Electron delocalization patterns in models of distorted (D2d) mixed-valence cubanes

Low-symmetry distortions are present in cubanes such as Fe(4)S(4), but their effects on electron delocalization properties are not well-understood. Mixed-valence cubanes often exhibit experimentally measurable "pair delocalization" of a delocalizable electron. An important question is, what is the role of physical interactions (vibronic, electronic, exchange) and symmetry distortions in determining the electron delocalization pattern? Semiclassical models are used to explore the electron delocalization patterns of S=1/2 tetragonally (D(2d)) distorted mixed-valence cubanes comprising four metal centers with bridging ligands, a single delocalizable "excess" electron, and either closed-shell or open-shell ion cores. Phase diagrams show that distorted S=1/2 ground state cubanes with antiferromagnetic exchange (as found in nature) have delocalization patterns qualitatively similar to those of an S=1/2 model with no Heisenberg exchange, suggesting that exchange is not necessarily a dominant factor in determining electron delocalization properties. The open-shell model reveals two types of pair delocalization for the S=1/2 ground state, with differing dimer subunit spins for compressed and elongated geometries. Previous studies emphasize the importance of exchange interactions for pair delocalization. Here, it is shown that electron exchange is not always necessary for pair delocalization and that it can be achieved with relatively small tetragonal distortions from tetrahedral (T(d)) symmetry. The results contradict those of an earlier theoretical study of distorted Fe(4)S(4) clusters, which concluded that distortions of lower symmetry than D(2d) are necessary to induce a transition to pair delocalization.