Structure and properties of the precursor/successor complex and transition state of the CrCl²⁺/Cr²⁺ electron self-exchange reaction via the inner-sphere pathway.

Abstract

The electron self-exchange reaction CrCl(OH2)5(2+) + Cr(OH2)6(2+) → Cr(OH2)6(2+) + CrCl(OH2)5(2+), proceeding via the inner-sphere pathway, was investigated with quantum-chemical methods. Geometry and vibrational frequencies of the precursor/successor (P/S) complex, (H2O)5Cr(III)ClCr(II)(OH2)5(4+)/(H2O)5Cr(II)ClCr(III)(OH2)5(4+), and the transition state (TS), (H2O)5CrClCr(OH2)5(4+‡), were computed with density functional theory (DFT) and conductor polarizable continuum model hydration. Consistent data were obtained solely with long-range-corrected functionals, whereby in this study, LC-BOP was used. Bent and linear structures were computed for the TS and P/S. The electronic coupling matrix element (H(ab)) and the reorganizational energy (λ) were calculated with multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory. The nuclear tunneling factor (Γ(n)), the nuclear frequency factor (ν(n)), the electronic frequency factor (ν(el)), the electron transmission coefficient (κ(el)), and the first-order rate constant (k(et)) for the electron-transfer step (the conversion of the precursor complex into the successor complex) were calculated based on the imaginary frequency (ν(‡)) of the TS, the Gibbs activation energy (ΔG(‡)), H(ab), and λ. The formation of the precursor complex via water substitution at Cr(OH2)6(2+) was also investigated with DFT and found to be very fast. Thus, the electron-transfer step is rate-determining. For the substitution reaction, only a bent TS structure could be obtained. The overall rate constant (k) was estimated as the product K(A)k(et), whereby K(A) is the equilibrium constant for the formation of the ion aggregate of the reactants Cr(OH2)6(2+) and CrCl(OH2)5(2+), Cr(H2O)6·CrCl(OH2)5(4+) (IAR). k calculated for the bent and linear isomers agrees with the experimental value.