Direct Evidence for a Geometrically Constrained “Entatic State” Effect on Copper(II/I) Electron-Transfer Kinetics As Manifested in Metastable Intermediates

The absolute magnitude of an “entatic” (constrained) state effect has never been quantitatively
demonstrated. In the current study, we have examined the electron-transfer kinetics for five closely related
copper(II/I) complexes formed with all possible diastereomers of [14]aneS4 (1,4,8,11-tetrathiacyclotetradecane)
in which both ethylene bridges have been replaced by cis- or trans-1,2-cyclohexane. The crystal structures of
all five Cu(II) complexes and a representative Cu(I) complex have been established by X-ray diffraction. For
each complex, the cross-reaction rate constants have been determined with six different oxidants and reductants
in aqueous solution at 25 °C, μ = 0.10 M. The value of the electron self-exchange rate constant (k11) has then
been calculated from each cross reaction rate constant using the Marcus cross relation. All five Cu(II/I) systems
show evidence of a dual-pathway square scheme mechanism for which the two individual k11 values have
been evaluated. In combination with similar values previously determined for the parent complex,
CuII/I([14]aneS4), and corresponding complexes with the two related monocyclohexanediyl derivatives, we
now have evaluated a total of 16 self-exchange rate constants which span nearly 6 orders of magnitude for
these 8 closely related Cu(II/I) systems. Application of the stability constants for the formation of the
corresponding 16 metastable intermediatesas previously determined by rapid-scan cyclic voltammetrymakes it possible to calculate the specific electron self-exchange rate constants representing the reaction of
each of the strained intermediate species exchanging electrons with their stable redox partnersthe first time
that calculations of this type have been possible. All but three of these 16 specific self-exchange rate constants
fall withinor very close tothe range of 105−106 M-1 s-1, values which are characteristic of the most labile
Cu(II/I) systems previously reported, including the blue copper proteins. The results of the current investigation
provide the first unequivocal demonstration of the efficacy of the entatic state concept as applied to Cu(II/I)
systems.