Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods , Dominik Marx and Jürg Hutter Cambridge U. Press, New York, 2009. $80.00 (567 pp.). ISBN 978-0-521-89863-8

The dynamics of molecules in a material or a chemical reaction can be simulated by calculating the time history of the internuclear coordinates according to the potential that governs internuclear motion. By the Born-Oppenheimer approximation, the potential is the electronic energy plus internuclear repulsion evaluated at a fixed internuclear configuration. Such simulations are useful in areas as diverse as nanoscale science, quantum photochemistry, combustion, biochemistry, catalysis, and atmospheric and environmental chemistry.

In the formative years of molecular dynamics simulations, the potential was represented by an analytic function, and only after hit-or-miss attempts to fit electronic-structure energy calculations or experimental data to potential functions could the dynamics be determined. However, about 35 years ago, a new approach began to replace that unsystematic, labor-intensive process. Direct dynamics, as it became known, does not require the fitting of the potential or force to an analytic function: The results of an electronic-structure calculation of the potential are used directly, without fitting, to advance the time step whenever the dynamics algorithm calls for energy or force. Direct dynamics began in the 1970s, and now a plethora of approaches are available in which either density functional theory or wavefunction theory is used to acquire the electronic energies. That this evolving field now has a pedagogical monograph in the form of Dominik Marx and Jürg Hutter’s * Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods* is a significant milestone.

The terms used in the book’s title, and in the field in general, are often open to interpretation and require discussion. For example, quantum chemists use the adjective “ab initio” to denote a calculation void of all but the most fundamental of empirical input, such as Planck’s constant and the charge of an electron. However, many physicists and materials scientists—including Marx and Hutter —apply the ab initio label to density functional theory, even though the density functional approximations that are most frequently used have some empirical character. Also, Marx and Hutter’s use of “molecular” in their title is too restrictive since the methods contained in their book can be applied to problems such as determining the structure of metallic nickel or of ceramic yttrium-doped strontium cerate—materials that do not contain molecules.

Even the term “quantum dynamics” is ambiguous. I use it to indicate that the dynamics, as opposed to the potential, is treated quantum mechanically. Some experts, though, use it even when the dynamics is classical, provided that the potential comes from explicitly quantal calculations. Marx and Hutter use the term “molecular dynamics” to denote any classical or semiclassical time-dependent method of propagating the coordinates of the nuclei in a system composed of atoms; for them, “ab initio” molecular dynamics means that the potential is obtained via an explicitly quantum treatment. Also, some experts refer to analytical potential functions as molecular mechanics, but Marx, Hutter, and others often call the same functions classical even if they were derived from fitting quantal electronic-structure calculations or from quantal experiments.

In most of * Ab Initio Molecular Dynamics *, the internuclear motion is treated as classical, but there is also an up-to-date 33-page section on path-integral approximations to quantal dynamics. Although direct dynamics can be applied with a variety of electronic-structure propagation algorithms, this book focuses squarely on Kohn-Sham density functional methods and the extended-Langrangian-type propagation schemes introduced in 1985 by Roberto Car and Michele Parrinello. Furthermore, even within that restriction, the density functionals considered are largely restricted to the generalized gradient approximation, which no longer represents the state of the art in density functional approximations. However, I applaud the authors for introducing the projector-augmented-wave method as an alternative to pseudopotentials for representing core electrons and for introducing the combined quantum mechanical and molecular mechanical method.

In a book replete with 1669 references, reviews of algorithmic developments, equations, flow charts, lines of code, and comments on software program organization, it is a mark of the field’s maturity that not all widely used approaches are covered. For example, * Ab Initio Molecular Dynamics * introduces metadynamics as the method for sampling rare events in statistical ensembles; the more standard approach of umbrella sampling is not mentioned. However, a student or newcomer to the field of molecular dynamics will find the approaches discussed in * Ab Initio Molecular Dynamics * a good place to start.

The section on excited electronic states is a useful overview of several approaches, but is disappointing in its treatment of dynamics. For example, the authors say that the Zhu-Nakamura approach cures the shortcomings of Landau-Zener-Stueckelberg theory, but neither captures the multidimensional nature of surface crossings and locally avoided crossings in polyatomic systems. Also missing is a discussion of decoherence.

* Ab Initio Molecular Dynamics * is not a self-contained work. In many cases the authors present equations without sufficient background to motivate the operations and without sufficient detail. Also, I found it hard to follow the book in places except by consulting its well-placed references. On the plus side, the text is written clearly and informed by the state-of-the-art research experiences of the authors themselves. Reading it is a valuable experience akin to spending time in their research groups.