Chemical Education Today edited by
Book & Media Reviews
Jeffrey Kovac University of Tennessee Knoxville, TN 37996-1600
Quantal Density Functional Theory by Viraht Sahni Springer-Verlag: Berlin, Heidelberg, New York, 2004. 256 pp. ISBN 3540408843 (cloth), $129. reviewed by Lou Massa
Is quantum chemistry ready for a paradigm shift in density functional theory (DFT)? To see the cover design of this book is to understand that a gauntlet is being thrown down and a line drawn in the sand of DFT practice. There on the cover of a book—including in its title the phrase Density Functional Theory—is the symbol for the wave function, ⌿. For decades, the holy grail of DFT (as some have pursued it) has been to rid quantum mechanics of the wave function ⌿ and all its complications, including its explicit anti-symmetric dependence upon all N particle coordinates at once. In contrast, the electron density is the simplest object in quantum mechanics, depending upon the coordinates of only one electron, no matter how many electrons the system under study may contain. To draw the electron density on a sheet of paper is to see an object as simple and intuitive as a landscape of the hills and valleys of ordinary 3-D experience. Yet there on the cover of a book dealing with the density is the wave function, ⌿. How can that be? The answer in part, is alluded to on the cover design, by showing the wave function as a functional of the density: ⌿ = ⌿[]. As the famous Hohenberg–Kohn theorem guarantees, the wave function is indeed a functional of the density. This book shows how, in an entirely new way, it becomes plausible to use the wave function within the broad context of DFT, thus redirecting the present computational approach of attempting to approximate the at present unknown, and thus largely mysterious, Hohenberg–Kohn energy functional of the density. The claim is that the simplicity of the equations of DFT is retained on the one hand, while on the other hand ridding them of their mystery, as contained in the Kohn–Sham local potential. Quantum chemists will notice in particular three important aspects of the book. First, it describes quantum chemistry in terms of quantal sources but classical force fields. Hence, atoms and molecules are pictured in a manner reminiscent of classical mechanics. Just as in classical mechanics, the potential energy plays a central role, and it is here described in terms of the classical concept of work. Just as raising a weight in a gravitational field requires work against the field, which is converted to a potential energy, so too for an electron in an atom or molecule. It acquires potential energy in an analogous way, although the field is, of course, not gravitational in origin. The book describes all quantum
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systems, including atoms and molecules, in terms of the fields inherent to the systems deriving from their quantal sources. Indeed, an innovation of quantal density functional theory is to identify all such fields and to explicitly write their dependence upon the various quantal sources. The result is a description of quantum chemistry that is as close to a classical description as one may imagine. Perhaps Einstein, who famously disliked the probabilities of quantum theory, might have liked this reformulation of Schrödinger theory in terms of the classical fields, so close to his own imagination. Second, the book gives a new physical understanding of DFT in terms of the various classical fields present in a quantum chemical system. In ordinary DFT the energy functional of the density is unknown. But this book explains how all the electron correlations that exist in the real system are accounted for and described within a model system of noninteracting electrons, having the same electron density as the real system. Third, a new computational scheme for electronic structure calculations is provided. The scheme is still within the broad context of DFT. One accounts explicitly for each of the electron correlations that exist in the system. And, in quantal DFT there is no approximation in the description of the physical system itself, as occurs with DFT, because there are no unknown functionals and no functional derivatives in the theory. The upshot of the book for quantum chemists is that it presents a complete quantum theory of atoms and molecules. One constructs a model system of non-interacting electrons with the same electron density as the real interacting quantum chemical system. Quantal DFT explicates each of the electron correlations of the system. In that sense, there is no guess work. There is a systematic way of incorporating the different types of electron correlation. There is a systematic way of improving on the approximations within the theory. One may separately examine each type of electron correlation for its contribution specifically to the energy, and generally to any other quantum property of interest. Faculty interested in rounding out the view of DFT presented in their quantum chemistry or computational chemistry courses will benefit from the clear presentation of fundamental ideas that are stressed in this book. Also, it would be appropriate as a special topics course for graduate and advanced undergraduate students. Of special interest, the book’s chapter on Schrödinger theory from the perspective of classical fields and quantal sources is an entirely new way of looking at Schrödinger theory. Undergraduates could well be taught quantum mechanics from this more tangible perspective, since after all, undergraduates learn classical mechanics and thus know about fields and work. Quantal DFT has this classical perspective, and only the sources are quantal. If such a perspective were taught to undergraduates, it
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Chemical Education Today
Book & Media Reviews might make quantum mechanics more tangible for them and therefore easier to understand. All readers interested in how DFT fits within the larger theoretical structure of quantum theory will profit from this book. It marshals an effective argument for the existence of a specifically quantal DFT view of the density as cardinal object of quantum theory. To accept that argument in its entirety is to see quantal DFT as the fulfillment of the HK theorem promise, to turn the density into all the quantum
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properties of a chemical system. That in turn could lead to a conceptual and computational revolution within quantum chemistry, the like of which has not been seen since the original Hohenberg–Kohn and Kohn–Sham papers of some 40 years ago. Lou Massa is in the Departments of Chemistry & Physics, Hunter College & the Graduate School, City University of New York, New York, NY 10021-5085;
[email protected].
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