Effect of Spin−Orbit Coupling on Reduction Potentials of Octahedral Ruthenium(II/III) and Osmium(II/III) Complexes

Abstract

Reduction potentials of several M(2+/3+) (M = Ru, Os) octahedral complexes, namely, [M(H2O)6](2+/3+), [MCl6](4-/3-), [M(NH3)6](2+/3+), [M(en)3](2+/3+) [M(bipy)3](2+/3+), and [M(CN)6](4-/3-), were calculated using the CASSCF/CASPT2/CASSI and MRCI methods including spin-orbit coupling (SOC) by means of first-order quasi-degenerate perturbation theory. It was shown that the effect of SOC accounts for a systematic shift of approximately -70 mV in the reduction potentials of the studied ruthenium (II/III) complexes and an approximately -300 mV shift for the osmium(II/III) complexes. SOC splits the sixfold-degenerate (2)T(2g) ground electronic state (in ideal octahedral symmetry) of the M(3+) ions into the E((5/2)g) Kramers doublet and G((3/2)g) quartet, which were calculated to split by 1354-1573 cm(-1) in the Ru(3+) complexes and 4155-5061 cm(-1) in the Os(3+) complexes. It was demonstrated that this splitting represents the main contribution to the stabilization of the M(3+) ground state with respect to the closed-shell (1)A(1g) ground state in M(2+) systems. Moreover, it was shown that the accuracy of the calculated reduction potentials depends on the calculated solvation energies of both the oxidized and reduced forms. For smaller ligands, it involves explicit inclusion of the second solvation sphere into the calculations, whereas implicit solvation models yield results of sufficient accuracy for complexes with larger ligands. In such cases (e.g., [M(bipy)3](2+/3+) and its derivatives), very good agreement between the calculated (SOC-corrected) values of the reduction potentials and the available experimental values was obtained. These results led us to the conclusion that especially for Os(2+/3+) complexes, inclusion of SOC is necessary to avoid systematic errors of approximately 300 mV in the calculated reduction potentials.

Computational Redox Potential Predictions: Applications to Inorganic and Organic Aqueous Complexes, and Complexes Adsorbed to Mineral Surfaces

“…This shows that even for the second row transition metal redox chemistry, the SO effect is not very significant since SO effect value found for the Ru(2+/3+) redox is −0.07 eV, which is negligible. However, for the fourth row transition metal redox chemistry, SO effects have to be taken into account since the SO value found for the Os(2+/3+) redox is −0.30 eV, which is significant [82]. For elements with unpaired f-electrons, spin orbit coupling can even be more significant, for instance, its value for f 1 electron of the uranyl(V) ion is about −0.31 eV [83].…”

Reduction Potentials and Acidity Constants of Mn Superoxide Dismutase Calculated by QM/MM Free‐Energy Methods

“…Non-scalar relativistic effects (spin-orbit coupling) are expected to be negligible. [121] MM and MD Calculations All MM calculations were run with the sander module in the Amber software, [122] using the Amber 1999 force field (FF99). [123,124] The QM system was represented by charges fitted to the electrostatic potential, sampled according to the Merz-Kollman scheme, [125] as implemented in Turbomole, but with a higher-thandefault density of points, 2000-3000 points/atom.…”

Electronic structure of Fe- vs. Ru-based dye molecules

“…The effect of the spin-orbit interaction on the electronic structure has been studied in detail for the Fe-, Ru-, and Os-tris(bipyridine) series which covers the 3d, 4d, and 5d shells. 12,[45][46][47] Here, we restrict ourselves to the Fe-Ru comparison, but extend the scope to a broader class of dye molecules, i.e., tris(phenanthroline) and OEP in addition to tris(bipyridine).…”