Structure-Property Relationships of Fe₄ S₄ Clusters

In this theoretical study, the sensitivity of Fe₄ S₄ cluster properties, such as potential energy, spin coupling, adiabatic detachment energy, inner-sphere reorganization energy, and reactivity, to structural distortions is investigated. [Fe₄ S₄ (SH)₄ ]^3-/2-/1- model clusters anchored by fixed hydrogen atoms are compared with Fe₄ S₄ clusters coordinated by ethyl thiolates with fixations according to cysteine residues in crystal structures. For the model system, a dependence of the ground-state spin-coupling scheme on the hydrogen-hydrogen distances is observed. The minima of the potential energy surface of [Fe₄ S₄ (SH)₄ ]^2-/1- clusters are located at slightly smaller hydrogen-hydrogen distances than those of the [Fe₄ S₄ (SH)₄ ]^3- cluster. For inner-sphere reorganization energies the spin-coupling scheme adopted by the broken-symmetry wave function plays an important role, since it can change the reorganization energies by up to 13 kcal mol^-1 . For most structures, [Fe₄ S₄ (SR)₄ ]^2- and [Fe₄ S₄ (SR)₄ ]^1- (R=H or ethyl, derived from cysteine) favor the same coupling scheme. Therefore, the reorganization energies for this redox couple are relatively low (6-12 kcal mol^-1 ) compared with the 2-/3- redox couple favoring different spin-coupling schemes before and after electron transfer (14-18 kcal mol^-1 ). However, one may argue that more reliable reorganization energies are obtained if always the same spin-coupling pattern is enforced. All theoretical observations and insights are discussed in the light of experimental results distilled from the literature.