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Principles and Practices of Molecular Properties

Principles and Practices of Molecular Properties

Authors
Publisher Blackwell Science
Year 01/03/2018
Edition First
Pages 480
Version hardback
Readership level Professional and scholarly
Language English
ISBN 9780470725627
Categories Quantum physics (quantum mechanics & quantum field theory), Chemistry, Quantum & theoretical chemistry, Mechanical engineering & materials
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Book description

Focusing on spectroscopic properties of molecular systems, Quantum Modeling of Molecular Materials presents the state-of-the-art methods in theoretical chemistry that are used to determine molecular properties relevant to different spectroscopies. This timely reference gives a basic presentation of response theory and its application to the simulation of spectroscopic properties of molecular materials. This in-depth presentation of time-dependent response theory and its applications in spectroscopy provides an important advance towards a modern vision of theoretical tools for researchers in academia and industry and postgraduate students.

Principles and Practices of Molecular Properties

Table of contents

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 Pr

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