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Low-cost, non-empirical corrections to semi-local density functional theoryare essential for accurately modeling transition metal chemistry. Here, wedemonstrate the judiciously-modified density functional theory (jmDFT) approachwith non-empirical U and J parameters obtained directly from frontier orbitalenergetics on a series of transition metal complexes. We curate a set of ninerepresentative Ti(III) and V(IV) $d^1$ transition metal complexes and evaluatetheir flat plane errors along the fractional spin and charge lines. Wedemonstrate that while jmDFT improves upon both DFT+U and semi-local DFT withthe standard atomic orbital projectors (AOPs), it does so inefficiently. Werationalize these inefficiencies by quantifying hybridization in the relevantfrontier orbitals for both the case of fractional spins and fractional charges.To overcome these limitations, we introduce a procedure for computing amolecular orbital projector (MOP) basis for use with jmDFT. We demonstrate thissingle set of $d^1$ MOPs to be suitable for nearly eliminating all energeticdelocalization error and static correlation error. In all cases, the MOP jmDFToutperforms AOP jmDFT, and it eliminates most flat plane errors atnon-empirical values. Unlike widely employed DFT+U or hybrid functionals, jmDFTnearly eliminates energetic delocalization error and static correlation errorwithin a non-empirical framework.

Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition metal chemistry