Microscopic expressions for interfacial bending constants and spontaneous curvature

We derive the interfacial-curvature free energy for a simple fluid from density-functional theory, and find a form matching that for a two-dimensional shearless elastic media. The fourth moment of the direct correlation function and the density gradient determine the bending moduli κ and κ¯, while the spontaneous curvature ${\mathit{c}}_0$ is given by asymmetry in the density. We obtain the critical indices of these quantities and corrections to the Laplace equation for curved interfaces.