On the relation between the form, force constants, and vibration frequencies of triatomic systems

Abstract

Within the past few years extensive contributions have been made to our knowledge of the architecture of polyatomic molecules. The some what indefinite bond diagrams of the chemists have been rep;aced by a more precise stereo-chemistry in which inter-atomic distances and valency angles are known with considerable accuracy. Most of this advance has come from the experimental side, particularly from vibration spectra and X-ray and electron diffraction measurements, but some progress has also been made on the purely theoretical side. For reasons of simplicity, attention up to the present has been mainly confined to two classes of molecule, namely those which possess a high degree of symmetry, e. g ., CH 4 , C 2 H 2 , and those which contain only three atoms, e. g ., SO 2 . There are, however, so many molecules belonging to the second of these classes that a detailed study of them alone is well worth while. It is the purpose of the present paper to make a critical survey of the experimental evidence on the shapes and fundamental frequencies of a number of triatomic molecules by studying the variations in the force constants from molecule to molecule. Our procedure is as follows. We begin by making a list of all the triatomic molecules and ions on which there is any experimental or theoretical evidence as regards size, shape, and vibration frequencies. These we divide roughly into three categories, "certain", "less certain", and "doubtful", and use the results on the first of these to guide us in dealing with the others. There is naturally no difficulty about evaluating the force constants for the molecules which are "certain"; in fact, for some of these various authors have already calculated all the force constants in the most general potential function of second degree consistent with the symmetry of the molecule. The present calculations, of course, do not aim at such accuracy as this because in most cases the data are not sufficient. We are more concerned with discovering whether the fundamental frequencies have been correctly assigned and whether we have adopted the right shape for the molecule.