Correlated electron behavior of metal-organic molecules: Insights from density functional theory combined with many-body effects using exact diagonalization

A proper theoretical description of the electronic structure of the $3d$ orbitals in the metal centers of functional metalorganics is a challenging problem. We apply density functional theory and an exact diagonalization method in a many-body approach to study the ground-state electronic configuration of an iron porphyrin (FeP) molecule. Our study reveals that the consideration of multiple Slater determinants is important, and FeP is a potential candidate for realizing a spin crossover due to a subtle balance of crystal-field effects, on-site Coulomb repulsion, and hybridization between the Fe-$d$ orbitals and ligand N-$p$ states. The mechanism of switching between two close-lying electronic configurations of Fe-$d$ orbitals is shown. We discuss the generality of the suggested approach and the possibility to properly describe the electronic structure and related low-energy physics of the whole class of correlated metal-centered organometallic molecules.