Ferrocene/ferrocenium, cobaltocene/cobaltocenium and nickelocene/nickelocenium : from gas phase ionization energy to one-electron reduction potential in solvated medium

We propose a theoretical procedure for accurate determination of reduction potentials for three metallocene couples, Cp₂M⁺/Cp₂M, where M = Fe, Co and Ni. This procedure first computes the gas phase ionization energy (IE) using the explicitly correlated CCSD(T)-F12 method and includes the zero-point energy correction, core-valence electronic correlation, and relativistic and spin-orbit coupling effects. By means of Born-Haber thermochemical cycle, the one-electron reduction potential is obtained as the sum of the gas phase IE and the corresponding Gibbs free energies of solvation (ΔG_solv) for both the neutral and cationic species. Among the three solvent models (PCM, SMD and uESE) investigated here, it turns out that only the SMD model (computed at the DFT level) gives the best estimation of the value for “ΔG_solv(cation) − ΔG_solv(neutral)” and thus, combining with the accurate IE values, the theoretical protocol is capable of yielding reliable values (in V) for E°_abs (Cp₂Fe⁺_/ CP₂Fe) = 4:616 (water) and and 4:644 (acetonitrile) , E°_abs (Cp₂Co⁺/ Cp₂Co) = 3:347 (water) and 3:369 (acetonitrile)  and E°_abs (Cp₂Ni⁺ / Cp₂Ni) = 4:289 (water) and 4:321 (acetonitrile).  These predictions compare favorably with the available experimental data (in V): E°_abs Cp2Fe⁺ / Cp₂Fe) 4:682 (water) and 4:763 (acetonitrile), E°_abs (Cp₂Co⁺/ Cp₂Co) = 3:321 (water) and 3:369 V, and E° _abs (Cp₂Ni⁺/ Cp₂Ni)  = 4:291 V (acetonitrile) . We show that our theoretical procedure is reliable for accurate reduction potential predictions of Cp₂Fe⁺ /Cp₂Fe, Cp₂Co⁺ /Cp₂Co and Cp₂Ni⁺/Cp₂Ni redox couples in aqueous and non-aqueous media; the maximum absolute deviation is as small as ≈120 mV, which outperforms those of the existing theoretical methods. 

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