The potential functions of polyatomic molecules

A polyatomic molecule may be considered as a system of heavy nuclei, the relative motions of which are strictly limited by a particular potential energy function. To a higher order of approximation the motion consists of a series of harmonic vibrations, whose amplitudes are small in comparison with the dimensions of the system. Certain of the spectroscopic frequencies (infra-red and Raman) may be identified with the normal frequencies of vibration, which frequencies may be readily be computed, provided the geometric form of the molecule and its potential energy function are known.Unfortunately it is very difficult to derive the potential energy function from purely theoretical considerations although some progress has been made in this direction, notably for H 2 O. It would appear that the converse problem of determining the potential energy from the experimentally known normal frequencies would be comparatively simple. This, however, is not usually the case, since in general the potential function contains more parameters than there are frequencies. Thus the molecule YX 2 has three normal modes of vibration, but its potential function depends on four constants; the molecule YX 3 has four frequencies, which are functions of six constants and so on.