DFT+ U -type functional derived to explicitly address the flat plane condition

Abstract

A $\text{DFT}+U\text{-type}$ corrective functional is derived from first principles to enforce the flat plane condition on localized subspaces, thus dispensing with the need for an ad hoc derivation from the Hubbard model. Small, molecular test systems at the dissociated limit are used to compare the functional form against several previously proposed $\text{DFT}+U\text{-type}$ functionals. The functional derived here yields relative errors below $0.6%$ in the total energy of the dissociated $s$-block dimers as well as the dissociated ${\mathrm{H}}_{5}^{+}$ ring system, a challenging test case in which the asymmetric, tilted flat plane condition applies. In comparison, bare PBE and $\text{PBE}+U$ (using Dudarev's 1998 Hubbard functional) yields relative energetic errors as high as $8.0%$ and $20.5%$, respectively.