A theory of solvent effects in infra-red spectra

The vibration frequencies of a molecule change on immersion in a solvent as a result of the forces between the molecule and the surrounding solvent molecules. For non-polar solvents, in the absence of strongly orientation-dependent forces such as hydrogen bonding, dipole-induced dipole and dispersion forces are probably most important. The former can be approximated by considering the solute molecule to be in a spherical cavity of radius a in a uniform dielectric. This over-simple model of the solvent facilitates consideration of the effect of varying solute parameters upon ∆ν/ν, the fractional decrease of frequency on solution in a given solvent from the vapour phase, and indicates, at least qualitatively, the character of the solute-solvent interaction in most cases. It can be shown (Pullin 1958) that if the dilute vapour phase potential and dipole moment functions of a diatomic molecule are given by V(x) = ½kx2 - bx3 + cx4, (1) μ(x) = μ0 + M'x + M"x2, (2) then the potential function Vs for the system, molecule and surrounding dielectric, is Vs(x) = V(x) - ½fμ02 - fμ0M'x - ½fM'2x2 - fμ0M"x2 - fM'M"x3 - ½fM"2x4, (3)