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

Abstract

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/CH 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.

Calculation of Ligand Dissociation Energies in Large Transition-Metal Complexes

“…A detailed assessment of approximate density functionals is crucial for drawing meaningful conclusions from quantum chemical studies of transitionmetal complexes and their reactions. [1][2][3][4][5][6][7][8][9][10][11] One of the few benchmark sets for large transition-metal complexes containing experimental gas-phase reference data is our WCCR10 reference set of ligand bonding energies. 12 The WCCR10 set comprises ten experimentally measured gas-phase ligand dissociation energies obtained from threshold collision-induced decay (T-CID) experiments.…”

Enumeration of de novo inorganic complexes for chemical discovery and machine learning

“…3). Although quantitative spin-state assignment remains an outstanding challenge for DFT, 97,[100][101][102][103][104][105][106] with no one-size-fits-all functional for spin-state energetics motivating more advanced methods, [107][108][109] ligand-dependent trends in relative spin-state ordering are expected to be less sensitive to method choice. From the 570 high-scoring ligands in sec.…”

Making machine learning a useful tool in the accelerated discovery of transition metal complexes

“…This revealed how changing DFT functionals changes the distribution of leads. In a similar vein, we predicted the xc‐sensitivity of lead compounds, bringing about the possibility of lead compound optimization through not just fitness maximization but also minimization of the sensitivity to xc functional.…”