Localized Orbital Scaling Correction with Linear Response in Materials

Density functional theory (DFT) is a powerful tool for quantum-mechanical calculations, but practical calculations suffer systematic errors like incorrect charge densities and total energies in molecular dissociation, underestimated band gaps in bulk materials, and poor energy level alignment at interfaces. These problems are due to delocalization error. The localized orbital scaling correction (LOSC) removes delocalization error in molecules effectively, but screening of the Hartree-exchange-correlation response is necessary to correct it in materials. We introduce LOSC with system-dependent linear-response screening (lrLOSC), which effectively corrects delocalization error in semiconductors and insulators. After correcting for electron-phonon effects, the band gaps of eleven test systems are predicted with a mean absolute error of 0.28 eV, comparable to self-consistent $GW$. This method represents a significant step forward in correcting densities and total energies across system sizes and solving the band gap and energy level alignment problems entirely within the DFT framework.