Holistic simulation of iron–sulfur cluster electronic and physical structures with hybrid density functional approximation reduced density matrix functional theory

[Fe–S] clusters are privileged and highly conserved metallocofactors that perform a wide range of biological functions, including redox catalysis and small molecule activation. Their reactivity is largely owed to their manifold of energetically low-lying, near-degenerate d-orbitals, resulting in a highly multi-reference, or strongly correlated, electronic structure. This results in not only a large number of electronic degrees of freedom but also a delicate interplay with the geometric configuration of the cluster core. Due to the size and computational complexity of these clusters, their larger-scale simulation has traditionally been limited to single-reference density functional theory (DFT), which struggles to capture strong-correlation effects. This approach leads to significant uncertainties not only in the predicted electronic properties of the [Fe–S] cluster but also in their optimized geometries, resulting in limitations to the ability of simulations to serve as a predictive tool in [Fe–S] chemistry. In a step to overcome these limitations, we employ a methodology based on combining existing, traditional density functionals with a 1-electron reduced density matrix functional (DFA 1-RDMFT), which captures strong correlation effects via fractional orbital occupation, while retaining the low computational scaling of DFT. We apply this approach to both simulate the electronic structure and optimize the geometries of a set of site-differentiated [Fe₄S₄]⁺ clusters coordinated by a series of electronically diverse ligands, demonstrating the ability of DFA 1-RDMFT to capture the delicate interplay between the electronic and physical structures in [Fe₄S₄] clusters.