  Density functional theories such as the Poniewierski-Stecki theory relate the
elastic properties of nematic liquid crystals with their local liquid
structure, i.e., with the direct correlation function (DCF) of the particles.
We propose a way to determine the DCF in the nematic state from simulations
without any approximations, taking into account the dependence of pair
correlations on the orientation of the director explicitly. Using this scheme,
we evaluate the Frank elastic constants K1, K2 and K3 in a system of soft
ellipsoids. The values are in good agreement with those obtained directly from
an analysis of order fluctuations. Our method thus establishes a reliable way
to calculate elastic constants from pair distributions in computer simulations.
