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" — 3 U' A / ω e ), where U' and U" are the first and second derivatives of U with respect to the normal co-ordinates and A / ω e 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, ( A s ) 0, n' is related to the frequency ω so that ( A s ) 0, n / ω n +1 is independent of isotopic substitution, as in the gas phase.
