A GGA+U approach to effective electronic correlations in thiolate-ligated iron-oxo (IV) porphyrin

High-valent oxo-metal complexes exhibit correlated electronic behavior on dense, low-lying electronic state manifolds, presenting challenging systems for electronic structure methods. Among these species, the iron-oxo (IV) porphyrin denoted Compound I occupies a privileged position, serving a broad spectrum of catalytic roles. The most reactive members of this family bear a thiolate axial ligand, exhibiting high activity toward molecular oxygen activation and substrate oxidation. The default approach to such systems has entailed the use of hybrid density functionals or multi-configurational/multireference methods to treat electronic correlation. An alternative approach is presented based on the GGA+U approximation to density functional theory, in which a generalized gradient approximation (GGA) functional is supplemented with a localization correction to treat on-site correlation as inspired by the Hubbard model. The electronic structure of thiolate-ligated iron-oxo (IV) porphyrin and corresponding Coulomb repulsion U are determined both empirically and self-consistently, yielding spin-distributions, state level splittings, and electronic densities of states consistent with prior hybrid functional calculations. Comparison of this detailed electronic structure with model Hamiltonian calculations suggests that the localized 3d iron moments induce correlation in the surrounding electron gas, strengthening local moment formation. This behavior is analogous to strongly correlated electronic systems such as Mott insulators, in which the GGA+U scheme serves as an effective single-particle representation for the full, correlated many-body problem.