Full Correlation in a Multiconfigurational Study of Bimetallic Clusters: Restricted Active Space Pair-Density Functional Theory Study of [2Fe–2S] Systems

Iron–sulfur clusters play a variety of important roles in protein chemistry, and understanding the energetics of their spin ladders is an important part of understanding these roles. Computational modeling can offer considerable insights into such problems; however, calculations performed thus far on systems with multiple transition metals have typically either been restricted to a single-configuration representation of the density, as in Kohn–Sham theory, or been limited to correlating excitations only within an active space, as in active-space self-consistent field methods. For greater reliability, a calculation should include full correlation, that is, not only correlation internal to the active space but also external correlation, and it is desirable to combine this full-electron correlation with a multiconfigurational representation of the wave function, but this has been impractical thus far. Here, we present an affordable way to do this by using restricted active-space pair-density functional theory. We show that with this method, it is possible to compute the entire spin ladder for systems containing two Fe centers bridged by two S atoms. On the other hand, with second-order perturbation theory, only the high-spin states can be computed. A key result is that, in agreement with some experiments, we find a high-spin ground state for a relaxed reduced [Fe₂S₂(SCH₃)₄]³– cluster, which is a novel result in computational studies.