Electrochemical proton-coupled electron transfer: Beyond the golden rule

Quantum Kinetic Rates within the Nonequilibrium Steady State

The nonequilibrium steady state (NESS) of a quantum network is central to a host of physical and biological scenarios. Examples include natural processes such as vision and photosynthesis as well as technical devices such as photocells, both activated by incoherent light (e.g., sunlight) and leading to quantum transport. Assessing time scales of the relevant chemical processes in the steady state is thus of utmost interest and is our goal in this paper. Here, a completely general approach to defining components of a quantum network in the NESS and obtaining rates of processes between these components is provided. Quantum effects are explicitly included throughout, both in (a) defining network components via projection operators and (b) determining the role of coherences in rate processes. As examples, the methodology is applied to model cases, two versions of the V-level system, and to the spin-boson model, wherein the roles of the environment and of internal system properties in determining the rates are examined. In addition, the role of Markovian vs non-Markovian contributions is quantified, exposing conditions under which NESS rates can be obtained by perturbing the nonequilibrium steady state.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

A non-perturbative approach to simulate heterogeneous electron transfer dynamics: Effective mode treatment of the continuum electronic states

We propose a non-perturbative method to simulate heterogeneous electron transfer dynamics in systems described by a Newns-Anderson type of model. The coupling between the molecule and the continuum electronic states at the metal or semiconductor surface is represented using a set of effective modes, by employing an exponential expansion of the bath correlation functions. Depending on the nature of the problems, the nuclear degrees of freedom are either treated explicitly using wave functions and density operators or as dissipative modes using the techniques from the hierarchical equations of the motion method. Numerical examples are also presented for applications in problems including (1) photo-induced charge transfer at the molecule-semiconductor interfaces, (2) heterogeneous electron transfer at the molecule-metal interface, and (3) vibrational relaxation on a metal surface.

Donor-Dependent Kinetics of Interfacial Proton-Coupled Electron Transfer

The effect of the proton donor on the kinetics of interfacial concerted proton-electron transfer (CPET) to polycrystalline Au was probed indirectly by studying the rate of hydrogen evolution from trialkylammonium donors with different steric profiles, but the same pKa. Detailed kinetic studies point to a mechanism for HER catalysis that involves rate-limiting CPET from the proton donor to the electrode surface, allowing this catalytic reaction to serve as a proxy for the rate of interfacial CPET. In acetonitrile electrolyte, triethylammonium (TEAH(+)) displays up to 20-fold faster CPET kinetics than diisopropylethylammonium (DIPEAH(+)) at all measured potentials. In aqueous electrolyte, this steric constraint is largely lifted, suggesting a key role for water in mediating interfacial CPET. In acetonitrile, TEAH(+) also displays a much larger transfer coefficient (β = 0.7) than DIPEAH(+) (β = 0.4), and TEAH(+) displays a potential-dependent H/D kinetic isotope effect that is not observed for DIPEAH(+). These results demonstrate that proton donor structure strongly impacts the free energy landscape for CPET to extended solid surfaces and highlight the crucial role of the proton donor in the kinetics of electrocatalytic energy conversion reactions.

Proton-Coupled Electron Transfer and a Tyrosine-Histidine Pair in a Photosystem II-Inspired β-Hairpin Maquette: Kinetics on the Picosecond Time Scale

Photosystem II (PSII) and ribonucleotide reductase employ oxidation and reduction of the tyrosine aromatic ring in radical transport pathways. Tyrosine-based reactions involve either proton-coupled electron transfer (PCET) or electron transfer (ET) alone, depending on the pH and the pKa of tyrosine's phenolic oxygen. In PSII, a subset of the PCET reactions are mediated by a tyrosine-histidine redox-driven proton relay, YD-His189. Peptide A is a PSII-inspired β-hairpin, which contains a single tyrosine (Y5) and histidine (H14). Previous electrochemical characterization indicated that Peptide A conducts a net PCET reaction between Y5 and H14, which have a cross-strand π-π interaction. The kinetic impact of H14 has not yet been explored. Here, we address this question through time-resolved absorption spectroscopy and 280-nm photolysis, which generates a neutral tyrosyl radical. The formation and decay of the neutral tyrosyl radical at 410 nm were monitored in Peptide A and its variant, Peptide C, in which H14 is replaced by cyclohexylalanine (Cha14). Significantly, both electron transfer (ET, pL 11, L = lyonium) and PCET (pL 9) were accelerated in Peptide A and C, compared to model tyrosinate or tyrosine at the same pL. Increased electronic coupling, mediated by the peptide backbone, can account for this rate acceleration. Deuterium exchange gave no significant solvent isotope effect in the peptides. At pL 9, but not at pL 11, the reaction rate decreased when H14 was mutated to Cha14. This decrease in rate is attributed to an increase in reorganization energy in the Cha14 mutant. The Y5-H14 mechanism in Peptide A is reminiscent of proton- and electron-transfer events involving YD-H189 in PSII. These results document a mechanism by which proton donors and acceptors can regulate the rate of PCET reactions.

Exploring Autoionization and Photoinduced Proton-Coupled Electron Transfer Pathways of Phenol in Aqueous Solution

The excited state dynamics of phenol in water have been investigated using transient absorption spectroscopy. Solvated electrons and vibrationally cold phenoxyl radicals are observed upon 200 and 267 nm excitation, but with formation time scales that differ by more than 4 orders of magnitude. The impact of these findings is assessed in terms of the relative importance of autoionization versus proton-coupled electron transfer mechanisms in this computationally tractable model system.

Proton-coupled electron transfer in molecular electrocatalysis: theoretical methods and design principles

Molecular electrocatalysts play an essential role in a wide range of energy conversion processes. The objective of electrocatalyst design is to maximize the turnover frequency and minimize the overpotential for the overall catalytic cycle. Typically, the catalytic cycle is dominated by key proton-coupled electron transfer (PCET) processes comprised of sequential or concerted electron and proton transfer steps. Theoretical methods have been developed to investigate the mechanisms, thermodynamics, and kinetics of PCET processes in electrocatalytic cycles. Electronic structure methods can be used to calculate the reduction potentials and pKa's and to generate thermodynamic schemes, free energy reaction pathways, and Pourbaix diagrams, which indicate the most stable species under certain conditions. These types of calculations have assisted in identifying the thermodynamically favorable mechanisms under specified experimental conditions, such as acid strength and overpotential. Such calculations have also revealed linear correlations among the thermodynamic properties, which can be used to predict the impact of modifying the ligands, substituents, or metal centers. The thermodynamic properties can be tuned with electron-withdrawing or electron-donating substituents. Ligand modification can exploit the role of noninnocent ligands. For example, ligand protonation typically decreases the overpotential. Calculations of rate constants for electron and proton transfer, as well as concerted PCET, have assisted in identifying the kinetically favorable mechanisms under specified conditions. The concerted PCET mechanism is thought to lower the overpotential required for catalysis by avoiding high-energy intermediates. Rate constant calculations have revealed that the concerted mechanism involving intramolecular proton transfer will be favored by designing more flexible ligands that facilitate the proton donor-acceptor motion while also maintaining a sufficiently short equilibrium proton donor-acceptor distance. Overall, theoretical methods have assisted in the interpretation of experimental data and the design of more effective molecular electrocatalysts.

Concerted proton-electron transfers: fundamentals and recent developments

Proton-coupled electron transfers (PCET) are ubiquitous in natural and synthetic processes. This review focuses on reactions where the two events are concerted. Semiclassical models of such reactions allow their kinetic characterization through activation versus driving force relationships, estimates of reorganization energies, effects of the nature of the proton acceptor, and H/D kinetic isotope effect as well as their discrimination from stepwise pathways. Several homogeneous reactions (through stopped-flow and laser flash-quench techniques) and electrochemical processes are discussed in this framework. Once the way has been rid of the improper notion of pH-dependent driving force, water appears as a remarkable proton acceptor in terms of reorganization energy and pre-exponential factor, thanks to its H-bonded and H-bonding properties, similarly to purposely synthesized "H-bond train" molecules. The most recent developments are in modeling and description of emblematic concerted proton-electron transfer (CPET) reactions associated with the breaking of a heavy-atom bond in an all-concerted process.

Ultrafast photochemistry in liquids

Ultrafast photochemical processes can occur in parallel with the relaxation of the optically populated excited state toward equilibrium. The latter involves both intra- and intermolecular modes, namely vibrational and solvent coordinates, and takes place on timescales ranging from a few tens of femtoseconds to up to hundreds of picoseconds, depending on the system. As a consequence, the reaction dynamics can substantially differ from those usually measured with slower photoinduced processes occurring from equilibrated excited states. For example, the decay of the excited-state population may become strongly nonexponential and depend on the excitation wavelength, contrary to the Kasha and Vavilov rules. In this article, we first give a brief account of our current understanding of vibrational and solvent relaxation processes. We then present an overview of important classes of ultrafast photochemical reactions, namely electron and proton transfer as well as isomerization, and illustrate with several examples how nonequilibrium effects can affect their dynamics.

Theory of proton-coupled electron transfer in energy conversion processes

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.