# Better band gaps for wide-gap semiconductors from a locally corrected exchange-correlation potential that nearly eliminates self-interaction errors

## TL;DR

This paper introduces a locally corrected exchange-correlation potential that significantly improves the accuracy of electronic structure calculations for wide-gap semiconductors and reduces self-interaction errors.

## Contribution

It develops and applies a van Leeuwen and Baerends exchange-corrected LDA that enforces correct asymptotic behavior, enhancing predictive accuracy for material properties.

## Key findings

- Lattice constants, bulk modulus, and band structures match experimental data well.
- Self-interaction errors are reduced to about 10%, much lower than standard LDA.
- Improved exchange potential representation enhances electronic structure calculations.

## Abstract

This work constitutes a comprehensive and improved account of electronic-structure and mechanical properties of silicon-nitride (Si3N4) polymorphs via van Leeuwen and Baerends (LB) exchange-corrected local density approximation (LDA) that enforces the exact exchange potential asymptotic behavior. The calculated lattice constant, bulk modulus, and electronic band structure of Si3N4 polymorphs are in good agreement with experimental results. We also show that, for a single electron in a hydrogen atom, spherical well, or harmonic oscillator, the LB-corrected LDA reduces the (self-interaction) error to exact total energy to ~10%, a factor of three to four lower than standard LDA, due to a dramatically improved representation of the exchange-potential.