Molecular Vibrations of Three Particle Systems with Special Applications to the Ethyl Halides and Ethyl Alcohol

The vibrational potential of polyatomic molecules is discussed in the light of the theory of directed valence. Andrews' assumptions of ``valence forces'' are seen to be rather special, but at the same time are fairly good approximations under certain conditions. The normal vibrations of three body systems are calculated for the potential function $$\mathrm{V=}\frac{1}{2}{\mathrm{[k}}_1{\mathrm{(\Delta r}}_1{)}^2{\mathrm{+k}}_2{\mathrm{(\Delta r}}_2{)}^2{\mathrm{+k}}_3{\mathrm{(r}}_1^{0^2}{\mathrm{+r}}_2^{0^2}{\mathrm{)(\Delta \gamma )}}^2]$$ with r₁, r₂ radial coordinates and γ an angular one. The potential terms proportional to Δr₁Δr₂, etc., are treated as perturbations. These calculations are applied to the ethyl halide and ethyl alcohol molecules by considering the CH₃, CH₂ and OH groups as dynamic units. Force constants were determined which gave approximately the experimental frequencies. The calculation of the normal modes of vibration illustrate the approximate validity of the designation of the modes of vibration of unsymmetrical three body systems as two independent radial motions and an angular motion.