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Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science

ISBN: 978-3-527-31292-4
690 pages
February 2009
Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science (3527312927) cover image
Written by two researchers in the field, this book is a reference to explain the principles and fundamentals in a self-contained, complete and consistent way. Much attention is paid to the didactical value, with the chapters interconnected and based on each other. From the contents:
* Fundamentals
* Relativistic Theory of a Free Electron: Diracīs Equation
* Dirac Theory of a Single Electron in a Central Potential
* Many-Electron Theory I: Quantum Electrodynamics
* Many-Electron Theory II: Dirac-Hartree-Fock 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.
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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.

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Prof. Dr. Markus Reiher obtained his PhD in Theoretical Chemistry in 1998, working in the group of Juergen Hinze at the University of Bielefeld. Since this time he has been working in relativistic many-electron theory. He completed his habilitation in Theoretical Chemistry at the University of Erlangen-Nuremberg in the group of Bernd Artur Hess in 2002. From 2003 to 2005, he was lecturer at the University of Bonn and then moved to the University of Jena as Professor for Physical Chemistry in 2005. Since the beginning of 2006 he has been Professor for Theoretical Chemistry at ETH Zurich. Markus Reiher's research interests are diverse and cover many topics in molecular physics and chemistry. His work has been awarded different prizes.

Dr. Alexander Wolf studied physics at the University of Erlangen-Nuremberg 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 Douglas-Kroll-Hess 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, two-component Hamiltonians. Since 2006 he has been engaged in financial risk management for various consultancies.
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"[This text] aims to be 'a reference to explain the principles and fundamentals in a self-contained, complete and consistent way'.... The authors have achieved their stated aims." (Chemistry World, June 2009)
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