Reviews of books

Abstract

In the development of unimolecular reaction rate theory it has been possible to achieve much in terms of the concept of averaged rate constants together with classical or semi-classical approximations for the sums and densities of the molecular states involved. Even the widely successful RRKM theory in its normal mode of application relies partly on a quantum-mechanical treatment of vibrational states and partly on a classical motion of the system over the potential barrier associated with an empirically assigned transition state.It has long been recognised that certain problems such as the incorporation of the concept of weak intermolecular collisions and more recently the adequate interpretation of laser-induced unimolecular processes require a state-to-state treatment and formulation of the unimolecular process as a master equation involving all the individual molecular energy states of interest.The vast number of vibrational-rotational states for most molecules near to the threshold energy for unimolecular reaction has made this formulation a formidable problem. Although with the advent of computer methods the ability to handle large numbers of simultaneous equations has increased, problems still remain in estimating associated transition probabilities and individual rate constants and in reducing such formulations to a tractable size. As explained in the Preface to the book, the work of Professor Pritchard and his coworkers in recent years has been parallel to the development of mainstream unimolecular theory. It is, therefore, very appropriate and timely that this book should appear to summarise his individual contribution to the subject and trace its progress in a logical sequence.The first chapter presents a very useful and concise summary of the main observed features of thermal unimolecular reactions, particularly in relation to factors affecting their fall-off behaviour. This is followed by the treatment of a unimolecular reaction as a perturbation of internal molecular relaxation processes. The mathematics of the master equation is recast into matrix form and is not particularly easy. The reader is, however, given help by ample references to the original papers and to mathematical texts and recourse to these will be essential to anyone wishing to pursue the theory in detail. The unimolecular rate constant is derived as the lowest eigenvalue of the perturbed matrix and the problem of its evaluation is aided by 'graining' the many energy levels into groups and treating all dissociations from a given group as having the same rate constant. These rate constants are evaluated as in the Forst procedure from the observed A and E values.Detailed comparisons with some known experimental data are made and computer programs appended to enable this method to be applied more generally. Further chapters in the book deal with attempts to apply a dynamic state-to-state process more rigorously in the case of some triatomic molecules and approximate methods for larger molecules are discussed. Related topics dealt with ...