Theoretical formulation for electron transfer coupled to multiple protons: Application to amidinium–carboxylate interfaces

Charge Regulation in a Rieske Proton Pump Pinpoints Zero, One, and Two Proton-Coupled Electron Transfer

The degree to which redox-driven proton pumps regulate net charge during electron transfer (ΔZET) remains undetermined due to difficulties in measuring the net charge of solvated proteins. Values of ΔZET can reflect reorganization energies or redox potentials associated with ET and can be used to distinguish ET from proton(s)-coupled electron transfer (PCET). Here, we synthesized protein "charge ladders" of a Rieske [2Fe-2S] subunit from Thermus thermophilus (truncTtRp) and made 120 electrostatic measurements of ΔZET across pH. Across pH 5-10, truncTtRp is suspected of transitioning from ET to PCET, and then to two proton-coupled ET (2PCET). Upon reduction, we found that truncTtRp became more negative at pH 6.0 by one unit (ΔZET = -1.01 ± 0.14), consistent with single ET; was isoelectric at pH 8.8 (ΔZET = -0.01 ± 0.45), consistent with PCET; and became more positive at pH 10.6 (ΔZET = +1.37 ± 0.60), consistent with 2PCET. These ΔZET values are attributed to protonation of H154 and H134. Across pH, redox potentials of TtRp (measured previously) correlated with protonation energies of H154 and H134 and ΔZET for truncTtRp, supporting a discrete proton pumping mechanism for Rieske proteins at the Fe-coordinating histidines.

Proton-Coupled Electron Transfer: Moving Together and Charging Forward

Proton-coupled electron transfer (PCET) is ubiquitous throughout chemistry and biology. This Perspective discusses recent advances and current challenges in the field of PCET, with an emphasis on the role of theory and computation. The fundamental theoretical concepts are summarized, and expressions for rate constants and kinetic isotope effects are provided. Computational methods for calculating reduction potentials and pKa's for molecular electrocatalysts, as well as insights into linear correlations and non-innocent ligands, are also described. In addition, computational methods for simulating the nonadiabatic dynamics of photoexcited PCET are discussed. Representative applications to PCET in solution, proteins, electrochemistry, and photoinduced processes are presented, highlighting the interplay between theoretical and experimental studies. The current challenges and suggested future directions are outlined for each type of application, concluding with an overall view to the future.

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.

The Possible Role of Proton-Coupled Electron Transfer (PCET) in Water Oxidation by Photosystem II

All higher life forms use oxygen and respiration as their primary energy source. The oxygen comes from water by solar-energy conversion in photosynthetic membranes. In green plants, light absorption in photosystem II (PSII) drives electron-transfer activation of the oxygen-evolving complex (OEC). The mechanism of water oxidation by the OEC has long been a subject of great interest to biologists and chemists. With the availability of new molecular-level protein structures from X-ray crystallography and EXAFS, as well as the accumulated results from numerous experiments and theoretical studies, it is possible to suggest how water may be oxidized at the OEC. An integrated sequence of light-driven reactions that exploit coupled electron-proton transfer (EPT) could be the key to water oxidation. When these reactions are combined with long-range proton transfer (by sequential local proton transfers), it may be possible to view the OEC as an intricate structure that is "wired for protons".

Anomalous temperature-isotope dependence in proton-coupled electron transfer

Motivated by the experiments of Hodgkiss et al. [J. Phys. Chem. (submitted)] on electron transfer (ET) through a H-bonding interface, we present a new theoretical model for proton-coupled electron transfer (PCET) in the condensed phase, that does not involve real proton transfer. These experiments, which directly probe the joint T-isotope effects in coupled charge transfer reactions, show anomalous T dependence in k(H)k(D), where k(H) and k(D) are the ET rates through the H-bonding interface with H-bonded protons and deuterons, respectively. We address the anomalous T dependence of the k(H)k(D) in our model by attributing the modulation of the electron tunneling dynamics to bath-induced fluctuations in the proton coordinate, so that the mechanism for coupled charge transfer might be better termed vibrationally assisted ET rather than PCET. We argue that such a mechanism may be relevant to understanding traditional PCET processes, i.e., those in which protons undergo a transfer from donor to acceptor during the course of ET, provided there is an appropriate time scale separating both coupled charge transfers. Likewise, it may also be useful in understanding long-range ET in proteins, where tunneling pathways between redox cofactors often pass through H-bonded amino acid residues, or other systems with sufficiently decoupled proton and electron donating functionalities.

Chemical approaches to artificial photosynthesis. 2

The goal of artificial photosynthesis is to use the energy of the sun to make high-energy chemicals for energy production. One approach, described here, is to use light absorption and excited-state electron transfer to create oxidative and reductive equivalents for driving relevant fuel-forming half-reactions such as the oxidation of water to O2 and its reduction to H2. In this "integrated modular assembly" approach, separate components for light absorption, energy transfer, and long-range electron transfer by use of free-energy gradients are integrated with oxidative and reductive catalysts into single molecular assemblies or on separate electrodes in photelectrochemical cells. Derivatized porphyrins and metalloporphyrins and metal polypyridyl complexes have been most commonly used in these assemblies, with the latter the focus of the current account. The underlying physical principles--light absorption, energy transfer, radiative and nonradiative excited-state decay, electron transfer, proton-coupled electron transfer, and catalysis--are outlined with an eye toward their roles in molecular assemblies for energy conversion. Synthetic approaches based on sequential covalent bond formation, derivatization of preformed polymers, and stepwise polypeptide synthesis have been used to prepare molecular assemblies. A higher level hierarchial "assembly of assemblies" strategy is required for a working device, and progress has been made for metal polypyridyl complex assemblies based on sol-gels, electropolymerized thin films, and chemical adsorption to thin films of metal oxide nanoparticles.

Quantum and dynamical effects of proton donor-acceptor vibrational motion in nonadiabatic proton-coupled electron transfer reactions

This paper presents a general theoretical formulation for proton-coupled electron transfer (PCET) reactions. The solute is represented by a multistate valence bond model, and the active electrons and transferring proton(s) are treated quantum mechanically. This formulation enables the classical or quantum mechanical treatment of the proton donor-acceptor vibrational mode, as well as the dynamical treatment of the proton donor-acceptor mode and the solvent. Nonadiabatic rate expressions are presented for PCET reactions in a number of well-defined limits for both dielectric continuum and molecular representations of the environment. The dynamical rate expressions account for correlations between the fluctuations of the proton donor-acceptor distance and the nonadiabatic PCET coupling. The quantities in the rate expressions can be calculated with a dielectric continuum model or a molecular dynamics simulation of the full system. The significance of the quantum and dynamical effects of the proton donor-acceptor mode is illustrated with applications to model PCET systems.

Theoretical studies of proton-coupled electron transfer reactions

A theoretical formulation for proton-coupled electron transfer (PCET) is described. This theory allows the calculation of rates and kinetic isotope effects and provides insight into the underlying fundamental principles of PCET reactions. Applications of this theory to PCET reactions in iron bi-imidazoline complexes, oxoruthenium polypyridyl complexes, osmium-benzoquinone systems, amidinium-carboxylate salt bridges, DNA-acrylamide complexes, and ruthenium polypyridyl-tyrosine systems are summarized. The mechanistic insight gained from theoretical calculations on these model systems is relevant to PCET in more complex biological processes such as photosynthesis and respiration.

Theoretical investigation of large kinetic isotope effects for proton-coupled electron transfer in ruthenium polypyridyl complexes

A theoretical investigation of proton-coupled electron transfer in ruthenium polypyridyl complexes is presented. The three reactions studied are as follows: (1) the comproportionation reaction of [(bpy)(2)(py)Ru(IV)O](2+) and [(bpy)(2)(py)Ru(II)OH(2)](2+) to produce [(bpy)(2)(py)Ru(III)OH](2+); (2) the comproportionation reaction of [(tpy)(bpy)Ru(IV)O](2+) and [(tpy)(bpy)Ru(II)OH(2)](2+) to produce [(tpy)(bpy)Ru(III)OH](2+); and (3) the cross reaction of [(tpy)(bpy)Ru(III)OH](2+) and [(bpy)(2)(py)Ru(II)OH(2)](2+) to produce [(tpy)(bpy)Ru(II)OH(2)](2+) and [(bpy)(2)(py)Ru(III)OH](2+). This investigation is motivated by experimental measurements of rates and kinetic isotope effects for these systems (Binstead, R. A.; Meyer, T. J. J. Am. Chem. Soc. 1987, 109, 3287. Farrer, B. T.; Thorp, H. H. Inorg. Chem. 1999, 38, 2497.). These experiments indicate that the second reaction is nearly one order of magnitude faster than the first reaction, and the third reaction is in the intermediate regime. The experimentally measured kinetic isotope effects for these three reactions are 16.1, 11.4, and 5.8, respectively. The theoretical calculations elucidate the physical basis for the experimentally observed trends in rates and kinetic isotope effects, as well as for the unusually high magnitude of the kinetic isotope effects. In this empirical model, the proton donor-acceptor distance is predicted to be largest for the first reaction and smallest for the third reaction. This prediction is consistent with the degree of steric crowding near the oxygen proton acceptor for the three reactions. The second reaction is faster than the first reaction since a smaller proton donor-acceptor distance leads to a larger overlap between the reactant and product proton vibrational wave functions. The intermediate rate of the third reaction is determined by a balance among several competing factors. The observed trend in the kinetic isotope effects arises from the higher ratio of the hydrogen to deuterium vibrational wave function overlap for larger proton donor-acceptor distances. Thus, the kinetic isotope effect increases for larger proton donor-acceptor distances. The unusually high magnitude of the kinetic isotope effects is due in part to the close proximity of the proton transfer interface to the electron donor and acceptor. This proximity results in strong electrostatic interactions that lead to a relatively small overlap between the reactant and product vibrational wave functions.

Comparison of hydride, hydrogen atom, and proton-coupled electron transfer reactions

A comparison of hydride, hydrogen atom, and proton-coupled electron transfer reactions is presented. Herein, hydride and hydrogen atom transfer refer to reactions in which the electrons and protons transfer between the same donor and acceptor, while proton-coupled electron transfer (PCET) refers to reactions in which the electrons and protons transfer between different centers. Within these definitions, hydride and hydrogen atom transfer reactions are typically electronically adiabatic, hence evolving on a single electronic surface. In contrast, PCET reactions are often electronically nonadiabatic since the electron transfers a longer distance through a proton transfer interface. For all three types of reactions, solute reorganization is important, particularly the hydrogen donor--acceptor mode. Solvent reorganization is critical for hydride transfer and PCET, which involve significant solute charge redistribution, but not for hydrogen atom transfer. Theoretical descriptions and simulation methodology for all three types of reactions are presented, as well as experimentally relevant applications to hydride transfer in enzymes and PCET in solution.