Markus Reiher, Alexander Wolf

While the theory of quantummechanics has been taught to chemistry students almost since the formulation of the theory in the beginning of the previous century, the equally old theory of relativity has long be considered to be of little relevance to chemistry. This conception changed in the past decades when many studies demonstrated that irregularities observed in the chemistry of heavy and superheavy elements can be explained by considering relativistic effects. At the same time, the tremendous increase in accuracy of the treatment of electron correlation brought the need to incorporate relativistic corrections in the underlying quantum mechanical model to reach quantitative agreement with spectroscopic measurements. Pushed by these two driving forces methods for relativistic quantumchemistry have rapidly evolved and entered mainstream electronic structure theory.

With the mature status of this field, specialized textbooks that provide a chemistry-oriented introduction to the field of relativistic quantum chemistry begin to appear. The most comprehensive book available this far was published by Dyall and Faegri a few years ago. While they filled the gap in the description of modern relativistic quantum chemical methods, readers still had to refer to the older textbooks on relativistic quantum mechanics to find derivations of the starting equations for these methods. The new book of Reiher andWolf provides this background as well, giving the interested chemist a self-contained and accessible treatment that even includes some of necessary mathematical background. The subtitle, The Fundamental Theory of Molecular Science, reveals the ambition of the authors, who advocate a first principles approach in which a few fundamental postulates suffice to obtain all the equations needed for the investigation of molecular systems.

They live up to this ambition by providing a structured and elucidating treatment of the theory of classical and quantum mechanics, electromagnetism and, of course, special relativity. The most important derivations found in physics textbooks are given in some detail, with appropriate reference to more elaborate treatments for the interested reader. A casual reader might be intimidated by the level of detail in this part of the book, but the serious student will appreciate that all of the material needed to master the concepts and techniques is present in one volume. The section on atomic solutions of the Dirac equation contains, for instance, not only the analytical solution of the hydrogen problem but describes also the techniques of numerical integration applied for many-electron atoms.

The consequence of this rigorous approach is that methods specifically developed for molecular systems are discussed relatively late in the book. This part starts by discussing the basis set expansion techniques used to expand the original four-component Dirac equation and then focuses attention on two-component approaches, in which the negative energy solutions of the Dirac equation are eliminated prior to the actual calculation. In particular the two-component Douglas-Kroll-Hess is treated in detail with all the insights that the authors, as prime developers of this method, can offer. Another important scheme, the relativistic effective core potential is only briefly discussed, however. This is an unfortunate omission, because many readers of the book are likely to apply this economical method in their calculations, warranting a more in-depth discussion of the different realizations of the effective core concept. The same brevity is also chosen for the discussion of the regular expansion method that is often used in relativistic density functional theory. For both subdisciplines of relativistic quantum chemistry readers will thus need to consult the original specialized literature.

The last two chapters of the book concern the relativistic calculation of molecular properties and the consequences of relativity for chemical structure and bonding. Both chapters give a good ‘‘feel’’ for the size of relativistic effects in practical calculations and provide guidelines for the application of the modern machinery of relativistic quantum chemistry.

As a teacher of relativistic quantum chemistry to master and Ph.D. students, I can recommend this book to all students entering the field of relativistic electronic structure theory. The clear and consistent notation and self-contained treatment of all the necessary physical and mathematical background makes the book also attractive for experienced researchers who learned the theory from scattered sources and are looking for the insights that this consistent treatment has to offer.


Wiley–VCH, Weinheim, 2009
ISBN: 978-3-527-31292-4
671 pp., hardcover, € 159

Reviewed by:
Prof. Lucas Visscher
Department of Theoretical Chemistry
Faculty of Sciences
Vrije Universiteit Amsterdam
De Boelelaan 1083
1081 HV Amsterdam, The Netherlands