  Low-cost, non-empirical corrections to semi-local density functional theory
are essential for accurately modeling transition metal chemistry. Here, we
demonstrate the judiciously-modified density functional theory (jmDFT) approach
with non-empirical U and J parameters obtained directly from frontier orbital
energetics on a series of transition metal complexes. We curate a set of nine
representative Ti(III) and V(IV) $d^1$ transition metal complexes and evaluate
their flat plane errors along the fractional spin and charge lines. We
demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with
the standard atomic orbital projectors (AOPs), it does so inefficiently. We
rationalize these inefficiencies by quantifying hybridization in the relevant
frontier orbitals for both the case of fractional spins and fractional charges.
To overcome these limitations, we introduce a procedure for computing a
molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this
single set of $d^1$ MOPs to be suitable for nearly eliminating all energetic
delocalization error and static correlation error. In all cases, the MOP jmDFT
outperforms AOP jmDFT, and it eliminates most flat plane errors at
non-empirical values. Unlike widely employed DFT+U or hybrid functionals, jmDFT
nearly eliminates energetic delocalization error and static correlation error
within a non-empirical framework.
