Rotational Spectroscopy of Diatomic Molecules , John M. Brown and Alan Carrington Cambridge U. Press, New York, 2003. $150.00, $75.00 paper (1013 pp.). ISBN 0-521-81009-4, ISBN 0-521-53078-4 paper
John Brown and Alan Carrington, leading molecular spectroscopists, are well known for their work on high-resolution spectroscopy, mostly on short-lived molecules in the gas phase. In Rotational Spectroscopy of Diatomic Molecules, they have produced a survey of the various kinds of spectra that one can observe without changing the electronic or vibrational state of a molecule.
Scientists began to understand the spectra of diatomic molecules in the early 20th century and were given a great boost by the advent of quantum mechanics in the 1920s. Researchers such as John H. Van Vleck, Friedrich Hund, and Robert S. Mulliken developed the general principles of the interpretation of spectra of diatomic molecules. Those principles were summarized in Gerhard Herzberg’s classic monograph, Molecular Spectra and Molecular Structure. Volume 1: Spectra of Diatomic Molecules (Prentice Hall, 1939). In 1989, Krieger Publishing revised and reprinted the second edition of the book. But Herzberg’s 1939 book was rapidly overtaken during and after World War II by new developments in spectroscopy, including the introduction of molecular-beam techniques using electric and magnetic resonance and the wide availability of ex-radar microwave equipment. The most important factor in those developments was increased resolution, which the use of Fourier transform techniques and lasers has since extended to shorter wavelengths. With high resolution, the hyperfine structure due to nuclear spin—a structure rarely resolved in conventional spectroscopy—becomes accessible.
Parallel to the experimental developments, new methods of fitting the data were introduced. Rather than use explicit formulas for the energy levels, researchers treated them as the eigenvalues of a (hopefully small) matrix representation of the effective Hamiltonian. For example, for a state with electron spin S but no orbital degeneracy, the effective Hamiltonian would be a matrix of dimension 2S+1, which can usually be factorized into two submatrices because of parity symmetry. For a doubly degenerate orbital state, the matrices would be twice as large. A nuclear spin I would increase the matrix size by a factor 2I+1, and so on. Extra symmetry exists for molecules containing two identical nuclei.
Brown and Carrington’s weighty volume is a paean to the effective Hamiltonian, which is developed in considerable detail from fairly basic principles. The essential technique is to transform the Hamiltonian to remove terms whose matrix elements connect states that are well separated in energy. For instance, different electronic states tend to be well separated in energy, and the interactions between them can be simulated by terms in the effective Hamiltonians of the two states, with coefficients that reflect the size of the interaction. A good example is the so-called ∇-type doubling of Π electronic states, produced by interactions with Σ states. The procedure is relatively simple for the purely electronic and rotational degrees of freedom but becomes quite involved when nuclear spin and electromagnetic fields have to be considered.
The treatment of the subject in Brown and Carrington’s book is exhaustive. For example, the formula for the full electronic Hamiltonian before transformation, including electric and magnetic fields but not nuclear spins, covers two full pages with 32 distinct terms identified. The systematic evaluation of the matrix elements of such terms requires spherical-tensor techniques, which the authors develop from scratch and use extensively. By way of contrast, I searched in vain in Herzberg’s book for the matrix elements of J + and J -, which are fundamental operators in the spherical-tensor algebra.
After the authors develop the theoretical tools, much of the second half of the book is devoted to case studies of spectra of particular molecules. The studies are often described in terms of classic experiments that introduced some of the observational techniques. These case studies often show the authors’ bias toward electric- and magnetic-field effects and hyperfine structure; not until chapter 10 (more than two-thirds of the way through the book) do readers finally reach the subject of pure rotational spectroscopy in a book on rotational spectroscopy!
Rotational Spectroscopy of Diatomic Molecules is carefully written and well produced. But a curious characteristic, partly responsible for the book’s great size, is its repetitiveness. For example, the authors introduce the Euler angles twice, in chapter 2 and again in chapter 5, using exactly the same diagram. Spherical harmonics are defined in table 5.1 with standard phases, but they reappear for no apparent reason in table 6.1, with different phases. In the case studies, the matrix elements of terms often duplicate previous equations. The authors sometimes repeat steps in the algebra as though their treatment of each molecule had to be self-contained. The formulas are useful for their intended purpose, but to the uninitiated they look like opaque jumbles of Wigner 3j, 6j, and occasionally 9j symbols, with strange sign factors that only a devotee could love; it is difficult to see why they should be repeated.
A significant error in the book is in the authors’ calculation of transition probabilities in chapter 6. The radiation density should be twice that given in the equation. As a result, the whole calculation is off by a factor of 2. In addition, the important statistical-weight factors are omitted from the calculation, but they appear later in chapter 10. The authors have the annoying habit of referring to some topic “as described elsewhere in this book,” but with more than 1000 pages to choose from, such things are not easy to find.
Among other books covering similar subject material, the closest to Brown and Carrington’s book is possibly The Theory of Rotating Diatomic Molecules (Wiley, 1975) by Masataka Mizushima, which is less useful for the working spectroscopist and may be difficult to find in print. Perturbations in the Spectra of Diatomic Molecules (Academic Press, 1986) by Hélène Lefebvre-Brion and Robert W. Field—or its revised version, The Spectra and Dynamics of Diatomic Molecules (Elsevier, 2004), by the same authors—is more concerned with excited electronic states that are nearly degenerate with each other. Walter Gordy and Robert L. Cook’s Microwave Molecular Spectra (Wiley, 1984) and Eiji Hirota’s High-Resolution Spectroscopy of Transient Molecules (Springer-Verlag, 1985) contain chapters on similar subjects, but those books are not restricted to diatomic molecules.
Rotational Spectroscopy of Diatomic Molecules is a detailed, wide-ranging presentation of all kinds of spectra within a given electronic-vibrational state of a diatomic molecule. All serious spectroscopists should have a copy, and the book’s price is reasonable. Besides, its sheer mass could be used to deter intruders.
