Environmental Effects on the Infrared Frequencies of Polyatomic Molecules. Evaluation of Perturbation-Theory Parameters for HCN and DCN

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Abstract
Buckingham's equations describing solvent‐induced vibrational frequency shifts for polyatomic solute molecules are applied to experimental solvent‐shift data for HCN and DCN. The equations were transformed to internal coordinates such that the expressions for the frequency shifts involve the first (Vi′) and second (Vii″) derivatives of the solute—solvent interaction energy with respect to the internal vibrational coordinates. Numerical values for these energy derivative terms were determined from the experimentally observed shifts of the six fundamentals of HCN—DCN in a series of solvents in a manner such that the problem was overdetermined. (Note that this method fails when applied to diatomic molecules.) It is found that second‐derivative terms make significant and often dominant contributions to the observed shifts and that solvent perturbation of a given internal vibration in a molecule materially affects the shifts of other vibrational bands in the molecule. The equations of Huong et al. relating the relative frequency shifts of the stretching vibrations of HCN and DCN are shown to be a consequence of the equations of Buckingham. Expressions are given for the solvent perturbation contribution to 〈Qi〉 and 〈Qi2〉. Quantitative estimates of average bond extensions and mean‐square vibrational amplitudes are given for certain cases.

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