Electric multipole moment fluctuations in polar liquids

A general expression for the distribution of the fluctuating $2ℓ$-pole moment $Mℓ$ 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 $Asolv$⁠, of the fluctuating electric moments to a surrounding dielectric medium. It turns out that the contribution to $Asolv$ 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 $Asolv$ for molecular media, which shows that the molecular nature of the surrounding medium effectively suppresses the divergence in the solvation free energy.