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, $\Delta \omega $, in the vibrational frequencies are found to be proportional to (U$^{\prime \prime}$ - 3U$^{\prime}\scr{A}$/$\omega _{e}$), where U$^{\prime}$ and U$^{\prime \prime}$ are the first and second derivatives of U with respect to the normal co-ordinates and $\scr{A}$/$\omega _{e}$ is an anharmonic constant obtainable from the spectrum of the gas. The theory indicates that $\Delta \omega $/$\omega $ 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, (A$_{s}$)$_{0,n}$, is related to the frequency $\omega $ so that (A$_{s}$)$_{0,n}$/$\omega ^{n+1}$ is independent of isotopic substitution, as in the gas phase.