Local-density-derived semiempirical pseudopotentials

Abstract

Transferable screened atomic pseudopotentials were developed 30 years ago in the context of the empirical pseudopotential method (EPM) by adjusting the potential to reproduce observed bulk electronic energies. While extremely useful, such potentials were not constrained to reproduce wave functions and related quantities, nor was there a systematic way to assure transferability to different crystal structures and coordination numbers. Yet, there is a significant contemporary demand for accurate screened pseudopotentials in the context of electronic structure theory of nanostructures, where local-density-approximation (LDA) approaches are both too costly and insufficiently accurate, while effective-mass band approaches are inapplicable when the structures are too small. We can now improve upon the traditional EPM by a two-step process: First, we invert a set of self-consistently determined screened LDA potentials for a range of bulk crystal structures and unit cell volumes, thus determining spherically symmetric and structurally averaged atomic potentials (SLDA). These potentials reproduce the LDA band structure to better than 0.1 eV, over a range of crystal structures and cell volumes. Second, we adjust the SLDA to reproduce observed excitation energies. We find that the adjustment represents a reasonably small perturbation over the SLDA potential, so that the ensuing fitted potential still reproduces a >99.9% overlap with the original LDA pseudowave functions despite the excitation energies being distinctly non-LDA. We apply the method to Si and CdSe in a range of crystal structures, finding excellent agreement with the experimentally determined band energies, optical spectra ${\mathrm{\ensuremath{\epsilon}}}_{2}$(E), static dielectric constants, deformation potentials, and, at the same time, LDA-quality wave functions.