The large and continually increasing importance of theoretical methods in the solution of chemical problems was impressively documented last year by the conferring of the Nobel price for chemistry on two extraordinary champions of this genre, John Pople and Walter Kohn. Of course, the appearance of Frank Jensen's textbook about computational chemistry could hardly have been better timed. In contrast to the numerous quantum-chemistry textbooks previously available, this book intends to cover the entire field of computational chemistry, although the main emphasis is clearly on the discussion of quantum-mechanical methods.

Jensen begins with an introductory, barely 50 page chapter about empirical force field methods. As in the rest of the book, the aspects being discussed are pleasantly geared toward the requirements of the potential user. In this manner, different parameterization strategies are discussed, and popular force fields are critically examined with regard to their fields of application and are compared to each other. Additional, modern approaches such as the determination of transition structures through force field calculations or the combination of force field methods with quantum-chemical strategies are introduced. Chapters follow in which a conventional, if also state of the art, introduction to the predominant tools of quantum chemistry - the Hartree-Fock approximations, important semiempirical methods (from the Hückel model to PM3 and SAM1_, and current methods for the inclusion of electron correlation (configuration interaction, perturbation theory, coupled cluster) - is given. These sections are sensibly supplemented by a chapter dedicated to the different basis sets and their characteristics, in which extrapolation methods such as the different Gaussian-1 and -2, CBS, or PCI-X methods are also included. A modern theoretical textbook can naturally not be without a chapter about density functional theory, so their fundamentals and popular functionals are on 15 pages concisely introduced. Somewhat more specialized sections follow about valence-bond methods, relativistic approaches, population analysis, and the calculation of molecular properties. Subsequently, an entire discusses the accuracies of the previous introduced methods, with respect to the calculation of energies, geometries, vibrational frequencies, dipole moments, and so on. Fortunately, this discussion is not limited to the ubiquitous water molecule, but rather treats several systems that are more difficult. In the last third of this work, further points important to the subject of the book are worked through, unfortunately rather disjointedly. The relationships between thermodynamic quantities or absolute rate constants and the calculation of molecular  quantities are established. The relevant methods for the optimization of minima and saddle points on potential energy surfaces are discussed and the qualitative concepts of frontier orbital theory and related approaches are expounded. Finally, simulation techniques such as the Monte-Carlo method or molecular dynamics, as well as approximate methods for the inclusion of solvent effect (COSMO, PCM, etc.) are introduced.

Based on the organization of the content and the elementary level of the presentation especially in the first part, this book serves as a useful accompanying text for application-oriented seminars and classes. As a rule, these cover a similar variety of subjects, and do not reduce the modeling and simulation methods to quantum chemistry. Beyond that, the efforts of the author to deliver a modern book that reflects the current state of the art are to be commended. Recent developments, such as hybrid strategies for the combination of force field and quantum-mechanical methods, the R12 approach in the calculations of electron correlation, or fast-multipole as well as pseudospectral methods for the efficient calculation of Columbic interactions are taken up in the discussion. Correspondingly up-to-date are the many useful references, which are as recent as 1998.

Despite this generally positive impression, there are some naturally some details that give rise to critical comments. For example, in some places the mathematical formalisms are described in great detail, while their interpretation is neglected. This is especially striking in the discussion of the density functionals. The highly complex expressions for, for example, Vosko, Wilk, and Nusair (VWN) or Lee, Yang, and Parr (LYP) correlation functionals are reproduced in all their beauty, although the actually do not reflect the underlying physics, but rather springs from purely pragmatic considerations. This reference fails, however, so that the complicated mathematics puts one off and do not impart any increased knowledge. Similar observations can be made about both the overly demanding sections about relativistic methods and the calculation of molecular properties. Here, the level is anything but elementary, much is assumed, and the description is far too compact. It is debatable, for instance, whether the highly complex discussion of propargators methods would be at all helpful to the reader of this book. Similarly, one can ask what the use the reader can make of the barely two-page appendix on the subject of ìsecond quantization.î which has no recognizable connection to the rest of the text. Here, less would surely have been more. Many smaller inconsistencies also blur the picture, such as when important concepts are used without comment many pages before they are introduced (e.g. ìnatural orbitalsî), or are never explained in greater detail (e.g. ìgradient normî). Many misprints have also unfortunately crept in. Apart from the omission of a factor of ìNî in the definition of electron density, these are luckily only distracting and do not invalidate the contents. In the reference section in particular, one finds many wayward spellings of the authorsí names. Also conspicuous is the clear and not always professionally understandable preference for Scandinavian authors in the selection of literature references.

Nevertheless, these critical comments should not obscure the fact that this book is an interesting new release. It covers the subject relevant to this area, is modern, and is over all pleasantly and understandably written. Jensenís book will, despite the small problems, live up to the claims of being a useful introduction to the techniques of computational chemistry. It can be recommended to students of general chemistry,a s well as those scientists interested in the subject, especially in the view of its pleasantly moderate price.

Wolfram Koch
Gesellshaft Deutscher Chemiker
Frankfurt a.M. (Germany)