Spin-State Energetics of Fe(III) and Ru(III) Aqua Complexes: Accurate ab Initio Calculations and Evidence for Huge Solvation Effects

Aqua complexes of transition metals are useful models for understanding the electronic structure of metal-oxide species relevant in photocatalytic water splitting. Moreover, spin-forbidden d-d transitions of aqua complexes provide valuable experimental data of spin-state energetics, which can be used for benchmarking of computational methods. Here, low-energy spin states of Fe(III) and Ru(III) aqua complexes are studied with an array of DFT and high-level wave function methods (CASPT2, RASPT2, NEVPT2, CCSD(T)-F12, and other coupled cluster methods up to full CCSDT). The results from single-reference and multireference methods are cross-checked, and the amount of multireference character for both considered spin states of Fe(H2O)6(3+) is carefully analyzed. In addition to small M(H2O)6(3+) clusters (M = Fe, Ru), we also employ larger models M(H2O)6·(H2O)12(3+), with explicit water molecules in the second coordination sphere, to describe the situation in aqueous solution. By comparing the results for both types of models, our calculations evidence large and systematic solvation effects on the spin-state energetics. It is found that, due to the interaction with hydrogen-bonded water molecules in the second coordination sphere, the first coordination sphere undergoes a noticeable contraction and deformation. In consequence, the presence of solvation shell affects the relative energies of spin states by as much as 3-4 × 10(3) cm(-1) (∼10 kcal/mol). Once this solvation effect is accounted for, the spin-state energetics from CCSD(T) and NEVPT2 calculations turn out to be in an excellent agreement with the experimental estimates, which was not the case for isolated M(H2O)6(3+) species is gas phase. We thus postulate that significant discrepancies between theory and experimental data for Fe(H2O)6(3+) that were previously reported in the literature may be plausibly resolved and attributed to the neglect of explicit solvation effects and also, to some extent, to incompleteness of the active space and/or basis set used in the previous theoretical studies. The findings of this work contradict an anecdotal conjecture that energies of ligand-field (d-d) transitions are almost unaffected by solvation. On the contrary, it is highlighted that medium effects may contribute very significantly to spin-state energetics of transition metal complexes.