Density-functional calculation of quadrupolar contributions to the atom-metal van der Waals interaction

The time-dependent extension of the density-functional approach is used to calculate the metal response function g(q,iu) which enters directly in the expression of the van der Waals attraction $E_{\mathrm{vdW}}$ between an atom and a metal surface. The long-wavelength behavior of this function, which is governed by the dynamic image plane, had been obtained previously in order to determine the lowest-order correction to the asymptotic form of $E_{\mathrm{vdW}}$. Here g(q,iu) is evaluated for arbitrary momenta in order to determine the attraction for short atom-metal separations (outside the region of charge-density overlap). For helium interacting with several simple-metal surfaces, $E_{\mathrm{vdW}}$ is found to become 5% to 10% more attractive as a result of these corrections. This enhancement is of similar magnitude as that caused by quadrupolar contributions to the atomic polarizability.