Better Band Gaps with Asymptotically Corrected Local Exchange Potentials

TL;DR

This paper introduces an asymptotically corrected local exchange potential that improves band gap predictions and electronic properties in various materials by enforcing the ionization potential theorem with minimal additional computational cost.

Contribution

The authors develop a spin-polarized vLB correction to the LDA exchange potential that enforces the IP theorem, replicates exact-exchange behavior, and enhances accuracy for diverse systems.

Findings

Significant improvement in eigenvalues over LDA due to correct asymptotics.

Accurate reproduction of spin-polarized properties in half-Heusler alloys.

Effective application to finite systems like B12N12 and graphene.

Abstract

We formulate a spin-polarized van Leeuwen and Baerends (vLB) correction to the local density approximation (LDA) exchange potential [Phys. Rev. A 49, 2421 (1994)] that enforces the ionization potential (IP) theorem following Stein et al. [Phys. Rev. Lett. 105, 266802 (2010)]. For electronic-structure problems, the vLB-correction replicates the behavior of exact-exchange potentials, with improved scaling and well-behaved asymptotics, but with the computational cost of semi-local functionals. The vLB+IP corrections produces large improvement in the eigenvalues over that from LDA due to correct asympotic behavior and atomic shell structures, as shown on rare-gas, alkaline-earth, zinc-based oxides, alkali-halides, sulphides, and nitrides. In half-Heusler alloys, this asymptotically-corrected LDA reproduces the spin-polarized properties correctly, including magnetism and half-metallicity. We also considered finite-sized systems [e.g., ringed boron-nitirde (B$_{12}$N$_{12}$) and graphene (C$_{24}$)] to emphasize the wide applicability of the method.