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[资源] A Chemist’s Guide to Density Functional Theory

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A Chemist’s Guide to Density Functional Theory

Wolfram Koch, Max C. Holthausen

Foreword ..................................................................................................................... V
Preface ....................................................................................................................... VII
Preface to the second edition .............................................................................. X
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
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 and Raman Intensities .................................................................... 191
11 Magnetic Properties .................................................................................. 197
11.1 Theoretical Background .............................................................................. 198
11.2 NMR Chemical Shifts ................................................................................. 201
11.3 NMR Nuclear Spin-Spin Coupling Constants ............................................. 209
11.4 ESR g-Tensors ............................................................................................. 211
11.5 Hyperfine Coupling Constants .................................................................... 211
11.6 Summary ...................................................................................................... 214
12 Hydrogen Bonds and Weakly Bound Systems ........................................ 217
12.1 The Water Dimer – A Worked Example ...................................................... 221
12.2 Larger Water Clusters .................................................................................. 230
12.3 Other Hydrogen Bonded Systems ............................................................... 232
12.4 The Dispersion Energy Problem .................................................................. 236
13 Chemical Reactivity: Exploration of Potential Energy Surfaces .......... 239
13.1 First Example: Pericyclic Reactions ............................................................ 240
13.1.1 Electrocyclic Ring Opening of Cyclobutene ............................................... 241
13.1.2 Cycloaddition of Ethylene to Butadiene ...................................................... 243
13.2 Second Example: The SN2 Reaction at Saturated Carbon ........................... 247
13.3 Third Example: Proton Transfer and Hydrogen Abstraction Reactions ...... 249
13.3.1 Proton Transfer in Malonaldehyde Enol ...................................................... 249
13.3.2 A Hydrogen Abstraction Reaction ............................................................... 252
13.4 Fourth Example: H2 Activation by FeO+ in the Gas Phase .......................... 255

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