Principles and Practices of Molecular Properties : Theory, Modeling, and Simulations.

Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction -- Chapter 2 Quantum Mechanics -- 2.1 Fundamentals -- 2.1.1 Postulates of Quantum Mechanics -- 2.1.2 Lagrangian and Hamiltonian Formalisms -- 2.1.3 Wave Functions and Operators -- 2.2 Time Evolution of Wave Functions -- 2.3 Time Evolution of Expectation Values -- 2.4 Variational Principle -- Further Reading -- Chapter 3 Particles and Fields -- 3.1 Microscopic Maxwell's Equations -- 3.1.1 General Considerations -- 3.1.2 The Stationary Case -- 3.1.3 The General Case -- 3.1.4 Electromagnetic Potentials and Gauge Freedom -- 3.1.5 Electromagnetic Waves and Polarization -- 3.1.6 Electrodynamics: Relativistic and Nonrelativistic Formulations -- 3.2 Particles in Electromagnetic Fields -- 3.2.1 The Classical Mechanical Hamiltonian -- 3.2.2 The Quantum‐Mechanical Hamiltonian -- 3.3 Electric and Magnetic Multipoles -- 3.3.1 Multipolar Gauge -- 3.3.2 Multipole Expansions -- 3.3.3 The Electric Dipole Approximation and Beyond -- 3.3.4 Origin Dependence of Electric and Magnetic Multipoles -- 3.3.5 Electric Multipoles -- 3.3.5.1 General Versus Traceless Forms -- 3.3.5.2 What We Can Learn from Symmetry -- 3.3.6 Magnetic Multipoles -- 3.3.7 Electric Dipole Radiation -- 3.4 Macroscopic Maxwell's Equations -- 3.4.1 Spatial Averaging -- 3.4.2 Polarization and Magnetization -- 3.4.3 Maxwell's Equations in Matter -- 3.4.4 Constitutive Relations -- 3.5 Linear Media -- 3.5.1 Boundary Conditions -- 3.5.2 Polarization in Linear Media -- 3.5.3 Electromagnetic Waves in a Linear Medium -- 3.5.4 Frequency Dependence of the Permittivity -- 3.5.4.1 Kramers-Kronig Relations -- 3.5.4.2 Relaxation in the Debye Model -- 3.5.4.3 Resonances in the Lorentz Model -- 3.5.4.4 Refraction and Absorption -- 3.5.5 Rotational Averages -- 3.5.6 A Note About Dimensions, Units, and Magnitudes -- Further Reading.

Chapter 4 Symmetry -- 4.1 Fundamentals -- 4.1.1 Symmetry Operations and Groups -- 4.1.2 Group Representation -- 4.2 Time Symmetries -- 4.3 Spatial Symmetries -- 4.3.1 Spatial Inversion -- 4.3.2 Rotations -- Further Reading -- Chapter 5 Exact‐State Response Theory -- 5.1 Responses in Two‐Level System -- 5.2 Molecular Electric Properties -- 5.3 Reference‐State Parameterizations -- 5.4 Equations of Motion -- 5.4.1 Time Evolution of Projection Amplitudes -- 5.4.2 Time Evolution of Rotation Amplitudes -- 5.5 Response Functions -- 5.5.1 First‐Order Properties -- 5.5.2 Second‐Order Properties -- 5.5.3 Third‐Order Properties -- 5.5.4 Fourth‐Order Properties -- 5.5.5 Higher‐Order Properties -- 5.6 Dispersion -- 5.7 Oscillator Strength and Sum Rules -- 5.8 Absorption -- 5.9 Residue Analysis -- 5.10 Relaxation -- 5.10.1 Density Operator -- 5.10.2 Liouville Equation -- 5.10.3 Density Matrix from Perturbation Theory -- 5.10.4 Linear Response Functions from the Density Matrix -- 5.10.5 Nonlinear Response Functions from the Density Matrix -- 5.10.6 Relaxation in Wave Function Theory -- 5.10.7 Absorption Cross Section -- 5.10.8 Einstein Coefficients -- Further Reading -- Chapter 6 Electronic and Nuclear Contributions to Molecular Properties -- 6.1 Born-Oppenheimer Approximation -- 6.2 Separation of Response Functions -- 6.3 Molecular Vibrations and Normal Coordinates -- 6.4 Perturbation Theory for Vibrational Wave Functions -- 6.5 Zero‐Point Vibrational Contributions to Properties -- 6.5.1 First‐Order Anharmonic Contributions -- 6.5.2 Importance of Zero‐Point Vibrational Corrections -- 6.5.3 Temperature Effects -- 6.6 Pure Vibrational Contributions to Properties -- 6.6.1 Perturbation Theory Approach -- 6.6.2 Pure Vibrational Effects from an Analysis of the Electric‐Field Dependence of the Molecular Geometry.

6.7 Adiabatic Vibronic Theory for Electronic Excitation Processes -- 6.7.1 Franck-Condon Integrals -- 6.7.2 Vibronic Effects in a Diatomic System -- 6.7.3 Linear Coupling Model -- 6.7.4 Herzberg-Teller Corrections and Vibronically Induced Transitions -- Further Reading -- Chapter 7 Approximate Electronic State Response Theory -- 7.1 Reference State Parameterizations -- 7.1.1 Single Determinant -- 7.1.2 Configuration Interaction -- 7.1.3 Multiconfiguration Self‐Consistent Field -- 7.1.4 Coupled Cluster -- 7.2 Equations of Motion -- 7.2.1 Ehrenfest Theorem -- 7.2.2 Quasi‐Energy Derivatives -- 7.3 Response Functions -- 7.3.1 Single Determinant Approaches -- 7.3.2 Configuration Interaction -- 7.3.3 Multiconfiguration Self‐Consistent Field -- 7.3.4 Matrix Structure in the SCF, CI, and MCSCF Approximations -- 7.3.5 Coupled Cluster -- 7.4 Residue Analysis -- 7.5 Relaxation -- Further Reading -- Chapter 8 Response Functions and Spectroscopies -- 8.1 Nuclear Interactions -- 8.1.1 Nuclear Charge Distribution -- 8.1.2 Hyperfine Structure -- 8.1.2.1 Nuclear Magnetic Dipole Moment -- 8.1.2.2 Nuclear Electric Quadrupole Moment -- 8.2 Zeeman Interaction and Electron Paramagnetic Resonance -- 8.3 Polarizabilities -- 8.3.1 Linear Polarizability -- 8.3.1.1 Weak Intermolecular Forces -- 8.3.2 Nonlinear Polarizabilities -- 8.4 Magnetizability -- 8.4.1 The Origin Dependence of the Magnetizability -- 8.4.2 Magnetizabilities from Magnetically Induced Currents -- 8.4.3 Isotropic Magnetizabilities and Pascal's Rule -- 8.5 Electronic Absorption and Emission Spectroscopies -- 8.5.1 Visible and Ultraviolet Absorption -- 8.5.2 Fluorescence Spectroscopy -- 8.5.3 Phosphorescence -- 8.5.4 Multiphoton Absorption -- 8.5.4.1 Multiphoton Absorption Cross Sections -- 8.5.4.2 Few‐State Models for Two‐Photon Absorption Cross Section -- 8.5.4.3 General Multiphoton Absorption Processes.

8.5.5 X‐ray Absorption -- 8.5.5.1 Core‐Excited States -- 8.5.5.2 Field Polarization -- 8.5.5.3 Static Exchange Approximation -- 8.5.5.4 Complex or Damped Response Theory -- 8.6 Birefringences and Dichroisms -- 8.6.1 Natural Optical Activity -- 8.6.2 Electronic Circular Dichroism -- 8.6.3 Nonlinear Birefringences -- 8.6.3.1 Magnetic Circular Dichroism -- 8.6.3.2 Electric Field Gradient‐Induced Birefringence -- 8.7 Vibrational Spectroscopies -- 8.7.1 Infrared Absorption -- 8.7.1.1 Double‐Harmonic Approximation -- 8.7.1.2 Anharmonic Corrections -- 8.7.2 Vibrational Circular Dichroism -- 8.7.3 Raman Scattering -- 8.7.3.1 Raman Scattering from a Classical Point of View -- 8.7.3.2 Raman Scattering from a Quantum Mechanical Point of View -- 8.7.4 Vibrational Raman Optical Activity -- 8.8 Nuclear Magnetic Resonance -- 8.8.1 The NMR Experiment -- 8.8.2 NMR Parameters -- Further Reading -- Appendix A Abbreviations -- Appendix B Units -- Appendix C Second Quantization -- C.1 Creation and Annihilation Operators -- C.2 Fock Space -- C.3 The Number Operator -- C.4 The Electronic Hamiltonian on Second‐Quantized Form -- C.5 Spin in Second Quantization -- Appendix D Fourier Transforms -- Appendix E Operator Algebra -- Appendix F Spin Matrix Algebra -- Appendix G Angular Momentum Algebra -- Appendix H Variational Perturbation Theory -- Appendix I Two‐Level Atom -- I.1 Rabi Oscillations -- I.2 Time‐Dependent Perturbation Theory -- I.3 The Quasi‐energy Approach -- Index -- EULA.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.