Quantum theory of polarizable quadrupolar fluids

Abstract

In this paper we investigate the dielectric and single particle thermodynamic properties of a polarizable quadrupolar fluid, employing a quantum mechanical theory of such developed previously. Numerical calculations of the renormalized electrical properties of a molecule in the condensed phase, and the solvation free energy of an impurity molecule dissolved in the fluid, are performed in § 2 using Padé approximant techniques. In § 3 we formulate a theory of the dielectric constant, ε, within a class of theories which include as examples the linear hypernetted chain equation or the single super chain approximation. Within such a class of theories, the dielectric constant of a polarizable quadrupolar fluid is shown to be identical to that of an equivalent non-polarizable fluid consisting of molecules possessing permanent (density dependent) dipoles and quadrupoles; we therefore use techniques available to us from the theory of non-polarizable multipolar fluids to formulate expressions for ε. Four different methods are used to calculate the dielectric constant, including an essentially rigorous virial expansion and a practical, albeit partial implementation of the single super chain approximation. Resultant numerical predictions of experimentally accessible deviations from pure Clausius-Mossotti behaviour are compared and contrasted in the final section. The effects of electrostatic interactions involving molecular quadrupoles, both permanent and induced, are found to contribute substantially to all properties calculated in this paper. For example, deviations from pure Clausius-Mossotti behaviour which result from such interactions often dominate those deviations whose origins are the familiar dipole-induced dipole interaction.