Heisenberg and double exchange in iron mixed valence [Fe6S6](+) supercluster

A theoretical model is presented of the Heisenberg exchange interaction and resonance delocalization (also called 'double exchange') for Fe/S protein containing six mixed valence iron ions. The model developed uses the reduced [Fe6S6](+) cluster in which there are five Fe(II) ions and one Fe(III) ion, and makes it possible to calculate the energies and describe the properties of the spin eigenstates of system investigated. The lowest energies presented on the correlation diagram depend on Heisenberg exchange coupling parameters J(i) (i = 1, 2, 3, 4) and the b parameter for the double exchange. The energies of the Lowest spin slates are presented in the form of analytical expressions obtained by using a third-order perturbation method. The most probable ground states of the cluster are determined as the antiferromagnetic states connected with the total spins S = 1/2, 3/2, 5/2, 7/2, depending on the values of parameter J(i). All these states are doubly degenerate. The double exchange leads to their splitting and strong decrease. The Heisenberg exchange parameters J(i) have been estimated based on parameters A and a for the Gaussian function Ae(-aR2) (R is the Fe-Fe distance).