Unifying Exchange Sensitivity in Transition-Metal Spin-State Ordering and Catalysis through Bond Valence Metrics

Accurate predictions of spin-state
ordering, reaction energetics,
and barrier heights are critical for the computational discovery of
open-shell transition-metal (TM) catalysts. Semilocal approximations
in density functional theory, such as the generalized gradient approximation
(GGA), suffer from delocalization error that causes them to overstabilize
strongly bonded states. Descriptions of energetics and bonding are
often improved by introducing a fraction of exact exchange (e.g.,
erroneous low-spin GGA ground states are instead correctly predicted
as high-spin with a hybrid functional). The degree of spin-splitting
sensitivity to exchange can be understood based on the chemical composition
of the complex, but the effect of exchange on reaction energetics
within a single spin state is less well-established. Across a number
of model iron complexes, we observe strong exchange sensitivities
of reaction barriers and energies that are of the same magnitude as
those for spin splitting energies. We rationalize trends in both reaction
and spin energetics by introducing a measure of delocalization, the
bond valence of the metal–ligand bonds in each complex. The
bond valence thus represents a simple-to-compute property that unifies
understanding of exchange sensitivity for catalytic properties and
spin-state ordering in TM complexes. Close agreement of the resulting
per-metal–organic-bond sensitivity estimates, together with
failure of alternative descriptors demonstrates the utility of the
bond valence as a robust descriptor of how differences in metal–ligand
delocalization produce differing relative energetics with exchange
tuning. Our unified description explains the overall effect of exact
exchange tuning on the paradigmatic two-state FeO+/CH4 reaction that combines challenges of spin-state and reactivity
predictions. This new descriptor-sensitivity relationship provides
a path to quantifying how predictions in transition-metal complex
screening are sensitive to the method used.