Kinetic model for reversible radical transfer in ribonucleotide reductase.

The enzyme ribonucleotide reductase (RNR), which catalyzes the reduction of ribonucleotides to deoxynucleotides, is vital for DNA synthesis, replication, and repair in all living organisms. Its mechanism requires long-range radical translocation over ∼32 Šthrough two protein subunits and the intervening aqueous interface. Herein, a kinetic model is designed to describe reversible radical transfer in Escherichia coli RNR. This model is based on experimentally studied photoRNR systems that allow the photochemical injection of a radical at a specific tyrosine residue, Y356, using a photosensitizer. The radical then transfers across the interface to another tyrosine residue, Y731, and continues until it reaches a cysteine residue, C439, which is primed for catalysis. This kinetic model includes radical injection, an off-pathway sink, radical transfer between pairs of residues along the pathway, and the conformational flipping motion of Y731 at the interface. Most of the input rate constants for this kinetic model are obtained from previous experimental measurements and quantum mechanical/molecular mechanical free-energy simulations. Ranges for the rate constants corresponding to radical transfer across the interface are determined by fitting to the experimentally measured Y356 radical decay times in photoRNR systems. This kinetic model illuminates the time evolution of radical transport along the tyrosine and cysteine residues following radical injection. Further analysis identifies the individual rate constants that may be tuned to alter the timescale and probability of the injected radical reaching C439. The insights gained from this kinetic model are relevant to biochemical understanding and protein-engineering efforts with potential pharmacological implications.

Proton-Coupled Electron Transfer upon Oxidation of Tyrosine in a De Novo Protein: Analysis of Proton Acceptor Candidates.

Redox-active residues, such as tyrosine and tryptophan, play important roles in a wide range of biological processes. The α3Y de novo protein, which is composed of three α helices and a tyrosine residue Y32, provides a platform for investigating the redox properties of tyrosine in a well-defined protein environment. Herein, the proton-coupled electron transfer (PCET) reaction that occurs upon oxidation of tyrosine in this model protein by a ruthenium photosensitizer is studied by using a vibronically nonadiabatic PCET theory that includes hydrogen tunneling and excited vibronic states. The input quantities to the analytical nonadiabatic rate constant expression, such as the diabatic proton potential energy curves and associated proton vibrational wave functions, reorganization energy, and proton donor-acceptor distribution functions, are obtained from density functional theory calculations on model systems and molecular dynamics simulations of the solvated α3Y protein. Two possible proton acceptors, namely, water or a glutamate residue in the protein scaffold, are explored. The PCET rate constant is greater when glutamate is the proton acceptor, mainly due to the more favorable driving force and shorter equilibrium proton donor-acceptor distance, although contributions from excited vibronic states mitigate these effects. Nevertheless, water could be the dominant proton acceptor if its equilibrium constant associated with hydrogen bond formation is significantly greater than that for glutamate. Although these calculations do not definitively identify the proton acceptor for this PCET reaction, they elucidate the conditions under which each proton acceptor can be favored. These insights have implications for tyrosine-based PCET in a wide variety of biochemical processes.

Direct Evidence for a Sequential Electron Transfer-Proton Transfer Mechanism in the PCET Reduction of a Metal Hydroxide Catalyst.

The proton-coupled electron transfer (PCET) mechanism for the reaction Mox-OH + e- + H+ → Mred-OH2 was determined through the kinetic resolution of the independent electron transfer (ET) and proton transfer (PT) steps. The reaction of interest was triggered by visible light excitation of [RuII(tpy)(bpy')H2O]2+, RuII-OH2, where tpy is 2,2':6',2″-terpyridine and bpy' is 4,4'-diaminopropylsilatrane-2,2'-bipyridine, anchored to In2O3:Sn (ITO) thin films in aqueous solutions. Interfacial kinetics for the PCET reduction reaction were quantified by nanosecond transient absorption spectroscopy as a function of solution pH and applied potential. Data acquired at pH = 5-10 revealed a stepwise electron transfer-proton transfer (ET-PT) mechanism, while kinetic measurements made below pKa(RuIII-OH/OH2) = 1.3 were used to study the analogous interfacial reaction, where electron transfer was the only mechanistic step. Analysis of this data with a recently reported multichannel kinetic model was used to construct a PCET zone diagram and supported the assignment of an ET-PT mechanism at pH = 5-10. Ultimately, this study represents a unique example among Mox-OH/Mred-OH2 reactivity where the protonation and oxidation states of the intermediate were kinetically and spectrally resolved to firmly establish the PCET mechanism.

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 pKa 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.

Electrocatalysis in Alkaline Media and Alkaline Membrane-Based Energy Technologies.

Hydrogen energy-based electrochemical energy conversion technologies offer the promise of enabling a transition of the global energy landscape from fossil fuels to renewable energy. Here, we present a comprehensive review of the fundamentals of electrocatalysis in alkaline media and applications in alkaline-based energy technologies, particularly alkaline fuel cells and water electrolyzers. Anion exchange (alkaline) membrane fuel cells (AEMFCs) enable the use of nonprecious electrocatalysts for the sluggish oxygen reduction reaction (ORR), relative to proton exchange membrane fuel cells (PEMFCs), which require Pt-based electrocatalysts. However, the hydrogen oxidation reaction (HOR) kinetics is significantly slower in alkaline media than in acidic media. Understanding these phenomena requires applying theoretical and experimental methods to unravel molecular-level thermodynamics and kinetics of hydrogen and oxygen electrocatalysis and, particularly, the proton-coupled electron transfer (PCET) process that takes place in a proton-deficient alkaline media. Extensive electrochemical and spectroscopic studies, on single-crystal Pt and metal oxides, have contributed to the development of activity descriptors, as well as the identification of the nature of active sites, and the rate-determining steps of the HOR and ORR. Among these, the structure and reactivity of interfacial water serve as key potential and pH-dependent kinetic factors that are helping elucidate the origins of the HOR and ORR activity differences in acids and bases. Additionally, deliberately modulating and controlling catalyst-support interactions have provided valuable insights for enhancing catalyst accessibility and durability during operation. The design and synthesis of highly conductive and durable alkaline membranes/ionomers have enabled AEMFCs to reach initial performance metrics equal to or higher than those of PEMFCs. We emphasize the importance of using membrane electrode assemblies (MEAs) to integrate the often separately pursued/optimized electrocatalyst/support and membranes/ionomer components. Operando/in situ methods, at multiscales, and ab initio simulations provide a mechanistic understanding of electron, ion, and mass transport at catalyst/ionomer/membrane interfaces and the necessary guidance to achieve fuel cell operation in air over thousands of hours. We hope that this Review will serve as a roadmap for advancing the scientific understanding of the fundamental factors governing electrochemical energy conversion in alkaline media with the ultimate goal of achieving ultralow Pt or precious-metal-free high-performance and durable alkaline fuel cells and related technologies.

General Kinetic Model for pH Dependence of Proton-Coupled Electron Transfer: Application to an Electrochemical Water Oxidation System.

The pH dependence of proton-coupled electron transfer (PCET) reactions, which are critical to many chemical and biological processes, is a powerful probe for elucidating their fundamental mechanisms. Herein, a general, multichannel kinetic model is introduced to describe the pH dependence of both homogeneous and electrochemical PCET reactions. According to this model, a weak pH dependence can arise from the competition among multiple sequential and concerted PCET channels involving different forms of the redox species, such as protonated and deprotonated forms, as well as different proton donors and acceptors. The contribution of each channel is influenced by the relative populations of the reactant species, which often depend strongly on pH, leading to complex pH dependence of PCET apparent rate constants. This model is used to explain the origins of the experimentally observed weak pH dependence of the electrochemical PCET apparent rate constant for a ruthenium-based water oxidation catalyst attached to a tin-doped In2O3 (ITO) surface. The weak pH dependence is found to arise from the intrinsic differences in the rate constants of participating channels and the dependence of their relative contributions on pH. This model predicts that the apparent maximum rate constant will become pH-independent at higher pH, which is confirmed by experimental measurements. Our analysis also suggests that the dominant channels are electron transfer at lower pH and sequential PCET via electron transfer followed by fast proton transfer at higher pH. This work highlights the importance of considering multiple competing channels simultaneously for PCET processes.

Computational Insights into the Mechanism of Nitric Oxide Generation from S-Nitrosoglutathione Catalyzed by a Copper Metal-Organic Framework.

The controlled generation of nitric oxide (NO) from endogenous sources, such as S-nitrosoglutathione (GSNO), has significant implications for biomedical implants due to the vasodilatory and other beneficial properties of NO. The water-stable metal-organic framework (MOF) Cu-1,3,5-tris[1H-1,2,3-triazol-5-yl]benzene has been shown to catalyze the production of NO and glutathione disulfide (GSSG) from GSNO in aqueous solution as well as in blood. Previous experimental work provided kinetic data for the catalysis of the 2GSNO → 2NO + GSSG reaction, leading to various proposed mechanisms. Herein, this catalytic process is examined using density functional theory. Minimal functional models of the Cu-MOF cluster and glutathione moieties are established, and three distinct catalytic mechanisms are explored. The most thermodynamically favorable mechanism studied is consistent with prior experimental findings. This mechanism involves coordination of GSNO to copper via sulfur rather than nitrogen and requires a reductive elimination that produces a Cu(I) intermediate, implicating a redox-active copper site. The experimentally observed inhibition of reactivity at high pH values is explained in terms of deprotonation of a triazole linker, which decreases the structural stability of the Cu(I) intermediate. These fundamental mechanistic insights may be generally applicable to other MOF catalysts for NO generation.

Reorganization Energies for Interfacial Proton-Coupled Electron Transfer to a Water Oxidation Catalyst.

The reorganization energy (λ) for interfacial electron transfer (ET) and proton-coupled ET (PCET) from a conductive metal oxide (In2O3:Sn, ITO) to a surface-bound water oxidation catalyst was extracted from kinetic data measured as a function of the thermodynamic driving force. Visible light excitation resulted in rapid excited-state injection (kinj > 108 s-1) to the ITO, which photo-initiated the two interfacial reactions of interest. The rate constants for both reactions increased with the driving force, -ΔG°, to a saturating limit, kmax, with rate constants consistently larger for ET than for PCET. Marcus-Gerischer analysis of the kinetic data provided the reorganization energy for interfacial PCET (0.90 ± 0.02 eV) and ET (0.40 ± 0.02 eV), respectively. The magnitude of kmax for PCET was found to decrease with pH, behavior that was absent for ET. Both the decrease in kmax and the larger reorganization energy for an unwanted competing PCET reaction from the ITO to the oxidized catalyst showcases a significant kinetic advantage for driving solar water oxidation at high pH. Computational analysis revealed a larger inner-sphere reorganization energy contribution for PCET than for ET arising from a more significant change in the Ru-O bond length for the PCET reaction. Extending the Marcus-Gerischer theory to PCET by including the excited electron-proton vibronic states and the proton donor-acceptor motion provided an apparent reorganization energy of 1.01 eV. This study demonstrates that the Marcus-Gerischer theory initially developed for ET can be reliably extended to PCET for quantifying and interpreting reorganization energies observed experimentally.

Theoretical Description of the Primary Proton-Coupled Electron Transfer Reaction in the Cytochrome bc1 Complex.

The cytochrome bc1 complex is a transmembrane enzymatic protein complex that plays a central role in cellular energy production and is present in both photosynthetic and respiratory chain organelles. Its reaction mechanism is initiated by the binding of a quinol molecule to an active site, followed by a series of charge transfer reactions between the quinol and protein subunits. Previous work hypothesized that the primary reaction was a concerted proton-coupled electron transfer (PCET) reaction because of the apparent absence of intermediate states associated with single proton or electron transfer reactions. In the present study, the kinetics of the primary bc1 complex PCET reaction is investigated with a vibronically nonadiabatic PCET theory in conjunction with all-atom molecular dynamics simulations and electronic structure calculations. The computed rate constants and relatively high kinetic isotope effects are consistent with experimental measurements on related biomimetic systems. The analysis implicates a concerted PCET mechanism with significant hydrogen tunneling and nonadiabatic effects in the bc1 complex. Moreover, the employed theoretical framework is shown to serve as a general strategy for describing PCET reactions in bioenergetic systems.

Theoretical Study of Shallow Distance Dependence of Proton-Coupled Electron Transfer in Oligoproline Peptides.

Long-range electron transfer is coupled to proton transfer in a wide range of chemically and biologically important processes. Recently the proton-coupled electron transfer (PCET) rate constants for a series of biomimetic oligoproline peptides linking Ru(bpy)32+ to tyrosine were shown to exhibit a substantially shallower dependence on the number of proline spacers compared to the analogous electron transfer (ET) systems. The experiments implicated a concerted PCET mechanism involving intramolecular electron transfer from tyrosine to Ru(bpy)33+ and proton transfer from tyrosine to a hydrogen phosphate dianion. Herein these PCET systems, as well as the analogous ET systems, are studied with microsecond molecular dynamics, and the ET and PCET rate constants are calculated with the corresponding nonadiabatic theories. The molecular dynamics simulations illustrate that smaller ET donor-acceptor distances are sampled by the PCET systems than by the analogous ET systems. The shallower dependence of the PCET rate constant on the ET donor-acceptor distance is explained in terms of an additional positive, distance-dependent electrostatic term in the PCET driving force, which attenuates the rate constant at smaller distances. This electrostatic term depends on the change in the electrostatic interaction between the charges on each end of the bridge and can be modified by altering these charges. On the basis of these insights, this theory predicted a less shallow distance dependence of the PCET rate constant when imidazole rather than hydrogen phosphate serves as the proton acceptor, even though their pKa values are similar. This theoretical prediction was subsequently validated experimentally, illustrating that long-range electron transfer processes can be tuned by modifying the nature of the proton acceptor in concerted PCET processes. This level of control has broad implications for the design of more effective charge-transfer systems.

Proton Discharge on a Gold Electrode from Triethylammonium in Acetonitrile: Theoretical Modeling of Potential-Dependent Kinetic Isotope Effects.

The discharge of protons on electrode surfaces, known as the Volmer reaction, is a ubiquitous reaction in heterogeneous electrocatalysis and plays an important role in renewable energy technologies. Recent experiments with triethylammonium (TEAH+) donating the proton to a gold electrode in acetonitrile demonstrate significantly different Tafel slopes for TEAH+ and its deuterated counterpart, TEAD+. As a result, the kinetic isotope effect (KIE) for the hydrogen evolution reaction changes considerably as a function of applied potential. Herein a vibronically nonadiabatic approach for proton-coupled electron transfer (PCET) at an electrode interface is extended to heterogeneous electrochemical processes and is applied to this system. This approach accounts for the key effects of the electrical double layer and spans the electronically adiabatic and nonadiabatic regimes, as found to be necessary for this reaction. The experimental Tafel plots for TEAH+ and TEAD+ are reproduced using physically reasonable parameters within this model. The potential-dependent KIE or, equivalently, isotope-dependent Tafel slope is found to be a consequence of contributions from excited electron-proton vibronic states that depend on both isotope and applied potential. Specifically, the contributions from excited reactant vibronic states are greater for TEAD+ than for TEAH+. Thus, the two reactions proceed by the same fundamental mechanism yet exhibit significantly different Tafel slopes. This theoretical approach may be applicable to a wide range of other heterogeneous electrochemical PCET reactions.

Theoretical analysis of the inverted region in photoinduced proton-coupled electron transfer.

Photoinduced proton-coupled electron transfer (PCET) plays a key role in a wide range of energy conversion processes, and understanding how to design systems to control the PCET rate constant is a significant challenge. Herein a theoretical formulation of PCET is utilized to identify the conditions under which photoinduced PCET may exhibit inverted region behavior. In the inverted region, the rate constant decreases as the driving force increases even though the reaction becomes more thermodynamically favorable. Photoinduced PCET will exhibit inverted region behavior when the following criteria are satisfied: (1) the overlap integrals corresponding to the ground reactant and the excited product proton vibrational wavefunctions become negligible for a low enough product vibronic state and (2) the reaction free energies associated with the lower excited product proton vibrational wavefunctions contributing significantly to the rate constant are negative with magnitudes greater than the reorganization energy. These criteria are typically not satisfied by harmonic or Morse potentials but are satisfied by more realistic asymmetric double well potentials because the proton vibrational states above the barrier correspond to more delocalized proton vibrational wavefunctions with nodal structures leading to destructive interference effects. Thus, this theoretical analysis predicts that inverted region behavior could be observed for systems with asymmetric double well potentials characteristic of hydrogen-bonded systems and that the hydrogen/deuterium kinetic isotope effect will approach unity and could even become inverse in this region due to the oscillatory nature of the highly excited vibrational wavefunctions. These insights may help guide the design of more effective energy conversion devices.

Fundamental Insights into Proton-Coupled Electron Transfer in Soybean Lipoxygenase from Quantum Mechanical/Molecular Mechanical Free Energy Simulations.

The proton-coupled electron transfer (PCET) reaction catalyzed by soybean lipoxygenase has served as a prototype for understanding hydrogen tunneling in enzymes. Herein this PCET reaction is studied with mixed quantum mechanical/molecular mechanical (QM/MM) free energy simulations. The free energy surfaces are computed as functions of the proton donor-acceptor (C-O) distance and the proton coordinate, and the potential of mean force is computed as a function of the C-O distance, inherently including anharmonicity. The simulation results are used to calculate the kinetic isotope effects for the wild-type enzyme (WT) and the L546A/L754A double mutant (DM), which have been measured experimentally to be ∼80 and ∼700, respectively. The PCET reaction is found to be exoergic for WT and slightly endoergic for the DM, and the equilibrium C-O distance for the reactant is found to be ∼0.2 Šgreater for the DM than for WT. The larger equilibrium distance for the DM, which is due mainly to less optimal substrate binding in the expanded binding cavity, is primarily responsible for its higher kinetic isotope effect. The calculated potentials of mean force are anharmonic and relatively soft at shorter C-O distances, allowing efficient thermal sampling of the shorter distances required for effective hydrogen tunneling. The primarily local electrostatic field at the transferring hydrogen is ∼100 MV/cm in the direction to facilitate proton transfer and increases dramatically as the C-O distance decreases. These simulations suggest that the overall protein environment is important for conformational sampling of active substrate configurations aligned for proton transfer, but the PCET reaction is influenced primarily by local electrostatic effects that facilitate conformational sampling of shorter proton donor-acceptor distances required for effective hydrogen tunneling.

Theoretical Insights into Proton-Coupled Electron Transfer from a Photoreduced ZnO Nanocrystal to an Organic Radical.

Proton-coupled electron transfer (PCET) at metal-oxide nanoparticle interfaces plays a critical role in many photocatalytic reactions and energy conversion processes. Recent experimental studies have shown that photoreduced ZnO nanocrystals react by PCET with organic hydrogen atom acceptors such as the nitroxyl radical TEMPO. Herein, the interfacial PCET rate constant is calculated in the framework of vibronically nonadiabatic PCET theory, which treats the electrons and transferring proton quantum mechanically. The input quantities to the PCET rate constant, including the electronic couplings, are calculated with density functional theory. The computed interfacial PCET rate constant is consistent with the experimentally measured value for this system, providing validation for this PCET theory. In this model, the electron transfers from the conduction band of the ZnO nanocrystal to TEMPO concertedly with proton transfer from a surface oxygen of the ZnO nanocrystal to the oxygen of TEMPO. Moreover, the proton tunneling at the interface is gated by the relatively low-frequency proton donor-acceptor motion between the TEMPO radical and the ZnO nanocrystal. The ZnO nanocrystal and TEMPO are found to contribute similar amounts to the inner-sphere reorganization energy, implicating structural reorganization at the nanocrystal surface. These fundamental mechanistic insights may guide the design of metal-oxide nanocatalysts for a wide range of energy conversion processes.

Proton-coupled electron transfer reactions: analytical rate constants and case study of kinetic isotope effects in lipoxygenase.

A general theory has been developed for proton-coupled electron transfer (PCET), which is vital to a wide range of chemical and biological processes. This theory describes PCET reactions in terms of nonadiabatic transitions between reactant and product electron-proton vibronic states and includes the effects of thermal fluctuations of the solvent or protein environment, as well as the proton donor-acceptor motion. Within the framework of this general PCET theory, a series of analytical rate constant expressions has been derived for PCET reactions in well-defined regimes. Herein, the application of this theory to PCET in the enzyme soybean lipoxygenase illustrates the regimes of validity for the various rate constant expressions and elucidates the fundamental physical principles dictating PCET reactions. Such theoretical studies provide significant physical insights that guide the interpretation of experimental data and lead to experimentally testable predictions. A combination of theoretical treatments with atomic-level simulations is essential to understanding PCET.

Dependence of Vibronic Coupling on Molecular Geometry and Environment: Bridging Hydrogen Atom Transfer and Electron-Proton Transfer.

The rate constants for typical concerted proton-coupled electron transfer (PCET) reactions depend on the vibronic coupling between the diabatic reactant and product states. The form of the vibronic coupling is different for electronically adiabatic and nonadiabatic reactions, which are associated with hydrogen atom transfer (HAT) and electron-proton transfer (EPT) mechanisms, respectively. Most PCET rate constant expressions rely on the Condon approximation, which assumes that the vibronic coupling is independent of the nuclear coordinates of the solute and the solvent or protein. Herein we test the Condon approximation for PCET vibronic couplings. The dependence of the vibronic coupling on molecular geometry is investigated for an open and a stacked transition state geometry of the phenoxyl-phenol self-exchange reaction. The calculations indicate that the open geometry is electronically nonadiabatic, corresponding to an EPT mechanism that involves significant electronic charge redistribution, while the stacked geometry is predominantly electronically adiabatic, corresponding primarily to an HAT mechanism. Consequently, a single molecular system can exhibit both HAT and EPT character. The dependence of the vibronic coupling on the solvent or protein configuration is examined for the soybean lipoxygenase enzyme. The calculations indicate that this PCET reaction is electronically nonadiabatic with a vibronic coupling that does not depend significantly on the protein environment. Thus, the Condon approximation is shown to be valid for the solvent and protein nuclear coordinates but invalid for the solute nuclear coordinates in certain PCET systems. These results have significant implications for the calculation of rate constants, as well as mechanistic interpretations, of PCET reactions.

Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion.

Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton transfer and proton-coupled electron transfer in chemical and biological processes.

Insights into proton-coupled electron transfer mechanisms of electrocatalytic H2 oxidation and production.

The design of molecular electrocatalysts for H(2) oxidation and production is important for the development of alternative renewable energy sources that are abundant, inexpensive, and environmentally benign. Recently, nickel-based molecular electrocatalysts with pendant amines that act as proton relays for the nickel center were shown to effectively catalyze H(2) oxidation and production. We developed a quantum mechanical approach for studying proton-coupled electron transfer processes in these types of molecular electrocatalysts. This theoretical approach is applied to a nickel-based catalyst in which phosphorous atoms are directly bonded to the nickel center, and nitrogen atoms of the ligand rings act as proton relays. The catalytic step of interest involves electron transfer between the nickel complex and the electrode as well as intramolecular proton transfer between the nickel and nitrogen atoms. This process can occur sequentially, with either the electron or proton transferring first, or concertedly, with the electron and proton transferring simultaneously without a stable intermediate. The electrochemical rate constants are calculated as functions of overpotential for the concerted electron-proton transfer reaction and the two electron transfer reactions in the sequential mechanisms. Our calculations illustrate that the concerted electron-proton transfer standard rate constant will increase as the equilibrium distance between the nickel and nitrogen atoms decreases and as the pendant amines become more flexible to facilitate the contraction of this distance with a lower energy penalty. This approach identifies the favored mechanisms under various experimental conditions and provides insight into the impact of substituents on the nitrogen and phosphorous atoms.

Extremely elevated room-temperature kinetic isotope effects quantify the critical role of barrier width in enzymatic C-H activation.

The enzyme soybean lipoxygenase (SLO) has served as a prototype for hydrogen-tunneling reactions, as a result of its unusual kinetic isotope effects (KIEs) and their temperature dependencies. Using a synergy of kinetic, structural, and theoretical studies, we show how the interplay between donor-acceptor distance and active-site flexibility leads to catalytic behavior previously predicted by quantum tunneling theory. Modification of the size of two hydrophobic residues by site-specific mutagenesis in SLO reduces the reaction rate 10(4)-fold and is accompanied by an enormous and unprecedented room-temperature KIE. Fitting of the kinetic data to a non-adiabatic model implicates an expansion of the active site that cannot be compensated by donor-acceptor distance sampling. A 1.7 Å resolution X-ray structure of the double mutant further indicates an unaltered backbone conformation, almost identical side-chain conformations, and a significantly enlarged active-site cavity. These findings show the compelling property of room-temperature hydrogen tunneling within a biological context and demonstrate the very high sensitivity of such tunneling to barrier width.

Nonadiabatic dynamics of electron transfer in solution: explicit and implicit solvent treatments that include multiple relaxation time scales.

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents for a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.