Relativistic Quantum Chemistry: The Fundamental Theory of Molecular ScienceISBN: 9783527312924
690 pages
February 2009

* Fundamentals
* Relativistic Theory of a Free Electron: Dirac´s Equation
* Dirac Theory of a Single Electron in a Central Potential
* ManyElectron Theory I: Quantum Electrodynamics
* ManyElectron Theory II: DiracHartreeFock Theory
* Elimination of the Small Component
* Unitary Transformation Schemes
* Relativistic Density Functional Theory
* Physical Observables and Molecular Properties
* Interpretive Approach to Relativistic Quantum Chemistry
From beginning to end, the authors deduce all the concepts and rules, such that readers are able to understand the fundamentals and principles behind the theory. Essential reading for theoretical chemists and physicists.
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 KleinGordon Equation.
Derivation of the Dirac Equation for a Freely Moving Electron.
Solution of the FreeElectron Dirac Equation.
Dirac Electron in External Electromagnetic Potentials.
Interpretation of NegativeEnergy 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 HydrogenLike 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 ManyElectron Theory.
QUANTUM ELECTRODYNAMICS.
Elementary Quantities and Notation.
Classical Hamiltonian Description.
SecondQuantized FieldTheoretical Formulation.
Implications for the Descriptions of Atoms and Molecules.
FIRSTQUANTIZED DIRACBASED MANYELECTRON THEORY.
TwoElectron Systems and the Breit Equation.
QuasiRelativistic ManyParticle Hamiltonians.
BornOppenheimer Approximation.
Tensor Structure of the ManyElectron Hamiltonian and Wave Function.
Approximations to the ManyElectron Wave Function.
Second Quantization for the ManyElectron Hamiltonian.
Derivation of Effective OneParticle Equations.
Relativistic Density Functional Theory.
Completion: The CoupledCluster Expansion.
MANYELECTRON ATOMS.
Transformation of the ManyElectron Hamiltonian to Polar Coordinates.
Atomic Manyelectron Wave Function and jjCoupling.
One and TwoElectron Integrals in Spherical Symmetry.
Total Expectation Values.
General SelfConsistentField 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.
DiracHartreeFock Electronic Energy in Basis Set Representation.
Molecular One and TwoElectron Integrals.
DiracHartreeFockRoothaan Matrix Equations.
Analytic Gradients.
PostHartreeFock Methods.
PART IV: TwoComponent Hamiltonians.
DECOUPLING THE NEGATIVEENERGY STATES.
Relation of Large and Small Components in OneElectron Equations.
ClosedForm Unitary Transformations of the Dirac Hamiltonian.
The FreeParticle FoldyWouthuysen Transformations.
General Parametrization of Unitary Transformations.
FoldyWouthuysen Expansion in Powers of 1/c.
The InfiniteOrder TwoComponent OneStep Protocol.
Toward WellDefined Analytic BlockDiagonal Hamiltonians.
DOUGLASKROLLHESS THEORY.
Sequential Unitary Decoupling Transformations.
Explicit Form of the DKH Hamiltonians.
InfiniteOrder DKH Hamiltonians and the ArbitraryOrder DKH Method.
ManyElectron DKH Hamiltonians.
Computational Aspects of DKH Calculations.
ELIMINATION TECHNIQUES.
Naïve Reduction: Pauli Elimination.
BreitPauli Theory.
The CowanGriffin and WoodBoring 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 SpinOrbit Coupling Effects.
Locality in FourComponent Methods.
Relativistic Effective Core Potentials.
EXTERNAL ELECTROMAGNETIC FIELDS AND MOLECULAR PROPERTIES.
FourComponent Perturbation and Response Theory.
Reduction to TwoComponent Form and Picture Change Artifacts.
DouglasKrollHess Property Transformations.
Magnetic Fields in Resonance Spectroscopies.
Electric Field Gradient and Nuclear Quadrupole Moment.
Parity Violation and ElectroWeak Chemistry.
RELATIVISTIC EFFECTS IN CHEMISTRY.
Effects in Atoms with Consequences for Chemical Bonding.
Is Spin a Relativistic Effect?.
ZDependence 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.
Dr. Alexander Wolf studied physics at the University of ErlangenNuremberg and Imperial College, London. In 2004, he earned his PhD in Theoretical Chemistry working with Bernd Artur Hess in Erlangen. His PhD thesis elaborated on the generalized DouglasKrollHess transformation and efficient decoupling schemes for the Dirac Hamiltonian. Afterwards he worked as as postdoc in the group of Markus Reiher at the universities of Bonn (2004) and Jena (2005). His main research interest is relativistic quantum chemsitry and, in particular, twocomponent Hamiltonians. Since 2006 he has been engaged in financial risk management for various consultancies.