Molecular Electromagnetism A Computational Chemistry Approach

by Sauer, Stephan P. A.

• ISBN13: 9780199575398
• ISBN10: 0199575398
• Format: Hardcover
• Copyright: 2011-11-01
• Publisher: Oxford University Press

Summary

This is a textbook on the theory and calculation of molecular electromagnetic and spectroscopic properties designed for a one-semester course with lectures and exercise classes. The idea of the book is to provide thorough background knowledge for the calculation of electromagnetic and spectroscopic properties of molecules with modern quantum chemical software packages. The book covers the derivation of the molecular Hamiltonian in the presence of electromagnetic fields, and of time-independent and time-dependent perturbation theory in the form of response theory. It defines many molecular properties and spectral parameters and gives an introduction to modern computational chemistry methods.

Author Biography

Stephan Sauer studied for his degrees in Germany and Denmark, and has worked since taking his doctorate at the IBM Almaden Research Centre, San Jose, California, USA, at Odense University, Denmark, and at the University of Copenhagen. He has authored more than 100 publications in peer-reviewed international journals.

Table of Contents

Introduction	p. 1
Quantum Mechanical Fundamentals
The Schrödinger Equation in the Presence of Fields	p. 5
The Time-Dependent Schrödinger Equation	p. 5
The Born-Oppenheimer Approximation	p. 7
Electron Charge and Current Density	p. 9
The Force due to Electromagnetic Fields	p. 12
Minimal CouplingùNon-Relativistically	p. 13
Minimal CouplingùRelativistically	p. 17
Elimination of the Small Component	p. 20
The Molecular Electronic Hamiltonian	p. 23
Gauge Transformations	p. 25
Further Reading	p. 28
Perturbation Theory	p. 30
The Hellmann-Feynman Theorem	p. 31
Time-Independent Perturbation Theory	p. 33
Time-Independent Response Theory	p. 37
Second Derivatives of the Energy	p. 38
Density Matrices	p. 39
The Ehrenfest Theorem	p. 41
The Off-Diagonal Hypervirial Theorem	p. 42
The Interaction Picture	p. 43
Time-Dependent Perturbation Theory	p. 44
Transition Probabilities and Rates	p. 47
Time-Dependent Response Theory	p. 49
Matrix Representation of the Propagator	p. 57
Pseudo-Perturbation Theory	p. 64
Further Reading	p. 66
Definition of Properties
Electric Properties	p. 71
Electric Multipole Expansion	p. 71
Potential Energy in an Electric Field	p. 75
Quantum Mechanical Expressions for Electric Moments	p. 77
Induced Electric Moments and Polarizabilities	p. 80
Quantum Mechanical Expressions for Polarizabilities	p. 85
Molecular Electric Fields and Field Gradients	p. 89
Further Reading	p. 91
Magnëtic Properties	p. 93
Magnetic Multipole Expansion	p. 93
Potential Energy in a Magnetic Induction	p. 96
Quantum Mechanical Expression for the Magnetic Moment	p. 97
Induced Magnetic Moment, Magnetizability, and Nuclear Magnetic Shielding	p. 100
Quantum Mechanical Expression for the Magnetizability	p. 102
Molecular Magnetic Fields and ESR Parameters	p. 105
Induced Magnetic Fields and NMR Parameters	p. 109
Quantum Mechanical Expression for the NMR Parameters	p. 112
Sum-over-States Expression for Diamagnetic Terms	p. 118
The Gauge-Origin Problem	p. 121
Further Reading	p. 124
Properties Related to Nuclear Motion	p. 126
Molecular Rotation as Source for Magnetic Moments	p. 126
Quantum Mechanical Expression for the Rotational g Tensor	p. 128
Rotational g Tensor and Electric Dipole Moment	p. 133
Rotational g Tensor and Electric Quadrupole Moment	p. 135
Molecular Rotation as Source for Magnetic Fields	p. 136
Quantum Mechanical Expression for the Spin Rotation Tensor	p. 138
Non-Adiabatic Rotational and Vibrational Reduced Masses	p. 141
Partitioning of the g Factors	p. 148
Further Reading	p. 152
Frequency-Dependent and Spectral Properties	p. 153
Time-Dependent Fields	p. 153
Frequency-Dependent Polarizability	p. 156
Optical Rotation	p. 157
Electronic Excitation Energies and Transition Moments	p. 161
Dipole Oscillator Strength Sums	p. 166
van der Waals Coefficients	p. 169
Further Reading	p. 172
Vibrational Contributions to Molecular Properties	p. 174
Sum-over-States Treatment	p. 175
Clamped-Nucleus Treatment	p. 177
Vibrational and Thermal Averaging	p. 179
Further Reading	p. 184
Computational Methods for the Calculation of Molecular Properties
Short Review of Electronic Structure Methods	p. 189
Hartree-Fock Theory	p. 191
Excited Determinants and Excitation Operators	p. 193
Multiconfigurational Self-Consistent Field Method	p. 196
Configuration Interaction	p. 197
Møller-Plesset Perturbation Theory	p. 198
Coupled Cluster Theory	p. 201
The Hellmann-Feynman Theorem for Approximate Wavefunctions	p. 203
Approximate Density Matrices	p. 207
Further Reading	p. 209
Approximations to Exact Perturbation and Response Theory Expressions	p. 210
Ground-State Expectation Values	p. 210
Sum-over-States Methods	p. 211
Møller-Plesset Perturbation Theory Polarization Propagator	p. 212
Multiconfigurational Polarization Propagator	p. 225
Further Reading	p. 226
Perturbation and Response Theory with Approximate Wavefunctions	p. 227
Coupled and Time-Dependent Hartree-Fock	p. 227
Multiconfigurational Linear Response Functions	p. 233
Second-Order Polarization Propagator Approximation	p. 235
Coupled Cluster Linear Response Functions	p. 236
Further Reading	p. 242
Derivative Methods	p. 243
The Finite-Field Method	p. 243
The Analytic Derivative Method	p. 245
Time-Dependent Analytical Derivatives	p. 248
Further Reading	p. 252
Examples of Calculations and Practical Issues	p. 253
Basis Sets for the Calculation of Molecular Properties	p. 253
Reduced Linear Equations	p. 259
Examples of Electron Correlation Effects	p. 260
Examples of Vibrational Averaging Effects	p. 266
Further Reading	p. 267
Appendices
Operators	p. 271
Perturbation Operators	p. 271
Other Electronic Operators	p. 277
Definitions of Properties	p. 278
Perturbation Theory Expressions for Properties	p. 280
References	p. 282
Index	p. 297
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