Detection and correction of delocalization errors for electron- and hole-polarons using density-corrected DFT

Modeling of polaron defects is an important aspect of computational materials science but the description of unpaired spins in density functional theory (DFT) suffers from delocalization error. To diagnose and correct the over-delocalization of unpaired spins, we report an implementation of density-corrected (DC-)DFT and its analytic energy gradient. In this approach, an exchange-correlation functional is evaluated using a Hartree-Fock density rather than the DFT density, to incorporate correlation while avoiding self-interaction error. Results for an electron-polaron in TiO2 and a hole-polaron in Al-doped silica demonstrate that geometry optimization with semilocal functionals drives significant structural distortion including elongation of several bonds, such that subsequent single-point calculations with hybrid functionals fail to afford a localized defect even when hybrid functional optimizations do localize the polaron. This has significant implications for the traditional workflow in computational materials science. DC-DFT calculations provide a mechanism to detect situations where delocalization error is likely to affect the results.