The Overlapping Muffin-Tin Approximation

We present the formalism and demonstrate the use of the overlapping muffin-tin approximation. This fits a full potential to a superposition of spherically symmetric short-ranged potential wells plus a constant. For one-electron potentials of this form, the standard multiple-scattering methods can solve Schrödingers’ equation correctly to 1st order in the potential overlap. Choosing an augmented-plane-wave method as the source of the full potential, we illustrate the procedure for diamond-structured Si. First, we compare the potential in the Si-centered overlapping muffin-tin approximation with the full potential, and then compare the corresponding overlapping muffin-tin approximation N -th order muffin-tin orbital and full-potential linear augmented plane wave band structures. We find that the two latter agree qualitatively for a wide range of overlaps and that the valence bands have a root mean squared deviation of 20 meV/electron for 30% radial overlap. Smaller overlaps give worse potentials and larger overlaps give larger 2nd-order errors of the multiple-scattering method. To further remove the mean error of the bands for small overlaps is simple.