Theoretical analysis of proton relays in electrochemical proton-coupled electron transfer

The coupling of long-range electron transfer to proton transport over multiple sites plays a vital role in many biological and chemical processes. Recently the concerted proton-coupled electron transfer (PCET) reaction in a molecule with a hydrogen-bond relay inserted between the proton donor and acceptor sites was studied electrochemically. The standard rate constants and kinetic isotope effects (KIEs) were measured experimentally for this double proton transfer system and a related single proton transfer system. In the present paper, these systems are studied theoretically using vibronically nonadiabatic rate constant expressions for electrochemical PCET. Application of this approach to proton relays requires the calculation of multidimensional proton vibrational wave functions and the incorporation of multiple proton donor-acceptor motions. The decrease in proton donor-acceptor distances due to thermal fluctuations and the contributions from excited electron-proton vibronic states play important roles in these systems. The calculated KIEs and the ratio of the standard rate constants for the single and double proton transfer systems are in agreement with the experimental data. The calculations indicate that the standard PCET rate constant is lower for the double proton transfer system because of the smaller overlap integral between the ground state reduced and oxidized proton vibrational wave functions, resulting in greater contributions from excited electron-proton vibronic states with higher free energy barriers. The theory predicts that this rate constant may be increased by modifying the molecule in a manner that decreases the equilibrium proton donor-acceptor distances or alters the molecular thermal motions to facilitate the concurrent decrease of these distances. These insights may guide the design of more efficient catalysts for energy conversion devices.     

Kinetic effects of hydrogen bonds on proton-coupled electron transfer from phenols

The kinetics and mechanism of proton-coupled electron transfer (PCET) from a series of phenols to a laser flash generated [Ru(bpy)(3)](3+) oxidant in aqueous solution was investigated. The reaction followed a concerted electron-proton transfer mechanism (CEP), both for the substituted phenols with an intramolecular hydrogen bond to a carboxylate group and for those where the proton was directly transferred to water. Without internal hydrogen bonds the concerted mechanism gave a characteristic pH-dependent rate for the phenol form that followed a Marcus free energy dependence, first reported for an intramolecular PCET in Sj?din, M. et al. J. Am. Chem. Soc. 2000, 122, 3932-3962 and now demonstrated also for a bimolecular oxidation of unsubstituted phenol. With internal hydrogen bonds instead, the rate was no longer pH-dependent, because the proton was transferred to the carboxylate base. The results suggest that while a concerted reaction has a relatively high reorganization energy (lambda), this may be significantly reduced by the hydrogen bonds, allowing for a lower barrier reaction path. It is further suggested that this is a general mechanism by which proton-coupled electron transfer in radical enzymes and model complexes may be promoted by hydrogen bonding. This is different from, and possibly in addition to, the generally suggested effect of hydrogen bonds on PCET in enhancing the proton vibrational wave function overlap between the reactant and donor states. In addition we demonstrate how the mechanism for phenol oxidation changes from a stepwise electron transfer-proton transfer with a stronger oxidant to a CEP with a weaker oxidant, for the same series of phenols. The hydrogen bonded CEP reaction may thus allow for a low energy barrier path that can operate efficiently at low driving forces, which is ideal for PCET reactions in biological systems.     

Proton-coupled electron transfer in solution, proteins, and electrochemistry

Recent advances in the theoretical treatment of proton-coupled electron transfer (PCET) reactions are reviewed. These reactions play an important role in a wide range of biological processes, as well as in fuel cells, solar cells, chemical sensors, and electrochemical devices. A unified theoretical framework has been developed to describe both sequential and concerted PCET, as well as hydrogen atom transfer (HAT). A quantitative diagnostic has been proposed to differentiate between HAT and PCET in terms of the degree of electronic nonadiabaticity, where HAT corresponds to electronically adiabatic proton transfer and PCET corresponds to electronically nonadiabatic proton transfer. In both cases, the overall reaction is typically vibronically nonadiabatic. A series of rate constant expressions have been derived in various limits by describing the PCET reactions in terms of nonadiabatic transitions between electron-proton vibronic states. These expressions account for the solvent response to both electron and proton transfer and the effects of the proton donor-acceptor vibrational motion. The solvent and protein environment can be represented by a dielectric continuum or described with explicit molecular dynamics. These theoretical treatments have been applied to numerous PCET reactions in solution and proteins. Expressions for heterogeneous rate constants and current densities for electrochemical PCET have also been derived and applied to model systems.     

Theoretical study of electron, proton, and proton-coupled electron transfer in iron bi-imidazoline complexes.

A comparative theoretical investigation of single electron transfer (ET), single proton transfer (PT), and proton-coupled electron transfer (PCET) reactions in iron bi-imidazoline complexes is presented. These calculations are motivated by experimental studies showing that the rates of ET and PCET are similar and are both slower than the rate of PT for these systems (Roth, J. P.; Lovel, S.; Mayer, J. M. J. Am. Chem. Soc. 2000, 122, 5486). The theoretical calculations are based on a multistate continuum theory, in which the solute is described by a multistate valence bond model, the transferring hydrogen nucleus is treated quantum mechanically, and the solvent is represented as a dielectric continuum. For electronically nonadiabatic electron transfer, the rate expressions for ET and PCET depend on the inner-sphere (solute) and outer-sphere (solvent) reorganization energies and on the electronic coupling, which is averaged over the reactant and product proton vibrational wave functions for PCET. The small overlap of the proton vibrational wave functions localized on opposite sides of the proton transfer interface decreases the coupling for PCET relative to ET. The theory accurately reproduces the experimentally measured rates and deuterium kinetic isotope effects for ET and PCET. The calculations indicate that the similarity of the rates for ET and PCET is due mainly to the compensation of the smaller outer-sphere solvent reorganization energy for PCET by the larger coupling for ET. The moderate kinetic isotope effect for PCET arises from the relatively short proton transfer distance. The PT reaction is found to be dominated by solute reorganization (with very small solvent reorganization energy) and to be electronically adiabatic, leading to a fundamentally different mechanism that accounts for the faster rate.     

Integrating proton coupled electron transfer (PCET) and excited states

In many of the chemical steps in photosynthesis and artificial photosynthesis, proton coupled electron transfer (PCET) plays an essential role. An important issue is how excited state reactivity can be integrated with PCET to carry out solar fuel reactions such as water splitting into hydrogen and oxygen or water reduction of CO₂ to methanol or hydrocarbons. The principles behind PCET and concerted electron–proton transfer (EPT) pathways are reasonably well understood. In Photosystem II antenna light absorption is followed by sensitization of chlorophyll P₆₈₀ and electron transfer quenching to give P₆₈₀⁺. The oxidized chlorophyll activates the oxygen evolving complex (OEC), a CaMn₄ cluster, through an intervening tyrosine–histidine pair, Y_Z. EPT plays a major role in a series of four activation steps that ultimately result in loss of 4e^?/4H⁺ from the OEC with oxygen evolution. The key elements in photosynthesis and artificial photosynthesis – light absorption, excited state energy and electron transfer, electron transfer activation of multiple-electron, multiple-proton catalysis – can also be assembled in dye sensitized photoelectrochemical synthesis cells (DS-PEC). In this approach, molecular or nanoscale assemblies are incorporated at separate electrodes for coupled, light driven oxidation and reduction. Separate excited state electron transfer followed by proton transfer can be combined in single semi-concerted steps (photo-EPT) by photolysis of organic charge transfer excited states with H-bonded bases or in metal-to-ligand charge transfer (MLCT) excited states in pre-associated assemblies with H-bonded electron transfer donors or acceptors. In these assemblies, photochemically induced electron and proton transfer occur in a single, semi-concerted event to give high-energy, redox active intermediates.     

Model system-bath Hamiltonian and nonadiabatic rate constants for proton-coupled electron transfer at electrode-solution interfaces

An extension of the Anderson-Newns-Schmickler model for electrochemical proton-coupled electron transfer (PCET) is presented. This model describes reactions in which electron transfer between a solute complex in solution and an electrode is coupled to proton transfer within the solute complex. The model Hamiltonian is derived in a basis of electron-proton vibronic states defined within a double adiabatic approximation for the electrons, transferring proton, and bath modes. The interaction term responsible for electronic transitions between the solute complex and the electrode depends on the proton donor-acceptor vibrational mode within the solute complex. This model Hamiltonian is used to derive the anodic and cathodic rate constants for nonadiabatic electrochemical PCET. The derivation is based on the master equations for the reduced density matrix of the electron-proton subsystem, which includes the electrons of the solute complex and the electrode, as well as the transferring proton. The rate constant expressions differ from analogous expressions for electrochemical electron transfer because of the summation over electron-proton vibronic states and the dependence of the couplings on the proton donor-acceptor vibrational motion. These differences lead to additional contributions to the total reorganization energy, an additional exponential temperature-dependent prefactor, and a temperature-dependent term in the effective activation energy that has different signs for the anodic and cathodic processes. This model can be generalized to describe both nonadiabatic and adiabatic electrochemical PCET reactions and provides the framework for the inclusion of additional effects, such as the breaking and forming of other chemical bonds.     

Switching the redox mechanism: models for proton-coupled electron transfer from tyrosine and tryptophan

The coupling of electron and proton transfer is an important controlling factor in radical proteins, such as photosystem II, ribinucleotide reductase, cytochrome oxidases, and DNA photolyase. This was investigated in model complexes in which a tyrosine or tryptophan residue was oxidized by a laser-flash generated trisbipyridine-Ru(III) moiety in an intramolecular, proton-coupled electron transfer (PCET) reaction. The PCET was found to proceed in a competition between a stepwise reaction, in which electron transfer is followed by deprotonation of the amino acid radical (ETPT), and a concerted reaction, in which both the electron and proton are transferred in a single reaction step (CEP). Moreover, we found that we could analyze the kinetic data for PCET by Marcus' theory for electron transfer. By altering the solution pH, the strength of the Ru(III) oxidant, or the identity of the amino acid, we could induce a switch between the two mechanisms and obtain quantitative data for the parameters that control which one will dominate. The characteristic pH-dependence of the CEP rate (M. Sjodin et al. J. Am. Chem. Soc. 2000, 122, 3932) reflects the pH-dependence of the driving force caused by proton release to the bulk. For the pH-independent ETPT on the other hand, the driving force of the rate-determining ET step is pH-independent and smaller. On the other hand, temperature-dependent data showed that the reorganization energy was higher for CEP, while the pre-exponential factors showed no significant difference between the mechanisms. Thus, the opposing effect of the differences in driving force and reorganization energy determines which of the mechanisms will dominate. Our results show that a concerted mechanism is in general quite likely and provides a low-barrier reaction pathway for weakly exoergonic reactions. In addition, the kinetic isotope effect was much higher for CEP (kH/kD > 10) than for ETPT (kH/kD = 2), consistent with significant changes along the proton reaction coordinate in the rate-determining step of CEP.     

Energetics of direct and water-mediated proton-coupled electron transfer

Proton-coupled electron transfer (PCET) is an elementary chemical reaction crucial for biological oxidoreduction. We perform quantum chemical calculations to study the direct and water-mediated PCET between two stacked tyrosines, TyrO(?) + TyrOH → TyrOH + TyrO(?), to mimic a key step in the catalytic reaction of class Ia ribonucleotide reductase (RNR). The energy surfaces of electronic ground and excited states are separated by a large gap of ~20 kcal mol(-1), indicative of an electronically adiabatic transfer mechanism. In response to chemical substitutions of the proton donor, the energy of the transition state for direct PCET shifts by exactly half of the change in energetic driving force, resulting in a linear free energy relation with a Br?nsted slope of ?. In contrast, for water-mediated PCET, we observe integer Br?nsted slopes of 1 and 0 for proton acceptor and donor modifications, respectively. Our calculations suggest that the π-stacking of the tyrosine dimer in RNR results in strong electronic coupling and adiabatic PCET. Water participation in the PCET can be identified perturbatively in a Br?nsted analysis.     

Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.     

Nonadiabatic proton-coupled electron transfer reactions: impact of donor-acceptor vibrations, reorganization energies, and couplings on dynamics and rates

Fundamental aspects of proton-coupled electron transfer (PCET) reactions in solution are analyzed with molecular dynamics simulations for a series of model systems. The analysis addresses the impact of the solvent reorganization energy, the proton donor-acceptor mode vibrational frequency, and the distance dependence of the nonadiabatic coupling on the dynamics of the reaction and the magnitude of the rate. The rate for nonadiabatic PCET is expressed in terms of a time-dependent probability flux correlation function. The time dependence of the probability flux correlation function is determined mainly by the solvent reorganization energy and is not significantly influenced by the proton donor-acceptor frequency or the distance dependence of the nonadiabatic coupling. The magnitude of the PCET rate becomes greater as the solvent reorganization energy decreases, the proton donor-acceptor frequency decreases, and the distance dependence of the nonadiabatic coupling increases. The approximations underlying a previously derived analytical PCET rate expression are also investigated. The short-time approximation for the solvent is valid for these types of systems. In addition, solvent damping effects on the proton donor-acceptor motion are not significant on the time scale of the probability flux. The rates calculated from the molecular dynamics simulations agree well with those calculated from the analytical rate expression.     

Bidirectional and unidirectional PCET in a molecular model of a cobalt-based oxygen-evolving catalyst

The oxidation of water to molecular oxygen is a kinetically demanding reaction that requires efficient coupling of proton and electron transfer. The key proton-coupled electron transfer (PCET) event in water oxidation mediated by a cobalt-phosphate-based heterogeneous catalyst is the one-electron, one-proton conversion of Co(III)-OH to Co(IV)-O. We now isolate the kinetics of this PCET step in a molecular Co(4)O(4) cubane model compound. Detailed electrochemical, stopped-flow, and NMR studies of the Co(III)-OH to Co(IV)-O reaction reveal distinct mechanisms for the unidirectional PCET self-exchange reaction and the corresponding bidirectional PCET. A stepwise mechanism, with rate-limiting electron transfer is observed for the bidirectional PCET at an electrode surface and in solution, whereas a concerted proton-electron transfer displaying a moderate KIE (4.3 ± 0.2), is observed for the unidirectional self-exchange reaction.     

Evidence for concerted electron proton transfer in charge recombination between FADH- and 306Trp• in Escherichia coli photolyase

Proton-coupled electron-transfer (PCET) is a mechanism of great importance in protein electron transfer and enzyme catalysis, and the involvement of aromatic amino acids in this process is of much interest. The DNA repair enzyme photolyase provides a natural system that allows for the study of PCET using a neutral radical tryptophan (Trp(?)). In Escherichia coli photolyase, photoreduction of the flavin adenine dinucleotide (FAD) cofactor in its neutral radical semiquinone form (FADH(?)) results in the formation of FADH(-) and (306)Trp(?). Charge recombination between these two intermediates requires the uptake of a proton by (306)Trp(?). The rate constant of charge recombination has been measured as a function of temperature in the pH range from 5.5 to 10.0, and the data are analyzed with both classical Marcus and semi-classical Hopfield electron transfer theory. The reorganization energy associated with the charge recombination process shows a pH dependence ranging from 2.3 eV at pH ≤ 7 and 1.2 eV at pH(D) 10.0. These findings indicate that at least two mechanisms are involved in the charge recombination reaction. Global analysis of the data supports the hypothesis that PCET during charge recombination can follow two different mechanisms with an apparent switch around pH 6.5. At lower pH, concerted electron proton transfer (CEPT) is the favorable mechanism with a reorganization energy of 2.1-2.3 eV. At higher pH, a sequential mechanism becomes dominant with rate-limiting electron-transfer followed by proton uptake which has a reorganization energy of 1.0-1.3 eV. The observed 'inverse' deuterium isotope effect at pH < 8 can be explained by a solvent isotope effect that affects the free energy change of the reaction and masks the normal, mass-related kinetic isotope effect that is expected for a CEPT mechanism. To the best of our knowledge, this is the first time that a switch in PCET mechanism has been observed in a protein.     

Distance Dependence of Bidirectional Concerted Proton–Electron Transfer in Phenol‐Ru(2,2′‐bipyridine)32+ Dyads

Proton‐coupled electron transfer (PCET) was investigated in three covalent donor–bridge–acceptor molecules with different bridge lengths. Upon photoexcitation of their Ru(bpy)₃²⁺ (bpy=2,2′‐bipyridine) photosensitizer in acetonitrile, intramolecular long‐range electron transfer from a phenolic unit to Ru(bpy)₃²⁺ occurs in concert with release of the phenolic proton to pyrrolidine base. The kinetics of this bidirectional concerted proton–electron transfer (CPET) reaction were studied as a function of phenol–Ru(bpy)₃²⁺ distance by increasing the number of bridging p‐xylene units. A distance decay constant (β) of 0.67±0.23 Å^?1 was determined. The distance dependence of the rates for CPET is thus not significantly steeper than that for ordinary (i.e., not proton coupled) electron transfer across the same bridges, despite the concerted motion of oppositely charged particles into different directions. Long‐range bidirectional CPET is an important reaction in many proteins and plays a key role in photosynthesis; our results are relevant in the context of photoinduced separation of protons and electrons as a means of light‐to‐chemical energy conversion. This is the first determination of β for a bidirectional CPET reaction.     

Step-wise proton-coupled electron transfer extended to aminobenzoquinone modified monolayers

The step-wise proton coupled electron transfer (SW-PCET) model has been expanded to describe instances where three protons are transferred with either one or two electrons. Expressions have been derived describing the pH dependence of the apparent formal potential, apparent standard rate constant, apparent transfer coefficient, and reaction pathway. The expressions can be applied to both Marcus density of states theory as well as Butler-Volmer kinetics depending on the assumptions made about the individual transfer coefficients. An example of 2e3H has been provided for an aminobenzoquinone monolayer system and experimental measurements have been compared to model predictions. Although the large reorganization energy of the benzoquinone system prevents differentiation between Butler-Volmer and Marcus DOS kinetic behaviour, results are consistent with the SW-PCET model. These results indicate how acid/base substituents on tethered organic molecules can participate in PCET even though they themselves are redox inactive.     

Proton-coupled electron transfer from tyrosine: a strong rate dependence on intramolecular proton transfer distance

Proton-coupled electron transfer (PCET) was examined in a series of biomimetic, covalently linked Ru(II)(bpy)(3)-tyrosine complexes where the phenolic proton was H-bonded to an internal base (a benzimidazyl or pyridyl group). Photooxidation in laser flash/quench experiments generated the Ru(III) species, which triggered long-range electron transfer from the tyrosine group concerted with short-range proton transfer to the base. The results give an experimental demonstration of the strong dependence of the rate constant and kinetic isotope effect for this intramolecular PCET reaction on the effective proton transfer distance, as reflected by the experimentally determined proton donor-acceptor distance.     

Tuning Excited‐State Reactivity by Proton‐Coupled Electron Transfer

The reactivity, and even reaction pathway, of excited states can be tuned by proton‐coupled electron transfer (PCET). The triplet state of benzophenone functionalized with a Brønsted acid (³*BP‐COOH) showed a more powerful oxidation capability over the simple triplet state of benzophenone (³*BP). ³*BP‐COOH could remove an electron from benzene at the rate of 8.0×10⁵ m ^?1 s^?1, in contrast to the reactivity of ³*BP which was inactive towards benzene oxidation. The origin of this great enhancement on the ability of the excited states to remove electrons from substrates is attributed to the intramolecular Brønsted acid, which enables the reductive quenching of ³*BP by concerted electron–proton transfer.     

The wave nature of the protonic conductivity mechanism in the active site of carboanhydrase

Quantum-chemical calculations were performed for the (NH₃)₃Zn²⁺...(H₂O)_n...NH₃ (n = 3–11) molecular complex to model the proton transfer system of the carboanhydrase enzyme. H-bond proton transfer along the chain connecting the donor and acceptor groups was shown to be concerted vibrational motion of all protons in the chain. A wave of H-bond deformations was related to the moving proton. The displacement of H-bond protons in the transition state of the proton transfer reaction with respect to their equilibrium positions corresponded to a structure that could be defined as a proton wave. The length of this wave found as the distance between H-bond contraction (O-H bond elongation) maxima was ～8 Å. Charge transfer from the donor to the acceptor occurred according to the mechanism of the concerted jump of H-bond protons as the wave reached the chain end. The barrier to transfer was independent of the number of chain links and equaled 10 kcal/mol.     

Photoreaction in BLUF receptors: proton-coupled electron transfer in the flavin-Gln-Tyr system

Photoinduced electron transfer from tyrosine to the flavin chromophore is involved in activation of BLUF (sensor of blue light using FAD) photoreceptors. We studied the electron transfer (ET) coupled with proton-transfer (PT) reactions, by means of XMCQDPT2//CASSCF calculations on a molecular cluster model. By defining a minimum active space in the CASSCF calculations, we could compute the entire photoreaction pathway. We find that the crossing of the locally excited and ET states is located along the flavin bond-stretching coordinate. The ET state is stabilized by a proton transfer from the electron donor to the electron acceptor. We mapped two different PT pathways from tyrosine to flavin via the conserved glutamine. These reactions generate a tautomeric form of glutamine. Along the PT coordinates, we find geometries where the ET and the electronic ground states degenerate. At the state crossing structures, either formation of the ground state biradical intermediate or a relaxation back to the Franck-Condon minimum takes places. The computed relaxation pathways reveal that the hydrogen bonds involving glutamine in the chromophore-binding pocket control BLUF photoefficiency.     

Buffer-assisted proton-coupled electron transfer in a model rhenium-tyrosine complex

The mechanism for tyrosyl radical generation in the [Re(P-Y)(phen)(CO)3]PF6 complex is investigated with a multistate continuum theory for proton-coupled electron transfer (PCET) reactions. Both water and the phosphate buffer are considered as potential proton acceptors. The calculations indicate that the model in which the proton acceptor is the phosphate buffer species HPO(4)2- can successfully reproduce the experimentally observed pH dependence of the overall rate and H/D kinetic isotope effect, whereas the model in which the proton acceptor is water is not physically reasonable for this system. The phosphate buffer species HPO4(2-) is favored over water as the proton acceptor in part because the proton donor-acceptor distance is approximately 0.2 A smaller for the phosphate acceptor due to its negative charge. The physical quantities impacting the overall rate constant, including the reorganization energies, reaction free energies, activation free energies, and vibronic couplings for the various pairs of reactant/product vibronic states, are analyzed for both hydrogen and deuterium transfer. The dominant contribution to the rate arises from nonadiabatic transitions between the ground reactant vibronic state and the third product vibronic state for hydrogen transfer and the fourth product vibronic state for deuterium transfer. These contributions dominate over contributions from lower product states because of the larger vibronic coupling, which arises from the greater overlap between the reactant and product vibrational wave functions. These calculations provide insight into the fundamental mechanism of tyrosyl radical generation, which plays an important role in a wide range of biologically important processes.