Multireference Ab initio study of ligand field d-d transitions in octahedral transition-metal oxide clusters

We have used multiconfigurational (MC) and multireference (MR) methods (CASSCF, CASPT2, and MRCI) to study d-d transitions and other optical excitations for octahedral [M(H₂O)₆]ⁿ⁺ clusters (M = Ti, V, Mn, Cr, Fe, Co, Ni, Cu) as models of hematite and other transition-metal oxides of interest in solar fuels. For [Fe(H₂O)₆]³⁺, all calculations substantially overestimate the d-d transition energies (∼3.0 versus ∼1.5 eV) compared to what has been experimentally assigned. This problem occurs even though theory accurately describes (1) the lowest d-d transition energy in the atomic ion Fe³⁺ (∼4.4 eV), (2) the t_2g-e_g splitting (∼1.4 eV) in [Fe(H₂O)₆]³⁺, and (3) the ligand-to-metal charge transfer (LMCT) energy in [Fe(H₂O)₆]³⁺. Indeed, the results for Fe³⁺ and the t_2g-e_g splitting suggest that the lowest d-d excitation energy in the hexa-aqua complex should be ∼3 eV (or slightly below because of Jahn-Teller stabilization), as we find. Possible origins for the d-d discrepancy are examined, including Fe²⁺ and low-spin Fe³⁺ impurities. For the [M(H₂O)₆]ⁿ⁺ clusters not involving Fe(III), our MR calculations show reasonable correlation (mostly within 0.5 eV) with experiments for the d-d transitions, including consistent trends for the intensities of spin-allowed and spin-forbidden transitions. Our calculations also greatly complement experimental data because (1) experimental results for some species are insufficient or even scarce, (2) some of the experimental peaks were not observed directly but were inferred, and (3) the nature or existence of some shoulder peaks and weak peaks is uncertain. Our MR calculations have also been used to study convergence of the results with choice of active space, including the importance of the "double shell" effect in which there are 10 active d orbitals per transition-metal atom rather than 5. The results show that the larger active space does not significantly change the excitation energy, although it lowers the absolute energies for complexes with high 3d occupations. This indicates that reasonable accuracy can be achieved using MR methods in studies of transition-metal oxide clusters using minimal active spaces. This study establishes fundamental principles for the further modeling of larger cluster models of pure and doped hematite and other metal oxides.