Density functional theory approximates quantum mechanics cheaply enough to use on real molecules and materials. But standard density functional approximations have a systematic flaw: they underlocalize electrons. Charges that should stay on one atom spread across several. Band gaps are underestimated. Energy levels at interfaces misalign. The delocalization error is well-known, pervasive, and the subject of decades of corrections.
Fan, Williams, and Yang (arXiv: 2603.21906) present olLOSC — a correction that works for both molecules and periodic materials with a single, unified framework. Previous fixes fell into two camps: molecular methods that don't scale to solids, and solid-state methods that don't apply to molecules. Treating an interface — where a molecule meets a material — required mixing incompatible correction schemes. olLOSC unifies them.
The method combines localized orbital scaling correction (which fixes the delocalization by applying orbital-specific corrections) with orbital-free electronic linear response (which computes the needed curvature information without expensive orbital-dependent calculations). The “orbital-free” part is what gives it the efficiency of standard DFT while achieving the accuracy of more expensive post-DFT methods.
The through-claim: the delocalization error was not two different problems in molecules and materials — it was one problem with two manifestations. Standard DFT spreads electrons too far in molecules (wrong charge distribution) and in solids (wrong band gaps). The same mathematical deficiency — incorrect behavior of the energy as a function of fractional electron number — causes both. A correction that targets the root cause rather than the symptom works everywhere the symptom appears.
Fan, Williams & Yang, 2603.21906. Chemical physics / density functional theory / delocalization error / electronic structure / band gaps.