Vibrational solvatochromism. III. Rigorous treatment of the dispersion interaction contribution

A rigorous first principles theory of vibrational solvatochromism including the intermolecular dispersion interaction, which is based on the effective fragment potential method, is developed. The present theory is an extended version of our previous vibrational solvatochromism model that took into account the Coulomb, exchange-repulsion, and induction interactions. We show that the frequency shifts of the amide I mode of N-methylacetamide in H2O and CDCl3, when combined with molecular dynamics simulations, can be quantitatively reproduced by the theory, which indicates that the dispersion interaction contribution to the vibrational frequency shift is not always negligibly small. Nonetheless, the reason that the purely Coulombic interaction model for vibrational solvatochromism works well for describing amide I mode frequency shifts in polar solvents is because the electrostatic contribution is strong and highly sensitive to the relative orientation of surrounding solvent molecules, which is in stark contrast with polarization, dispersion, and exchange-repulsion contributions. It is believed that the theory presented and discussed here will be of great use in quantitatively describing vibrational solvatochromism and electrochromism of infrared probes in not just polar solvent environments but also in biopolymers such as proteins.