The Overlapping Muffin-Tin Approximation

TL;DR

This paper introduces the overlapping muffin-tin approximation (OMTA), a method for fitting full potentials with overlapping spherical wells, and demonstrates its effectiveness in band structure calculations for silicon.

Contribution

The paper presents a formalism for OMTA and compares its band structure results with full-potential methods, showing good qualitative agreement and quantifying errors related to potential overlap.

Findings

Valence band rms deviation of 20 meV/electron at 30% overlap

Qualitative agreement between OMTA and full-potential band structures

Smaller overlaps lead to worse potentials, larger overlaps increase second-order errors

Abstract

We present the formalism and demonstrate the use of the overlapping muffin-tin approximation (OMTA). 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 Schr\"{o}dingers' 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 OMTA with the full potential, and then compare the corresponding OMTA $N$-th order muffin-tin orbital and full-potential LAPW band structures. We find that the two latter agree qualitatively for a wide range of overlaps and that the valence bands have an rms 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.