Chemists and physicists are both concerned with how atoms stick together to give the myriad molecules and solids that are known to exist. Chemists are particularly interested in how to make new combinations of atoms which will have such desirable properties as biological activity or zero electrical resistance at easily accessible temperatures. There is a great deal of art in these activities but they increasingly rely on some sort of theory as a guide. To understand the behaviour of atoms we need quantum mechanics, the central equation of which is the famous Schrodinger equation.

The snag is that the equation can only be solved exactly for the simplest atom, the hydrogen atom, which has only one electron. In all other atoms and all molecules the electrons interfere with each other's motion in a complicated way, making the equation insoluble. For all but the simplest molecules, accurate calculations are not possible at present. The solution would seem to be to use, to quote the preface, "as simple as possible but not simpler" models of molecular structure that have secure physical basis but which lead to tractable equations. This is the topic of David Pettifor's book.

All good science begins by surveying the experimental facts that need to be explained; in this case they are the types of structures that are observed. The end cover of the book also has a useful structure map for most binary compounds. There is a concise, lucid explanation of the origins of quantum mechanics. The problem of "many electron atoms" is discussed using the Hartree-Fock model in which each electron is regarded as moving in the averaged out field of the other electrons. This so-called "self-consistent field theory", while not an exact theory, is the basis for most of today's electronic structure calculations. The free-electron gas theory, which appears to be a good model for some metals is discussed, together with the ideas of bands. The more recent density functional theory using the local density approximation is introduced. This is based on a theorem that the energy of a many-electron system depends, in a complicated way, on the electron density.

This theory is shown to be a very satisfactory way of dealing with electron interaction and many accurate calculations have been carried out using it, at about the same cost as a Hartree-Fock type calculation, but with greater accuracy. It is unusual and gratifying to find it described in an undergraduate text. The hallmark of this book is originality; this is a distillation of the author's original efforts over the last 20 or so years.

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The next two chapters consider molecules and their structures. The first deals with the simplest cases of homonuclear and heteronuclear diatomic molecules and the question of how the electrons are distributed between them. In this regard, Pauling's idea of electronegativity dates back to 1932, not 1960.

The fourth chapter points out the delicate balance between different possible structures for a molecule, and that any theory that seeks to explain it needs to be carefully constructed. This the author proceeds to do. It is not easy bedtime reading and, for the reviewer, at least, required a pencil and a large pile of paper to follow the intricate argument. The effort, however, is well worth while. The principles of band theory are derived from the free-electron gas theory and the use of pseudo-potentials developed. The so-called tight binding approximation is introduced and applied to transition metals and semiconductors. At each stage reference is made to the experimental facts about real materials.

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Most of the compounds considered are simple, in that they contain either only one kind of atom or at most two; yet so many useful and important molecules and solids contain more different atoms, that one hopes a similar book might be written about them too.

John Binks lectures in chemistry, the University of Aberdeen.