Electronic Structure of a Rieske Iron−Sulfur Complex and the Calculation of Its Reduction Potential

Benchmark Study of Redox Potential Calculations for Iron-Sulfur Clusters in Proteins

Redox potentials have been calculated for 12 different iron–sulfur sites of 6 different types with 1–4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated using the QM/MM energies, single-point QM methods in a continuum solvent or by QM/MM thermodynamic cycle perturbations. We show that the best results are obtained with a large QM system (∼300 atoms, but a smaller QM system, ∼150 atoms, can be used for the QM/MM geometry optimization) and a large value of the dielectric constant (80). For absolute redox potentials, the B3LYP density functional method gives better results than TPSS, and the results are improved with a larger basis set. However, for relative redox potentials, the opposite is true. The results are insensitive to the force field (charges of the surroundings) used for the QM/MM calculations or whether the protein and solvent outside the QM system are relaxed or kept fixed at the crystal structure. With the best approach for relative potentials, mean absolute and maximum deviations of 0.17 and 0.44 V, respectively, are obtained after removing a systematic error of −0.55 V. Such an approach can be used to identify the correct oxidation states involved in a certain redox reaction.

We have studied redox potentials of 12 iron−sulfur sites of 6 types with 1−4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated with QM/MM, QM calculations in a continuum solvent or by QM/MM thermodynamic cycle perturbations. The best results are obtained with the second approach using ∼300 atoms in the QM model and a large dielectric constant.

Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods

We used two theoretical methods to estimate reduction potentials and acidity constants in Mn superoxide dismutase (MnSOD), namely combined quantum mechanical and molecular mechanics (QM/MM) thermodynamic cycle perturbation (QTCP) and the QM/MM-PBSA approach. In the latter, QM/MM energies are combined with continuum solvation energies calculated by solving the Poisson-Boltzmann equation (PB) or by the generalised Born approach (GB) and non-polar solvation energies calculated from the solvent-exposed surface area. We show that using the QTCP method, we can obtain accurate and precise estimates of the proton-coupled reduction potential for MnSOD, 0.30±0.01 V, which compares favourably with experimental estimates of 0.26-0.40 V. However, the calculated potentials depend strongly on the DFT functional used: The B3LYP functional gives 0.6 V more positive potentials than the PBE functional. The QM/MM-PBSA approach leads to somewhat too high reduction potentials for the coupled reaction and the results depend on the solvation model used. For reactions involving a change in the net charge of the metal site, the corresponding results differ by up to 1.3 V or 24 pK(a) units, rendering the QM/MM-PBSA method useless to determine absolute potentials. However, it may still be useful to estimate relative shifts, although the QTCP method is expected to be more accurate.

On the electronic origins of structural isomerism in the iron-sulfur cubane, [(C(5)H(5))(4)Fe(4)S(4)](2+)

Density functional theory provides new insights into the structural isomerism observed in the cyclopentadienyl-capped iron-sulfur cluster, [(C(5)H(5))(4)Fe(4)S(4)](2+). Two distinct, closely spaced minima have been located, a triplet with D(2) symmetry and a C(2)-symmetric singlet, both of which correspond closely to the structure of one of the known crystal forms of the cation. Thus, the structural diversity in these species reflects genuine molecular bistability rather than simple solid-state packing effects. In contrast, no stable D(2)(d)()-symmetric minimum has been located, suggesting that the reported D(2)(d)() symmetry of the cation in [(C(5)H(5))(4)Fe(4)S(4)][PF(6)](2) may be a crystallographic artifact. In the ruthenium analogue, the more diffuse 4d orbitals stabilize the C(2)-symmetric singlet, which is unambiguously the ground state, but the D(2)-symmetric potential energy surface provides a viable low-energy pathway for the dynamic exchange of the Ru-Ru bonds.