Quantum theory of polarizable quadrupolar fluids. I

Using the path integral representation of quantum theory, we construct a simple quantum mechanical model for a polarizable quadrupolar molecule, which represents a generalization of the dipolar Drude model and which takes full account of molecular quadrupoles, both permanent and induced. We consider the predictions of the model in the condensed phase within a class of linear theories which include as examples the mean spherical approximation and the linear hypernetted chain equation. We analyse both the pair correlation function of the model fluid and the renormalized, frequency dependent electrical properties of the molecule in the condensed phase; a simple practical method of calculating the latter quantities is described. The physical implications of the model are discussed and it is pointed out that a number of non-trivial predictions result from the model, including the predicted appearance of a collision-induced electronic dipolar absorption band. We discuss the relationship of the model here presented to the classical Yvon-Kirkwood model of polarization, and discuss a possible extension to the case of polarizable dipolar-quadrupolar fluids.