Leviathons that don't quite cover the expanse

There are four volumes under this single title: thermodynamics, quantum theory, statistical mechanics (in fact, statistical thermodynamics) and a relatively skinny volume on kinetics. Overall, there are 1,284 pages of physical chemistry and it is little wonder the publishers elected to split it into fragments. But even this huge amount of paper does not cover the whole of what the world in general thinks of as physical chemistry.

Like most textbooks, this one sprang from the discontent of the author (who is at the University of California, Santa Barbara) with those available, and in particular a discontent with the fact that they make use of model systems, most notably the perfect gas, that are far removed from the complexity of real systems. In Horia Metiu's case, the discontent was allied with the recognition that most mathematics of physical chemistry can now be carried out efficiently and painlessly by using mathematical software. No longer is it necessary to wade through formal solutions of differential equations or plot data in formats that give straight lines: software can deal with the work of symbolic manipulation and numerical analysis. To that end, the text and the worked examples are built around the use of Mathematica, and there are CDs in each volume with all the workbooks. For those who use Mathcad, the CDs also contain versions of the workbooks translated by Jeffry Madura. Those who use neither will have to fend for themselves, but that in itself will be a good education.

The reliance on software will not appeal to everyone, especially when it is a part of the core structure of the book, and the author's obsession with it might be perceived as a distraction from the establishment of fundamental principles. However, I have sympathy with the general philosophy of the approach, with the fear of mathematics off-loaded on to a screen and the concomitant advantage of being able to explore even quite complex systems. In these volumes, though, the balance seems to be wrong, with physical chemistry emerging as a computation discipline with scant attention paid to its experimental aspects. There are passing references to techniques, but the author's heart lies in equations and their consequences.

One sign of the commitment to software is the dearth of illustrations. I estimate that there is only about one illustration for every ten pages, and many of these are rather trivial. Many chapters have no illustrations, despite the capacity of mathematical software to generate graphs that reveal trends in pedagogically interesting ways. Instructors who favour a touch of reality will be surprised that there is not a single illustration in the chapter on nuclear magnetic resonance.

As is regrettably common in many texts that originate in the US, scant attention is made to the correct use of units that, although perhaps irksomely pedantic, is in my view a component of the precise communication that our international subject demands. For a book that claims to be the bee's knees in a modern approach, it is odd to see Boltzmann's constant expressed in ergs per kelvin (on page 8 of Statistical Mechanics ; there is a confusing typo when it is expressed more appropriately in joules per kelvin on page 142 of Quantum Mechanics ), and the widespread use of calories, dynes and electrostatic units.

This blindness to international standards extends to the style of the text, which is written in the first person singular. It certainly gives the reader a sense of being present at one of the author's lectures, but in places it goes too far. For instance, in the kinetics volume we read:

"Don't worry if you don't know what di-tert-butylperoxide is; we can study its decomposition kinetics even if we don't know what we are talking about (isn't kinetics wonderful?)." That is inappropriate in a scholarly volume, as is the remark in Quantum Mechanics that "spectroscopists have a habit of inventing strange units and they use cm-1 as a unit for vibrational energy [they don't]. Do not ask why, the story is too long..."

Informality is perhaps acceptable in this modern world, but not when it segues into misleading remarks. A good touchstone for accuracy is the definition of the standard state, which Metiu gets doubly wrong in the thermodynamics volume (it is no longer at 1 atm, and temperature is not a part of the definition). I am also surprised at non-standard uses of notations, such as l s for the spin quantum number and O for frequency in spectroscopy. At one stage (in Quantum Mechanics ), the quantum number for a particle in a box is allowed to take negative values.

I remarked earlier that despite its 1,284 pages, this text is incomplete.

The treatment of molecular structure is superficial, and rather oddly symmetry is mentioned only in the most casual way (in Quantum Mechanics), where it is implied that because computers can evaluate integrals so swiftly, there is no need to worry about the implications of symmetry.

That, it seems to me, is a black box too far. (Incidentally, the description of g and u symmetry that precedes this remark is just plain wrong.) This is not a book for courses that consider that the structure of solids is an important part of physical chemistry: band theory does not appear in the index. Diffraction techniques do not sit comfortably in physical chemistry, despite being a major investigative technique, and these volumes are perhaps understandably, but nevertheless regrettably, blind to them, despite them being a good romping ground for numerical calculations. You will not be pleased if you consider that intermolecular forces are relevant to an understanding of the structure of matter.

This is not a text likely to appeal to many instructors in the UK, as its level is inappropriate, its exposition too imprecise and its attempts to convey insight almost non-existent. The style will not be to everyone's taste. But there are some good things about it, not least the large number of examples showing how mathematical software may augment and even enliven a physical chemistry course. This lengthy text is a huge supplement, and perhaps a pointer to the future, but not at present a core.

Peter Atkins is professor of chemistry, Oxford University, and author of Physical Chemistry .