Effect of spin-orbit coupling on reduction potentials of octahedral ruthenium(II/III) and osmium(II/III) complexes

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.