Relativistic Quantum Theory Of Atoms And Molecules

This book is intended for physicists and chemists who need to understand the theory of atomic and molecular structure and processes, and who wish to apply the theory to practical problems. As far as practicable, the book provides a self-contained account of the theory of relativistic atomic and molecular structure, based on the accepted formalism of bound-state Quantum Electrodynamics. The author was elected a Fellow of the Royal Society of London in 1992.

Written by two researchers in the field, this book is a reference to explain the principles and fundamentals in a self-contained, complete and consistent way. Much attention is paid to the didactical value, with the chapters interconnected and based on each other. From the contents: * Fundamentals * Relativistic Theory of a Free Electron: Diracï¿1⁄2s Equation * Dirac Theory of a Single Electron in a Central Potential * Many-Electron Theory I: Quantum Electrodynamics * Many-Electron Theory II: Dirac-Hartree-Fock Theory * Elimination of the Small Component * Unitary Transformation Schemes * Relativistic Density Functional Theory * Physical Observables and Molecular Properties * Interpretive Approach to Relativistic Quantum Chemistry From beginning to end, the authors deduce all the concepts and rules, such that readers are able to understand the fundamentals and principles behind the theory. Essential reading for theoretical chemists and physicists.

Recent years have seen a growing interest in the effects of relativity in atoms, molecules and solids. On the one hand, this can be seen as result of the growing awareness of the importance of relativity in describing the properties of heavy atoms and systems containing them. This has been fueled by the inadequacy of physical models which either neglect relativity or which treat it as a small perturbation. On the other hand, it is dependent upon the technological developments which have resulted in computers powerful enough to make calculations on heavy atoms and on systems containing heavy atoms meaningful. Vector processing and, more recently, parallel processing techniques are playing an increasingly vital role in rendering the algorithms which arise in relativistic studies tractable. This has been exemplified in atomic structure theory, where the dominant role of the central nuclear charge simplifies the problem enough to permit some prediction to be made with high precision, especially for the highly ionized atoms of importance in plasma physics and in laser confinement studies. Today's sophisticated physical models of the atom derived from quantum electrodynamics would be intractable without recourse to modern computational machinery. Relativistic atomic structure calculations have a history dating from the early attempts of Swirles in the mid 1930's but continue to provide one of the primary test beds of modern theoretical physics.

This book is primarily intended for graduate chemists and chemical physicists. Indeed, it is based on a graduate course that I give in the Chemistry Depart ment of Southampton University. Nowadays undergraduate chemistry courses usually include an introduction to quantum mechanics with particular reference to molecular properties and there are a number of excellent textbooks aimed specifically at undergraduate chemists. In valence theory and molecular spectroscopy physical concepts are often encountered that are normally taken on trust. For example, electron spin and the anomalous magnetic moment of the electron are usually accepted as postulates, although they are well understood by physicists. In addition, the advent of new techniques has led to experimental situations that can only be accounted for adequately by relatively sophisticated physical theory. Relativis tic corrections to molecular orbital energies are needed to explain X-ray photo electron spectra, while the use oflasers can give rise to multiphoton transitions, which are not easy to understand using the classical theory of radiation. Of course, the relevant equations may be extracted from the literature, but, if the underlying physics is not understood, this is a practice that is at best dissatisfy ing and at worst dangerous. One instance where great care must be taken is in the use of spectroscopically determined parameters to test the accuracy of elec tronic wave functions.

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.

An understanding of the collisions between micro particles is of great importance for the number of fields belonging to physics, chemistry, astrophysics, biophysics etc. The present book, a theory for electron-atom and molecule collisions is developed using non-relativistic quantum mechanics in a systematic and lucid manner. The scattering theory is an essential part of the quantum mechanics course of all universities. During the last 30 years, the author has lectured on the topics presented in this book (collisions physics, photon-atom collisions, electron-atom and electron-molecule collisions, "electron-photon delayed coincidence technique", etc.) at many institutions including Wayne State University, Detroit, MI, The University of Western Ontario, Canada, and The Meerut University, India. The present book is the outcome of those lectures and is written to serve as a textbook for post-graduate and pre-PhD students and as a reference book for researchers.

Quantum mechanics provides the fundamental theoretical apparatus for describing the structure and properties of atoms and molecules in terms of the behaviour of their fundamental components, electrons and nudeL For heavy atoms and molecules containing them, the electrons can move at speeds which represent a substantial fraction of the speed of light, and thus relativity must be taken into account. Relativistic quantum mechanics therefore provides the basic formalism for calculating the properties of heavy-atom systems. The purpose of this book is to provide a detailed description of the application of relativistic quantum mechanics to the many-body prob lem in the theoretical chemistry and physics of heavy and superheavy elements. Recent years have witnessed a continued and growing interest in relativistic quantum chemical methods and the associated computa tional algorithms which facilitate their application. This interest is fu elled by the need to develop robust, yet efficient theoretical approaches, together with efficient algorithms, which can be applied to atoms in the lower part of the Periodic Table and, more particularly, molecules and molecular entities containing such atoms. Such relativistic theories and computational algorithms are an essential ingredient for the description of heavy element chemistry, becoming even more important in the case of superheavy elements. They are destined to become an indispensable tool in the quantum chemist's armoury. Indeed, since relativity influences the structure of every atom in the Periodic Table, relativistic molecular structure methods may replace in many applications the non-relativistic techniques widely used in contemporary research.