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

The
theoretical calculations of reduction potentials for the [M­(H2O)6]2+/3+, [M­(NH3)6]2+/3+, [M­(en)3]2+/3+, [M­(bipy)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.