Scaling correction approaches for reducing delocalization error in density functional approximations

Abstract

Delocalization error associated with the presently used density functional approximations is one of the main sources of errors which plague density functional theory calculations. In this paper, we give a comprehensive review on scaling correction (SC) approaches developed recently for reducing the delocalization error. The global and local SC approaches impose the rigorous Perdew-Parr-Levy-Balduz condition that the total electronic energy should scale linearly between integer electron numbers, on systems involving global and local fractional electron distributions, respectively. After presenting the theoretical background and mathematical formulation of scaling corrections, we demonstrate that they lead to universal alleviation of delocalization error. This is exemplified by the substantial improvement for the prediction of a wide range of electronic properties, including Kohn-Sham frontier orbital energies and band gaps, dissociation behavior of molecules, reaction barriers, electric polarizabilities, and charge-transfer species. The encouraging performances of SC approaches highlight their practicality and usefulness, and also affirm that an explicit treatment of fractional electron distributions is essentially important for reducing the intrinsic delocalization error. The existing limitations, the remaining challenges, and the future perspectives of SC are also discussed. Moreover, the SC approaches are compared with some existing methods attempting to remove the self-interaction error, such as the Perdew-Zunger self-interaction correction, the local hybrid hyper-generalized gradient approximations, and the rangeseparated density functional approximations. The unique advantages of SC suggest that it could open a novel and potentially paradigm-changing route for advancing density functional theory methods towards chemical accuracy.