## Structure and Properties of the Precursor/Successor Complex and Transition State of the CrCl<sup>2+</sup>/Cr<sup>2+</sup> Electron Self-Exchange Reaction via the Inner-Sphere Pathway

2014-09-15T00:00:00Z (GMT)
The electron self-exchange reaction <b>Cr</b>Cl­(OH<sub>2</sub>)<sub>5</sub><sup>2+</sup> + Cr­(OH<sub>2</sub>)<sub>6</sub><sup>2+</sup> → <b>Cr</b>(OH<sub>2</sub>)<sub>6</sub><sup>2+</sup> + CrCl­(OH<sub>2</sub>)<sub>5</sub><sup>2+</sup>, proceeding via the inner-sphere pathway, was investigated with quantum-chemical methods. Geometry and vibrational frequencies of the precursor/successor (P/S) complex, (H<sub>2</sub>O)<sub>5</sub>Cr<sup>III</sup>ClCr<sup>II</sup>(OH<sub>2</sub>)<sub>5</sub><sup>4+</sup>/(H<sub>2</sub>O)<sub>5</sub>Cr<sup>II</sup>ClCr<sup>III</sup>(OH<sub>2</sub>)<sub>5</sub><sup>4+</sup>, and the transition state (TS), (H<sub>2</sub>O)<sub>5</sub>CrClCr­(OH<sub>2</sub>)<sub>5</sub><sup>4+ ⧧</sup>, 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 (<i>H</i><sub>ab</sub>) and the reorganizational energy (λ) were calculated with multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory. The nuclear tunneling factor (Γ<sub>n</sub>), the nuclear frequency factor (ν<sub>n</sub>), the electronic frequency factor (ν<sub>el</sub>), the electron transmission coefficient (κ<sub>el</sub>), and the first-order rate constant (<i>k</i><sub>et</sub>) for the electron-transfer step (the conversion of the precursor complex into the successor complex) were calculated based on the imaginary frequency (ν<sup>⧧</sup>) of the TS, the Gibbs activation energy (Δ<i>G</i><sup>⧧</sup>), <i>H</i><sub>ab</sub>, and λ. The formation of the precursor complex via water substitution at Cr­(OH<sub>2</sub>)<sub>6</sub><sup>2+</sup> 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 (<i>k</i>) was estimated as the product <i>K</i><sub>A</sub><i>k</i><sub>et</sub>, whereby <i>K</i><sub>A</sub> is the equilibrium constant for the formation of the ion aggregate of the reactants Cr­(OH<sub>2</sub>)<sub>6</sub><sup>2+</sup> and CrCl­(OH<sub>2</sub>)<sub>5</sub><sup>2+</sup>, Cr­(H<sub>2</sub>O)<sub>6</sub>·CrCl­(OH<sub>2</sub>)<sub>5</sub><sup>4+</sup> (IAR). <i>k</i> calculated for the bent and linear isomers agrees with the experimental value.