Methods of molecular quantum mechanics

목차 (Table of Contents)

• CONTENTS
• Preface to Second Edition = ⅴ
• Units = xiv
• 1 Introductory Surver = 1
• 1.1 Schr$$\ddot o$$dinger's equation = 1
• 1.2 Example : the helium atom = 6
• 1.3 Example : the hydrogen molecule = 17
• Problems 1 = 21
• 2 Mathematical Methods = 25
• 2.1 Complete set expansions = 25
• 2.2 Vector spaces and matrices = 29
• 2.3 The eigenvalue equation = 34
• 2.4 Vartitioning theory = 40
• 2.5 Partitioning and perturbation methods = 45
• Problems 2 = 50
• 3 Many-Electron Wavefunctions = 55
• 3.1 Antisymmerty and the Slater Method = 55
• 3.2 Calulation of the enery : helim atom = 58
• 3.3 Matrix elements between antisymmetrized products = 61
• 3.4 Configuration interaction = 66
• 3.5 An example : the hydrogen molecale = 71
• 3.6 An alternative approach : Fock space = 76
• Problems 3 = 82
• 4 Spin and Permutation Symmetry = 87
• 4.1 Spin eigenfunctions = 87
• 4.2 Methods for constructing spin eigenfunctions = 90
• 4.3 Permutatio symmetry and its implications = 97
• 4.4 Uoung tableaux = 100
• 4.5 The standard irreps of $$S_N$$ = 103
• 4.6 Connections between different bases = 110
• Problems 4 = 113
• 5 Digression : The Electron Distribution = 115
• 5.1 Electron density functions = 115
• 5.2 Density matrices = 119
• 5.3 Density functions for 1-determinant wavefunctiopns = 125
• 5.4 Transition densiies. Generalizations = 128
• 5.5 Localized orbitals. Population analysis = 133
• 5.6 Natural expansions = 135
• 5.7 Molecular properties : An introduction = 137
• 5.8 The pair function. Electron correlation = 142
• 5.9 Spin density = 146
• 5.10 Other density functions = 152
• Problems 5 = 154
• 6 Self-Consistent Field Theory = 159
• 6.1 Hartree-Fock theory. The independent-particle model = 159
• 6.2 Finite-basis approximations. Closed-shell systems = 166
• 6.3 Unrestriced Hartree-Fock Theory = 172
• 6.4 Some futther properties. An open-shell system = 175
• 6.5 Restricted HF theory. An open-shell system = 181
• 6.6 Other open-shell situations. Ensemble averaging = 187
• 6.7 States of given spin = 194
• 6.8 Physical significance of MOs. Localization = 200
• Problems 6 = 206
• 7 Valence Bond Theory = 211
• 7.1 The Heitler-London calculation = 211
• 7.2 Generalizations = 215
• 7.3 Perfect Pairing and resonance = 216
• 7.4 One-configuration VB theory. Non-orthogonal orbitals = 223
• 7.5 Multocofiguration VB theory. Orthogonal orbitals = 234
• 7.6 Multocofiguration VB theory. VB theory. Non-orthogonal orbitals = 239
• 7.7 A non-variational method = 247
• Problems 7 = 251
• 8 Multiconfiguration SCF Theory = 255
• 8.1 The optimization problem = 255
• 8.2 Orbital variation. Stationary-value conditions = 256
• 8.3 Solution of the stationary-value equations = 263
• 8.4 Gradient methods = 267
• 8.5 Use of the Brillouin-Levy-Berthier theorem = 274
• 8.6 Variation of all parameters = 278
• Problems 8 = 282
• 9 Perturbation Theory and Diagram Techniques = 285
• 9.1 Perturbation methods = 285
• 9.2 The Hartree-Fock reference function = 286
• 9.3 The cluster develoment = 294
• 9.4 Diagrammatic perturbation theory = 300
• 9.5 The inked-cluster (Goldston's) theorem = 309
• 9.6 Extensions of the diagrammatic approach = 314
• 9.7 Generalizations = 322
• Problems 9 = 324
• 10 Lager-Scale CI and the Unitary-Group Approach = 327
• 10.1 The general approach = 327
• 10.2 Transformations and tensors = 328
• 10.3 Irreducible bases in CI space = 333
• 10.4 Generators of the unitary group. The Hamiltonian = 341
• 10.5 The matrix-eigenvalue problem Direct CI = 347
• Problems 10 = 352
• 11 Small Terms in the Hamiltionian. Static Properties = 357
• 11.1 Electronic and magnetic interactions. The classical approach = 357
• 11.2 Relativistic effects : one particle = 363
• 11.3 Relativistic treatment of many-particle systems = 366
• 11.4 A variation-perturbation approach = 371
• 11.5 Effect of a uniform electric field = 377
• 11.6 Effect of a uniform magnetic field = 381
• 11.7 Some spin-coupling effects (first-order) = 386
• 11.8 Some spin-coupling effects (second-order) = 394
• 11.9 Variational methods. Coupled Hartree-Fock theory = 404
• 11.10 Generalizations of CHF theory = 410
• Problems 11 = 415
• 12 Dynamic Properties and Response Theory = 419
• 12.1 Preliminaries. Linear response = 419
• 12.2 Time-dependent variation theory = 425
• 12.3 Free and forced Oscillations = 428
• 12.4 Significance of the response matrix = 433
• 12.5 Time-dependent Hartree-Fock theory = 435
• 12.6 Density-matrix form of TDHF theory = 438
• 12.7 Multiconfiguration (MC) TDHF theory = 442
• Probems 12 = 446
• 13 Propagator and Equation-of-Motion Methods = 449
• 13.1 Preliminary notions = 449
• 13.2 Propagators. The polarization propagator = 451
• 13.3 Propagator, Green's functions and density matrices = 457
• 13.4 Some properties of electron propagators = 460
• 13.5 The calculation of propagators = 464
• 13.6 Equation-of-motion (EOM) methods = 475
• Problems 13 = 481
• 14 Intermolecular Forces = 485
• 14.1 Weak interactions. Generalized product functions = 485
• 14.2 Variation theory for subsystems = 491
• 14.3 Configuration interication. Interpretation of the terms = 496
• 14.4 Long-range effects. The dispersion energy = 499
• 14.5 Non-orthegonality and short-range effects = 507
• 14.6 Excited states and resonance interactions = 514
• Problems 14 = 517
• Appendix 1 : Atomic Orbitals = 521
• Appendix 2 : Angular Momentum = 527
• Appendix 3 : Symmetry and Group Concepts = 531
• Appendix 4 : Relativistic terms in the Hamiltonian = 545
• References = 553
• Index = 565