Patrick Norman, Kenneth Ruud, Trond Saue

Principles and Practices of Molecular Properties (eBook, PDF)

Theory, Modeling, and Simulations

• Format: PDF

Produktbeschreibung

A comprehensive yet accessible exploration of quantum chemical methods for the determination of molecular properties of spectroscopic relevance Molecular properties can be probed both through experiment and simulation. This book bridges these two worlds, connecting the experimentalist's macroscopic view of responses of the electromagnetic field to the theoretician's microscopic description of the molecular responses. Comprehensive in scope, it also offers conceptual illustrations of molecular response theory by means of time-dependent simulations of simple systems. This important resource in physical chemistry offers: * A journey in electrodynamics from the molecular microscopic perspective to the conventional macroscopic viewpoint * The construction of Hamiltonians that are appropriate for the quantum mechanical description of molecular properties * Time- and frequency-domain perspectives of light-matter interactions and molecular responses of both electrons and nuclei * An introduction to approximate state response theory that serves as an everyday tool for computational chemists * A unified presentation of prominent molecular properties Principles and Practices of Molecular Properties: Theory, Modeling and Simulations is written by noted experts in the field. It is a guide for graduate students, postdoctoral researchers and professionals in academia and industry alike, providing a set of keys to the research literature.

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Produktdetails

• Verlag: John Wiley & Sons
• Erscheinungstermin: 11. Januar 2018
• Englisch
• ISBN-13: 9781118794838
• Artikelnr.: 52579115

Autorenporträt

Patrick Norman is Professor and Head of Theoretical Chemistry and Biology at KTH Royal Institute of Technology, Stockholm, Sweden. His research interests include response theory for non-resonant and resonant external fields in the UV/vis and X-ray regions. He is a co-author of the Dalton program.

Kenneth Ruud is Professor of Theoretical Chemistry at the University of Tromsø ¿ The Arctic University of Norway. His research interests include linear and nonlinear response theory for mixed electric and magnetic fields as well as vibrational and medium effects. He is a co-author of the Dalton program.

Trond Saue is a directeur de recherché of the French National Center for Scientific Research (CNRS) working at Université Toulouse III-Paul Sabatier in France. His research focuses on relativistic methods in theoretical chemistry. He is a principal author of the DIRAC program.

Inhaltsangabe

Preface xi

1 Introduction 1

2 Quantum Mechanics 11

2.1 Fundamentals 11

2.1.1 Postulates of Quantum Mechanics 11

2.1.2 Lagrangian and Hamiltonian Formalisms 11

2.1.3 Wave Functions and Operators 18

2.2 Time Evolution ofWave Functions 22

2.3 Time Evolution of Expectation Values 25

2.4 Variational Principle 27

Further Reading 29

3 Particles and Fields 31

3.1 Microscopic Maxwell's Equations 32

3.1.1 General Considerations 32

3.1.2 The Stationary Case 34

3.1.3 The General Case 38

3.1.4 Electromagnetic Potentials and Gauge Freedom 39

3.1.5 ElectromagneticWaves and Polarization 41

3.1.6 Electrodynamics: Relativistic and Nonrelativistic Formulations 45

3.2 Particles in Electromagnetic Fields 48

3.2.1 The Classical Mechanical Hamiltonian 48

3.2.2 The Quantum-Mechanical Hamiltonian 52

3.3 Electric and Magnetic Multipoles 57

3.3.1 Multipolar Gauge 57

3.3.2 Multipole Expansions 59

3.3.3 The Electric Dipole Approximation and Beyond 63

3.3.4 Origin Dependence of Electric and MagneticMultipoles 64

3.3.5 Electric Multipoles 65

3.3.5.1 General Versus Traceless Forms 65

3.3.5.2 WhatWe Can Learn from Symmetry 68

3.3.6 MagneticMultipoles 69

3.3.7 Electric Dipole Radiation 70

3.4 Macroscopic Maxwell's Equations 72

3.4.1 Spatial Averaging 72

3.4.2 Polarization and Magnetization 73

3.4.3 Maxwell's Equations in Matter 77

3.4.4 Constitutive Relations 79

3.5 Linear Media 81

3.5.1 Boundary Conditions 82

3.5.2 Polarization in LinearMedia 86

3.5.3 ElectromagneticWaves in a Linear Medium 92

3.5.4 Frequency Dependence of the Permittivity 96

3.5.4.1 Kramers-Kronig Relations 97

3.5.4.2 Relaxation in the Debye Model 98

3.5.4.3 Resonances in the LorentzModel 101

3.5.4.4 Refraction and Absorption 104

3.5.5 Rotational Averages 107

3.5.6 A Note About Dimensions, Units, and Magnitudes 110

Further Reading 111

4 Symmetry 113

4.1 Fundamentals 113

4.1.1 Symmetry Operations and Groups 113

4.1.2 Group Representation 117

4.2 Time Symmetries 120

4.3 Spatial Symmetries 125

4.3.1 Spatial Inversion 125

4.3.2 Rotations 127

Further Reading 134

5 Exact-State Response Theory 135

5.1 Responses in Two-Level System 135

5.2 Molecular Electric Properties 145

5.3 Reference-State Parameterizations 151

5.4 Equations of Motion 156

5.4.1 Time Evolution of Projection Amplitudes 157

5.4.2 Time Evolution of Rotation Amplitudes 159

5.5 Response Functions 163

5.5.1 First-Order Properties 166

5.5.2 Second-Order Properties 166

5.5.3 Third-Order Properties 169

5.5.4 Fourth-Order Properties 174

5.5.5 Higher-Order Properties 179

5.6 Dispersion 179

5.7 Oscillator Strength and Sum Rules 183

5.8 Absorption 185

5.9 Residue Analysis 190

5.10 Relaxation 194

5.10.1 Density Operator 195

5.10.2 Liouville Equation 196

5.10.3 Density Matrix from PerturbationTheory 200

5.10.4 Linear Response Functions from the Density Matrix 201

5.10.5 Nonlinear Response Functions from the Density Matrix 204

5.10.6 Relaxation inWave FunctionTheory 204

5.10.7 Absorption Cross Section