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Preface
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
Kinematic 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 Electronic Motion in a Nuclear Central Field
Schrödinger Hydrogen Atom
Total Angular Momentum
Separation of Angular Coordinates in the Dirac Hamiltonian
Radical 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 Description 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
Relations of Large and Small Components in One-Electron Equations
Closed-Form Unitary Transformations of the Dirac Hamiltonian
The Free-Particle Foldy-Wouthuysen Transformation
General Parametrization of Unitary Transformation
Fold-Wouthuysen Expansion in Powers of 1/c
The Infinite-Order Two-Component Two-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
Naive Reduction: Pauli Elimination
Breit-Pauli Theory
The Cowan-Griffin and Wood-Boring Approaches
Elimination for Different Representations of Dirac Matrices
Regular Approximations
PART V: Chemistry with Relativistic Hamiltonians
SPECIAL COMPUTATIONAL TECHNIQUES
From the Modified Dir

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