Relativistic Quantum Chemistry
The Fundamental Theory of Molecular Science
(Sprache: Englisch)
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.
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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.
Klappentext zu „Relativistic Quantum Chemistry “
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.
Inhaltsverzeichnis zu „Relativistic Quantum Chemistry “
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
... mehr
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 Eliminati
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 Eliminati
... weniger
Autoren-Porträt von M. Reiher, A. Wolf
Markus Reiher is working as a professor for Theoretical Chemistry at the ETH Zurich, Switzerland. During his career he has published more than 120 papers and his research is concentrating on various aspects of theoretical chemistry, in particular, on relativistic quantum chemistry.Alexander Wolf has been a co-worker in the group of Markus Reiher, now working for a consulting company.
Rezension zu „Relativistic Quantum Chemistry “
"[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)
Pressezitat
"[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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