Local exact exchange potentials within the all-electron FLAPW method and a comparison with pseudopotential results

TL;DR

This paper develops a numerical method within the all-electron FLAPW framework to construct local exchange potentials from orbital-dependent functionals, demonstrating good agreement with pseudopotential results and clarifying previous discrepancies.

Contribution

It introduces a balanced basis set approach for accurate, smooth EXX potentials in all-electron FLAPW calculations and compares these with pseudopotential results.

Findings

All-electron FLAPW results agree with pseudopotential calculations.

Proper basis set balancing is crucial for smooth potentials.

Confirms pseudopotential approximation validity in EXX-OEP context.

Abstract

We present a general numerical approach to construct local Kohn-Sham potentials from orbital-dependent functionals within the all-electron full-potential linearized augmented-plane-wave (FLAPW) method, in which core and valence electrons are treated on an equal footing. As a practical example, we present a treatment of the orbital-dependent exact-exchange (EXX) energy and potential. A formulation in terms of a mixed product basis, which is constructed from products of LAPW basis functions, enables a solution of the optimized-effective-potential (OEP) equation with standard numerical algebraic tools and without shape approximations for the resulting potential. We find that the mixed product and LAPW basis sets must be properly balanced to obtain smooth and converged EXX potentials without spurious oscillations. The construction and convergence of the exchange potential is analyzed in detail for diamond. Our all-electron results for C, Si, SiC, Ge, GaAs semiconductors as well as Ne and Ar noble-gas solids are in very favorable agreement with plane-wave pseudopotential calculations. This confirms the adequacy of the pseudopotential approximation in the context of the EXX-OEP formalism and clarifies a previous contradiction between FLAPW and pseudopotential results.