Reexamination of the Rehm–Weller Data Set Reveals Electron Transfer Quenching That Follows a Sandros–Boltzmann Dependence on Free Energy

Abstract

In a landmark publication over 40 years ago, Rehm and Weller (RW) showed that the electron transfer quenching constants for excited-state molecules in acetonitrile could be correlated with the excited-state energies and the redox potentials of the electron donors and acceptors. The correlation was interpreted in terms of electron transfer between the molecules in the encounter pair (A*/D ⇌ A(•-)/D(•+) for acceptor A and donor D) and expressed by a semiempirical formula relating the quenching constant, k(q), to the free energy of reaction, ΔG. We have reinvestigated the mechanism for many Rehm and Weller reactions in the endergonic or weakly exergonic regions. We find they are not simple electron transfer processes. Rather, they involve exciplexes as the dominant, kinetically and spectroscopically observable intermediate. Thus, the Rehm-Weller formula rests on an incorrect mechanism. We have remeasured k(q) for many of these reactions and also reevaluated the ΔG values using accurately determined redox potentials and revised excitation energies. We found significant discrepancies in both ΔG and k(q), including A*/D pairs at high endergonicity that did not exhibit any quenching. The revised data were found to obey the Sandros-Boltzmann (SB) equation k(q) = k(lim)/[1 + exp[(ΔG + s)/RT]]. This behavior is attributed to rapid interconversion among the encounter pairs and the exciplex (A*/D ⇌ exciplex ⇌ A(•-)/D(•+)). The quantity k(lim) represents approximately the diffusion-limited rate constant, and s the free energy difference between the radical ion encounter pair and the free radical ions (A(•-)/D(•+) vs A(•-) + D(•+)). The shift relative to ΔG for the overall reaction is positive, s = 0.06 eV, rather than the negative value of -0.06 eV assumed by RW. The positive value of s involves the poorer solvation of A(•-)/D(•+) relative to the free A(•-) + D(•+), which opposes the Coulombic stabilization of A(•-)/D(•+). The SB equation does not involve the microscopic rate constants for interconversion among the encounter pairs and the exciplex. Data that fit this equation contain no information about such rate constants except that they are faster than dissociation of the encounter pairs to (re-)form the corresponding free species (A* + D or A(•-) + D(•+)). All of the present conclusions agree with our recent results for quenching of excited cyanoaromatic acceptors by aromatic donors, with the two data sets showing indistinguishable dependencies of k(q) on ΔG.