Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics

Density functional theory (DFT) is widely used in transition-metal chemistry, yet essential properties such as spin-state energetics in transition-metal complexes (TMCs) are well known to be sensitive to the choice of the exchange-correlation functional. Increasing the amount of exchange in a functional typically shifts the preferred ground state in first-row TMCs from low-spin to high-spin by penalizing delocalization error, but the effect on properties of second-row complexes is less well known. We compare the exchange sensitivity of adiabatic spin-splitting energies in pairs of mononuclear 3d and 4d mid-row octahedral transition-metal complexes. We analyze hundreds of complexes assembled from four metals in two oxidation states with ten small monodentate ligands that span a wide range of field strengths expected to favor a variety of ground states. We observe consistently lower but proportional sensitivity to exchange fraction among 4d TMCs with respect to their isovalent 3d TMC counterparts, leading to the largest difference in sensitivities for the strongest field ligands. The combined effect of reduced exchange sensitivities and the greater low-spin bias of most 4d TMCs means that while over one-third of 3d TMCs change ground states over a modest variation (ca.0.0-0.3) in exchange fraction, almost no 4d TMCs do. Differences in delocalization, as judged through changes in the metal-ligand bond lengths between spin states, do not explain the distinct behavior of 4d TMCs. Instead, evaluation of potential energy curves in 3d and 4d TMCs reveals that higher exchange sensitivities in 3d TMCs are likely due to the opposing effect of exchange on the low-spin and high-spin states, whereas the effect on both spin states is more comparable in 4d TMCs.