Microscopic derivation of fluctuation formulas for calculating dielectric constants by simulation

A microscopic derivation using the average Maxwell electric field is given for fluctuation formulas for the dielectric constant of a simulation sample for both periodic and reaction field boundary conditions. The reaction field case is for a spherical cavity reaction field. The derivations put both boundary conditions on an equal footing of microscopic theory and the only nonrigorous part of the derivation is the assumption that the region used to average the electric field is large enough. The fluctuation formula for reaction field boundary conditions is rather different from that used heretofore. The method is applied to a subregion of an isolated spherical system.