Relativistic Quantum Chemistry

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) Schrödinger 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.

Auteur
Markus Reiher obtained his PhD in Theoretical Chemistry in 1998, working in the group of Juergen Hinze at the University of Bielefeld on relativistic atomic structure theory. He completed his habilitation on transition-metal catalysis and vibrational spectroscopy at the University of Erlangen in the group of Bernd Artur Hess in 2002. During that time he had the opportunity to return to relativistic theories when working with Bernd Hess and Alex Wolf. From 2003 to 2005, Markus Reiher was Privatdozent 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 in molecular physics and chemistry are broad and diverse.

Alexander Wolf studied physics at the University of Erlangen and at Imperial College, London. In 2004, he completed his PhD in Theoretical Chemistry in the group of Bernd Artur Hess in Erlangen. His thesis elaborated on the generalized Douglas-Kroll-Hess transformation and efficient decoupling schemes for the Dirac Hamiltonian. As a postdoc he continued to work on these topics in the group of Markus Reiher at the universities of Bonn (2004) and Jena (2005). Since 2006 he has been engaged in financial risk management for various consultancies and is currently working in the area of structuring and modeling of life insurance products. On a regular basis he has been using his spare time to delve into his old passion, relativistic quantum mechanics and quantum chemistry.

Contenu

Preface xxi

1 Introduction 1

1.1 Philosophy of this Book 1

1.2 Short Reader's Guide 4

1.3 Notational Conventions and Choice of Units 6

Part I Fundamentals 9

2 Elements of Classical Mechanics and Electrodynamics 11

2.1 Elementary Newtonian Mechanics 11

2.1.1 Newton's Laws of Motion 11

2.1.2 Galilean Transformations 14

2.1.2.1 Relativity Principle of Galilei 14

2.1.2.2 General Galilean Transformations and Boosts 16

2.1.2.3 Galilei Covariance of Newton's Laws 17

2.1.2.4 Scalars, Vectors, Tensors in 3-Dimensional Space 17

2.1.3 Conservation Laws for One Particle in Three Dimensions 20

2.1.4 Collection of N Particles 21

2.2 Lagrangian Formulation 22

2.2.1 Generalized Coordinates and Constraints 22

2.2.2 Hamiltonian Principle and EulerLagrange Equations 24

2.2.2.1 Discrete System of Point Particles 24

2.2.2.2 Example: Planar Pendulum 26

2.2.2.3 Continuous Systems of Fields 27

2.2.3 Symmetries and Conservation Laws 28

2.2.3.1 Gauge Transformations of the Lagrangian 28

2.2.3.2 Energy and Momentum Conservation 29

2.2.3.3 General SpaceTime Symmetries 30

2.3 Hamiltonian Mechanics 31

2.3.1 Hamiltonian Principle and Canonical Equations 31

2.3.1.1 System of Point Particles 31

2.3.1.2 Continuous System of Fields 32

2.3.2 Poisson Brackets and Conservation Laws 33

2.3.3 Canonical Transformations 34

2.4 Elementary Electrodynamics 35

2.4.1 Maxwell's Equations 36

2.4.2 Energy and Momentum of the Electromagnetic Field 38

2.4.2.1 Energy and Poynting's Theorem 38

2.4.2.2 Momentum and Maxwell's Stress Tensor 39

2.4.2.3 Angular Momentum 40

2.4.3 Plane Electromagnetic Waves in Vacuum 40

2.4.4 Potentials and Gauge Symmetry 42

2.4.4.1 Lorenz Gauge 44

2.4.4.2 Coulomb Gauge 44

2.4.4.3 Retarded Potentials 45

2.4.5 Survey of Electro and Magnetostatics 45

2.4.5.1 Electrostatics 45

2.4.5.2 Magnetostatics 47

2.4.6 One Classical Particle Subject to Electromagnetic Fields 47

2.4.7 Interaction of Two Moving Charged Particles 50

3 Concepts of Special Relativity 53

3.1 Einstein's Relativity Principle and Lorentz Transformations 53

3.1.1 Deficiencies of Newtonian Mechanics 53

3.1.2 Relativity Principle of Einstein 55

3.1.3 Lorentz Transformations 58

3.1.3.1 Definition of General Lorentz Transformations 58

3.1.3.2 Classification of Lorentz Transformations 59

3.1.3.3 Inverse Lorentz Transformation 60

3.1.4 Scalars, Vectors, and Tensors in Minkowski Space 62

3.1.4.1 Contra- and Covariant Components 62

3.1.4.2 Properties of Scalars, Vectors, and Tensors 63

3.2 Kinematic Effects in Special Relativity 67

3.2.1 Explicit Form of Special Lorentz Transformations 67

3.2.1.1 Lorentz Boost in One Direction 67

3.2.1.2 General Lorentz Boost 70

3.2.2 Length Contraction, Time Dilation, and Proper Time 72

3.2.2.1 Length Contraction 72

3.2.2.2 Time Dilation 73

3.2.2.3 Proper Time 74

3.2.3 Addition of Velocities 75

3.2.3.1 Parallel Velocities 75

3.2.3.2 General Velocities 77

3.3 Relativistic Dynamics 78

3.3.1 Elementary Relativistic Dynamics 79

3.3.1.1 Trajectories and Relativistic Velocity 79

3.3.1.2 Relativistic Momentum and Energy 79

3.3.1.3 EnergyMomentum Relation 81

3.3.2 Equation of Motion 83

3.3.2.1 Minkowski Force 83

3.3.2.2 Lorentz Force 85

3.3.3 Lagrangian and Hamiltonian Formulation 86

3.3.3.1 Relativistic Free Particle 86

3.3.3.2 Particle in Electromagnetic Fields 89

3.4 Covariant Electrodynamics 90

3.4.1 Ingredients 91 <p...