Bibliography

M. V. Volkenstein. Structure of Molecules. Publishing House of the Academy of Sciences of the USSR, popular-science series—monographs, 1947, 270 pp., 133 figures, 49 tables, with a subject index.

The purpose of this book, as the author writes in the preface, is to interest the scientific worker and the student of physics or chemistry in the field of molecular structure. Having such a reader in mind, the author did not aim at a popular exposition in the full sense of the word. To read the book one must know mathematics approximately as a second- or third-year chemistry student knows it, one must know the course of physics taught in a higher educational institution, and also, perhaps, one must read one or two books devoted to atomic structure.

A reader possessing such preparation has been waiting for a book of the kind under review with great impatience and will greet Volkenstein’s book with great satisfaction. This, perhaps, is the first book presenting the subject sufficiently comprehensively and at the same time without details of interest only to a narrow specialist. The book by Syrkin and Dyatkina, recently published, cannot compete with the book under review—their aims are entirely different. The former is intended for scientific workers engaged in the study of molecular structure; it is, so to speak, a working manual. By contrast, the book under review is an outline of the subject, intended to give only a general idea of it.

The book is divided into eight chapters. In the first, introductory chapter, the foundations of quantum mechanics and atomic physics are set forth in a quite condensed form. The aim of such an introduction can be only one—to remind the reader of information already known to him but forgotten.

The second chapter is entitled “The Nature of the Chemical Bond.” The chapter is undoubtedly successful: the chemical theories of valence are presented simply and clearly on the basis of only indisputable physical concepts. The exposition in this chapter of the Born–Haber process is appropriate. Throughout, the author strives to give a physical definition to the concepts used by chemists qualitatively only (for example, electron affinity). The author approaches the theory of electron resonance from the side of a mechanical analogue of this phenomenon. The resonance of oscillations of two coupled pendulums is considered, and it is shown that the imposition of coupling leads to the splitting of identical frequencies into two different frequencies for the coupled system. This energetic approach is maintained throughout the discussion of questions of the electron bond.

The third chapter, devoted to the geometry of molecules, seems to us unsatisfactory. Speaking of the geometry of a molecule, we are entitled to pose the following questions: what is the mutual arrangement of the atoms in a given molecule, what are the dimensions of the molecule and its external form? The last question is, of course, subject to several conditions: the external dimensions of molecules can be determined from the distances to which atoms belonging to different molecules can approach one another. It may be considered firmly

established that a definite volume falls to the share of one atom or another—the intermolecular, or, as they are called in the American literature, van der Waals radii are in any case known for many atoms with an accuracy of up to 0.1 Å. By assigning to the atoms of a molecule a definite volume bounded by intermolecular radii, we can explain a number of details in the structure of molecules. At present the term “steric factor” is widely used to describe those distortions in structure which deviate from normal valence angles and which arise because the sizes of the atoms prevent them from being situated too close to one another.

Unfortunately, we do not find such a treatment in the chapter “Geometry of Molecules.” In the paragraph on the sizes of molecules, figures for the effective diameter of a molecule, calculated from the van der Waals equation and from internal friction, are given which have no significance for the question of structure. Contrary to what the author writes, it may be stated with confidence that gas-kinetic properties give no information about molecular dimensions that would have any significance for general questions of molecular structure.

In the subsequent exposition the author, of course, does not use these data on molecular sizes (precisely because they have no significance for the subject under consideration); nor does the book contain any other considerations about the sizes of atoms in a molecule. As a result, throughout the further exposition we are dealing with bodiless molecules—systems of points. This circumstance greatly impoverishes the subsequent exposition. It seems to us quite inappropriate, as one may state, to present the question of free rotation in molecules without saying anything about the steric factor.

In the fourth chapter, chemical bonds in polyatomic molecules are considered. In this chapter the clear separation of experimental facts, of consequences from the general principles of the theory, and of general hypotheses makes a very pleasant impression. The author never regards the absence of confirmation as an explanation of one fact or another by quantum chemistry. The author always notes the speculative character of a significant number of quantum-mechanical arguments and theories, which subject to discussion questions that cannot have experimental verification. Thus, for example, on p. 111 it is stated directly that attempts to find a dependence between bond length and fractional order have no meaning, since the accuracy of determining the bond length is 0.02–0.03 Å, while all these “theories” try to find the “true” course of the curve between the points 1.39 Å (benzene) and 1.42 Å (graphite). Such a restrained exposition of the foundations of the theory of electronic resonance (see, for example, p. 120), with a clear indication of the possibilities of the theory and of the limits of its applicability, is a great merit of the book.

A drawback of the fourth chapter is the excessive number of details; it seems to us that it would have made sense to set forth the basic ideas in greater detail.

In the fifth chapter the foundations of the theory of dipole moments and of the polarizability of molecules are presented, and it is explained how these quantities can be obtained from measurements of the dielectric constant and refractive index. The author needlessly begins his exposition “from afar” and makes the reader recall the foundations of the theory of electricity.

In the sixth chapter, certain phenomena connected with the anisotropy of molecules are set forth, namely the Kerr effect, anisotropic absorption of light, and the polarization of fluorescence.

The seventh chapter, “Spectra of Molecules,” is very well written. On reading these 30 pages, one is left with a completely clear and precise picture of the whole field. The reviewer read this chapter very attentively and can point out only a few, quite insignificant defects, for example, the absence

Bibliography

explanation of the intensity distribution shown in Fig. 106, and a somewhat unsatisfactory explanation of the Franck–Condon principle.

The last, eighth, chapter sets forth the theory of vibrational spectra “in the form in which it has taken shape in the works of M. A. Elyashevich, B. I. Stepanov, and the author.” The interesting and original material of this chapter should have been presented in greater detail and made somewhat more popular. In the first paragraphs of the chapter, a series of examples shows how the structure of a molecule can be established merely by counting the number of lines in the spectrum. Next the question is considered of the connection between the forces acting between atoms and the spectra of molecules. Using the example of a nonlinear triatomic molecule, the basic idea of calculating molecular vibrations is shown. The mathematical material of these paragraphs, unfortunately, is fairly considerable. After a detailed consideration of all the information that can be obtained by studying the frequencies of spectral lines (in particular, molecular isomerism, the hydrogen bond, intermolecular interaction, and the thermal properties of molecules), the author concludes his exposition with a brief treatment of the theory of the intensities and polarization of the lines of a vibrational spectrum. The author points out that the experimental material available in this respect is still very meager, and believes that the chief task in the study of molecular spectra is the accumulation and analysis of this material.

At the end of the book there is an index of the literature (74 titles).

Despite the indicated shortcomings, as well as certain unevenness in the presentation, M. V. Volkenstein’s book leaves a very good impression. It will be of great benefit to the chemist and physicist wishing to “enter into the subject.”

A. I. Kitaigorodsky