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A Chemist’s Guide to Density Functional Theory
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分享一本书，论坛09年有人传过纳米盘的，纳米盘~~大家懂的。。。 这里重新上传分享 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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