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Chapter 1 Computational Quantum Chemistry |
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1.1 What Does Computational Quantum Chemistry Offer? |
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1 | (2) |
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1.2 The Model: Quantum Mechanics |
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3 | (12) |
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1.2.1 The Schrodinger Equation and the Born-Oppenheimer Approximation |
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5 | (6) |
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1.2.2 Electronic Wavefunctions and the Antisymmetry Principle |
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11 | (2) |
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1.2.3 Molecular Orbitals and Basis Set Expansions |
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13 | (2) |
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1.3 Chemistry in Silico: Where Do You Start? |
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15 | (12) |
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1.3.1 Potential Energy Curves, Forces and Force Constants |
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15 | (2) |
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1.3.2 Potential Energy Surfaces, Stationary Points and Reactivity |
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17 | (6) |
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1.3.3 Linking the Electronic Energy with Thermodynamic State Functions |
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23 | (4) |
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1.4 Standard Models of Electronic Structure |
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27 | (20) |
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1.4.1 The Hartree-Fock Model and Electron Correlation |
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28 | (7) |
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1.4.2 Configuration Interaction Methods |
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35 | (2) |
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1.4.3 Perturbation Theory Methods |
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37 | (2) |
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1.4.4 Coupled-Cluster Methods |
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39 | (2) |
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1.4.5 Multiconfigurational and Multireference Methods |
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41 | (5) |
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1.4.6 Density Functional Methods |
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46 | (1) |
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1.5 How Do You Select a Theoretical Model? |
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47 | (1) |
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1.6 The. Apparatus: Hardware and Software |
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48 | (15) |
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Appendix 1A Physical Constants, Atomic Units and Conversion Factors |
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52 | (1) |
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Appendix 1B Elementary Properties of Determinants |
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53 | (3) |
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Appendix 1C Diagonalisation of Matrices |
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56 | (4) |
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Appendix 1D Moments of Inertia and the Inertia Tensor |
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60 | (2) |
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62 | (1) |
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Chapter 2 Computational Electronic Structure Theory |
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2.1 A Few Essential Notions and Requirements |
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63 | (11) |
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2.1.1 Matrix Elements and Integrals |
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65 | (4) |
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2.1.2 Permutational Symmetry of One-and Two - Electron Integrals |
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69 | (1) |
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70 | (2) |
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2.1.4 The Variation Theorem |
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72 | (2) |
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74 | (13) |
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2.2.1 Minimisation of the Hartree-Fock Energy |
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77 | (3) |
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2.2.2 The Canonical Hartree-Fock Equations |
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80 | (1) |
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2.2.3 Understanding Solutions to the Hartree-Fock Equations: Canonical Molecular Orbitals |
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81 | (1) |
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2.2.4 Understanding Solutions to the Hartree-Fock Equations: Orbital Energies |
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82 | (1) |
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2.2.5 The Total Hartree-Fock Energy |
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83 | (2) |
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2.2.6 Ionisation Energies: Koopmans' Theorem |
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85 | (2) |
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2.3 Open-Shell Systems in Hartree-Fock Theory |
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87 | (7) |
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2.3.1 The Restricted Open-Shell Hartree-Fock (ROHF) Method |
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87 | (1) |
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2.3.2 The Unrestricted Hartree-Fock (UHF) Method |
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88 | (3) |
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2.3.3 UHF Method for S = 0 and the Dissociation Problem |
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91 | (1) |
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92 | (2) |
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2.4 Computational Realisation of the Hartree-Fock Theory |
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94 | (12) |
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2.4.1 The Roothaan-Hall Equations and Basis Set Expansions |
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94 | (5) |
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2.4.2 Orbital Optimisation: The Self-Consistent Field (SCF) Procedure for Closed Shells |
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99 | (1) |
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2.4.3 Basis Set Expansions in the UHF Method |
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99 | (3) |
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2.4.4 Convergence of the SCF Process |
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102 | (2) |
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2.4.5 The Direct SCF Method |
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104 | (2) |
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106 | (12) |
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2.5.1 Gaussian Type Functions |
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106 | (7) |
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2.5.2 Types of Contracted Basis Sets |
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113 | (3) |
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2.5.3 Basis Set Superposition Error: Non-Covalent Interactions |
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116 | (2) |
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2.6 Electron Correlation: Background to Post Hartree-Fock Methods |
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118 | (20) |
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2.6.1 Brillouin's Theorem |
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121 | (1) |
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2.6.2 Spin Eigenfunctions/Configuration State Functions |
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122 | (5) |
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2.6.3 Integral Approximations: Density Fitting Configuration Interaction Methods |
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127 | (5) |
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2.7.1 Density Matrices and Natural Orbitals |
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132 | (1) |
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2.7.2 Truncated Configuration Interaction Methods |
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133 | (4) |
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2.7.3 The Frozen Core Approximation |
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137 | (1) |
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138 | (10) |
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2.8.1 Maller-Plesset Perturbation Theory |
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143 | (4) |
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2.8.2 Improvements in Low-Order Perturbation Theory: Spin Component Scaling and Orbital Optimisation |
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147 | (1) |
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2.9 Coupled-Cluster Methods |
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148 | (5) |
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2.9.1 The Coupled-Cluster Doubles Equations |
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149 | (3) |
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2.9.2 Higher Order Methods |
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152 | (1) |
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2.10 Localised Orbital Formulations of Post Hartree-Fock Techniques |
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153 | (4) |
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2.11 Non-Dynamic Electron Correlation and Multi-configurational Reference Wavefunctions |
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157 | (11) |
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2.11.1 The MCSCF Method and Associated Optimisation Problems |
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160 | (5) |
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2.11.2 Electron Correlation Methods Based on a CASSCF Reference Wavefunction |
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165 | (3) |
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2.12 Density Functional Theory |
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168 | (23) |
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2.12.1 The Hohenberg-Kohn Theorems |
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170 | (2) |
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2.12.2 The Kohn-Sham Method |
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172 | (3) |
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2.12.3 The Local Density Approximation |
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175 | (1) |
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2.12.4 Generalised Gradient Approximation |
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176 | (2) |
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2.12.5 Meta-Generalised Gradient Approximation |
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178 | (1) |
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2.12.6 Adiabatic Connection: Hybrid Functional |
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178 | (1) |
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2.12.7 Double Hybrid Functionals |
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179 | (1) |
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2.12.8 Non-Covalent Interactions |
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180 | (1) |
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2.12.9 Ionisation Energies in Density Functional Theory |
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181 | (2) |
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Appendix 2A The Method of Lagrange Multipliers |
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183 | (1) |
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Appendix 2B Orthogonalisation Methods |
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184 | (3) |
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Appendix 2C Computing Eigenvalues and Eigenvectors of Large Matrices |
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187 | (1) |
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188 | (3) |
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Chapter 3 The Computation of Molecular Properties |
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3.1 Molecular Properties as Derivatives of the Potential Energy |
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191 | (3) |
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3.2 Analytic Differentiation of the Energy Expression |
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194 | (4) |
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3.2.1 Variational Wavefunctions |
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195 | (2) |
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3.2.2 Non-Variational Wavefunctions |
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197 | (1) |
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3.3 First Derivative with Respect to Geometric Coordinates: Variational Case |
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198 | (3) |
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3.4 Second Derivative with Respect to Geometric Coordinates: Variational Case |
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201 | (3) |
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3.5 Application of Energy Derivatives with Respect to Geometric Coordinates: Geometry Optimisation |
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204 | (4) |
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3.6 Electric and Magnetic Field Perturbations |
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208 | (9) |
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3.6.1 External Electric Fields |
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208 | (1) |
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3.6.2 External Magnetic Fields and Internal Magnetic Moments |
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209 | (8) |
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3.7 Time-Dependent Linear Response Methods: Excited States |
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217 | (4) |
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3.8 Continuum Methods of Solvation |
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221 | (7) |
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225 | (3) |
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Chapter 4 Understanding Molecular Wavefunctions, Orbitals and Densities |
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4.1 Isosurface Representations |
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228 | (2) |
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4.2 Canonical Orbitals, Density Matrices and Natural Orbitals |
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230 | (3) |
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4.3 Natural Bond Orbitals |
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233 | (1) |
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4.4 Localised Molecular Orbitals |
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234 | (3) |
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4.5 Natural Transition Orbitals |
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237 | (2) |
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4.6 Electronic Population Analysis |
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239 | (3) |
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4.7 Mayer Bond Orders and Valencies |
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242 | (1) |
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4.8 Electrostatic Potential |
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242 | (2) |
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4.9 Energy Decomposition Analysis |
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244 | (5) |
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248 | (1) |
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Chapter 5 Relativistic Effects and Electronic Structure Theory |
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5.1 Relativistic Effects and Chemistry |
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249 | (3) |
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5.2 Special Relativity and the Dirac Equation |
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252 | (5) |
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5.3 Elimination of the Small Component: The Pauli Approximation |
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257 | (3) |
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5.4 Elimination of the Small Component: Regular Approximations |
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260 | (3) |
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5.5 Elimination of the Small Component: Unitary Decoupling of the Dirac Equation |
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263 | (3) |
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5.6 Elimination of the Small Component: The Picture Change Transformation of Operators |
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266 | (1) |
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267 | (3) |
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270 | (2) |
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270 | (2) |
Subject Index |
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272 | |