# Calculation of the dielectric constant of a fluid by a cluster expansion method

## Abstract

A method is developed for calculating the static dielectric constant of a fluid of polar but, at the present state of the treatment, nonpolarizable molecules by cluster expansion methods. The dielectric constant is obtained as the inverse of the coefficient in the Coulomb potential between two charged spherical probes immersed in the fluid. This yields a new derivation of the Kirkwood expression for the dielectric constant in terms of the moment of a sample inside a larger sphere produced by a fixed molecular dipole, showing that the sample may be taken infinite in size without shape-dependence problems. The Onsager result (for nonpolarizable molecules) is obtained from a partial summation of the diagrams without any use of classical electrostatics.