  Despite its widespread use, the predictive accuracy of density functional
theory (DFT) is hampered by delocalization errors, especially for correlated
systems such as transition-metal complexes. Two complementary tuning strategies
have been developed to reduce delocalization error: eliminating the global
curvature with respect to charge addition or removal, and computing a linear
response Hubbard U as a measure of local curvature at the metal center at fixed
charge and applying it to the transition-metal complex in a DFT+U framework. We
investigate the relationship between the two measures of delocalization error
as we manipulate the ligand field strength by varying the number of
strong-field ligands in a series of heteroleptic complexes or by geometrically
constraining the metal-ligand bond length in homoleptic octahedral complexes.
We show that across these sets of complexes with varying ligand fields, an
inverse relationship generally exists between global and local curvatures. We
find that effects of ligand substitution on both measures of delocalization are
typically additive, but the two quantities seldom coincide. The observation of
ligand additivity suggests opportunities for evaluating errors on homoleptic
complexes to infer corrections for lower-symmetry complexes.
