Review ofRelativistic Effects in Chemistry Part A: Theory and Techniques

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Book Review

Relativistic Effects in Chemistry Part A: Theoryand Techniques. By Krishnan Balasubramanian, John

( )Wiley & Sons, New York, 1997, 301pp. $84.95 HB .ISBN 0-471-30400-X.

There has been a great deal of interest lately inthe inclusion of relativistic effects in quantumchemical calculations, stemming from the realiza-tion that these may not only affect the quantitativeprediction of chemical properties but even alterthe qualitative description. With more powerfulcomputers it is now possible to incorporate rela-tivistic effects into high-level calculations. The ap-pearance of a book on relativistic effects in chem-istry is therefore very timely.

The preface gives two discernible goals for thetwo volumes of the book. The first is to provideanswers to questions concerning relativistic effectsin chemistry. The second is to compile currenttechniques for relativistic quantum chemical com-putations and results accumulated to the present.The intention to present relativity in a chemicalcontext is also implied in comments on quantummechanics texts. The first volume, the subject ofthis review, is divided into five chapters: an intro-duction; a chapter on special relativity; a chapteron relativistic quantum mechanics; a chapter onrelativistic quantum chemistry; and a chapter ondouble group symmetry.

In the introduction the author gives an overviewof the importance of relativity in chemistry. Theprincipal effects are treated at a basic, descriptivelevel of understanding illustrated with numerousexamples. The presentation is marred by someoversimplifications and overstatements, a numberof errors, the presence of material in tables that isnot discussed in the text, and some irrelevantmaterial. The chapter commences well, but be-comes bogged down in a sequence of exampleswith no connecting thread between them, andsimply ends in the details of an example, withoutever surfacing to the general picture. Regardless

of the somewhat meandering presentation, theimportance of relativity in chemistry is certainlyestablished.

The chapter on special relativity is treated onthe assumption, stated in the preface, that thereader has had no exposure to the topic, andcovers all the aspects of an undergraduate specialrelativity text and in much the same fashion. As anintroduction to these topics, one would be betterserved by standard physics texts, which are moreclearly presented, have many fewer errors, aremore consistent in their notation and the level atwhich derivations are presented, and much betterin their explanations of phenomena. For a bookwhose primary goal is the presentation of relativis-tic effects in chemistry this chapter has a lot ofmaterial that is irrelevant, and does not present atall well the relevant sections, such as the sectionson electromagnetism and on angular momentum.In its favor it does make connections to chemistryfrom time to time, but does not really have thechemistry in view as a goal towards which thechapter is directed.

In a similar vein to the second, the third chaptercontains the kind of material expected in a stan-dard physics text introducing relativistic quantummechanics, covering such topics as the Klein]Gordon and Dirac equations, solutions of the Diracequation, the Foldy]Wouthuysen transformation,and the Breit]Pauli approximation. Like its prede-cessor, it is inferior to the standard physics texts.Inconsistent notation and missing definitions cre-ate confusion, along with the inaccuracies anderrors that are sprinkled throughout the chapter.The same unevenness in the level of explanation asin the second chapter is evident. Some sections,such as that on relativistic angular momentum, arefairly well explained, but others such as theFoldy]Wouthuysen transformation, are not. Thechoice of the relativistic unit system in which c s 1seems antithetical to the goal of a presentation tochemists who almost invariably use Hartree atomicunits.

( )Journal of Computational Chemistry, Vol. 19, No. 13, 1553]1554 1998Q 1998 John Wiley & Sons, Inc. CCC 0192-8651 / 98 / 131553-02

BOOK REVIEW

The fourth chapter is extremely brief. After avery short description of the Dirac Hamiltonian foran atom and the Breit]Pauli Hamiltonian, the the-

Ž .ory of effective core potentials ECPs is presented,followed by a summary description of configura-tion interaction methods and a small three-pagesection on semiempirical and density functionalmethods. The previous two chapters were intro-ductory, preparing for the major focus of the book,which is the theory and techniques of relativisticquantum chemistry. To find a chapter that, apartfrom the ECP section, is largely a prose overviewof methods is odd, to say the least. The assump-tion of a high level of familiarity with quantumchemical methods and the resultant lack of de-tailed description does not fit with the intention tomake a compilation of current techniques. Eventhe derivation of effective core potentials is morefully and lucidly developed in the original papers.It is quite incongruous that the author should gointo great detail on topics that have little bearingon quantum chemistry, and skimp on the sectionsthat have a direct bearing. It is also obvious thatthe author is mainly concerned with his ownmethods: some of the main developers of four-component methods are ignored entirely, and thedescription of methods other than ECP methods isvery sketchy.

The final chapter, on double group theory, is themost well-written chapter. It presents a derivationof character tables for the extra irreducible repre-sentations in the double groups and the develop-ment of relativistic wave functions in terms of

spatial and spin functions. It is amply illustratedand contains character tables for a number ofgroups, including those of the highest symmetry.It anything the explanations are a bit labored attimes, and the chapter would have benefited froma brief introduction to group theory before launch-ing into the construction of character tables, butthe development is, in general, quite clear. As inthe other chapters, there are some obscurities,omissions, and errors, but these are much fewer.One notable omission is the treatment of time-reversal symmetry and its connection to the dou-ble group.

After reading the book, the impression gained isnot of a cohesive whole, but of a collection ofseparate sets of notes related to the theme but onlyloosely connected. Given the errors, the inconsis-tencies and the lack of clarity of many parts of thebook, it is hard to judge the value of having thesenotes together in one volume. As a compilation ofthe author’s own methods it has partially suc-ceeded, and the group theory chapter containsuseful information. As an introduction of relativis-tic quantum chemistry to the novice, it is far fromadequate and liable to cause confusion. The needfor such an introduction remains: this book may betimely, but timeliness alone is not enough.

KENNETH G. DYALL

Thermosciences Institute atNASA Ames Research Center

VOL. 19, NO. 131554