Iron-sulfur bond covalency from electronic structure calculations for classical iron-sulfur clusters

The covalent character of iron-sulfur bonds is a fundamental electronic structural feature for understanding the electronic and magnetic properties and the reactivity of biological and biomimetic iron-sulfur clusters. Conceptually, bond covalency obtained from X-ray absorption spectroscopy (XAS) can be directly related to orbital compositions from electronic structure calculations, providing a standard for evaluation of density functional theoretical methods. Typically, a combination of functional and basis set that optimally reproduces experimental bond covalency is chosen, but its dependence on the population analysis method is often neglected, despite its important role in deriving theoretical bond covalency. In this study of iron tetrathiolates, and classical [2Fe-2S] and [4Fe-4S] clusters with only thiolate ligands, we find that orbital compositions can vary significantly depending on whether they are derived from frontier orbitals, spin densities, or electron sharing indexes from "Átoms in Molecules" (ÁIM) theory. The benefits and limitations of Mulliken, Minimum Basis Set Mulliken, Natural, Coefficients-Squared, Hirshfeld, and AIM population analyses are described using ab initio wave function-based (QCISD) and experimental (S K-edge XAS) bond covalency. We find that the AIM theory coupled with a triple-ζ basis set and the hybrid functional B(5%HF)P86 gives the most reasonable electronic structure for the studied Fe-S clusters.