Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes
Polynuclear transition-metal (PNTM) clusters, ubiquitous in biological systems, owe their catalytic activity to the presence of a large manifold of low-lying spin states, and a number of stable oxidation states. The ab initio description of such systems - starting from the electronic Schrodinger equation - represents one of the greatest challenges of modern quantum chemistry, requiring highly multiconfigurational treatments. We propose a theoretical framework of simple and physically motivated molecular-orbital transformations that enable the resolution and characterization of targeted electronic wave functions with ease. This paradigm allows us to unravel the complicated electronic correlations in PNTM clusters. We apply it to two super-oxidized iron-sulfur cubane [Fe4S4] structures, and accurately characterize their singlet ground and low-lying excited states. Through direct access to their wave functions, we identify the important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters. Our results unambiguously reveal a hidden magnetic order in the manifold of singlet states. Namely, that in all low-energy singlet states of the two compounds, well-defined spin structures are formed within two pairs of magnetic sites. For instance, in the ground state of one compound two iron sites of local S = 5/2 spins are strongly ferromagnetically correlated to form two S = 5 intermediate pair states; two such pairs are then anti-ferromagnetically coupled to yield an overall singlet. In the five excited singlets, the spin of these hidden pair-states is reduced in steps to zero. We find that the ab initio results for these compounds can be mapped with high fidelity onto a four-site Heisenberg–Dirac–van Vleck Hamiltonian with two anti-ferromagnetic coupling constants. Thus, the complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures, together with the geometrical distortions represent two possible ways to release spin frustration. The geometrical distortions may be seen as the result of a spin-driven Jahn-Teller distortion, that lifts the electronic ground state degeneracies. Our paradigm provides a simple yet rigorous wave function-based route to uncover the electronic structure of PNTM clusters, and may be applied to a wide variety of such clusters.