Solvent effects in infra-red spectroscopy

The effects of solute-solvent interactions on the vibrational spectrum of a dissolved molecule are evaluated by supposing that the interaction energy U can be expanded as a power series in the normal co-ordinates of the active molecule. By treating U and the anharmonic terms in the potential energy function of the free molecule as small perturbations to the harmonic oscillator Hamiltonian, the solvent shifts, ∆ω, in the vibrational frequencies are found to be proportional to (U" — 3U'A/ωe), where U' and U" are the first and second derivatives of U with respect to the normal co-ordinates and A/ωe is an anharmonic constant obtainable from the spectrum of the gas. The theory indicates that ∆ω/ω is independent of isotopic sub­stitution as well as of the order of the transition; experimental data for HCl and DCl support these conclusions. The intensities of vibrational bands of dissolved molecules are shown to be proportional to a factor involving the refractive index of the solvent and to be dependent upon the derivatives with respect to the normal co-ordinates of the dipole moment of the solute molecule and its near neighbours. It is predicted that for diatomic molecules the intensity of the (n — 1)th overtone, (As)0,n' is related to the frequency ω so that (As)0,n/ωn+1 is independent of isotopic substitution, as in the gas phase.