As we reported recently, endergonic to mildly exergonic electron transfer between neutral aromatics (benzenes and biphenyls) and their radical cations in acetonitrile follows a Sandros–Boltzmann (SB) dependency on the reaction free energy (ΔG); i.e., the rate constant is proportional to 1/[1 + exp(ΔG/RT)]. We now report deviations from this dependency when one reactant is sterically crowded: 1,4-di-tert-butylbenzene (C1), 1,3,5-tri-tert-butylbenzene (C2), or hexaethylbenzene (C3). Obvious deviation from SB behavior is observed with C1. Stronger deviation is observed with the more crowded C2 and C3, where steric hindrance increases the interplanar separation at contact by ∼1 Å, significantly decreasing the π orbital overlap. Consequently, electron transfer (ket) within the contact pair becomes slower than diffusional separation (k–d), causing deviation from the SB dependency, especially near ΔG = 0. Fitting the data to a standard electron-transfer theory gives small matrix elements (∼5–7 meV) and reasonable reorganization energies. A small systematic difference between reactions of C3 with benzenes vs biphenyls is rationalized in terms of small differences in the electron-transfer parameters that are consistent with previous data. The influence of solvent viscosity on the competition between ket and k–d was investigated by comparing reactions in acetonitrile and propylene carbonate.

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 klim 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 kq) 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 (Eredox − Eexcit). 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 kq 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.

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, kq, 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 kq 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 kq, 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 kq = klim/[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 klim 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 kq on ΔG.