Self-Consistent Electronic Structure of Solid Surfaces

We have developed a method for calculating electron states in the surface region of a semi-infinite solid taking full account of the three-dimensional nature of the lattice potential. The Schr\"odinger equation is integrated numerically in a region consisting of the last few atomic layers and the vacuum, and optimally matched to a linear combination of Bloch (pseudo) wave functions in the interior. The potential in the surface region is computed self-consistently from the valence-charge density by solving Poisson's equation, using a local approximation to the exchange and correlation contribution, and representing the cores by a model potential. As an illustration of the practical applicability of the method, the electronic structure of the (100) surface of Na has been calculated.