION OF SOLIDS 122
5.7 SUMMARY 122
6 ORBITAL FUNCTIONALS 125
6.1 WHY ORBITAL FUNCTIONALS ARE NEEDED 125
6.2 USING ORBITAL FUNCTIONALS IN TDDFT: SOME CHOICES TO MAKE 129
6.3 THE TIME-DEPENDENT OPTIMIZED EFFECTIVE POTENTIAL 131
6.4 A FEW EXAMPLES 137
7 RESPONSE FUNCTIONS IN TDDFT: CONCEPTS AND IMPLEMENTATION 139
7.1 INTRODUCTION 139
7.2 RESPONSE FUNCTIONS 140
7.2.1 LINEAR DENSITY RESPONSE 141
7.2.2 HIGHER-ORDER DENSITY RESPONSE 143
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X V I C O N T E N T S
7.3 METHODS FOR CALCULATING RESPONSE FUNCTIONS 144
7.3.1 TIME-PROPAGATION METHOD 145
7.3.2 STERNHEIMER METHOD 147
7.3.3 CASIDA METHOD 153
7.3.4 GENERALIZATIONS AND DISCUSSION 156
7.4 APPLICATIONS OF LINEAR RESPONSE 157
7.4.1 RESPONSE TO ELECTRIC PERTURBATIONS 157
7.4.2 RESPONSE TO MAGNETIC PERTURBATIONS 160
7.4.3 RESPONSE TO STRUCTURAL PERTURBATIONS 162
7.4.4 MIXED ELECTRIC AND STRUCTURAL RESPONSE TO STRUCTURAL PERTURBATIONS
164
7.4.5 RESPONSE TO K * P PERTURBATIONS 165
8 MEMORY: HISTORY, INITIAL-STATE DEPENDENCE, AND DOUBLE-EXCITATIONS 167
8.1 INTRODUCTION 167
8.2 HISTORY DEPENDENCE: AN EXAMPLE 169
8.3 INITIAL-STATE DEPENDENCE 171
8.4 MEMORY: AN EXACT CONDITION 174
8.5 MEMORY IN QUANTUM CONTROL PHENOMENA 177
8.6 MEMORY EFFECTS IN EXCITATION SPECTRA 180
8.7 OUTLOOK 184
PART III ADVANCED CONCEPTS
9 BEYOND THE RUNGE-GROSS THEOREM 187
9.1 INTRODUCTION 187
9.2 THE EXTENDED RUNGE-GROSS THEOREM: DIFFERENT INTERACTIONS AND INITIAL
STATES 188
9.3 RUNGE-GROSS THEOREM FOR DIPOLE FIELDS 194
9.4 INVERTIBILITY OF THE LINEAR DENSITY RESPONSE FUNCTION 195
9.5 GLOBAL FIXED-POINT PROOF OF TDDFT 200
9.6 CONSEQUENCES OF V-REPRESENTABILITY FOR THE QUANTUM MECHANICAL ACTION
206
10 OPEN QUANTUM SYSTEMS: DENSITY MATRIX FORMALISM AND APPLICATIONS 211
10.1 INTRODUCTION 211
10.2 THE GENERALIZED QUANTUM MASTER EQUATION 213
10.2.1 DERIVATION O F THE QUANTUM MASTER EQUATION USING THE
NAKAJIMA-ZWANZIG PROJECTION OPERATOR FORMALISM 213
10.2.2 THE MARKOV APPROXIMATION 214
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CONTENTS X V I I
10.3 RIGOROUS FOUNDATIONS O F OQS-TDDFT 215
10.3.1 THE OQS-TDDFT VAN LEEUWEN CONSTRUCTION . . . . 215
10.3.2 THE DOUBLE ADIABATIC CONNECTION 218
10.4 SIMULATING REAL-TIME DISSIPATIVE DYNAMICS WITH A UNITARILY EVOLVING
KOHN-SHAM SYSTEM 220
10.5 OQS-TDDFT IN THE LINEAR RESPONSE REGIME USING THE OPEN KOHN-SHAM
SCHEME 222
10.6 POSITIVITY OF THE LINDBLAD MASTER EQUATION FOR TIME-DEPENDENT
HAMILTONIANS 225
10.7 COMPARISON OF OQS-TDDFT IN THE STOCHASTIC SCHRODINGER EQUATION AND
MASTER EQUATION APPROACHES 228
10.8 CONCLUSIONS AND OUTLOOK 229
11 OPEN QUANTUM SYSTEMS: A STOCHASTIC PERSPECTIVE 231
11.1 INTRODUCTION 231
11.2 GENERAL REMARKS ON OPEN QUANTUM SYSTEMS 233
11.2.1 PARTITIONING INTO SYSTEM AND ENVIRONMENT 233
11.2.2 PHYSICAL ASSUMPTIONS 234
11.3 STOCHASTIC SCHRODINGER EQUATIONS 234
11.4 DERIVATION O F MASTER EQUATIONS FROM STOCHASTIC SCHRODINGER
EQUATIONS 239
11.5 STOCHASTIC CURRENT DENSITY FUNCTIONAL THEORY 241
11.5.1 FORMAL ASPECTS OF STOCHASTIC CURRENT DENSITY FUNCTIONAL THEORY
241
11.5.2 PRACTICAL ASPECTS O F A STOCHASTIC SIMULATION: QUANTUM JUMP
ALGORITHM 243
11.5.3 STOCHASTIC QUANTUM MOLECULAR DYNAMICS 244
11.6 OPEN QUESTIONS IN TDDFT FOR OPEN QUANTUM SYSTEMS AND OUTLOOK 246
12 MULTICOMPONENT DENSITY-FUNCTIONAL THEORY 249
12.1 INTRODUCTION 249
12.2 FUNDAMENTALS 250
12.2.1 DEFINITION O F THE DENSITIES 253
12.3 THE RUNGE-GROSS THEOREM FOR MULTICOMPONENT SYSTEMS . . . 253 12.4
THE KOHN-SHAM SCHEME FOR MULTICOMPONENT SYSTEMS 254
12.5 THE MULTICOMPONENT ACTION 256
12.6 LINEAR RESPONSE AND MULTICOMPONENT SYSTEMS 258
12.7 EXAMPLE 260
12.8 CONCLUSIONS 263
13 QUANTUM OPTIMAL CONTROL 265
13.1 INTRODUCTION 265
13.2 THE ESSENTIAL QOCT EQUATIONS 266
13.3 OPTIMIZATION FOR THE TDKS SYSTEM 270
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XVIII
C O N T E N T S
PART IV REAL-TIME DYNAMICS
14 NON-BORN-OPPENHEIMER DYNAMICS AND CONICAL INTERSECTIONS . . . 279
14.1 INTRODUCTION 279
14.2 WAVE-FUNCTION THEORY 282
14.2.1 BORN-OPPENHEIMER APPROXIMATION AND BEYOND . . . 283 14.2.2 MIXED
QUANTUM/CLASSICAL DYNAMICS 286
14.2.3 PATHWAY METHOD 288
14.3 TDDFT 290
14.4 PERSPECTIVES 298
15 ON THE COMBINATION O F TDDFT WITH MOLECULAR DYNAMICS: NEW
DEVELOPMENTS 301
15.1 INTRODUCTION 301
15.2 FAST EHRENFEST MOLECULAR DYNAMICS 302
15.3 MD AT FINITE ELECTRONIC TEMPERATURE 309
16 EXCITED-STATE PROPERTIES AND DYNAMICS 317
16.1 DERIVATIVES O F EXCITED-STATE ENERGIES IN TDDFT 318
16.2 IMPLEMENTATION OF EXCITED-STATE ENERGY DERIVATIVES 323
16.2.1 ATOM-CENTERED BASIS SETS 323
16.2.2 PLANE-WAVE BASIS SETS 325
16.2.3 TAMM-DANCOFF APPROXIMATION 325
16.3.4 RESOLUTION-OF-THE-IDENTITY APPROXIMATION 326
16.3 PERFORMANCE OF TDDFT FOR EXCITED-STATE ENERGIES AND THEIR
DERIVATIVES 326
16.3.1 SINGLET EXCITATIONS 326
16.3.2 CHARGE-TRANSFER EXCITATIONS IN TDDFT 329
16.3.3 RYDBERG, TRIPLET EXCITATIONS AND EXCITATIONS WITH DOUBLES
CHARACTER 331
16.4 NON-ADIABATIC COUPLING MATRIX ELEMENTS 332
16.5 EXCITED-STATE DYNAMICS 334
16.6 SOLVATION EFFECTS AND COUPLING TO CLASSICAL FORCE FIELDS . . . 335
17 ELECTRONIC TRANSPORT 337
17.1 INTRODUCTION 337
17.2 TDDFT APPROACHES TO TRANSPORT 339
17.2.1 FINITE SYSTEMS 339
17.2.2 INFINITE SYSTEMS VIA EMBEDDING TECHNIQUE 340
17.2.3 QUANTUM KINETIC APPROACH 348
17.3 CONCLUSIONS 350
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CONTENTS X I X
18 ATOMS AND MOLECULES IN STRONG LASER FIELDS 351
18.1 INTRODUCTION: NEW LIGHT SOURCES FOR THE TWENTY-FIRST CENTURY 351
18.2 ATOMS IN STRONG LASER FIELDS: AN OVERVIEW 353
18.2.1 MULTIPHOTON IONIZATION 353
18.2.2 ABOVE-THRESHOLD IONIZATION 355
18.2.3 HARMONIC GENERATION 356
18.2.4 THEORETICAL METHODS 357
18.3 TDDFT FOR ATOMS IN STRONG LASER FIELDS 358
18.4 MOLECULES IN STRONG FIELDS 362
18.4.1 OVERVIEW 362
18.4.2 A ID EXAMPLE: H 2 WITH FIXED NUCLEI 364
18.4.3 TDDFT FOR MOLECULES IN STRONG FIELDS 367
18.5 CONCLUSION AND PERSPECTIVES 370
PART V NUMERICAL ASPECTS
19 THE LIOUVILLE-LANCZOS APPROACH TO TIME-DEPENDENT DENSITY-FUNCTIONAL
(PERTURBATION) THEORY 375
19.1 INTRODUCTION 375
19.2 STATEMENT O F THE PROBLEM, MINIMAL THEORETICAL BACKGROUND, AND
NOTATION 377
19.2.1 REPRESENTATION O F THE RESPONSE DENSITY MATRIX AND O F OTHER
OPERATORS 377
19.2.2 DIPOLE OPERATOR IN PERIODIC BOUNDARY CONDITIONS 381
19.3 ALGORITHM 382
19.3.1 LANCZOS BI-ORTHOGONALIZATION ALGORITHM 382
19.3.2 CALCULATION OF THE POLARIZABILITY 383
19.3.3 EXTRAPOLATING THE LANCZOS RECURSION 385
19.4 OPTICAL SUM RULES 386
19.5 APPLICATION TO AN ORGANIC DYE MOLECULE 388
19.6 CONCLUSIONS 389
20 THE PROJECTOR AUGMENTED WAVE METHOD 391
20.1 INTRODUCTION 391
20.2 THE PAW METHOD 392
20.3 OPERATORS 395
20.4 GROUND-STATE KOHN-SHAM EQUATION AND FORCES 396
20.4.1 CONNECTION TO NONLOCAL PSEUDOPOTENTIALS 397
20.5 TIME-DEPENDENT DFT 397
20.5.1 TIME-PROPAGATION 398
20.5.2 LINEAR-RESPONSE TDDFT 399
20.6 APPLICATIONS 399
IMAGE 8
X X
C O N T E N T S
21 HARNESSING THE POWER O F GRAPHIC PROCESSING UNITS 401
21.1 INTRODUCTION 401
21.2 BASIC CONCEPTS IN GPU ARCHITECTURES 402
21.3 GPU PROGRAMMING 403
21.3.1 THE OPENCL LANGUAGE 404
21.3.2 EVALUATION OF BENEFITS: PERFORMANCE WITH COMPLEX CODES 404
21.4 GPUS FOR DFT AND TDDFT 405
2 1 . 5 G P U IMPLEMENTATION IN THE B I G D F T CODE 4 0 5
21.5.1 THE CODE STRUCTURE: PRELIMINARY
CPU INVESTIGATION 406
21.5.2 GPU CONVOLUTION ROUTINES AND CUBLAS LINEAR ALGEBRA 406
21.5.3 PERFORMANCE EVALUATION O F HYBRID CODE 407
21.6 TDDFT ON GPUS: IMPLEMENTATION IN OCTOPUS 407
21.6.1 WORKING WITH BLOCKS OF KOHN-SHAM ORBITALS 409
21.6.2 APPLICATION OF THE KOHN-SHAM HAMILTONIAN 410
21.6.3 THE KINETIC ENERGY OPERATOR IN REAL-SPACE 410
21.6.4 OVERALL PERFORMANCE IMPROVEMENTS 411
21.7 FUTURE DEVELOPMENTS IN TDDFT 411
21.8 CONCLUSIONS 412
PART VI TDDFT VERSUS OTHER THEORITICAL TECHNIQUES
22 DISPERSION (VAN DER WAALS) FORCES AND TDDFT 417
22.1 INTRODUCTION 417
22.2 SIMPLE MODELS O F THE VDW INTERACTION BETWEEN SMALL SYSTEMS 418
22.2.1 COUPLED-FLUCTUATION PICTURE 418
22.2.2 PICTURE BASED ON THE STATIC CORRELATION HOLE: FAILURE OF LDA/GGA
AT LARGE SEPARATIONS 418
22.2.3 PICTURE BASED ON SMALL DISTORTIONS O F THE GROUNDSTATE DENSITY
419
22.2.4 COUPLED-PLASMON PICTURE 419
22.3 THE SIMPLEST MODELS FOR VDW ENERGETICS OF LARGER SYSTEMS 420
22.4 FORMAL PERTURBATION THEORY APPROACH 420
22.4.1 CASIMIR-POLDER FORMULA: SECOND ORDER PERTURBATION THEORY FOR TWO
FINITE NONOVERLAPPING SYSTEMS. . . 420 22.4.2 VDW AND HIGHER-ORDER
PERTURBATION THEORY 422
22.4.3 SYMMETRY-ADAPTED PERTURBATION THEORY 423
22.5 NONUNIVERSALITY OF VDW ASYMPTOTICS IN LAYERED AND STRIATED SYSTEMS
423
IMAGE 9
CONTENTS X X I
22.6 CORRELATION ENERGIES FROM RESPONSE FUNCTIONS:
THE FLUCTUATION-DISSIPATION THEOREM 424
22.6.1 BASIC ADIABATIC CONNECTION FLUCTUATION-DISSIPATION THEORY 425
22.6.2 EXACT EXCHANGE: A STRENGTH OF THE ACFD APPROACH 428
22.7 THE XC ENERGY IN THE DIRECT RANDOM PHASE APPROXIMATION 431
22.7.1 CASIMIR-POLDER CONSISTENCY: A GOOD FEATURE OF THE DRPA FOR VDW
CALCULATIONS IN THE WELL SEPARATED LIMIT 431
22.7.2 PROBLEMS WITH THE DRPA 433
22.8 BEYOND DRPA: NON-TDDFT METHODS 434
22.9 BEYOND THE DRPA: ACFD WITH A NONZERO XC KERNEL 434
22.9.1 THE CASE OF TWO SMALL DISTANT SYSTEMS IN THE ACFD WITH A NONZERO
XC KERNEL 434
22.9.2 BEYOND THE DRPA IN THE ACFD: ENERGY-OPTIMIZED/ XC KERNELS 435
22.9.3 BEYOND THE RPA IN THE ACFD: MORE REALISTIC UNIFORM-GAS BASED / X
C KERNELS 436
22.9.4 XC KERNELS NOT BASED ON THE UNIFORM ELECTRON GAS 437
22.10 DENSITY-BASED APPROXIMATIONS FOR THE RESPONSE FUNCTIONS IN ACFD
VDW THEORY 438
22.10.1 DENSITY-BASED APPROXIMATIONS FOR THE NON-OVERLAPPING REGIME 438
22.10.2 "SEAMLESS" DENSITY-BASED VDW APPROXIMATIONS VALID INTO THE
OVERLAPPED REGIME 439
22.11 SUMMARY 440
23 NONLOCAL VAN DER WAALS DENSITY FUNCTIONALS BASED ON LOCAL RESPONSE
MODELS 443
23.1 INTRODUCTION 443
23.2 LONG-RANGE ASYMPTOTE OF DISPERSION INTERACTION 444
23.2.1 LOCAL POLARIZABILITY FORMALISM 444
23.2.2 PRACTICAL LOCAL POLARIZABILITY MODELS 445
23.3 GENERAL AND SEAMLESS NONLOCAL VAN DER WAALS DENSITY FUNCTIONALS 448
23.3.1 FUNCTIONAL FORM 448
23.3.2 VDW-DF-04 AND ITS VARIANTS 449
23.3.3 VV09 AND VV10 450
23.3.4 IMPLEMENTATION 452
23.4 DISPERSIONLESS CORRELATION AND EXCHANGE COMPONENTS 453
23.5 BENCHMARK TESTS ON BINDING ENERGIES 455
23.6 KNOWN LIMITATIONS AND AVENUES FOR IMPROVEMENT 456
IMAGE 10
XXII C O N T E N T S
24 TIME-DEPENDENT CURRENT DENSITY FUNCTIONAL THEORY 457
24.1 INTRODUCTION 457
24.2 FIRST HINTS OF ULTRANONLOCALITY: THE HARMONIC POTENTIAL THEOREM 458
24.3 TDDFT AND HYDRODYNAMICS 459
24.4 CURRENT DENSITY FUNCTIONAL THEORY 462
24.5 THE XC VECTOR POTENTIAL FOR THE HOMOGENEOUS ELECTRON LIQUID 463
24.6 THE XC VECTOR POTENTIAL FOR THE INHOMOGENEOUS ELECTRON LIQUID 467
24.7 IRREVERSIBILITY IN TDCDFT 468
25 TIME-DEPENDENT DEFORMATION FUNCTIONAL THEORY 471
25.1 INTRODUCTION 471
25.2 HYDRODYNAMIC FORMULATION O F TDCDFT 472
25.2.1 LOCAL CONSERVATION LAWS AND TDCDFT HYDRODYNAMICS IN EULERIAN
FORMULATION 472
25.2.2 KOHN-SHAM CONSTRUCTION IN TDCDFT 474
25.2.3 TDCDFT HYDRODYNAMICS IN THE LAGRANGIAN FORM 475
25.3 TIME-DEPENDENT DEFORMATION FUNCTIONAL THEORY 477
25.3.1 MANY-BODY THEORY IN A CO-MOVING REFERENCE FRAME 477
25.3.2 EMERGENCE OF TDDEFFT: A UNIVERSAL MANY-BODY PROBLEM 479
25.4 APPROXIMATE FUNCTIONALS FROM TDDEFFT 482
26 TIME-DEPENDENT REDUCED DENSITY MATRIX FUNCTIONAL THEORY. . . . 485
26.1 INTRODUCTION 485
26.2 THE ONE-BODY REDUCED DENSITY MATRIX 487
26.3 1RDM FUNCTIONALS 489
26.4 THE EQUATION OF MOTION 492
26.5 RESPONSE EQUATIONS 493
26.6 EXCITATIONS OF H 2 4 9 5
26.7 FURTHER READING 496
REFERENCE 499
INDEX 555 |
| any_adam_object | 1 |
| author2 | Marques, Miguel 1974- |
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| author2_variant | m m mm |
| author_GND | (DE-588)123388201 |
| author_facet | Marques, Miguel 1974- |
| building | Verbundindex |
| bvnumber | BV039902243 |
| classification_rvk | UD 8220 UL 2000 VE 5650 |
| ctrlnum | (OCoLC)785830422 (DE-599)DNB1013868625 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
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| dewey-tens | 530 - Physics |
| discipline | Chemie / Pharmazie Physik |
| format | Book |
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| id | DE-604.BV039902243 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:25:06Z |
| institution | BVB |
| isbn | 3642235174 9783642235177 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024761084 |
| oclc_num | 785830422 |
| open_access_boolean | |
| owner | DE-11 DE-384 DE-703 DE-355 DE-BY-UBR DE-29T |
| owner_facet | DE-11 DE-384 DE-703 DE-355 DE-BY-UBR DE-29T |
| physical | XXXII, 559 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Fundamentals of time-dependent density functional theory Miguel A. L. Marques ... eds. Berlin [u.a.] Springer 2012 XXXII, 559 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 837 Dichtefunktionalformalismus (DE-588)4258514-4 gnd rswk-swf Zeitabhängige Methode (DE-588)4279451-1 gnd rswk-swf Dichtefunktionalformalismus (DE-588)4258514-4 s Zeitabhängige Methode (DE-588)4279451-1 s DE-604 Marques, Miguel 1974- (DE-588)123388201 edt Erscheint auch als Online-Ausgabe 978-3-642-23518-4 Lecture notes in physics 837 (DE-604)BV000003166 837 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3859676&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=024761084&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fundamentals of time-dependent density functional theory Lecture notes in physics Dichtefunktionalformalismus (DE-588)4258514-4 gnd Zeitabhängige Methode (DE-588)4279451-1 gnd |
| subject_GND | (DE-588)4258514-4 (DE-588)4279451-1 |
| title | Fundamentals of time-dependent density functional theory |
| title_auth | Fundamentals of time-dependent density functional theory |
| title_exact_search | Fundamentals of time-dependent density functional theory |
| title_full | Fundamentals of time-dependent density functional theory Miguel A. L. Marques ... eds. |
| title_fullStr | Fundamentals of time-dependent density functional theory Miguel A. L. Marques ... eds. |
| title_full_unstemmed | Fundamentals of time-dependent density functional theory Miguel A. L. Marques ... eds. |
| title_short | Fundamentals of time-dependent density functional theory |
| title_sort | fundamentals of time dependent density functional theory |
| topic | Dichtefunktionalformalismus (DE-588)4258514-4 gnd Zeitabhängige Methode (DE-588)4279451-1 gnd |
| topic_facet | Dichtefunktionalformalismus Zeitabhängige Methode |
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| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT marquesmiguel fundamentalsoftimedependentdensityfunctionaltheory |