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

Proton transfer kinetics of transition metal hydride complexes and implications for fuel-forming reactions

Proton transfer reactions involving transition metal hydride complexes are prevalent in a number of catalytic fuel-forming reactions, where the proton transfer kinetics to or from the metal center can have significant impacts on the efficiency, selectivity, and stability associated with the catalytic cycle. This review correlates the often slow proton transfer rate constants of transition metal hydride complexes to their electronic and structural descriptors and provides perspective on how to exploit these parameters to control proton transfer kinetics to and from the metal center. A toolbox of techniques for experimental determination of proton transfer rate constants is discussed, and case studies where proton transfer rate constant determination informs fuel-forming reactions are highlighted. Opportunities for extending proton transfer kinetic measurements to additional systems are presented, and the importance of synergizing the thermodynamics and kinetics of proton transfer involving transition metal hydride complexes is emphasized.

Nonadiabatic quantum dynamics of the coherent excited state intramolecular proton transfer of 10-hydroxybenzo[h]quinoline

The photoinduced nonadiabatic dynamics of the enol-keto isomerization of 10-hydroxybenzo[h]quinoline (HBQ) are studied computationally using high-dimensional quantum dynamics. The simulations are based on a diabatic vibronic coupling Hamiltonian, which includes the two lowest [Formula: see text] excited states and a [Formula: see text] state, which has high energy in the Franck-Condon zone, but significantly stabilizes upon excited state intramolecular proton transfer. A procedure, applicable to large classes of excited state proton transfer reactions, is presented to parametrize this model using potential energies, forces and force constants, which, in this case, are obtained by time-dependent density functional theory. The wave packet calculations predict a time scale of 10-15 fs for the photoreaction, and reproduce the time constants and the coherent oscillations observed in time-resolved spectroscopic studies performed on HBQ. In contrast to the interpretation given to the most recent experiments, it is found that the reaction initiated by [Formula: see text] photoexcitation proceeds essentially on a single potential energy surface, and the observed coherences bear signatures of Duschinsky mode-mixing along the reaction path. The dynamics after the [Formula: see text] excitation are instead nonadiabatic, and the [Formula: see text] state plays a major role in the relaxation process. The simulations suggest a mainly active role of the proton in the isomerization, rather than a passive migration assisted by the vibrations of the benzoquinoline backbone.

Understanding the Large Kinetic Isotope Effect of Hydrogen Tunneling in Condensed Phases by Using Double-Well Model Systems

In recent years, many experiments have shown large kinetic isotope effects (KIEs) for hydrogen transfer reactions in condensed phases as evidence of strong quantum tunneling effects. Since accurate calculation of the tunneling dynamics in such systems still present significant challenges, previous studies have employed different types of approximations to estimate the tunneling effects and KIEs. In this work, by employing model systems consisting of a double-well coupled to a harmonic bath, we calculate the tunneling effects and KIEs using the numerically exact hierarchical equations of motion (HEOM) method. It is found that hydrogen and deuterium transfer reactions in the same system may show rather different behaviors, where hydrogen transfer is dominated by tunneling between the two lowest vibrational states and deuterium transfer is controlled by excited vibrational states close to the barrier top. The simulation results are also used to test the validity of various approximate methods. It is shown that the Wolynes theory of dissipative tunneling gives a good estimation of rate constants in the over-the-barrier regime, while the nonadiabatic reaction rate theory based on the Landau-Zener formula is more suitable for deep tunneling reactions.

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 pK_a 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.

Modeling voltammetry curves for proton coupled electron transfer: The importance of nuclear quantum effects

We investigate rates of proton-coupled electron transfer (PCET) in potential sweep experiments for a generalized Anderson-Holstein model with the inclusion of a quantized proton coordinate. To model this system, we utilize a quantum classical Liouville equation embedded inside of a classical master equation, which can be solved approximately with a recently developed algorithm combining diffusional effects and surface hopping between electronic states. We find that the addition of nuclear quantum effects through the proton coordinate can yield quantitatively (but not qualitatively) different IV curves under a potential sweep compared to electron transfer (ET). Additionally, we find that kinetic isotope effects give rise to a shift in the peak potential, but not the peak current, which would allow for quantification of whether an electrochemical ET event is proton-coupled or not. These findings suggest that it will be very difficult to completely understand coupled nuclear-electronic effects in electrochemical voltammetry experiments using only IV curves, and new experimental techniques will be needed to draw inferences about the nature of electrochemical PCET.

The Soybean Lipoxygenase-Substrate Complex: Correlation between the Properties of Tunneling-Ready States and ENDOR-Detected Structures of Ground States

Hydrogen tunneling in enzymatic C-H activation requires a dynamical sampling among ground-state enzyme-substrate (E-S) conformations, which transiently generates a tunneling-ready state (TRS). The TRS is characterized by a hydrogen donor-acceptor distance (DAD) of 2.7 Å, ∼0.5 Å shorter than the dominant DAD of optimized ground states. Recently, a high-resolution, 13C electron-nuclear double-resonance (ENDOR) approach was developed to characterize the ground-state structure of the complex of the linoleic acid (LA) substrate with soybean lipoxygenase (SLO). The resulting enzyme-substrate model revealed two ground-state conformers with different distances between the target C11 of LA and the catalytically active cofactor [Fe(III)-OH]: the active conformer "a", with a van der Waals DAD of 3.1 Å between C11 and metal-bound hydroxide, and an inactive conformer "b", with a distance that is almost 1 Å longer. Herein, the structure of the E-S complex is examined for a series of six variants in which subtle structural modifications of SLO have been introduced either at a hydrophobic side chain near the bound substrate or at a remote residue within a protein network whose flexibility influences hydrogen transfer. A remarkable correlation is found between the ENDOR-derived population of the active ground-state conformer a and the kinetically derived differential enthalpic barrier for D versus H transfer, ΔEa, with the latter increasing as the fraction of conformer a decreases. As proposed, ΔEa provides a "ruler" for the DAD within the TRS. ENDOR measurements further corroborate the previous identification of a dynamical network coupling the buried active site of SLO to the surface. This study shows that subtle imperfections within the initial ground-state structures of E-S complexes are accompanied by compromised geometries at the TRS.

Controlling Electrons and Protons through Theory: Molecular Electrocatalysts to Nanoparticles

The development of renewable energy sources that are environmentally friendly and economical is of critical importance. The effective utilization of such energy sources relies on catalysts to facilitate the interconversion between electrical and chemical energy through multielectron, multiproton reactions. The design of effective catalysts for these types of energy conversion processes requires the ability to control the localization and movement of electrons and protons, as well as the coupling between them. Theoretical calculations, in conjunction with experimental validation and feedback, are playing a key role in these catalyst design efforts. A general theory has been developed for describing proton-coupled electron transfer (PCET) reactions, which encompass all reactions involving the coupled transfer of electrons and protons, including sequential and concerted mechanisms for multielectron, multiproton processes. In addition, computational methods have been devised to compute the input quantities for the PCET rate constant expressions and to generate free energy pathways for molecular electrocatalysts. These methods have been extended to heterogeneous PCET reactions to enable the modeling of PCET processes at electrode and nanoparticle surfaces. Three distinct theoretical studies of PCET reactions relevant to catalyst design for energy conversion processes are discussed. In the first application, theoretical calculations of hydrogen production catalyzed by hangman metalloporphyrins predicted that the porphyrin ligand is reduced, leading to dearomatization and proton transfer from the carboxylic acid hanging group to the meso carbon of the porphyrin rather than the metal center, producing a phlorin intermediate. Subsequent experiments isolated and characterized the phlorin intermediate, validating this theoretical prediction. These molecular electrocatalysts exemplify the potential use of noninnocent ligands to localize electrons and protons on different parts of the catalyst and to direct their motions accordingly. In the second application, theoretical calculations on substituted benzimidazole phenol molecules predicted that certain substituents would lead to multiple intramolecular proton transfer reactions upon oxidation. Subsequent experiments verified these multiproton reactions, as well as the predicted shifts in the redox potentials and kinetic isotope effects. These bioinspired molecular systems demonstrate the potential use of multiproton relays to enable the transport of protons over longer distances along specified pathways, as well as the tuning of redox potentials through this movement of positive charge. In the third application, theoretical studies of heterogeneous PCET in photoreduced ZnO nanoparticles illustrated the significance of proton diffusion through the bulk of the nanoparticle as well as interfacial PCET to an organic radical in solution at its surface. These theoretical calculations were consistent with prior experimental studies of this system, although theoretical methods for heterogeneous PCET have not yet attained the level of predictive capability highlighted for the molecular electrocatalysts. These examples suggest that theory will play a significant role in the design of both molecular and heterogeneous catalysts to control the movement and coupling of electrons and protons. The resulting catalysts will be essential for the development of renewable energy sources to address current energy challenges.

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.

A qualitative quantum rate model for hydrogen transfer in soybean lipoxygenase

The hydrogen transfer reaction catalysed by soybean lipoxygenase (SLO) has been the focus of intense study following observations of a high kinetic isotope effect (KIE). Today high KIEs are generally thought to indicate departure from classical rate theory and are seen as a strong signature of tunnelling of the transferring particle, hydrogen or one of its isotopes, through the reaction energy barrier. In this paper, we build a qualitative quantum rate model with few free parameters that describes the dynamics of the transferring particle when it is exposed to energetic potentials exerted by the donor and the acceptor. The enzyme's impact on the dynamics is modelled by an additional energetic term, an oscillatory contribution known as "gating." By varying two key parameters, the gating frequency and the mean donor-acceptor separation, the model is able to reproduce well the KIE data for SLO wild-type and a variety of SLO mutants over the experimentally accessible temperature range. While SLO-specific constants have been considered here, it is possible to adapt these for other enzymes.

Enhanced Rigidification within a Double Mutant of Soybean Lipoxygenase Provides Experimental Support for Vibronically Nonadiabatic Proton-Coupled Electron Transfer Models

Soybean lipoxygenase (SLO) is a prototype for nonadiabatic hydrogen tunneling reactions and, as such, has served as the subject of numerous theoretical studies. In this work, we report a nearly temperature-independent kinetic isotope effect (KIE) with an average KIE value of 661 ± 27 for a double mutant (DM) of SLO at six temperatures. The data are well-reproduced within a vibronically nonadiabatic proton-coupled electron transfer model in which the active site has become rigidified compared to wild-type enzyme and single-site mutants. A combined temperature-pressure perturbation further shows that temperature-dependent global motions within DM-SLO are more resistant to perturbation by elevated pressure. These findings provide strong experimental support for the model of hydrogen tunneling in SLO, where optimization of both local protein and ligand motions and distal conformational rearrangements is a prerequisite for effective proton vibrational wave function overlap between the substrate and the active-site iron cofactor.

Hydrostatic Pressure Studies Distinguish Global from Local Protein Motions in C-H Activation by Soybean Lipoxygenase-1

The proposed contributions of distinct classes of local versus global protein motions during enzymatic bond making/breaking processes has been difficult to verify. We employed soybean lipoxygenase-1 as a model system to investigate the impact of high pressure at variable temperatures on the hydrogen-tunneling properties of the wild-type protein and three single-site mutants. For all variants, pressure dramatically elevates the enthalpies of activation for the C-H activation. In contrast, the primary kinetic isotope effects (KIEs) for C-H activation and their corresponding temperature dependencies remain unchanged up to ca. 700 bar. The differential impact of elevated hydrostatic pressure on the temperature dependencies of rate constants versus substrate KIEs provides direct evidence for two distinct classes of protein motions: local, isotope-dependent donor-acceptor distance-sampling modes, and a more global, isotope-independent search for productive protein conformational sub-states.