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| | Contents | |
| | | |
| |
| | Foreword | V |
| | Preface | VII |
| | | |
| |
| Part A | The Definition of the Model | 1 |
| 1 | Elementary Quantum Chemistry | 3 |
| 1.1 | The Schrödinger Equation | 3 |
| 1.2 | The Variational Principle | 6 |
| 1.3 | The Hartree-Fock Approximation | 8 |
| 1.4 | The Restricted and Unrestricted Hartree-Fock Models | 13 |
| 1.5 | Electron Correlation | 14 |
| 2 | Electron Density and Hole Functions | 19 |
| 2.1 | The Electron Density | 19 |
| 2.2 | The Pair Density | 20 |
| 2.3 | Fermi and Coulomb Holes | 24 |
| 2.3.1 | The Fermi Hole | 25 |
| 2.3.2 | The Coulomb Hole | 27 |
| 3 | The Electron Density as Basic Variable: Early Attempts | 29 |
| 3.1 | Does it Make Sense? | 29 |
| 3.2 | The Thomas-Fermi Model | 30 |
| 3.3 | Slater's Approximation of Hartree-Fock Exchange | 31 |
| 4 | The Hohenberg-Kohn Theorems | 33 |
| 4.1 | The First Hohenberg-Kohn Theorem: Proof of Existence | 33 |
| 4.2 | The Second Hohenberg-Kohn Theorem: Variational Principle | 36 |
| 4.3 | The Constrained-Search Approach | 37 |
| 4.4 | Do We Know the Ground State Wave Function in Density Functional Theory? | 39 |
| 4.5 | Discussion | 39 |
| 5 | The Kohn-Sham Approach | 41 |
| 5.1 | Orbitals and the Non-Interacting Reference System | 41 |
| 5.2 | The Kohn-Sham Equations | 43 |
| 5.3 | Discussion | 47 |
| 5.3.1 | The Kohn-Sham Potential is Local | 47 |
| 5.3.2 | The Exchange-Correlation Energy in the Kohn-Sham and Hartree-Fock Schemes | 48 |
| 5.3.3 | Do the Kohn-Sham Orbitals Mean Anything? | 49 |
| 5.3.4 | Is the Kohn-Sham Approach a Single Determinant Method? | 50 |
| 5.3.5 | The Unrestricted Kohn-Sham Formalism | 52 |
| 5.3.6 | On Degeneracy, Ensembles and other Oddities | 55 |
| 5.3.7 | Excited States and the Multiplet Problem | 59 |
| 6 | The Quest for Approximate Exchange-Correlation Functionals | 65 |
| 6.1 | Is There a Systematic Strategy? | 65 |
| 6.2 | The Adiabatic Connection | 67 |
| 6.3 | From Holes to Functionals | 69 |
| 6.4 | The Local Density and Local Spin-Density Approximations | 70 |
| 6.5 | The Generalized Gradient Approximation | 75 |
| 6.6 | Hybrid Functionals | 78 |
| 6.7 | Self-Interaction | 85 |
| 6.8 | Asymptotic Behavior of Exchange-Correlation Potentials | 88 |
| 6.9 | Discussion | 89 |
| 7 | The Basic Machinery of Density Functional Programs | 93 |
| 7.1 | Introduction of a Basis: The LCAO Ansatz in the Kohn-Sham Equations | 93 |
| 7.2 | Basis Sets | 97 |
| 7.3 | The Calculation of the Coulomb Term | 102 |
| 7.4 | Numerical Quadrature Techniques to Handle the Exchange-Correlation Potential | 105 |
| 7.5 | Grid-Free Techniques to Handle the Exchange-Correlation Potential | 110 |
| 7.6 | Towards Linear Scaling Kohn-Sham Theory | 113 |
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| Part B | The Performance of the Model | 117 |
| 8 | Molecular Structures and Vibrational Frequencies | 119 |
| 8.1 | Molecular Structures | 119 |
| 8.1.1 | Molecular Structures of Covalently Bound Main Group Elements | 119 |
| 8.1.2 | Molecular Structures of Transition Metal Complexes | 127 |
| 8.2 | Vibrational Frequencies | 130 |
| 8.2.1 | Vibrational Frequencies of Main Group Compounds | 131 |
| 8.2.2 | Vibrational Frequencies of Transition Metal Complexes | 135 |
| 9 | Relative Energies and Thermochemistry | 137 |
| 9.1 | Atomization Energies | 137 |
| 9.2 | Atomic Energies | 149 |
| 9.3 | Bond Strengths in Transition Metal Complexes | 157 |
| 9.4 | Ionization Energies | 163 |
| 9.5 | Electron Affinities | 166 |
| 9.6 | Electronic Excitation Energies and the Singlet/Triplet Splitting in Carbenes | 168 |
| 10 | Electric Properties | 177 |
| 10.1 | Population Analysis | 178 |
| 10.2 | Dipole Moments | 180 |
| 10.3 | Polarizabilities | 183 |
| 10.4 | Hyperpolarizabilites | 188 |
| 10.5 | Infrared Intensities | 191 |
| 11 | Magnetic Properties | 195 |
| 11.1 | Theoretical Background | 196 |
| 11.2 | NMR Chemical Shifts | 199 |
| 11.3 | NMR Nuclear Spin-Spin Coupling Constants | 207 |
| 11.4 | ESR g-Tensors | 209 |
| 11.5 | Hyperfine Coupling Constants | 209 |
| 11.6 | Summary | 212 |
| 12 | Hydrogen Bonds and Weakly Bound Systems | 213 |
| 12.1 | The Water Dimer - A Worked Example | 217 |
| 12.2 | Larger Water Clusters | 226 |
| 12.3 | Other Hydrogen Bonded Systems | 228 |
| 12.4 | The Dispersion Energy Problem | 232 |
| 13 | Chemical Reactivity: Exploration of Potential Energy Surfaces | 235 |
| 13.1 | First Example: Pericyclic Reactions | 236 |
| 13.1.1 | Electrocyclic Ring Opening of Cyclobutene | 237 |
| 13.1.2 | Cycloaddition of Ethylene to Butadiene | 240 |
| 13.2 | Second Example: The SN2 Reaction at Saturated Carbon | 243 |
| 13.3 | Third Example: Proton Transfer and Hydrogen Abstraction Reactions | 245 |
| 13.3.1 | Proton Transfer in Malonaldehyde Enol | 245 |
| 13.3.2 | A Hydrogen Abstraction Reaction | 248 |
| 13.4 | Fourth Example: H2 Activation by FeO+ in the Gas Phase | 251 |
| | Bibliography | 261 |
| | Index | 289 |
