Electric multipole moment fluctuations in polar liquids

A general expression for the distribution of the fluctuating 2(l)-pole moment M(l) of a spherical sample of dielectric material is derived on the basis of dielectric theory combined with statistical mechanics. The formulas are compared with results from computer simulations of a weakly coupled Stockmayer fluid and the agreement is shown to be excellent. Furthermore, we calculate the size of the coupling, quantified through the free energy of solvation A(solv), of the fluctuating electric moments to a surrounding dielectric medium. It turns out that the contribution to A(solv) from each fluctuating electric moment actually increases with increasing order l of the moment, resulting in a formally infinite free energy of solvation. We also present a correction to A(solv) for molecular media, which shows that the molecular nature of the surrounding medium effectively suppresses the divergence in the solvation free energy.