The effective Hamiltonian H-cap for a liquid-vapor interface is constructed by using the "experimental" direct correlation function obtained from molecular-dynamics simulation. The density fluctuation is parametrized according to: (a) The standard shift of the density profile, parallel and small; (b) the parallel shift; and (c) the shift with rotation as recently introduced, used in a density functional theory and compared with experiment. We find a universal shape of H-cap, discussed in some detail. The shape strongly suggests the existence of two regions of low wave-vector q and of high q corresponding to microscopic distances. Although bending and nonzero curvature of the fluctuating interface are present, the apparent bending (rigidity) coefficient is always negative, thus supporting the contention that the membrane Hamiltonians are not applicable to normal liquid-vapor interfaces. Several definitions of the momentum-dependent surface tension are also discussed.