DOUBLE EXCHANGE AND VIBRONIC COUPLING IN MIXED-VALENCE SYSTEMS - ORIGIN OF THE BROKEN-SYMMETRY GROUND-STATE OF [FE3S4]0 CORES IN PROTEINS AND MODELS

The origin of the pair-delocalized ground state of spin S = 2, observe d in chemically symmetric mixed-valence [Fe3S4]0 cores present in prot eins and synthetic models, is analyzed in the framework of an effectiv e-Hamiltonian model, comprising terms for excess-electron transfer (le ading to double-exchange coupling of the paramagnetic Fe(III) cores), vibronic coupling (trapping the excess electron), and antiferromagneti c 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 determine d and their extremal points, corresponding to definite electron distri butions, are ascertained. The electron distributions depend essentiall y on the ratio of transfer parameter and vibronic trapping energy: bet a/(lambda2/2kappa). For small ratios, the excess electron is site-trap ped; 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 represe ntations (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 (r epresented by electronic structure d5-ds-d6) reveals, for beta > 0, a highly degenerate electronic ground state, including spin levels rangi ng 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-delocaliz ed 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 (an d strongest vibronic stabilization) is found for spin S = 2: the conju nction of electron-transfer interaction and vibronic coupling leads to a pair-delocalized ground state of spin S = 2 for beta/(lambda2/2kapp a) greater-than-or-equal-to 1. The condition is satisfied by estimates of the ratio in trinuclear iron-sulfur clusters, which explains the g round state observed therein. The calculated magnetic hyperfine parame ters are in good agreement with experiment. Introduction of antiferrom agnetic exchange does not change the main conclusions obtained without this interaction.