DENSITY-FUNCTIONAL POISSON-BOLTZMANN CALCULATIONS OF REDOX POTENTIALS FOR IRON-SULFUR CLUSTERS

Density functional calculations for 1Fe, 2Fe, and 4Fe iron-sulfur clusters are reported. From broken symmetry and high spin state calculations, the energies of the spin ground states can be calculated, along with spin Hamiltonian parameters J, B, and B' for Heisenberg coupling, resonance delocalization within a mixed valence pair, and resonance between pairs, respectively. Environmental effects are modeled through a continuum dielectric, so that the solvent contribution to the redox potential can be calculated. There is a good correlation between predicted and measured redox potentials. The concepts of spin and electron delocalization barycenter states are introduced, which are analogous to the ideas of ligand field stabilization theory, but now applied to spin coupling Hamiltonians. The Heisenberg spin coupling produces a negative redox potential shift for the 2Fe redox couple compared with one iron clusters. Both spin coupling and resonance delocalization contribute to the much higher redox potential found for the 4Fe high potential (HPox,red) couple compared to the reduced ferrodoxin couple (Fd(ox,red)) in synthetic analogues, and probably in proteins as well. The solvation contribution is large in all clusters and for all redox couples, but the calculations suggest that solvation mainly compensates for differences in electron-electron repulsion energies in vacuum. For the HPox state, we find three low lying electronic states with redox potentials within 0.3 eV, which could contribute to the two redox potential peaks observed by differential pulse polarography. The HPox clusters in synthetic systems and in proteins could involve any of these three states and are, therefore, probably more complicated than previously thought.