Short description Written by two researchers, this book presents the fascinating field of relativistic quantum chemistry in a unique, self-contained way. For the first time this new topic is combined in one book, essential for theoretical chemists and physicists.
From the contents INTRODUCTION Philosophy of this Book Short Reader's Guide Notational Conventions and Choice of Units
PART I: Fundamentals
ELEMENTS OF CLASSICAL MECHANICS AND ELECTRODYNAMICS Elementary Newtonian Mechanics Lagrangian Formulation Hamiltonian Mechanics Elementary Electrodynamics CONCEPTS OF SPECIAL RELATIVITY Einstein's Relativity Principle and Lorentz Transformations Kinematical Effects in Special Relativity Relativistic Dynamics Covariant Electrodynamics Interaction of Two Moving Charged Particles BASICS OF QUANTUM MECHANICS The Quantum Mechanical State The Equation of Motion Observables Angular Momentum and Rotations Pauli Antisymmetry Principle
PART II: Dirac's Theory of the Electron
RELATIVISTIC THEORY OF THE ELECTRON Correspondence Principle and Klein-Gordon Equation Derivation of the Dirac Equation for a Freely Moving Electron Solution of the Free-Electron Dirac Equation Dirac Electron in External Electromagnetic Potentials Interpretation of Negative-Energy States: Dirac's Hole Theory THE DIRAC HYDROGEN ATOM Separation of Electron Motion in a Nuclear Central Field Schrödinger Hydrogen Atom Total Angular Momentum Separation of Angular Coordinates in the Dirac Hamiltonian Radial Dirac Equation for Hydrogen-Like Atoms The Nonrelativistic Limit Choice of the Energy Reference and Matching Energy Scales Wave Functions and Energy Eigenvalues in the Coulomb Potential Finite Nuclear Size Effects Momentum Space Representation
PART III: Four Component Many-Electron Theory
QUANTUM ELECTRODYNAMICS Elementary Quantities and Notation Classical Hamiltonian Description Second-Quantized Field-Theoretical Formulation Implications for the Descriptions of Atoms and Molecules FIRST-QUANTIZED DIRAC-BASED MANY-ELECTRON THEORY Two-Electron Systems and the Breit Equation Quasi-Relativistic Many-Particle Hamiltonians Born-Oppenheimer Approximation Tensor Structure of the Many-Electron Hamiltonian and Wave Function Approximations to the Many-Electron Wave Function Second Quantization for the Many-Electron Hamiltonian Derivation of Effective One-Particle Equations Relativistic Density Functional Theory Completion: The Coupled-Cluster Expansion MANY-ELECTRON ATOMS Transformation of the Many-Electron Hamiltonian to Polar Coordinates Atomic Many-electron Wave Function and jj-Coupling One- and Two-Electron Integrals in Spherical Symmetry Total Expectation Values General Self-Consistent-Field Equations and Atomic Spinors Analysis of Radial Functions and Potentials at Short and Long Distances Numerical Discretization and Solution Techniques Results for Total Energies and Radial Functions GENERAL MOLECULES AND MOLECULAR AGGREGATES Basis Set Expansion of Molecular Spinors Dirac-Hartree-Fock Electronic Energy in Basis Set Representation Molecular One- and Two-Electron Integrals Dirac-Hartree-Fock-Roothaan Matrix Equations Analytic Gradients Post-Hartree-Fock Methods
PART IV: Two-Component Hamiltonians
DECOUPLING THE NEGATIVE-ENERGY STATES Relation of Large and Small Components in One-Electron Equations Closed-Form Unitary Transformations of the Dirac Hamiltonian The Free-Particle Foldy-Wouthuysen Transformations General Parametrization of Unitary Transformations Foldy-Wouthuysen Expansion in Powers of 1/c The Infinite-Order Two-Component One-Step Protocol Toward Well-Defined Analytic Block-Diagonal Hamiltonians DOUGLAS-KROLL-HESS THEORY Sequential Unitary Decoupling Transformations Explicit Form of the DKH Hamiltonians Infinite-Order DKH Hamiltonians and the Arbitrary-Order DKH Method Many-Electron DKH Hamiltonians Computational Aspects of DKH Calculations ELIMINATION TECHNIQUES Naïve Reduction: Pauli Elimination Breit-Pauli Theory The Cowan-Griffin and Wood-Boring Approach Elimination for Different Representations of Dirac Matrices Regular Approximations
PART V: Chemistry with Relativistic Hamiltonians
SPECIAL COMPUTATIONAL TECHNIQUES The Modified Dirac Equation Efficient Calculation of Spin-Orbit Coupling Effects Locality in Four-Component Methods Relativistic Effective Core Potentials EXTERNAL ELECTROMAGNETIC FIELDS AND MOLECULAR PROPERTIES Four-Component Perturbation and Response Theory Reduction to Two-Component Form and Picture Change Artifacts Douglas-Kroll-Hess Property Transformations Magnetic Fields in Resonance Spectroscopies Electric Field Gradient and Nuclear Quadrupole Moment Parity Violation and Electro-Weak Chemistry RELATIVISTIC EFFECTS IN CHEMISTRY Effects in Atoms with Consequences for Chemical Bonding Is Spin a Relativistic Effect? Z-Dependence of Relativistic Effects: Perturbation Theory Potential Energy Surfaces and Spectroscopic Parameters Lanthanides and Actinides Electron Density of Transition Metal Complexes Relativistic Quantum Chemical Calculations in Practice
APPENDIX Vector and Tensor Calculus Kinetic Energy in Generalized Coordinates Technical Proofs for Special Relativity Relations for Pauli and Dirac Matrices Fourier Transformations Discretization and Quadrature Schemes List of Abbreviations and Acronyms List of Symbols
