Probing ligand effects on the redox energies of [4Fe-4S] clusters using broken-symmetry density functional theory

A central issue in understanding redox properties of iron-sulfur proteins is determining the factors that tune the reduction potentials of the Fe-S clusters. Recently, Solomon and coworkers have shown that the Fe-S bond covalency of protein analogs measured by %L, the percent ligand character of the Fe 3d orbitals, from ligand K-edge X-ray absorption spectroscopy (XAS) correlates with the electrochemical redox potentials. Also, Wang and coworkers have measured electron detachment energies for iron-sulfur clusters without environmental perturbations by gas-phase photoelectron spectroscopy (PES). Here the correlations of the ligand character with redox energy and %L character are examined in [Fe(4)S(4)L(4)](2-) clusters with different ligands by broken symmetry density functional theory (BS-DFT) calculations using the B3LYP functional together with PES and XAS experimental results. These gas-phase studies assess ligand effects independently of environmental perturbations and thus provide essential information for computational studies of iron-sulfur proteins. The B3LYP oxidation energies agree well with PES data, and the %L character obtained from natural bond orbital analysis correlates with XAS values, although it systematically underestimates them because of basis set effects. The results show that stronger electron-donating terminal ligands increase %L(t), the percent ligand character from terminal ligands, but decrease %S(b), the percent ligand character from the bridging sulfurs. Because the oxidized orbital has significant Fe-L(t) antibonding character, the oxidation energy correlates well with %L(t). However, because the reduced orbital has varying contributions of both Fe-L(t) and Fe-S(b) antibonding character, the reduction energy does not correlate with either %L(t) or %S(b). Overall, BS-DFT calculations together with XAS and PES experiments can unravel the complex underlying factors in the redox energy and chemical bonding of the [4Fe-4S] clusters in iron-sulfur proteins.