PCET proton-coupled electron acceptor

As demonstrated in this chapter, there have always been the fundamental mechanistic questions in oxidation of C-H bonds whether the rate-determining step is ET, PCET, one-step HAT, or one-step hydride transfer. When the ET step is thermodynamically feasible, ET occurs first, followed by proton transfer for the overall HAT reactions, and the HAT step is followed by subsequent rapid ET for the overall hydride transfer reactions. In such a case, ET products, that is, radical cations of electron donors and radical anions of electron acceptors, can be detected as the intermediates in the overall HAT and hydride transfer reactions. The ET process can be coupled by proton transfer and also by hydrogen bonding or by binding of metal ions to the radical anions produced by ET to control the ET process. The borderline between a sequential PCET pathway and a one-step HAT pathway has been related to the borderline between the outer-sphere and inner-sphere ET pathways. In HAT reactions, the proton is provided by radical cations of electron donors because the acidity is significantly enhanced by the one-electron oxidation of electron donors. An electron and a proton are transferred by a one-step pathway or a sequential pathway depending on the types of electron donors and acceptors. When proton is provided externally, ET from an electron donor that has no proton to be transferred to an electron acceptor (A) is coupled with protonation of A -, when the one-electron reduction and protonation of A occur simultaneously. The mechanistic discussion described in this chapter will provide useful guide to control oxidation of C-H bonds. 

The distance between the electron donor and acceptor affects the rates and mechanisms of PCET reactions in two different ways. First, an increase in this distance results in a decrease in the coupling between ET states (la/2a, aj2b, bj2a, bj2b). In the limit of electronically non-adiabatic electron transfer, a decrease in this coupling results in a decrease in the rate. Moreover, as the distance between the electron donor and acceptor increases, the interaction between the proton and the electron decreases. Thus, for a symmetric PT system with an initial state of la, EPT is favorable for short electron donor-acceptor distances and ET becomes equally favorable as this distance increases. 

In the simplest case, the R mode is characterized by a low frequency and is not dynamically coupled to the fluctuations of the solvent. The system is assumed to maintain an equilibrium distribution along the R coordinate. In this case, ve can exclude the R mode from the dynamical description and consider an equilibrium ensemble of PCET systems with fixed proton donor-acceptor distances. The electrons and transferring proton are assumed to be adiabatic with respect to the R coordinate and solvent coordinates within the reactant and product states. Thus, the reaction is described in terms of nonadiabatic transitions between two sets of intersecting free energy surfaces ( R, and ej, Zp, corresponding to... 

PCET can occur when the electron and proton are site-differentiated on both the donor and acceptor sides of the reaction. The PT coordinate must still be constrained to a hydrogen bond length scale, however, it is feasible for the ET coordinate to span an extended distance [79-81]. Nevertheless, coupling between the electron and proton may be strong since the redox potentials depend on the protonation state and the pfQ,s depend on the redox state. Consequently, the square scheme of Eig. 17.1 must be used to evaluate the attendant thermodynamics. 

Theoretical treatments of PCET reactions typically have equation (1.2) as a conceptual starting point. In Hammes-Schiffer s multistate continuum theory for PCET, the pre-exponential factor includes both electronic coupling and vibrational overlaps, and the rate is a sum over initial and final vibrational states integrated over a range of proton-donor acceptor distances. This theory has been elegantly applied to understand the intimate details of a variety of PCET reactions, but many of its parameters are essentially unattainable experimentally. 

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