The DFT-$\frac{1}{2}$ method is a band-gap correction with GW precision at a density functional theory (DFT) computational cost. The method was also extended to correct the gap between defect levels, allowing for the calculation of optical transitions. However, this method fails when the atomic character of the occupied and unoccupied defect levels is similar as we illustrate by two examples, the tetrahedral hydrogen interstitial and the negatively charged vacancy in diamond. We solve this problem by decoupling the effect of the occupied and unoccupied defect levels and call this the decoupled DFT-$\frac{1}{2}$ method for defects.

• Received 13 June 2023
• Revised 30 August 2023
• Accepted 6 September 2023

DOI:https://doi.org/10.1103/PhysRevB.108.125306