Molecular Simulation/Dielectric constants

The dielectric constant of a liquid can be calculated from the magnitude of the variance in the net dipole moment of a cubic simulation cell, M,

$ϵ={ϵ}_{\mathrm{\infty }}+\frac{4\pi (⟨M^2⟩-⟨M{⟩}^2)}{3⟨V⟩k_{B}T}$

where V is the volume of the simulation cell. ${ϵ}_{\mathrm{\infty }}$ is the infinite frequency dielectric constant. For non-polarizable models, this term is equal to 1.