Introduction to Relativistic Quantum Chemistry
Kenneth G. Dyall, Knut Faegri
This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.
Table of Contents
PART I: Foundations1. Introduction 32. Basic Special Relativity3. Relativistic Electromagnetic Interactions 17PART II: The Dirac Equation: Solutions and Properties4. The Dirac Equation 335. Negative-Energy States and Quantum Electrodynamics 516. Relativistic Symmetry 6578.PART III: Four-Component Methodology9. Operators, Matrix Elements and Wave Functions under Time Reversal10. Matrices and Wave Functions under Double-Group Symmetry 14711. Basis Set Expansions of Relativistic Electronic Wave Functions 17312. Correlation Methods 20713. Molecular properties 23314. Density Functional Approaches to Relativistic Quantum Mechanics 261PART IV: Approximations to the Dirac equation15. Spin Separation and the Modified Dirac Equation 27716. Unitary Transformations of the Dirac Hamiltonian 29517. Perturbation Methods 32118. Regular Approximations 35319. Matrix Approximations 37720. Core Approximations 39321. Spin-orbit Configuration Interaction Methods 423PART V: The nature of the relativistic chemical bond22. Relativistic Effects on Molecular Bonding and Structure 449Appendix A: Four-vector quantities 473Appendix B: Vector relations 474Appendix C: Elements of group theory 475Appendix D: Group tables 477Appendix E: Change of Metric for Modified Wave Functions 483Appendix F: Two-Electron Gauge Terms for the Modified Dirac Operator 485Appendix G: The Second-Order Term of the Douglas-Kroll Expansion 487Appendix H: Transformed Operators for Electric and Magnetic Properties 489Appendix I: Gauge Term Contributions from the Breit Interaction to the Breit- Pauli Hamiltonian 492Appendix J: Approximations in Relativistic Density Functional Theory 494Appendix K: The Cowan-Griffin and Wood-Boring Equations. 496Appendix L: Supplementary Reading 497Bibliography 500