Dichtefunktionaltheorie (DFT) ist der Shooting-star unter den quantenchemischen Berechnungsmethoden, die in der Computer-Chemie verwendet werden. Besonders das exzellente Preis-Leistungsverhältnis stimuliert das explosionsartige Wachstum von DFT-Anwendungen in praktisch allen Gebieten der Chemie. Allerdings laufen Anwender, deren Spezialgebiet nicht die Quantentheorie ist, bei der Benutzung von DFT-Programmen als Black-Box-Werkzeug Gefahr, dass sie die Stärken und die Grenzen der Methode falsch einschätzen. Genau für solche Anwender ist dieses Buch geschrieben. Es ist ein zuverlässiger Führer durch das Minenfeld der Fehlinterpretation. Chemiker, denen die konventionelle Quantentheorie geläufig ist, werden dieses Buch begrüßen und von ihm sehr profitieren. Es ist eine besonders instruktive, solide und klar geschriebene Darstellung der Dichtefunktionaltheorie, ihres Fundaments, ihrer Konzepte, Terminologie und Leistungsfähigkeit in vielen Anwendungen. Nutzer von DFT für Struktur-, Energie- und Moleküleigenschaftsberechnungen sowie Untersuchungen von Reaktionsmechanismen werden angeleitet, die optimale Entscheidung für die effektivste Methode zu treffen. Gut gemacht! Paul von Ragu chleyer Many use Density Functional Theory (DFT) programs as black-box tools without having a quantum theoretical background or a concise knowledge about the strength and weaknesses of this approach. This text is designed to bridge the gap and to guide the non-expert user. Foreword v Preface vii Preface to the second edition x Part A The Definition of the Model 1(116) Elementary Quantum Chemistry 3(16) The Schrodinger Equation 3(3) The Variational Principle 6(2) The Hartree-Fock Approximation 8(5) The Restricted and Unrestricted Hartree-Fock Models 13(1) Electron Correlation 14(5) Electron Density and Hole Functions 19(10) The Electron Density 19(1) The Pair Density 20(4) Fermi and Coulomb Holes 24(5) The Fermi Hole 25(2) The Coulomb Hole 27(2) The Electron Density as Basic Variable: Early Attempts 29(4) Does it Make Sense? 29(1) The Thomas-Fermi Model 30(1) Slater's Approximation of Hartree-Fock Exchange 31(2) The Hohenberg-Kohn Theorems 33(8) The First Hohenberg-Kohn Theorem: Proof of Existence 33(3) The Second Hohenberg-Kohn Theorem: Variational Principle 36(1) The Constrained-Search Approach 37(2) Do We Know the Ground State Wave Function in Density Functional Theory? 39(1) Discussion 39(2) The Kohn-Sham Approach 41(24) Orbitals and the Non-Interacting Reference System 41(2) The Kohn-Sham Equations 43(4) Discussion 47(18) The Kohn-Sham Potential is Local 47(1) The Exchange-Correlation Energy in the Kohn-Sham and Hartree-Fock Schemes 48(1) Do the Kohn-Sham Orbitals Mean Anything? 49(1) Is the Kohn-Sham Approach a Single Determinant Method? 50(2) The Unrestricted Kohn-Sham Formalism 52(3) On Degeneracy, Ensembles and other Oddities 55(4) Excited States and the Multiplet Problem 59(6) The Quest for Approximate Exchange-Correlation Functionals 65(28) Is There a Systematic Strategy? 65(2) The Adiabatic Connection 67(2) From Holes to Functionals 69(1) The Local Density and Local Spin-Density Approximations 70(5) The Generalized Gradient Approximation 75(3) Hybrid Functionals 78(7) Self-Interaction 85(3) Asymptotic Behavior of Exchange-Correlation Potentials 88(1) Discussion 89(4) The Basic Machinery of Density Functional Programs 93(24) Introduction of a Basis: The LCAO Ansatz in the Kohn-Sham Equations 93(4) Basis Sets 97(5) The Calculation of the Coulomb Term 102(3) Numerical Quadrature Techniques to Handle the Exchange-Correlation Potential 105(5) Grid-Free Techniques to Handle the Exchange-Correlation Potential 110(3) Towards Linear Scaling Kohn-Sham Theory 113(4) Part B The Performance of the Model 117(148) Molecular Structures and Vibrational Frequencies 119(18) Molecular Structures 119(11) Molecular Structures of Covalently Bound Main Group Elements 119(8) Molecular Structures of Transition Metal Complexes 127(3) Vibrational Frequencies 130(7) Vibrational Frequencies of Main Group Compounds 131(4) Vibrational Frequencies of Transition Metal Complexes 135(2) Relative Energies and Thermochemistry 137(40) Atomization Energies 137(12) Atomic Energies 149(8) Bond Strengths in Transition Metal Complexes 157(6) Ionization Energies 163(3) Electron Affinities 166(2) Electron Excitation Energies and the Singlet/Triplet Splitting in Carbenes 168(9) Electric Properties 177(20) Population Analysis 178(2) Dipole Moments 180(3) Polarizabilities 183(5) Hyperpolarizabilities 188(3) Infrared and Raman Intensities 191(6) Magnetic Properties 197(20) Theoretical Background 198(3) NMR Chemical Shifts 201(8) NMR Nuclear Spin-Spin Coupling Constants 209(2) ESR g-Tensors 211(1) Hyperfine Coupling Constants 211(3) Summary 214(3) Hydrogen Bonds and Weakly Bound Systems 217(22) The Water Dimer---A Worked Example 221(9) Larger Water Clusters 230(2) Other Hydrogen Bonded Systems 232(4) The Dispersion Energy Problem 236(3) Chemical Reactivity: Exploration of Potential Energy Surfaces 239(26) First Example: Pericyclic Reactions 240(7) Electrocyclic Ring Opening of Cyclobutene 241(2) Cycloaddition of Ethylene to Butadiene 243(4) Second Example: The SN2 Reaction at Saturated Carbon 247(2) Third Example: Proton Transfer and Hydrogen Abstraction Reactions 249(6) Proton Transfer in Malonaldehyde Enol 249(3) A Hydrogen Abstraction Reaction 252(3) Fourth Example: H2 Activation by FeO+ in the Gas Phase 255(10) Bibliography 265(30) Index 295