Title:

Some problems in the theory of molecular vibrations

This thesis embodies the results of theoretical investigations into a number of branches of molecular physics in which molecular vibrations are involved. The broad divisions into which it falls are as follows: spectroscopy (Chapters I, II and III), chemical kinetics (Chapter IV), Xray crystallography (Appendices I and II), and thermodynamics (Appendix III). In Chapter I a new form of matrix perturbation theory is developed for calculating the vibration frequencies of molecules whose vibration spectra fall roughly into two classes, namely, a high and a low frequency class. By this method the single exact secular equation for the frequencies is replaced by two approximate equations of lower order, in terms of whose solutions the exact frequencies are obtained as analytical but infinite series. In Chapter II it is shown that the method leads to an explicit expression for the first order effect of a bending force constant upon the skeletal stretching frequencies of normal paraffins in the zigzag configuration. Chapter III consists of a discussion of the infrared and Raman spectra of helical molecules: the selection rules for fundamentals in the vibration spectra are derived from considerations of symmetry, approximate intensity relationships are found for a model containing strongly boded atomic groupings weakly coupled together, and the perturbation theory is applied to the same model to obtain relations between the allowed fundamental frequencies and the angle of the helix. The problem in chemical kinetics discussed in Chapter IV is that of calculating unimolecular reaction rates. An attempt is made to find a satisfactory quantum mechanical analogue of the existing classical theory. The first two Appendices are concerned with the influence of the thermal motion of atoms in a crystal upon the electron density distributions obtained by the Fourier synthesis of Xray diffraction data. The problem falls naturally into two parts: in I the dependence of the distribution in a carbon atom upon its thermal r.m.s. vibration amplitude is found; in II the variation of this amplitude from atom to atom within a molecular crystal is investigated. Finally, Appendix III consists of a short note outlining a method for computing the zeropoint energy of a vibrating molecule whose geometry and force field are known without first solving the secular equation for the individual frequencies. With the exception of a few sections which summarise previous work, the material in this thesis is entirely original. Most of Chapters I and III has already been published in the form of papers (J. Chem. Phys. 21, 1151 (1953) and Proc. Roy. Soc. A220, 472 (1953), respectively). Appendices I and II contain some material which formed part of the author's M.Sc. Thesis, but there is also a considerable portion which is fresh.
