Ebook
Relativistic Quantum Chemistry: The Fundamental Theory of Molecular ScienceISBN: 9783527627493
690 pages
May 2009

Description
Written by two researchers in the field, this book is a reference to explain the principles and fundamentals in a selfcontained, 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
* 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.
* Fundamentals
* Relativistic Theory of a Free Electron: Diracīs 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.
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Table of 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 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
Schrodinger 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
Naive 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
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
Schrodinger 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
Naive 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
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Author Information
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 manyelectron theory. He completed his habilitation in Theoretical Chemistry at the University of ErlangenNuremberg 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 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.
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.
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