The origin of the pair-delocalized ground state of spin S = 2, observed in chemically symmetric mixed-valence [Fe3S4]0 cores present in proteins and synthetic models, is analyzed in the framework of an effective-Hamiltonian model, comprising terms for excess-electron transfer (leading to double-exchange coupling of the paramagnetic Fe(III) cores), vibronic coupling (trapping the excess electron), and antiferromagnetic exchange. The basic mechanisms underlying the inhomogeneous electron distributions in trinuclear mixed-valence clusters with paramagnetic ion cores are illustrated in a simple model with electronic structure d1-d1-d2. The adiabatic potential surfaces of the system are determined and their extremal points, corresponding to definite electron distributions, are ascertained. The electron distributions depend essentially on the ratio of transfer parameter and vibronic trapping energy: beta/(lambda2/2kappa). For small ratios, the excess electron is site-trapped; for larger values (greater-than-or-equal-to 1) the delocalization behavior depends on the nature of the electronic state considered. In case of a degenerate manifold including different irreducible representations (A + E in C3v symmetry), the excess electron is trapped in a pair-delocalized state, in which the electronic charge is accumulated at two sites of the trinuclear system. Analysis of the triiron unit (represented by electronic structure d5-ds-d6) reveals, for beta > 0, a highly degenerate electronic ground state, including spin levels ranging from S=0-6. The ground manifolds for S = 1, ..., 4 are, for beta > 0, 'A + E'-degenerate and give rise to broken-symmetry, pair-delocalized ground states. The excess electron in these states is not strictly confined to a pair of sites; there is a finite probability density of finding the electron at the remaining center. The smallest density (and strongest vibronic stabilization) is found for spin S = 2: the conjunction of electron-transfer interaction and vibronic coupling leads to a pair-delocalized ground state of spin S = 2 for beta/(lambda2/2kappa) greater-than-or-equal-to 1. The condition is satisfied by estimates of the ratio in trinuclear iron-sulfur clusters, which explains the ground state observed therein. The calculated magnetic hyperfine parameters are in good agreement with experiment. Introduction of antiferromagnetic exchange does not change the main conclusions obtained without this interaction.
