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1 | (5) |
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1.1 Importance of Second Quantization |
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1 | (1) |
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1.2 The One-Electron Model |
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2 | (4) |
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2 Concept of Creation and Annihilation Operators |
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6 | (12) |
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6 | (1) |
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6 | (3) |
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2.3 Particle Number Representation |
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9 | (1) |
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2.4 Annihilating Electrons |
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10 | (2) |
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2.5 Commutator Relation between Creation and Annihilation Operators |
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12 | (2) |
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2.6 The Adjoint Relation -- Role of Orthogonality of One-Particle States |
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14 | (2) |
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2.7 Summary of the Properties of Creation/Annihilation Operators |
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16 | (2) |
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3 Particle Number Operators |
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18 | (4) |
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4 Second Quantized Representation of Quantum Mechanical Operators |
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22 | (11) |
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22 | (1) |
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4.2 One-Electron Operators |
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23 | (3) |
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4.3 Two-Electron Operators |
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26 | (3) |
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4.4 Second Quantized Form of the Born-Oppenheimer Hamiltonian |
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29 | (1) |
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4.5 Hermiticity of Second Quantized Operators |
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30 | (3) |
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5 Evaluation of Matrix Elements |
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33 | (7) |
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5.1 Basic Matrix Elements |
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33 | (2) |
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5.2 Concept of the Fermi Vacuum |
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35 | (5) |
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6 Advantages of Second Quantization - Illustrative Examples |
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40 | (6) |
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40 | (1) |
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6.2 Overlap of two Determinants |
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41 | (1) |
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6.3 Huckel Energy Expression |
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42 | (2) |
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6.4 Interaction of Two Electrons |
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44 | (2) |
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46 | (7) |
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7.1 First-Order Density Matrix |
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46 | (3) |
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7.2 Second-Order Density Matrix |
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49 | (2) |
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7.3 Hartree-Fock Energy Expression |
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51 | (2) |
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8 Connection to "Bra and Ket" Formalism |
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53 | (6) |
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59 | (7) |
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10 Some Model Hamiltonians in Second Quantized Form |
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66 | (21) |
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10.1 π-Electron Hamiltonians |
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66 | (7) |
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66 | (4) |
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70 | (2) |
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10.1.3 Pariser-Parr-Pople (PPP) Model |
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72 | (1) |
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10.2 Particle-Hole Symmetry |
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73 | (7) |
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10.3 All-Valence Electron Hamiltonians |
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80 | (3) |
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10.4 The Hartree-Fock Hamiltonian |
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83 | (4) |
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87 | (6) |
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12 Many-Body Perturbation Theory |
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93 | (10) |
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13 Second Quantization for Nonorthogonal Orbitals |
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103 | (11) |
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13.1 Anticommutation Rules |
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103 | (5) |
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13.2 The Hamiltonian in Nonorthogonal Representations |
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108 | (3) |
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13.3 Extended Huckel Theory |
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111 | (3) |
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14 Second Quantization and Hellmann-Feynman Theorem |
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114 | (7) |
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114 | (2) |
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14.2 Variation of Energy-Orthogonal Basis Set |
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116 | (1) |
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14.3 Variation of Energy-Nonorthogonal Basis Set |
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117 | (2) |
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14.4 Special Case: The SCF Gradient Formula |
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119 | (2) |
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15 Intermolecular Interactions |
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121 | (16) |
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15.1 The Operator for Interaction |
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121 | (10) |
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15.2 Symmetry-Adapted Perturbation Theory |
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131 | (6) |
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16 Quasiparticle Transformations |
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137 | (16) |
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16.1 One-Particle Transformations |
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137 | (4) |
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16.2 Two-Particle Transformations |
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141 | (4) |
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16.3 A Theory of the Local Chemical Bond |
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145 | (8) |
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17 Miscellaneous Topics Related to Second Quantization |
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153 | (10) |
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17.1 Spin Operators and Spin Hamiltonians |
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153 | (6) |
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17.2 Unitary Group Approach |
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159 | (4) |
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163 | (12) |
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175 | (6) |
Index |
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181 | |