Model for the effects of a condensed phase on the infrared spectra of hydrogen-bonded systems

A formal scheme is developed for treating the effects of a condensed phase on the vibrational spectrum of hydrogen-bonded systems. A coupling of the moving proton to the bath is assumed responsible for the broadening, and is taken as simply the electrostatic interaction between the protonic dipole and the random local field set up by the internal modes of the bath or solvent. This corresponds to the electrostatic broadening. A strong-coupling treatment is employed. The spectrum is found by a cumulant expansion of the dipole-dipole correlation function. Expressions for the shift and broadening of the individual lines are given. The dynamics, as well as the strength, of the system-bath coupling are important for determining lineshape. The lineshape is thus related to the microscopic dynamic behavior of the hydrogen-bonded system in solution.