Vibrational solvatochromism and electrochromism: coarse-grained models and their relationships

A theoretical description of vibrational solvatochromism and electrochromism is presented by using a coarse-grained model based on a distributed charge and multipole interaction theory. Solvatochromic frequency shift has been described by considering the interaction between distributed charges of a solute and electrostatic potential due to distributed charges of solvent molecules. Another approach was based on the expansion of the solvatochromic frequency shift in terms of solvent electric field and its gradient at distributed sites on solute. The relationship between these two approaches is elucidated and their validities are discussed. It is also shown that the distributed charge and multipole model for solvatochromism developed here can be used to describe vibrational Stark effects on frequency and transition dipole moment. The relationship between the vibrational Stark tuning rate and the parameters obtained from recent vibrational solvatochromism studies is clarified and used to determine the vibrational Stark tuning rates of a few stretching modes, which are then directly compared with experimentally measured values. We anticipate that the present theoretical model can be used to study a variety of vibrational solvatochromic and electrochromic phenomena and to extract critical information on local electrostatic environment around a small IR probe in solution or protein from linear and nonlinear IR spectroscopic studies.