  We analyze a one-component simple fluid in a liquid-vapor coexistence state,
which forms an arbitrarily curved interface. By using an approach based on
density functional theory, we obtain an exact and simple expression for the
grand potential at the level of mean field approximation that depends on the
density profile and the short-range interaction potential. By introducing the
step-function approximation for the density profile, and using general
geometric arguments, we expand the grand potential in powers of the principal
curvatures of the surface and find consistency with the Helfrich
phenomenological model in the second order approximation.
