On the Accuracy of Calculated Reduction Potentials of Selected Group 8 (Fe, Ru, and Os) Octahedral Complexes

Abstract

The theoretical calculations of reduction potentials for the [M­(H₂O)₆]^2+/3+, [M­(NH₃)₆]^2+/3+, [M­(<i>en</i>)₃]^2+/3+, [M­(<i>bipy</i>)₃]^2+/3+, [M­(CN)₆]^4–/3–, and [MCl₆]^4–/3– systems (M = Fe, Os, Ru) were carried out. The DFT­(PBE)/def2-TZVP//DFT­(PBE)/def2-SVP quantum chemical method was employed to obtain presumably accurate ionization energies, whereas the conductor-like screening model for real solvents (COSMO-RS) was selected as the most suitable method for calculations of solvation energies of the oxidized and reduced forms of the studied species. It has been shown that COSMO-RS may overcome problems related to directionality of hydrogen bonds in the second solvation sphere that previously led to errors of ∼1 V for the [Ru­(H₂O)₆]²⁺ complex employing PCM-like models. Thus, most of the values for (2+) → (3+) oxidations are now within 0.1–0.2 V from the experimental data, once the anticipated spin–orbit coupling effects in Os complexes (downshifting the calculated reduction potentials by ∼0.3 V) are taken into account. The robustness of the DFT­(PBE)/COSMO-RS computational protocol is further verified by showing that reduction potentials obtained for selected 2+/3+ redox pairs with and without the inclusion of explicit second-sphere water molecules are almost identical. At the same time, it must be admitted that the calculated values of reduction potentials for systems involving quadruple charged species, exemplified here by [M­(CN)₆]^4–/3– and [MCl₆]^4–/3– redox pairs, might still not be within the grasp of contemporary solvation models, possibly due to the large values of solvation energies of their reduced (4−) forms that are in the range of 700–750 kcal mol^–1 (30–33 eV) and possibly larger errors inherent in their calculations. Finally, a comparison is made with M06-L//SMD computational protocol, which is also shown to correct some of the deficiencies of previous PCM models