Molecular expression for dielectric friction on a rotating dipole: Reduction to the continuum theory

Recently we presented a microscopic expression for dielectric friction on a rotating dipole. This expression has a rather curious structure, involving the contributions of the transverse polarization modes of the solvent and also of the molecular length scale processes. It is shown here that under proper limiting conditions, this expression reduces exactly to the classical continuum model expression of Nee and Zwanzig [J. Chem. Phys. 52, 6353 (1970)]. The derivation requires the use of the asymptotic form of the orientation-dependent total pair correlation function, the neglect of the contributions of translational modes of the solvent, and also the use of the limit that the size of the solvent molecules goes to zero. Thus, the derivation can be important in understanding the validity of the continuum model and can also help in explaining the results of a recent computer simulation study of dielectric relaxation in a Brownian dipolar lattice.