Electron-scattering states at solid surfaces calculated with realistic potentials

Scattering states with low-energy-electron diffraction asymptotics are calculated for a general non-muffin-tin potential, as, e.g., for a pseudopotential with a suitable barrier and image potential part. The latter applies especially to the case of low lying conduction bands. The wave function is described with a reciprocal lattice representation parallel to the surface and a discretization of the real space perpendicular to the surface. The Schrodinger equation leads to a system of linear one-dimensional equations. The asymptotic boundary value problem is confined via the quantum transmitting boundary method to a finite interval. The solutions are obtained based on a multigrid technique that yields a fast and reliable algorithm. The influence of the boundary conditions, the accuracy, and the rate of convergence with several solvers are discussed. The resulting charge densities are investigated.