Vibrational spectrum of an ion pair in a non-polar solvent

Abstract

The vibrational spectrum of an ion pair dissolved in a low polarity solvent is investigated. The analysis presented is phenomenological and concentrates on one particular system: namely, an ion pair composed of a rigid charged ring, e.g., the benzene radical anion, and a spherical counter ion. The potential energy function for the system consists (1) of an electrostatic component which is formulated in terms of continuous charge distributions, and (2) a simple exponential, short ranged repulsion term. The complete interaction energy depends parametrically upon several parameters, and the adjustment of these parameters can be carried out based on physical arguments. Vibrational force constants, the associated frequencies, and the oscillator strengths for the first allowed dipole transitions are determined with the use of the harmonic term in a general Taylor expansion of the interaction energy. Stable force constants are found for a limited range of values of the ring radius, the equilibrium separation between the ring and counter ion, and the repulsion parameter. The vibrations of the spherical counter ion in the plane of the ring, which are of importance for coupled electron-ion transport processes, have predicted frequencies in the range of 30 to 550 cm^–1.