A Breathing Sphere Model for Calculating Frequency Shifts of Polyatomic Molecules in Solution

Abstract

Molecular vibrational frequency shifts are modeled by treating the vibrating solute as a breathing sphere with repulsive (hard-core) and attractive (mean field) solvent−solute interactions. The solvent-induced repulsive force exerted on the normal mode of a vibrating solute molecule is obtained using the derivative of the molecular volume with respect to the normal mode coordinate in conjunction with an analytical expression for the chemical potential of a hard sphere solute immersed in a solvent of hard spheres. The volume derivative of the vibrating solute molecule is calculated by considering the solvent molecule as an assembly of interpenetrating or fused hard spheres whose individual motions are given by normal mode coordinates. The calculation of the repulsive force is simplified by equating the normal mode volume change of the multisphere solute to a volume change of a spherical solute. The anisotropy of the solute−solvent system is used to adjust the spherical solute diameter so its chemical potential matches the chemical potential of the multisphere solute. This adjustment is critical to correctly scale the spherical volume change to the anisotropy of the polyatomic solute. For the diatomic solutes, N2 and HCl, the breathing sphere model predicts repulsive forces and frequency shifts that closely agree with a near exact diatomic hard sphere model. Applied to the three different CO2 vibrations, the explicit calculation of the different excluded volume changes associated with each vibration gives predicted frequency shifts that agree with available pressure-dependent frequency data.