Theory and application of quantum molecular dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
1999
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 366 S. graph. Darst. |
| ISBN: | 9810233884 |
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Datensatz im Suchindex
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| adam_text | THEORY AND APPLICATION OF QUANTUM MOLECULAR DYNAMICS JOHN ZENG HUI ZHANG
DEPARTMENT OF CHEMISTRY NEW YORK UNIVERSITY S% WORLD SCIENTIFIC &
SINGAPORE * NEW JERSEY LONDON * SINGAPORE * NEW JERSEY * LONDON * HONG
KONG CONTENTS PREFACE V 1 SEPARATION OF ELECTRONIC AND NUCLEAR MOTIONS 1
1.1 ADIABATIC REPRESENTATION 1 1.2 BORN-OPPENHEIMER APPROXIMATION 3 1.3
HELLMANN-FEYNMAN THEORY 5 1.4 DIABATIC REPRESENTATION 6 1.5
TRANSFORMATION BETWEEN REPRESENTATIONS 8 1.6 CROSSING OF ADIABATIC
POTENTIALS 10 2 AB INITIO THEORY FOR ELECTRONS 13 2.1 HARTREE-FOCK
THEORY 13 2.1.1 HARTREE-FOCK EQUATION 13 2.1.2 RESTRICTED HARTREE-FOCK
(RHF) 18 2.1.3 UNRESTRICTED HARTREE-FOCK (UHF) 19 2.1.4 KOOPMANS
THEOREM 20 2.1.5 SCF SOLUTION TO HF EQUATION 21 2.2 ELECTRON CORRELATION
23 2.2.1 MULTICONFIGURATION 23 2.2.2 PERTURBATION METHODS 24 3
ROVIBRATIONAL MOTIONS OF MOLECULES 27 3.1 VIBRATION IN ONE-DIMENSION 27
3.1.1 HARMONIE POTENTIAL 27 3.1.2 MORSE POTENTIAL 29 3.1.3 GENERAL
POTENTIAL 29 3.1.4 DISCRETE VARIABLE REPRESENTATION 31 3.1.5 GAUSSIAN
BASIS FUNCTIONS 33 3.2 VIBRATION-ROTATION IN MANY DIMENSIONS 36 IX X
CONTENTS 3.2.1 DIATOMIC MOLECULES 36 3.2.2 TRIATOMIC MOLECULES 37 3.2.3
TETRAATOMIC MOLECULES 41 3.2.4 BOUND STATE CALCULATION OF (HF) 2 45 3.3
TIME-DEPENDENT SPECTRUM METHOD 50 3.3.1 AUTOCORRELATION FUNCTION 50
3.3.2 ENERGY SPECTRUM 51 3.3.3 SPECTRUM OF H0 2 56 4 FUNDAMENTAL THEORY
OF QUANTUM SCATTERING 59 4.1 TIME-DEPENDENT SCATTERING THEORY 59 4.1.1
MILLER OPERATOR 59 4.1.2 SCATTERING OPERATOR 63 4.2 TIME-INDEPENDENT
SCATTERING THEORY 64 4.2.1 GREEN S FUNCTION 64 4.2.2 LIPPMANN-SCHWINGER
EQUATION 66 4.2.3 THE S MATRIX 67 4.2.4 DISTORTED WAVE 71 4.3 ELASTIC
SCATTERING 74 4.3.1 RADIAL SCHROEDINGER EQUATION 74 4.3.2 FREE RADIAL
FUNCTIONS 75 4.3.3 RADIAL GREEN S FUNCTION 76 4.3.4 SCATTERING PHASE
SHIFT 78 4.3.5 SCATTERING CROSS SECTION 82 4.4 INELASTIC SCATTERING 85
4.4.1 COUPLED CHANNEL EQUATIONS 85 4.4.2 MULTICHANNEL GREEN S FUNCTION
86 4.4.3 S, T AND K MATRICES 88 4.4.4 SCATTERING CROSS SECTION 89 4.4.5
R MATRIX METHOD 95 4.4.6 OTHER METHODS 99 4.5 REACTIVE SCATTERING 99
4.5.1 PARTITIONING OF THE HAMILTONIAN 99 4.5.2 SCATTERING MATRIX AND
CROSS SECTION 100 4.5.3 JACOBI COORDINATES 104 4.5.4 A NOTE ON REACTIVE
SCATTERING 106 5 TIME-INDEPENDENT APPROACH TO REACTIVE SCATTERING 107
5.1 INTRODUCTION 107 5.2 DISTORTED-WAVE BORN APPROXIMATION 108 5.3
HYPERSPHERICAL COORDINATE APPROACH 109 CONTENTS XI 5.4 VARIATIONAL
ALGEBRAIC APPROACH 111 5.4.1 MULTI-ARRANGEMENT EXPANSION OF WAVEFUNCTION
. . . 111 5.4.2 COUPLED ARRANGEMENT INTEGRAL EQUATION 112 5.4.3
ALGEBRAIC METHOD 115 5.4.4 SCHWINGER VARIATIONAL METHOD 118 5.4.5 KOHN
VARIATIONAL METHOD 120 5.5 ATOM-DIATOM REACTIVE SCATTERING 127 5.5.1
HAMILTONIAN AND BASIS SET 128 5.5.2 CALCULATION OF DIRECT MATRIX
ELEMENTS 129 5.5.3 CALCULATION OF EXCHANGE MATRIX ELEMENTS 131 5.5.4 H +
H 2 REACTION 134 5.5.5 F + H 2 REACTION 140 6 TIME-DEPENDENT APPROACH TO
REACTIVE SCATTERING 145 6.1 INTRODUCTION 145 6.2 REPRESENTATIONS 146 6.3
METHODS OF TIME PROPAGATION 147 6.3.1 FINITE DIFFERENCE METHOD 147 6.3.2
SPLIT-OPERATOR METHOD 148 6.3.3 CHEBYCHEV POLYNOMIAL METHOD 149 6.3.4
GAUSSIAN WAVEPACKETS 151 6.4 APPLICATION TO REACTIVE SCATTERING 153
6.4.1 EXTRACTION OF SCATTERING INFORMATION 154 6.4.2 REACTIVE FLUX AND
TOTAL REACTION PROBABILITY . . . . 155 6.4.3 USE OF ABSORBING POTENTIALS
157 6.5 TRIATOMIC REACTION: A + BC 158 6.5.1 HAMILTONIAN AND WAVEPACKET
PROPAGATION 158 6.5.2 REACTION OF H + 0 2 160 6.6 TETRAATOMIC REACTION:
AB + CD 163 6.6.1 BEYOND TRIATOMIC SYSTEMS 163 6.6.2 HAMILTONIAN AND
BASIS FUNCTIONS 165 6.6.3 TREATMENT FOR SPECTATOR BONDS 169 6.6.4
REACTION OF H 2 + OH 170 6.6.5 REACTION OF HO + CO 175 7 STATE-TO-STATE
REACTIVE SCATTERING 179 7.1 INTRODUCTION 179 7.2 STATE-TO-STATE S MATRIX
ELEMENTS 180 7.2.1 TIME-INDEPENDENT EXPRESSIONS OF S MATRIX ELEMENTS 180
7.2.2 TIME-DEPENDENT EXPRESSIONS OF S MATRIX ELEMENTS . 182 7.2.3
STATE-TO-STATE REACTIVE SCATTERING OF H + 0 2 . . . . 187 7.3 RPD
APPROACH TO STATE-TO-STATE REACTIONS 189 7.3.1 THE RPD EQUATIONS 191
7.3.2 REACTANT COMPONENT WAVEFUNCTION 192 7.3.3 PRODUCT COMPONENT
WAVEFUNCTION 193 7.3.4 EXTRACTION OF STATE-TO-STATE S MATRIX ELEMENTS .
. . 195 7.3.5 A COLLOCATION QUADRATURE SCHEME 195 7.4 RPD METHOD FOR
TRIATOMIC REACTIONS 196 7.4.1 TRANSFORMATION OF JACOBI COORDINATES 196
7.4.2 NUMERICAL TEST FOR H -I- H 2 REACTION 197 DYNAMICS OF CHEMICAL
REACTIONS 201 8.1 SCATTERING RESONANCE . 201 8.1.1 INTRODUCTION 201
8.1.2 PHASE SHIFT AND TIME DELAY 202 8.1.3 LIFETIME MATRIX 204 8.1.4
IMPLICATION OF RESONANCE IN CROSS SECTIONS 205 8.2 FORMAL THEORY OF
RESONANCE 206 8.2.1 COMPLEX SYMMETRIE OPERATOR 206 8.2.2 PROJECTION
OPERATORS AND FESHBACH PARTITIONING . . 207 8.2.3 RESONANCE STATES 210
8.2.4 DECAY OF RESONANCE 213 8.2.5 CALCULATION OF RESONANCE 215 8.3
REACTION RATES AND TRANSITION STATE THEORY 216 8.3.1 CUMULATIVE REACTION
PROBABILITY 216 8.3.2 RELATION TO TRANSITION STATE THEORY 218 PHOTON
INDUCED MOLECULAR PROCESSES 223 9.1 INTRODUCTION 223 9.2 TIME-DEPENDENT
PERTURBATION THEORY 224 9.3 INTERACTION OF MOLECULES WITH THE RADIATION
FIELD 227 9.3.1 VECTOR POTENTIALS IN QUANTUM MECHANICS 227 9.3.2
QUANTIZED RADIATION FIELD 230 9.3.3 ONE PHOTON PROCESSES 232 9.3.4 TWO
PHOTON PROCESSES: LIGHT SCATTERING 234 9.4 PHOTODISSOCIATION OF
MOLECULES 238 9.4.1 HALF COLLISION DYNAMICS 238 9.4.2 THEORETICAL
TREATMENT 239 9.4.3 DISSOCIATION OF H 2 0 241 9.4.4 DISSOCIATION OF H 2
0 2 242 9.5 VIBRATIONAL PREDISSOCIATION OF MOLECULES 246 9.5.1
INTRODUCTION 246 CONTENTS XIII 9.5.2 TIME-DEPENDENT GOLDEN RULE
TREATMENT 248 9.5.3 HECL 2 (U) -FHE + CL 2 (V - 1) 250 9.5.4 D 2 HF(U =
1) -+ D 2 + HF(V = 0) 252 9.6 FLUX METHOD FOR PHOTOFRAGMENTATION 254
9.6.1 SINGLE ARRANGEMENT 254 9.6.2 MULTI-ARRANGEMENT 257 9.6.3
TIME-DEPENDENT FLUX CALCULATION 258 9.7 THE RPD APPROACH TO
PHOTOFRAGMENTATION DYNAMICS . . . 261 9.7.1 THEORETICAL FORMULATION 261
10 MOLECULAR REACTIONS ON SURFACES 265 10.1 INTRODUCTION 265 10.2
THEORETICAL MODELS 266 10.2.1 DISSOCIATIVE ADSORPTION ON METAL SURFACES
266 10.2.2 FIAT SURFACE MODEL 267 10.2.3 FIXED SITE CORRUGATED SURFACE
MODEL 270 10.2.4 A SELECTION RULE FOR HOMONUCLEAR DIATOMS 271 10.2.5
FULLY CORRUGATED SURFACE MODEL 273 10.3 THE H 2 /CU(LLL) SYSTEM 275
10.3.1 BACKGROUND 275 10.3.2 POTENTIAL ENERGY SURFACE FOR H 2 /CU(LLL)
276 10.3.3 RESULTS OF QUANTUM DYNAMICS STUDIES 278 11 SEMICLASSICAL
DESCRIPTIONS OF QUANTUM MECHANICS 285 11.1 WKB APPROXIMATION 285 11.1.1
GENERAL FORMALISM 285 11.1.2 TURNING POINTS AND CONNECTION FORMULAE 287
11.2 UNIFORM SEMICLASSICAL APPROXIMATION 290 11.2.1 COMPARISON EQUATIONS
290 11.2.2 APPLICATIONS OF THE UNIFORM APPROXIMATION 292 11.2.3 LANGER
MODIFICATION 299 11.3 SEMICLASSICAL SCATTERING 301 11.3.1 PHASE SHIFT IN
ELASTIC SCATTERING 301 11.3.2 ELASTIC CROSS SECTIONS 302 11.4 PATH
INTEGRAL AND STATIONARY PHASE APPROXIMATION 305 11.4.1 STATIONARY PHASE
APPROXIMATION 305 11.4.2 PATH INTEGRAL REPRESENTATION OF QUANTUM
MECHANICS 306 11.4.3 STATIONARY PHASE APPROXIMATION OF THE PATH INTEGRAL
309 11.4.4 INITIAL VALUE REPRESENTATION 311 XIV CONTENTS APPENDIX A
ORTHOGONAL POLYNOMIALS AND SPECIAL FUNCTIONS 315 A.L HERMITE POLYNOMIALS
315 A.2 LEGENDRE POLYNOMIALS 317 A.3 SPHERICAL HARMONICS 318 A.4
CHEBYCHEV POLYNOMIALS 320 A.5 SPHERICAL BESSEL FUNCTIONS 321 A.6 USEFUL
MATHEMATICAL FORMULAE 323 APPENDIX B GAUSSIAN QUADRATURE 325 APPENDIX C
CLEBSCH-GORDON COEFFICIENTS 329 APPENDIX D SPACE-FIXED AND BODY-FIXED
FRAMES 333 D.L COORDINATE ROTATIONS AND ANGULAR MOMENTUM 333 D.2
ROTATION MATRIX 334 D.3 TRANSFORMATION BETWEEN SF AND BF BASIS 337 D.4
TOTAL ANGULAR MOMENTUM IN THE BF FRAME 340 BIBLIOGRAPHY 345 INDEX 359
|
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| indexdate | 2024-07-09T20:06:56Z |
| institution | BVB |
| isbn | 9810233884 |
| language | English |
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| spelling | Zhang, John Zeng-hui Verfasser aut Theory and application of quantum molecular dynamics John Zeng Hui Zhang Singapore [u.a.] World Scientific 1999 XIV, 366 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Reaktionskinetik (DE-588)4048655-2 gnd rswk-swf Molekulardynamik (DE-588)4170370-4 gnd rswk-swf Quantenchemie (DE-588)4047979-1 gnd rswk-swf Reaktionsdynamik (DE-588)4301792-7 gnd rswk-swf Molekulardynamik (DE-588)4170370-4 s Quantenchemie (DE-588)4047979-1 s DE-604 Reaktionskinetik (DE-588)4048655-2 s Reaktionsdynamik (DE-588)4301792-7 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013147877&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhang, John Zeng-hui Theory and application of quantum molecular dynamics Reaktionskinetik (DE-588)4048655-2 gnd Molekulardynamik (DE-588)4170370-4 gnd Quantenchemie (DE-588)4047979-1 gnd Reaktionsdynamik (DE-588)4301792-7 gnd |
| subject_GND | (DE-588)4048655-2 (DE-588)4170370-4 (DE-588)4047979-1 (DE-588)4301792-7 |
| title | Theory and application of quantum molecular dynamics |
| title_auth | Theory and application of quantum molecular dynamics |
| title_exact_search | Theory and application of quantum molecular dynamics |
| title_full | Theory and application of quantum molecular dynamics John Zeng Hui Zhang |
| title_fullStr | Theory and application of quantum molecular dynamics John Zeng Hui Zhang |
| title_full_unstemmed | Theory and application of quantum molecular dynamics John Zeng Hui Zhang |
| title_short | Theory and application of quantum molecular dynamics |
| title_sort | theory and application of quantum molecular dynamics |
| topic | Reaktionskinetik (DE-588)4048655-2 gnd Molekulardynamik (DE-588)4170370-4 gnd Quantenchemie (DE-588)4047979-1 gnd Reaktionsdynamik (DE-588)4301792-7 gnd |
| topic_facet | Reaktionskinetik Molekulardynamik Quantenchemie Reaktionsdynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013147877&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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