Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error

While density functional theory (DFT)
is widely applied for its
combination of cost and accuracy, corrections (e.g., DFT+U) that improve
it are often needed to tackle correlated transition-metal chemistry.
In principle, the functional form of DFT+U, consisting of a set of
localized atomic orbitals (AOs) and a quadratic energy penalty for
deviation from integer occupations of those AOs, enables the recovery
of the exact conditions of piecewise linearity and the derivative
discontinuity. Nevertheless, for practical transition-metal complexes,
where both atomic states and ligand orbitals participate in bonding,
standard DFT+U can fail to eliminate delocalization error (DE). Here,
we show that by introducing an alternative valence-state (i.e., molecular
orbital or MO) basis to the DFT+U approach, we recover exact conditions
in cases for which standard DFT+U corrections have no error-reducing
effect. This MO-based DFT+U also eliminates DE where standard AO-based
DFT+U is already successful. We demonstrate the transferability of
our approach on representative transition-metal complexes with a range
of ligand field strengths, electron configurations (i.e., from Sc
to Zn), and spin states.