Non-empirical corrections for simultaneous elimination of delocalization and static correlation errors in density functional theory

Presently available exchange-correlation functionals in density functional theory (DFT) suffer from a number of errors, including many electron self-interaction error or delocalization error. Eliminating delocalization error (i.e., deviation from piecewise linearity) has been shown to improve property estimation, including relative energies and especially properties directly tied to the improved orbital energies. However, all common approaches of mediating this delocalization error (e.g., global or range-separated hybrid functionals or DFT+U) do so at the cost of increasing fractional spin (i.e., static correlation) errors that should worsen other essential properties (e.g., bond dissociation energies). We develop a general approach to avoid this trade-off by returning to the flat-plane condition that arises from the union of the fractional spin and piecewise linearity constraints. We examine the shapes of semi-local DFT errors with respect to the flat plane condition and use these deviations to construct new, approximate, functional forms that can recover the flat-plane condition. Our judiciously-modified DFT (jmDFT) approach for constructing few-parameter, low-order corrections to conventional xc-functionals adds no computational overhead to semi-local DFT while recovering the flat-plane constraint. We describe how our approach relates to commonly used Hubbard corrections (i.e., DFT+U and DFT+U+J), thereby emphasizing their relation to improving DFT+U. Finally, using this observation, we outline expressions that can be used to extract jmDFT parameters in a first-principles manner and study how such expressions compare with those employed in the ab initio computation of Hubbard parameters.