Dielectric Constant and Fluctuation Formulae for Molecular Dynamics

The dielectric constant $$\epsilon $$ ϵ of a material describes the collective response of its constituent molecules to electric fields, which is of fundamental importance in the study of electromagnetic phenomena in materials. In this chapter, we will present the statistical molecular theory for the dielectric constant. First, a brief review of the classical electrostatic theory of charges and dipoles is given. Then we present the classical Clausius–Mossotti theory for non-polar dielectrics, i.e., materials that do not have molecular dipole moments in the absence of external fields, and the Onsager theory for dipolar dielectrics, specifically for dipolar liquids. Finally, we discuss the statistical molecular theory for the dielectric constant and dielectric formula in terms of dipole moment fluctuations; the latter can be obtained over molecular trajectories in molecular dynamics simulations of dielectric materials.