Dirac and beyond

Introduction to relativistic quantum chemistry 

K G Dyall and K Faegri 

Oxford, UK: Oxford University Press 2007 | 544pp | ?58.00 (HB) ISBN 9780195140866 

Reviewed by Fred Manby

I suppose it was always inevitable that this book would start with the quote from Dirac about the completeness of quantum theory, and the challenge of its approximate application. But after this predictable start, the authors plunge into an outstanding introduction, containing very clear expositions of relevant aspects of special relativity, and of relativistic quantum theory. Anyone familiar with non-relativistic quantum chemistry should find it easy to follow the arguments that lead the reader from basic special relativity, through relativistic electrostatics and the Dirac equation, and on to the relativistic quantum theory of many-electron systems. In particular, it is clear that considerable efforts have been invested in striking an appropriate balance between rigour and clarity; and in any case where rigour is compromised, extensive suggestions for further reading are provided. 

Numerous chapters of the book are then devoted to the theory behind practical formulations of relativistic quantum chemistry. The authors deal concisely and clearly with kinetic balance in finite basis set expansions, and dispense summarily with any concerns about variational stability. The chapter on relativistic density functional theory is brief but serves as an adequate introduction. Subsequent chapters cover all of the main approximate approaches to the treatment of relativistic effects, and form a useful and up-to-date reference. 

In summary, this book is an excellent guide to the theoretical background and the computational application of relativistic quantum chemistry. It lives up to the claim of being readable by the non-relativistic quantum chemist, and I can recommend it to anyone interested in using or developing these methods.