Koch W., Holthausen M.C. A Chemist’s Guide to Density Functional Theory

2nd edition. Wiley-VCH Verlag GmbH. 2001. - 293 p.
A full appreciation of DFT is only gained through an understanding of how the theory, in spite of working with an orbital model and a single determinantal wave function for a model system of noninteracting electrons, still achieves to incorporate electron correlation. The authors justly put emphasis on the pictorial approach, by way of Fermi and Coulomb correlation holes, to understanding exchange and correlation. The present success of DFT proves that modelling of these holes, even if rather crudely, can provide very good energetics. It is also in the simple physical language of shape and extent (localized or delocalized) of these holes that we can understand where the problems of that modelling with only local input (local density, gradient, Laplacian, etc. ) arise. It is because of the well equilibrated treatment of physical principles and chemical applications that this book does a good and very timely service to the computational and quantum chemists as well as to the chemistry community at large.

Contents

Foreword

Preface

Preface to the second edition

Part A The Definition of the Model

Elementary Quantum Chemistry

The Schr?dinger Equation
The Variational Principle
The Hartree-Fock Approximation
The Restricted and Unrestricted Hartree-Fock Models
Electron Correlation

Electron Density and Hole Functions

The Electron Density
The Pair Density
Fermi and Coulomb Holes
The Fermi Hole
The Coulomb Hole

The Electron Density as Basic Variable: Early Attempts

Does it Make Sense?
The Thomas-Fermi Model
Slater’s Approximation of Hartree-Fock Exchange

The Hohenberg-Kohn Theorems

The First Hohenberg-Kohn Theorem: Proof of Existence
The Second Hohenberg-Kohn Theorem: Variational Principle
The Constrained-Search Approach
Do We Know the Ground State Wave Function in Density Functional Theory?
Discussion

The Kohn-Sham Approach

Orbitals and the Non-Interacting Reference System
The Kohn-Sham Equations
Discussion
The Kohn-Sham Potential is Local
The Exchange-Correlation Energy in the Kohn-Sham and Hartree-Fock Schemes
Do the Kohn-Sham Orbitals Mean Anything?
Is the Kohn-Sham Approach a Single Determinant Method?
The Unrestricted Kohn-Sham Formalism On Degeneracy, Ensembles and other Oddities
Excited States and the Multiplet Problem

The Quest for Approximate Exchange-Correlation Functionals

Is There a Systematic Strategy?
The Adiabatic Connection
From Holes to Functionals
The Local Density and Local Spin-Density Approximations
The Generalized Gradient Approximation
Hybrid Functionals
Self-Interaction
Asymptotic Behavior of Exchange-Correlation Potentials
Discussion

The Basic Machinery of Density Functional Programs

Introduction of a Basis: The LCAO Ansatz in the Kohn-Sham Equations
Basis Sets
The Calculation of the Coulomb Term
Numerical Quadrature Techniques to Handle the Exchange-Correlation Potential
Grid-Free Techniques to Handle the Exchange-Correlation Potential
Towards Linear Scaling Kohn-Sham Theory

Part B The Performance of the Model

Molecular Structures and Vibrational Frequencies

Molecular Structures
Molecular Structures of Covalently Bound Main Group Elements
Molecular Structures of Transition Metal Complexes
Vibrational Frequencies
Vibrational Frequencies of Main Group Compounds
Vibrational Frequencies of Transition Metal Complexes

Relative Energies and Thermochemistry

Atomization Energies
Atomic Energies
Bond Strengths in Transition Metal Complexes
Ionization Energies
Electron Affinities
Electronic Excitation Energies and the Singlet/Triplet Splitting in Carbenes

Electric Properties

Population Analysis
Dipole Moments
Polarizabilities
Hyperpolarizabilites
Infrared and Raman Intensities

Magnetic Properties

Theoretical Background
NMR Chemical Shifts
NMR Nuclear Spin-Spin Coupling Constants
ESR g-Tensors
Hyperfine Coupling Constants
Summary

Hydrogen Bonds and Weakly Bound Systems

The Water Dimer – A Worked Example
Larger Water Clusters
Other Hydrogen Bonded Systems
The Dispersion Energy Problem

Chemical Reactivity: Exploration of Potential Energy Surfaces

First Example: Pericyclic Reactions
Electrocyclic Ring Opening of Cyclobutene
Cycloaddition of Ethylene to Butadiene
Second Example: The S_N2 Reaction at Saturated Carbon
Third Example: Proton Transfer and Hydrogen Abstraction Reactions
Proton Transfer in Malonaldehyde Enol
A Hydrogen Abstraction Reaction
Fourth Example: H₂ Activation by FeO⁺ in the Gas Phase

Bibliography

Index