Correcting Delocalization Error in Materials with Localized Orbitals and Linear-Response Screening

TL;DR

Delocalization error in DFAs undermines accurate band gaps and energy-level alignment, especially at interfaces. The authors introduce lrLOSC, a method that combines localization via DLWFs with linear-response screening to produce a total-energy correction and a Hamiltonian correction, restoring correct derivative discontinuities and improving orbital energies across wide band gaps. In benchmarks on eleven materials, lrLOSC achieves a mean absolute error of $MAE = 0.22$ eV for the fundamental gap, outperforming PBE and rivaling some many-body approaches, while also providing a consistent energy correction that enables a unified treatment of molecules and solids. This framework promises improved interfaces modeling and energy-level alignment within a parameter-light DFT paradigm, with future work aimed at self-consistency and efficiency.

Abstract

Delocalization error prevents density functional theory (DFT) from reaching its full potential, causing problems like systematically underestimated band gaps and misaligned energy levels at interfaces. We introduce lrLOSC to correct delocalization error in materials over a wide range of band gaps. We predict eleven materials' fundamental gaps to within 0.22 eV, while offering a nonzero total energy correction; molecular properties are improved with a parallel implementation of the same theory [J. Phys. Chem. Lett. 16, 2492 (2025)]. lrLOSC is an essential step toward modeling molecules, materials, and their interfaces within the same DFT framework.

Figures (3)

• Figure 1: Fundamental gaps predicted by lrLOSC vs. by PBE. Reference: experimental gaps $-$ zero-point renormalization.
• Figure 2: LiF band structure by PBE and lrLOSC. Purple dashed lines (top to bottom): Experimental gaps adjusted by ZPR; experimental energies for F 2s, Li 1s states.
• Figure 3: SiC band structure, with the Fermi energy set to zero. Purple dashed line: Experimental gap adjusted for ZPR.