# Finite-size corrections for defect-involving vertical transitions in supercell calculations

## TL;DR

This paper introduces a correction method for defect-related vertical transition levels in supercell calculations, significantly reducing errors from about 1 eV to below 0.12 eV across multiple materials.

## Contribution

A general correction scheme for defect-involving vertical transition levels in supercell calculations is formulated and validated on various materials.

## Key findings

- Errors reduced from ~1 eV to <0.12 eV with correction
- Method verified on ten different defects in multiple materials
- Potential for wide application in defect level calculations

## Abstract

A correction method for vertical transition levels (VTLs) involving defect states calculated with a supercell technique is formulated and its effectiveness is systematically verified with ten defects in prototypical materials: cubic-BN, GaN, MgO, and 3C-SiC. Without any corrections, the absolute errors are around 1 eV with moderate size supercells in most cases. In contrast, when our correction method is adopted, the absolute errors are reduced and become less than 0.12 eV in all the cases. Our correction scheme is general and will have the potential for wide application as it is adaptive for evaluating various quantities at fixed geometry, as represented by those relevant to the generalized Koopmans' theorem.