Theory of proton-coupled electron transfer in energy conversion processes

Abstract

Proton-coupled electron transfer (PCET) reactions play an essential role in a broad range of energy conversion processes, including photosynthesis and respiration. These reactions also form the basis of many types of solar fuel cells and electrochemical devices. Recent advances in the theory of PCET enable the prediction of the impact of system properties on the reaction rates. These predictions may guide the design of more efficient catalysts for energy production, including those based on artificial photosynthesis and solar energy conversion. This Account summarizes the theoretically predicted dependence of PCET rates on system properties and illustrates potential approaches for tuning the reaction rates in chemical systems. A general theoretical formulation for PCET reactions has been developed over the past decade. In this theory, PCET reactions are described in terms of nonadiabatic transitions between the reactant and product electron-proton vibronic states. A series of nonadiabatic rate constant expressions for both homogeneous and electrochemical PCET reactions have been derived in various well-defined limits. Recently this theory has been extended to include the effects of solvent dynamics and to describe ultrafast interfacial PCET. Analysis of the rate constant expressions provides insight into the underlying physical principles of PCET and enables the prediction of the dependence of the rates on the physical properties of the system. Moreover, the kinetic isotope effect, which is the ratio of the rates for hydrogen and deuterium, provides a useful mechanistic probe. Typically the PCET rate will increase as the electronic coupling and temperature increase and as the total reorganization energy and equilibrium proton donor-acceptor distance decrease. The rate constant is predicted to increase as the driving force becomes more negative, rather than exhibit turnover behavior in the inverted region, because excited vibronic product states associated with low free energy barriers and relatively large vibronic couplings become accessible. The physical basis for the experimentally observed pH dependence of PCET reactions has been debated in the literature. When the proton acceptor is a buffer species, the pH dependence may arise from the protonation equilibrium of the buffer. It could also arise from kinetic complexity of competing concerted and sequential PCET reaction pathways. In electrochemical PCET, the heterogeneous rate constants and current densities depend strongly on the overpotential. The change in equilibrium proton donor-acceptor distance upon electron transfer may lead to asymmetries in the Tafel plots and deviations of the transfer coefficient from the standard value of one-half at zero overpotential. Applications of this theory to experimentally studied systems illustrate approaches that can be utilized to tune the PCET rate. For example, the rate can be tuned by changing the pH or using different buffer species as proton acceptors. The rate can also be tuned with site-specific mutagenesis in biological systems or chemical modifications that vary the substituents on the redox species in chemical systems. Understanding the impact of these changes on the PCET rate may assist experimental efforts to enhance energy conversion processes.

Figure 1

Slices of the free energy surfaces for the ground reactant (I) and product (II) vibronic states along a collective solvent coordinate. The proton potential energy curves and ground state proton vibrational wavefunctions with energies corresponding to open circles on the free energy curves are depicted. Figure reproduced with permission from Ref. .

Figure 2

Driving force dependence of (a) the rate constant in the low-frequency R-mode regime, (b) the associated KIE, and (c) the contributions of pairs of reactant/product vibronic states for a model system. In (a) and (b), the dashed red curve corresponds to the calculation including only the ground reactant and product vibronic states, and the solid black curve corresponds to the calculation converged with respect to excited vibronic states. In (c), the color code for pairs of reactant/product vibronic states is as follows: 0/0 (black), 1/0 (blue), 2/0 (magenta), 0/1 (red), and 0/2 (green). Figure reproduced with permission from Ref. .

Figure 3

Logarithm of the scaled current density as a function of overpotential for a model electrochemical PCET system. The solid red and dashed blue curves correspond to δR = 0.05 Å and δR = 0, respectively. Figure reproduced with permission from Ref. .

Figure 4

PCET reaction induced by photoexcitation of the rhenium-tyrosine complex to a metal-to-ligand charge transfer state. The proton transfers to a hydrogen-bonded phosphate HPO₄²⁻ buffer. Figure reproduced with permission from Ref. .

Figure 5

The hydrogen abstraction step of the reaction catalyzed by soybean lipoxygenase with linoleic acid substrate. Figure reproduced with permission from Ref. .

Figure 6

PCET reaction corresponding to oxidation of UQH₂ following photoexcitation of the ruthenium-bipyridyl complex to a metal-to-ligand charge transfer state. Figure reproduced with permission from Ref. .

Figure 7

Free energy curves as functions of a collective solvent coordinate for the UQH₂ system. The lowest energy reactant vibronic state (µ=0) and lowest two product vibronic states (ν=0, 1) are shown for H (left) and D (right). All states are shifted so the lowest energy reactant vibronic state has zero energy for both H and D. The free energy barrier for the (0/1) pair of reactant/product vibronic states is smaller for D than for H because of the smaller vibronic energy level splittings for D. Figure reproduced with permission from Ref. .

Figure 8

Electrochemical PCET reaction for a system comprised of an osmium-bipyridyl-aquo complex attached to a mixed self-assembled monolayer on a gold electrode. The proton acceptor has been proposed to be a carboxylate group of the monolayer.