Bimolecular Electron Transfers That Follow a Sandros−Boltzmann Dependence on Free Energy

Abstract

Rate constants (k) for exergonic and endergonic electron-transfer reactions of equilibrating radical cations (A(•+) + B ⇌ A + B(•+)) in acetonitrile could be fit well by a simple Sandros-Boltzmann (SB) function of the reaction free energy (ΔG) having a plateau with a limiting rate constant k(lim) in the exergonic region, followed, near the thermoneutral point, by a steep drop in log k vs ΔG with a slope of 1/RT. Similar behavior was observed for another charge shift reaction, the electron-transfer quenching of excited pyrylium cations (P(+)*) by neutral donors (P(+)* + D → P(•) + D(•+)). In this case, SB dependence was observed when the logarithm of the quenching constant (log k(q)) was plotted vs ΔG + s, where the shift term, s, equals +0.08 eV and ΔG is the free energy change for the net reaction (E(redox) - E(excit)). The shift term is attributed to partial desolvation of the radical cation in the product encounter pair (P(•)/D(•+)), which raises its free energy relative to the free species. Remarkably, electron-transfer quenching of neutral reactants (A* + D → A(•-) + D(•+)) using excited cyanoaromatic acceptors and aromatic hydrocarbon donors was also found to follow an SB dependence of log k(q) on ΔG, with a positive s, +0.06 eV. This positive shift contrasts with the long-accepted prediction of a negative value, -0.06 eV, for the free energy of an A(•-)/D(•+) encounter pair relative to the free radical ions. That prediction incorporated only a Coulombic stabilization of the A(•-)/D(•+) encounter pair relative to the free radical ions. In contrast, the results presented here show that the positive value of s indicates a decrease in solvent stabilization of the A(•-)/D(•+) encounter pair, which outweighs Coulombic stabilization in acetonitrile. These quenching reactions are proposed to proceed via rapidly interconverting encounter pairs with an exciplex as intermediate, A*/D ⇌ exciplex ⇌ A(•-)/D(•+). Weak exciplex fluorescence was observed in each case. For several reactions in the endergonic region, rate constants for the reversible formation and decay of the exciplexes were determined using time-correlated single-photon counting. The quenching constants derived from the transient kinetics agreed well with those from the conventional Stern-Volmer plots. For excited-state electron-transfer processes, caution is required in correlating quenching constants vs reaction free energies when ΔG exceeds ∼+0.1 eV. Beyond this point, additional exciplex deactivation pathways-fluorescence, intersystem crossing, and nonradiative decay-are likely to dominate, resulting in a change in mechanism.