Relativistic Quantum Chemistry : The Fundamental Theory of Molecular Science.
Title:
Relativistic Quantum Chemistry : The Fundamental Theory of Molecular Science.
Author:
Reiher, Markus.
ISBN:
9783527667574
Personal Author:
Edition:
2nd ed.
Physical Description:
1 online resource (765 pages)
Contents:
Cover -- Title Page -- Contents -- Preface -- Preface to the Second Edition -- Preface to the First Edition -- 1 Introduction -- 1.1 Philosophy of this Book -- 1.2 Short Reader's Guide -- 1.3 Notational Conventions and Choice of Units -- Part I: FUNDAMENTALS -- 2 Elements of Classical Mechanics and Electrodynamics -- 2.1 Elementary Newtonian Mechanics -- 2.1.1 Newton's Laws of Motion -- 2.1.2 Galilean Transformations -- 2.1.2.1 Relativity Principle of Galilei -- 2.1.2.2 General Galilean Transformations and Boosts -- 2.1.2.3 Galilei Covariance of Newton's Laws -- 2.1.2.4 Scalars, Vectors, and Tensors in Three-Dimensional Space -- 2.1.3 Basic Conservation Laws for One Particle in Three Dimensions -- 2.1.4 Collection of N Particles -- 2.2 Lagrangian Formulation -- 2.2.1 Generalized Coordinates and Constraints -- 2.2.2 Hamiltonian Principle and Euler-Lagrange Equations -- 2.2.2.1 Discrete System of Point Particles -- 2.2.2.2 Example: Planar Pendulum -- 2.2.2.3 Continuous Systems of Fields -- 2.2.3 Symmetries and Conservation Laws -- 2.2.3.1 Gauge Transformations of the Lagrangian -- 2.2.3.2 Energy and Momentum Conservation -- 2.2.3.3 General Space-Time Symmetries -- 2.3 Hamiltonian Mechanics -- 2.3.1 Hamiltonian Principle and Canonical Equations -- 2.3.1.1 System of Point Particles -- 2.3.1.2 Continuous System of Fields -- 2.3.2 Poisson Brackets and Conservation Laws -- 2.3.3 Canonical Transformations -- 2.4 Elementary Electrodynamics -- 2.4.1 Maxwell's Equations -- 2.4.2 Energy and Momentum of the Electromagnetic Field -- 2.4.2.1 Energy and Poynting's Theorem -- 2.4.2.2 Momentum and Maxwell's Stress Tensor -- 2.4.2.3 Angular Momentum -- 2.4.3 Plane Electromagnetic Waves in Vacuum -- 2.4.4 Potentials and Gauge Symmetry -- 2.4.4.1 Lorenz Gauge -- 2.4.4.2 Coulomb Gauge -- 2.4.4.3 Retarded Potentials -- 2.4.5 Survey of Electro- and Magnetostatics.
2.4.5.1 Electrostatics -- 2.4.5.2 Magnetostatics -- 2.4.6 One Classical Particle Subject to Electromagnetic Fields -- 2.4.7 Interaction of Two Moving Charged Particles -- Further Reading -- 3 Concepts of Special Relativity -- 3.1 Einstein's Relativity Principle and Lorentz Transformations -- 3.1.1 Deficiencies of Newtonian Mechanics -- 3.1.2 Relativity Principle of Einstein -- 3.1.3 Lorentz Transformations -- 3.1.3.1 Definition of General Lorentz Transformations -- 3.1.3.2 Classification of Lorentz Transformations -- 3.1.3.3 Inverse Lorentz Transformation -- 3.1.4 Scalars, Vectors, and Tensors in Minkowski Space -- 3.1.4.1 Contraand Covariant Components -- 3.1.4.2 Transformation Properties of Scalars, Vectors, and Tensors -- 3.2 Kinematic Effects in Special Relativity -- 3.2.1 Explicit Form of Special Lorentz Transformations -- 3.2.1.1 Lorentz Boost in One Direction -- 3.2.1.2 General Lorentz Boost -- 3.2.2 Length Contraction, Time Dilation, and Proper Time -- 3.2.2.1 Length Contraction -- 3.2.2.2 Time Dilation -- 3.2.2.3 Proper Time -- 3.2.3 Addition of Velocities -- 3.2.3.1 Parallel Velocities -- 3.2.3.2 General Velocities -- 3.3 Relativistic Dynamics -- 3.3.1 Elementary Relativistic Dynamics -- 3.3.1.1 Trajectories and Relativistic Velocity -- 3.3.1.2 Relativistic Momentum and Energy -- 3.3.1.3 Energy-Momentum Relation -- 3.3.2 Equation of Motion -- 3.3.2.1 Minkowski Force -- 3.3.2.2 Lorentz Force -- 3.3.3 Lagrangian and Hamiltonian Formulation -- 3.3.3.1 Relativistic Free Particle -- 3.3.3.2 Relativistic Particle Subject to External Electromagnetic Fields -- 3.4 Covariant Electrodynamics -- 3.4.1 Ingredients -- 3.4.1.1 Charge-Current Density -- 3.4.1.2 Gauge Field -- 3.4.1.3 Field Strength Tensor -- 3.4.2 Transformation of Electromagnetic Fields -- 3.4.3 Lagrangian Formulation and Equations of Motion.
3.4.3.1 Lagrangian for the Electrodynamic Field -- 3.4.3.2 Minimal Coupling -- 3.4.3.3 Euler-Lagrange Equations -- 3.5 Interaction of Two Moving Charged Particles -- 3.5.1 Scalar and Vector Potentials of a Charge at Rest -- 3.5.2 Retardation from Lorentz Transformation -- 3.5.3 General Expression for the Interaction Energy -- 3.5.4 Interaction Energy at One Instant of Time -- 3.5.4.1 Taylor Expansion of Potential and Energy -- 3.5.4.2 Variables of Charge Two at Time of Charge One -- 3.5.4.3 Final Expansion of the Interaction Energy -- 3.5.4.4 Expansion of the Retardation Time -- 3.5.4.5 General Darwin Interaction Energy -- 3.5.5 Symmetrized Darwin Interaction Energy -- Further Reading -- 4 Basics of Quantum Mechanics -- 4.1 The Quantum Mechanical State -- 4.4.1 Bracket Notation -- 4.1.2 Expansion in a Complete Basis Set -- 4.1.3 Born Interpretation -- 4.1.4 State Vectors in Hilbert Space -- 4.2 The Equation of Motion -- 4.2.1 Restrictions on the Fundamental Quantum Mechanical Equation -- 4.2.2 Time Evolution and Probabilistic Character -- 4.2.3 Stationary States -- 4.3 Observables -- 4.3.1 Expectation Values -- 4.3.2 Hermitean Operators -- 4.3.3 Unitary Transformations -- 4.3.4 Heisenberg Equation of Motion -- 4.3.5 Hamiltonian in Nonrelativistic Quantum Theory -- 4.3.6 Commutation Relations for Position and Momentum Operators -- 4.3.7 The Schrödinger Velocity Operator -- 4.3.8 Ehrenfest and Hellmann-Feynman Theorems -- 4.3.9 Current Density and Continuity Equation -- 4.4 Angular Momentum and Rotations -- 4.4.1 Classical Angular Momentum -- 4.4.2 Orbital Angular Momentum -- 4.4.3 Coupling of Angular Momenta -- 4.4.4 Spin -- 4.4.5 Coupling of Orbital and Spin Angular Momenta -- 4.5 Pauli Antisymmetry Principle -- Further Reading -- Part II: DIRAC'S THEORY OF THE ELECTRON -- 5 Relativistic Theory of the Electron.
5.1 Correspondence Principle and Klein-Gordon Equation -- 5.1.1 Classical Energy Expression and First Hints from the Correspondence Principle -- 5.1.2 Solutions of the Klein-Gordon Equation -- 5.1.3 The Klein-Gordon Density Distribution -- 5.2 Derivation of the Dirac Equation for a Freely Moving Electron -- 5.2.1 Relation to the Klein-Gordon Equation -- 5.2.2 Explicit Expressions for the Dirac Parameters -- 5.2.3 Continuity Equation and Definition of the 4-Current -- 5.2.4 Lorentz Covariance of the Field-Free Dirac Equation -- 5.2.4.1 Covariant Form -- 5.2.4.2 Lorentz Transformation of the Dirac Spinor -- 5.2.4.3 Higher Level of Abstraction and Clifford Algebra -- 5.3 Solution of the Free-Electron Dirac Equation -- 5.3.1 Particle at Rest -- 5.3.2 Freely Moving Particle -- 5.3.3 The Dirac Velocity Operator -- 5.4 Dirac Electron in External Electromagnetic Potentials -- 5.4.1 Kinematic Momentum -- 5.4.2 Electromagnetic Interaction Energy Operator -- 5.4.3 Nonrelativistic Limit and Pauli Equation -- 5.5 Interpretation of Negative-Energy States: Dirac's Hole Theory -- Further Reading -- 6 The Dirac Hydrogen Atom -- 6.1 Separation of Electronic Motion in a Nuclear Central Field -- 6.2 Schrödinger Hydrogen Atom -- 6.3 Total Angular Momentum -- 6.4 Separation of Angular Coordinates in the Dirac Hamiltonian -- 6.4.1 Spin-Orbit Coupling -- 6.4.2 Relativistic Azimuthal Quantum Number Analog -- 6.4.3 Four-Dimensional Generalization -- 6.4.4 Ansatz for the Spinor -- 6.5 Radial Dirac Equation for Hydrogen-Like Atoms -- 6.5.1 Radial Functions and Orthonormality -- 6.5.2 Radial Eigenvalue Equations -- 6.5.3 Solution of the Coupled Dirac Radial Equations -- 6.5.4 Energy Eigenvalue, Quantization and the Principal Quantum Number -- 6.5.5 The Four-Component Ground State Wave Function -- 6.6 The Nonrelativistic Limit.
6.7 Choice of the Energy Reference and Matching Energy Scales -- 6.8 Wave Functions and Energy Eigenvalues in the Coulomb Potential -- 6.8.1 Features of Dirac Radial Functions -- 6.8.2 Spectrum of Dirac Hydrogen-like Atoms with Coulombic Potential -- 6.8.3 Radial Density and Expectation Values -- 6.9 Finite Nuclear Size Effects -- 6.9.1 Consequences of the Nuclear Charge Distribution -- 6.9.2 Spinors in External Scalar Potentials of Varying Depth -- 6.10 Momentum Space Representation -- Further Reading -- Part III: FOUR-COMPONENT MANY-ELECTRON THEORY -- 7 Quantum Electrodynamics -- 7.1 Elementary Quantities and Notation -- 7.1.1 Lagrangian for Electromagnetic Interactions -- 7.1.2 Lorentz and Gauge Symmetry and Equations of Motion -- 7.2 Classical Hamiltonian Description -- 7.2.1 Exact Hamiltonian -- 7.2.2 The Electron-Electron Interaction -- 7.3 Second-Quantized Field-Theoretical Formulation -- 7.4 Implications for the Description of Atoms and Molecules -- Further reading -- 8 First-Quantized Dirac-Based Many-Electron Theory -- 8.1 Two-Electron Systems and the Breit Equation -- 8.1.1 Dirac Equation Generalized for Two Bound-State Electrons -- 8.1.2 The Gaunt Operator for Unretarded Interactions -- 8.1.3 The Breit Operator for Retarded Interactions -- 8.1.4 Exact Retarded Electromagnetic Interaction Energy -- 8.1.5 Breit Interaction from Quantum Electrodynamics -- 8.2 Quasi-Relativistic Many-Particle Hamiltonians -- 8.2.1 Nonrelativistic Hamiltonian for a Molecular System -- 8.2.2 First-Quantized Relativistic Many-Particle Hamiltonian -- 8.2.3 Pathologies of the First-Quantized Formulation -- 8.2.3.1 Continuum Dissolution -- 8.2.3.2 Projection and No-Pair Hamiltonians -- 8.2.4 Local Model Potentials for One-Particle QED Corrections -- 8.3 Separation of Nuclear and Electronic Degrees of Freedom: The Born-Oppenheimer Approximation.
8.4 Tensor Structure of the Many-Electron Hamiltonian and Wave Function.
Abstract:
Einstein proposed his theory of special relativity in 1905. For a long time it was believed that this theory has no significant impact on chemistry. This view changed in the 1970s when it was realized that (nonrelativistic) Schrodinger quantum mechanics yields results on molecular properties that depart significantly from experimental results. Especially when heavy elements are involved, these quantitative deviations can be so large that qualitative chemical reasoning and understanding is affected. For this to grasp the appropriate many-electron theory has rapidly evolved. Nowadays relativistic approaches are routinely implemented and applied in standard quantum chemical software packages. As it is essential for chemists and physicists to understand relativistic effects in molecules, the first edition of "Relativistic Quantum Chemistry - The fundamental Theory of Molecular Science" had set out to provide a concise, comprehensive, and complete presentation of this theory. This second edition expands on some of the latest developments in this fascinating field. The text retains its clear and consistent style, allowing for a readily accessible overview of the complex topic. It is also self-contained, building on the fundamental equations and providing the mathematical background necessary. While some parts of the text have been restructured for the sake of clarity a significant amount of new content has also been added. This includes, for example, an in-depth discussion of the Brown-Ravenhall disease, of spin in current-density functional theory, and of exact two-component methods and its local variants. A strength of the first edition of this textbook was its list of almost 1000 references to the original research literature, which has made it a valuable reference also for experts in the field. In the second edition, more than 100 additional key
references have been added - most of them considering the recent developments in the field. Thus, the book is a must-have for everyone entering the field, as well as for experienced researchers searching for a consistent review.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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