  We estimate the prediction sensitivity with respect to Hartree-Fock exchange
in approximate density functionals for representative Fe(II) and Fe(III)
octahedral complexes. Based on the observation that the range of parameters
spanned by the most widely-employed functionals is relatively narrow, we
compute electronic structure property and spin-state orderings across a
relatively broad range of Hartree-Fock exchange (0-50%) ratios. For the entire
range considered, we consistently observe linear relationships between
spin-state ordering that differ only based on the element of the direct ligand
and thus may be broadly employed as measures of functional sensitivity in
predictions of organometallic compounds. The role Hartree-Fock exchange in
hybrid functionals is often assumed to play is to correct self-interaction
error-driven electron delocalization (e.g. from transition metal centers to
neighboring ligands). Surprisingly, we instead observe that increasing
Hartree-Fock exchange reduces charge on iron centers, corresponding to
effective delocalization of charge to ligands, thus challenging notions of the
role of Hartree-Fock exchange in shifting predictions of spin-state ordering.
