Fact-checked by Grok 2 weeks ago

Proton-coupled electron transfer

Proton-coupled electron transfer (PCET) is a fundamental redox process in which the transfer of an electron from a donor to an acceptor is coupled with the concomitant transfer of a proton, which may occur concertedly in a single kinetic step or sequentially through intermediates.^[1] This coupling can involve transfers between the same or different sites and in the same or opposite directions, enabling efficient charge separation and neutralization to avoid high-energy charged intermediates.^[2] PCET underpins energy conversion and storage in both natural biological systems and artificial devices, such as photosynthesis, respiration, and electrocatalytic fuel production.^[3] In biological contexts, PCET facilitates critical reactions like water oxidation in photosystem II, where tyrosine residues undergo oxidation via proton-coupled mechanisms involving hydrogen bonding and proton tunneling to generate oxygen-evolving radicals.^[3] Similarly, enzymes such as soybean lipoxygenase and ribonucleotide reductase employ PCET for C-H bond activation and long-range radical propagation, respectively, with kinetic isotope effects highlighting the role of proton tunneling in enhancing reaction efficiency at low barriers.^[3] These processes often proceed through concerted pathways, such as hydrogen atom transfer (HAT), where the electron and proton move in the same direction adiabatically, or multiple-site electron-proton transfer (MS-EPT), allowing asynchronous motion over extended distances.^[1] Mechanistically, PCET can be distinguished from pure electron transfer (ET) or proton transfer (PT) by thermodynamic driving forces, with concerted PCET favored when sequential pathways involve unstable intermediates, as mapped in PCET-zone diagrams based on free energy changes (ΔG°_PT and ΔG°_ET).^[4] Theoretical frameworks describe these reactions via nonadiabatic transitions between electron-proton vibronic states, influenced by solvent reorganization, hydrogen bond networks, and quantum effects like tunneling.^[5] In artificial systems, PCET enables overpotential reduction in electrocatalysis, such as CO2 reduction to methanol using cobalt phthalocyanine catalysts or water splitting with ruthenium-porphyrin complexes, mimicking biological efficiency for sustainable energy technologies.^[4]

Fundamentals

Definition and basic concepts

Proton-coupled electron transfer (PCET) refers to chemical reactions in which the transfer of an electron and a proton are coupled, occurring either simultaneously in a single elementary step or in linked sequential steps, often facilitating redox processes across interfaces or in biological systems.^[1] This coupling influences both the thermodynamics and kinetics of the reaction, enabling the accumulation of multiple charges or the modulation of pH-dependent redox potentials.^[6] Electrons and protons, both fundamental charged particles, exhibit distinct transfer behaviors: electron transfer typically involves quantum mechanical tunneling over distances of several angstroms, while proton transfer is governed by classical over-barrier motion, often facilitated by hydrogen-bonded networks. The coupling in PCET mitigates high energy barriers associated with charge separation or solvation penalties that would hinder uncoupled transfers, thereby promoting efficient reaction pathways in energy conversion.^[6] Central terminology distinguishes PCET as the overarching process, encompassing subtypes such as hydrogen atom transfer (HAT), in which the electron and proton originate from the same donor atom (e.g., an X–H bond) and transfer to the same acceptor site, resulting in net movement of a hydrogen atom; and electron-proton transfer (EPT) or concerted proton-electron transfer (CPET), where the proton and electron transfer from/to different sites or orbitals without forming a stable intermediate.^[1] The foundational concepts of PCET emerged in the early 1980s, initially coined by Moyer and Meyer in 1981 to describe concerted transfers in ruthenium complex reactions, with pivotal advancements by James Mayer through thermochemical analyses that extended Marcus theory to coupled electron-proton dynamics.^[7]^[8] A generic representation of PCET illustrates the coupling of an electron transfer step,

\ce{A + B -> A^+ + B^-}

with a proton transfer step,

\ce{AH + B -> A + BH^+},

which can yield a net hydrogen atom transfer in certain cases:

\ce{AH + B -> A + BH}.

Thermodynamic principles

Proton-coupled electron transfer (PCET) is governed by a thermodynamic framework that integrates the driving forces for both electron transfer (ET) and proton transfer (PT), primarily through redox potentials (E°) for electrons and pKa values for protons. The overall standard free energy change (ΔG°) for PCET determines its feasibility, combining the electrochemical potential difference for ET and the proton affinity difference for PT. This coupling allows PCET to achieve charge balance in a single step, often making it more thermodynamically favorable than decoupled processes, especially in systems where charge separation would otherwise incur high energetic penalties.^[4] The key equation for the standard free energy of PCET, derived from adaptations of the Nernst equation for ET and the Henderson-Hasselbalch equation for PT, is:

\Delta G^\circ_\text{PCET} = -nF(E^\circ_\text{acceptor} - E^\circ_\text{donor}) + RT \ln\left(10^{{\rm p}K_\text{a,donor} - {\rm p}K_\text{a,acceptor}}\right)

Here, n is the number of electrons transferred (typically 1), F is the Faraday constant, R is the gas constant, and T is the temperature in Kelvin; the logarithmic term equates to 2.303 RT (pKa_donor - pKa_acceptor) at standard conditions. For a favorable PCET (ΔG° < 0), the ET term dominates if the acceptor has a higher reduction potential, while the PT term favors transfer from a stronger acid (lower pKa_donor) to a stronger base (higher pKa_acceptor). This equation highlights how pH modulates effective potentials via proton concentrations, with acidic conditions (low pH) enhancing proton donation and basic conditions aiding acceptance.^[4]^[6] Driving forces in PCET arise from electrostatic coupling between the electron and proton, which neutralizes charges and reduces unfavorable interactions, particularly in low-dielectric environments. Solvent effects, such as hydrogen bonding in aqueous media, stabilize charged intermediates and lower effective ΔG° by screening electrostatics, while pH influences the proton availability and shifts the proton-coupled redox potentials (e.g., via Pourbaix diagrams). These factors collectively make PCET exergonic under physiological or catalytic conditions where pure ET or PT would be endergonic.^[4]^[9] Proton involvement modifies the reorganization energy (λ), the energy required to restructure the donor-acceptor system and solvent upon transfer, compared to pure ET. In ET alone, λ primarily involves outer-sphere solvent reorganization (~0.5–1 eV in water), but PCET adds significant inner-sphere contributions from proton motion along hydrogen-bonded networks, often increasing λ to 1–2 eV. However, concerted PCET can effectively lower the activation barrier relative to stepwise mechanisms by optimizing the transition state through charge compensation, avoiding high-energy charged intermediates. In aqueous media, this results in barrier reductions of 10–100 kJ/mol compared to decoupled ET or PT.^[6]^[4]^[9]

Mechanisms

Stepwise PCET

In stepwise proton-coupled electron transfer (PCET), the electron and proton transfers occur sequentially rather than simultaneously, allowing for the formation of transient intermediates. This mechanism encompasses two primary variants: electron transfer followed by proton transfer (EPT) or proton transfer followed by electron transfer (PET).^[6] In EPT, an initial electron transfer generates a radical intermediate, which then undergoes proton transfer to yield the final product, while PET involves deprotonation or protonation first, creating a charged species that subsequently transfers an electron.^[6] These sequential processes are distinguished from concerted PCET by the temporal separation of the transfers, often observable through kinetic isotope effects or pH-dependent rate profiles.^[10] The kinetics of stepwise PCET are described using Marcus theory applied to each individual step, treating electron and proton transfers as distinct events. The rate constant for each step follows the form

k = Z \exp\left(-\frac{\Delta G^\ddagger}{RT}\right),

where Z is the pre-exponential factor, \Delta G^\ddagger is the activation free energy, R is the gas constant, and T is the temperature; \Delta G^\ddagger incorporates contributions from inner-sphere reorganization (bond length changes) and outer-sphere reorganization (solvent polarization).^[6] The overall rate is often limited by the slower, rate-determining step, with the electron transfer typically following non-adiabatic pathways when electronic coupling between donor and acceptor is weak.^[11] Proton transfer rates in the second step can be enhanced by hydrogen-bonded networks, but the process requires careful alignment of driving forces to avoid kinetic bottlenecks.^[6] Stepwise PCET offers the advantage of enabling charge separation in the intermediate, which can facilitate long-range transfers in certain environments, but it carries the disadvantage of forming high-energy charged intermediates that raise activation barriers and reduce overall efficiency.^[6] This mechanism predominates in non-adiabatic regimes where direct overlap between electron and proton pathways is minimal, contrasting with concerted PCET that avoids such intermediates for lower barriers.^[10] A representative example is EPT in acid-base catalyzed reductions, such as the reduction of quinones or metal complexes, where protonation of the reduced species follows initial electron uptake. In these systems, base catalysis can accelerate the proton transfer step, yielding rate enhancements of up to $10^6 compared to uncoupled electron transfer alone.^[6] Key influencing factors include distance dependence for electron transfer, governed by tunneling probability \kappa = \exp(-\beta r) with \beta \approx 1.4 \, \AA^{-1} in aqueous or protein environments, which decays rates exponentially over distances beyond 10 Å.^[6] Proton transfer in stepwise processes is facilitated by the Grotthuss mechanism, involving sequential hydrogen bond rearrangements in water or solvent networks, enabling rapid diffusion over longer distances without direct donor-acceptor contact.^[6]

Concerted PCET

Concerted proton-coupled electron transfer (PCET), also known as concerted EPT or HAT, involves the synchronous transfer of a proton and an electron in a single kinetic step, thereby avoiding the formation of high-energy charged intermediates that characterize stepwise pathways.^[12] This mechanism is particularly relevant in systems where the proton and electron transfers are tightly coupled, such as in certain redox reactions involving hydrogen bonds or direct atom transfers. The theoretical foundation of concerted PCET relies on adiabatic coupling facilitated by vibronic interactions between the electronic and nuclear degrees of freedom. In this framework, the proton vibrational modes play a crucial role in promoting electron transfer by modulating the potential energy surface, allowing the system to evolve along a reaction coordinate that combines both transfers without crossing to diabatic states.^[12] The Cukier-Savéant model provides a semiclassical description of the kinetics, incorporating electronic (V_el) and protonic (V_prot) couplings as key parameters. The rate constant is expressed as:

k_{\text{PCET}} = \frac{2\pi}{\hbar} \frac{|V_{\text{el}}|^2 |V_{\text{prot}}|^2}{\sqrt{2\pi k_B T \lambda}} \exp\left(-\frac{\Delta G^\ddagger}{RT}\right)

where \lambda is the reorganization energy and \Delta G^\ddagger is the activation free energy. Experimental and computational evidence supports the occurrence of concerted PCET through distinct signatures. Spectroscopic studies reveal broadened infrared (IR) bands, particularly in the N-H or O-H stretching regions, indicative of dynamic proton motion coupled to electron transfer during the reaction.^[13] Density functional theory (DFT) computations further demonstrate transition states with delocalized partial electron and proton character, confirming the synchronous nature of the transfer rather than sequential steps.^[12] Concerted PCET becomes the dominant mechanism when the difference between the pK_a change and the standard potential shift is small, specifically |ΔpK_a - ΔE°| < 0.2 V, which minimizes energy barriers and reduces overpotentials in electrocatalytic processes. This condition highlights the mechanism's efficiency in systems requiring low-energy pathways for coupled transfers.

The square scheme model

The square scheme model provides a kinetic framework for understanding proton-coupled electron transfer (PCET) as a four-state system involving coupled redox and protonation equilibria.^[6] In this model, the states are represented in a square diagram: the neutral state (A/B), the electron-transfer (ET) intermediate (A⁺/B), the proton-transfer (PT) intermediate (AH/B⁻), and the dually coupled state (AH⁺/B).^[6] Vertical arrows denote ET processes, horizontal arrows denote PT processes, and the diagonal represents the concerted PCET pathway.^[4] This diagrammatic approach, developed by Cukier in 1994, captures the competition between sequential and concerted mechanisms in coupled redox-protonation cycles.^[14] The model outlines four primary kinetic pathways: ET followed by PT, PT followed by ET, concerted PCET, and reverse processes.^[6] Branching ratios between these routes depend on the relative magnitudes of the rate constants for ET (k_{ET}) and PT (k_{PT}), which are influenced by thermodynamic driving forces and reorganization energies.^[14] For instance, if k_{ET} >> k_{PT}, the system favors the ET-PT sequence, whereas comparable rates may promote the concerted pathway to avoid high-energy intermediates.^[6] This framework explains observed pH-dependent voltammetry peaks in model complexes, where shifts in peak potentials arise from varying protonation states.^[14] To derive effective PCET rates, the model employs a steady-state approximation for the populations of short-lived intermediates. For the ET-PT pathway, the concentration of the oxidized intermediate is given by

[A^+ B] = \frac{k_1 [A B]}{k_{-1} + k_2},

where k_1 is the forward ET rate, k_{-1} is the reverse ET rate, and k_2 is the subsequent PT rate from the intermediate.^[6] The overall PCET rate then emerges as k_{PCET} = k_1 k_2 / (k_{-1} + k_2), highlighting how intermediate stability dictates the effective kinetics.^[14] Similar expressions apply to the PT-ET pathway by symmetry. The model assumes an isotropic medium where solvent reorganization energies are equivalent for parallel pathways, simplifying the Marcus-like rate expressions.^[6] Validation often involves kinetic isotope effects, with k_H / k_D ratios of approximately 2-5 indicating proton involvement in the rate-limiting step.^[14] These features make the square scheme a foundational tool for analyzing PCET in both solution and interfacial environments.^[6]

Examples

Synthetic and model systems

Synthetic and model systems for proton-coupled electron transfer (PCET) have been developed to probe the fundamental mechanisms in controlled environments, distinct from complex biological matrices. Ruthenium polypyridyl complexes, such as those based on [Ru(bpy)₃]²⁺ scaffolds (bpy = 2,2'-bipyridine), serve as versatile probes due to their tunable redox potentials and ability to incorporate protonatable sites like aqua or pendant groups. Similarly, quinone-hydroquinone pairs provide simple organic models for studying PCET, mimicking redox-active cofactors with well-defined two-electron/two-proton transfers. These systems allow isolation of stepwise versus concerted pathways through variation of pH, solvent, and structural features.^[6]^[15] Experimental investigations of PCET in these models often employ electrochemical and spectroscopic techniques to characterize kinetics and intermediates. Cyclic voltammetry reveals pH-dependent redox potentials, where a Nernstian shift of approximately 60 mV per pH unit indicates coupled proton transfer accompanying the electron transfer, as observed in Ru polypyridyl systems. Transient absorption spectroscopy detects short-lived intermediates, such as radical species from concerted PCET, enabling rate measurements on picosecond to microsecond timescales. These methods, combined with isotope labeling, distinguish PCET from pure electron or proton transfer.^[6] A seminal example is the PCET reaction between [Ru(bpy)₂(py)OH₂]²⁺ and [Ru(bpy)₂(py)O]²⁺ (py = pyridine), where the aqua ligand acts as a pendant proton source. This system demonstrates electron-proton transfer (EPT) with a solvent kinetic isotope effect (k_{H₂O}/k_{D₂O}) of 16.1, confirming proton involvement, and exhibits pH-dependent voltammetric shifts near 60 mV/pH, reflecting thermodynamic coupling. Observed in the late 1980s by the Meyer group, this represents one of the earliest synthetic demonstrations of PCET in coordination complexes.^[16] Design principles in these models emphasize control over electron-proton distances and environmental factors to favor concerted PCET. Spacer lengths between the redox center and proton site, typically 1-10 Å via alkyl or peptide linkers in Ru-tyrosine complexes, modulate tunneling probabilities and rates, with shorter distances enhancing concerted pathways. Solvent effects, such as deuterium oxide substitution, yield kinetic isotope effects up to 4, indicating proton motion in the rate-limiting step. In optimized systems, concerted PCET rates reach ~10⁸ s⁻¹, as measured in Ru-linked tyrosine models using flash-quench techniques. These synthetic designs highlight how structural tuning influences PCET efficiency, providing insights applicable to mechanistic studies.^[17]

Biological systems

Proton-coupled electron transfer (PCET) plays a crucial role in biological systems by facilitating efficient charge separation in enzymes and proteins, preventing dissipative buildup of charges that could otherwise lead to energy loss or structural damage. This process is essential for maintaining redox balance in cellular environments, where PCET coordinates electron and proton movements to support vital metabolic functions without generating high-energy intermediates that might react indiscriminately. In natural systems, PCET is finely tuned by evolutionary pressures to operate under physiological conditions, enabling processes like energy conversion and biosynthesis with high fidelity.^[3] A prominent example of PCET in biology occurs in Photosystem II (PSII) during water oxidation, where the oxygen-evolving complex (OEC) undergoes a cycle involving concerted PCET steps to generate oxygen from water. In this process, tyrosine residues (such as TyrZ) act as intermediaries, undergoing PCET to transfer electrons to the oxidized P680 chlorophyll while protons are relayed through hydrogen-bonded networks, ensuring minimal charge separation.^[3] Similarly, in cytochrome c oxidase (CcO), PCET is integral to proton pumping mechanisms that couple electron transfer from cytochrome c to oxygen reduction, translocating protons across the membrane to drive ATP synthesis; here, concerted PCET at the binuclear center involving His-Tyr motifs facilitates vectorial proton transfer without net charge accumulation.^[18] These examples highlight how PCET enables multi-electron, multi-proton reactions critical for respiration and photosynthesis. Structural features in biological PCET systems often involve intricate hydrogen-bonded networks, such as chains of histidine (His), tyrosine (Tyr), and asparagine (Asn) residues, which provide pathways for proton transfer coupled to electron movement. Active site geometries are precisely arranged, with electron and proton transfer paths typically separated by less than 5 Å to promote concerted mechanisms and reduce reorganization energies. These networks, embedded in protein scaffolds, allow for directional charge flow and electrostatic gating, as seen in the OEC of PSII where water molecules and amino acid side chains form a proton wire.^[3] Experimental evidence for PCET in these systems comes from mutagenesis studies, which demonstrate dramatic rate reductions upon disruption of key residues; for instance, mutating the redox-active tyrosine in PSII leads to a 10^4-fold decrease in electron transfer rates, underscoring the necessity of PCET for efficient catalysis.^[3] Techniques like electron paramagnetic resonance (EPR) and Fourier-transform infrared (FTIR) spectroscopy have identified radical intermediates, such as tyrosyl radicals, confirming the formation of protonated or deprotonated states during PCET events in enzymes like ribonucleotide reductase (RNR). In RNR, PCET propagates a radical over distances exceeding 40 Å through a chain of amino acid radicals, enabling deoxyribonucleotide synthesis essential for DNA replication; this long-range mechanism is believed to have evolved around 3.5 billion years ago, reflecting its ancient origins in early life forms.^[3]^[19]

Applications and Significance

In bioenergetics

Proton-coupled electron transfer (PCET) plays a central role in bioenergetics by linking redox reactions to the establishment of proton gradients across biological membranes, which drive ATP synthesis according to the chemiosmotic theory. In this framework, PCET enables the vectorial transport of protons, converting the energy from electron flow into a transmembrane electrochemical potential that powers oxidative phosphorylation. This coupling is essential for efficient energy transduction in cellular respiration and photosynthesis, where PCET reactions ensure that electron transfer is synchronized with proton movement to maximize energy conservation.^[18]^[20] In photosynthesis, PCET is critical within the reaction centers of photosystems I and II, where light-induced charge separation initiates electron transfer from the primary donor P680⁺ to pheophytin (Pheo⁻), followed by reduction of quinones with concomitant proton uptake. This process achieves charge separation efficiencies exceeding 90%, allowing nearly complete conversion of absorbed photons into stable charge-separated states that fuel subsequent proton translocation and ATP/NADPH production. These PCET steps not only prevent wasteful charge recombination but also contribute to the proton gradient formation across the thylakoid membrane.^[21]^[22]^[23] In cellular respiration, PCET facilitates proton pumping along the mitochondrial electron transport chain, particularly at Complexes I and IV, and in the Q-cycle mechanism of Complex III during ubiquinol oxidation and oxygen reduction. At Complex I, PCET couples NADH oxidation to ubiquinone reduction, driving the translocation of approximately 4 protons per 2 electrons (or ~2 H⁺ per e⁻), while Complex IV's PCET reactions during O₂ reduction to water translocate ~1 H⁺ per e⁻ in addition to scalar protons consumed. Overall, these processes yield approximately 5 H⁺ translocated per electron (10 H⁺ per 2 electrons from NADH) across the chain, enabling vectorial proton transport that sustains the mitochondrial membrane potential; this mechanism is evolutionarily conserved across bacterial, archaeal, and eukaryotic domains. Disruptions in PCET, such as those in Complex I subunits, are implicated in mitochondrial diseases like Leigh syndrome, where impaired proton pumping leads to energy deficits; such pathologies are often analyzed using flux balance analysis to model metabolic fluxes and identify therapeutic targets.^[24]^[25]^[26]^[27]^[28]^[29]

In artificial systems and catalysis

Proton-coupled electron transfer (PCET) plays a pivotal role in artificial photosynthesis, particularly in dye-sensitized solar cells (DSSCs) designed for water splitting. In these systems, ruthenium-based sensitizers adsorbed on TiO₂ electrodes facilitate photoinduced electron injection into the semiconductor, followed by PCET processes that enable water oxidation at co-catalysts such as ruthenium complexes or IrO₂ clusters. For instance, malonate-linked Ru polypyridyl dyes coupled to IrO₂ on porous TiO₂ achieve efficient proton and electron transfer, yielding solar-to-hydrogen efficiencies approaching 2% under AM 1.5G illumination, with incident photon-to-current efficiencies (IPCE) up to 80% in the visible range. These configurations mimic natural photosystems by integrating PCET to regenerate the sensitizer and drive four-electron water oxidation, though overall device efficiencies remain below 10% due to recombination losses.^[30]^[31] In electrocatalysis, PCET enhances the efficiency of CO₂ reduction to fuels by facilitating concerted proton-electron transfers that lower activation barriers and improve selectivity. Nickel cyclam complexes, often modified with pendant amines, exemplify this approach, where the pendant groups act as proton relays to stabilize intermediates and promote CO production from CO₂ with overpotentials around 0.6 V in aqueous media. These catalysts achieve faradaic efficiencies exceeding 90% for CO at modest potentials, outperforming unmodified analogs by reducing the energy penalty for C-O bond cleavage through PCET-mediated pathways. Such designs draw brief inspiration from enzymatic motifs but focus on scalable synthetic applications for carbon capture and utilization.^[32]^[33]^[34] Effective design strategies for PCET in artificial systems incorporate proton relays to control the timing and site of protonation relative to electron transfer. Molecular dyads, such as porphyrin-quinone assemblies, enable photoinduced PCET where the quinone acceptor couples electron uptake with protonation via hydrogen-bonded networks, mimicking charge separation in photosynthesis and achieving charge-separated state lifetimes on the order of microseconds. Heterogeneous catalysts like metal-organic frameworks (MOFs) extend this to solid-state platforms; for example, Zr-based MOFs support bulk-to-surface PCET for redox reactions, allowing reversible proton-coupled oxidation of phenols with minimal structural degradation. These strategies emphasize tunable proton pathways to optimize thermodynamics and kinetics in both homogeneous and immobilized environments.^[35]^[36]^[37] Despite progress, challenges in PCET-based catalysts include limited long-term stability under operational conditions, arising from catalyst degradation and side reactions like hydrogen evolution competing with target transformations. Recent advances in the 2020s have addressed these through stabilized homogeneous catalysts, such as modified cobalt porphyrins, achieving high turnover frequencies (TOFs) on the order of 1 s⁻¹ for CO₂ reduction while maintaining selectivity over hours of electrolysis. A landmark contribution from the Savéant group in the 2010s demonstrated concerted PCET mechanisms for hydrogen evolution from acids, inspired by photosystem II tyrosine oxidation, enabling low-overpotential HER with cobaloxime catalysts and turnover numbers over 10⁴. Recent 2025 advances include Zr-cage platforms enhancing PCET for photocatalytic reductions with higher quantum yields.^[38]^[39]^[40]^[41] These developments underscore PCET's potential for practical energy conversion, though scaling to industrial levels requires further enhancements in durability and cost-effectiveness.

Pure electron transfer

Pure electron transfer (ET) involves the movement of an electron between redox-active species without any net proton transfer, distinguishing it from proton-coupled processes. According to Marcus theory, ET can proceed via outer-sphere or inner-sphere mechanisms. In outer-sphere ET, the electron tunnels between intact coordination spheres of the donor and acceptor without bond breaking or forming, often mediated by solvent or vacuum.^[42] Inner-sphere ET, as conceptualized by Taube, requires a bridging ligand to facilitate electron transfer, involving temporary coordination changes but no net proton motion.^[42] These mechanisms apply to both homogeneous and heterogeneous ET, with rates governed by quantum mechanical tunneling and classical reorganization. The kinetics of pure ET are described by the Marcus equation for nonadiabatic transfer:

k_\text{ET} = \frac{2\pi}{\hbar} |V|^2 \sqrt{\frac{1}{4\pi \lambda k_B T}} \exp\left( -\frac{(\lambda + \Delta G^\circ)^2}{4\lambda k_B T} \right)

where |V| is the electronic coupling, \lambda is the reorganization energy, \Delta G^\circ is the standard free energy change, k_B is Boltzmann's constant, T is temperature, and \hbar is the reduced Planck's constant.^[43] A key principle is the exponential distance decay of |V|, expressed as |V| \propto \exp(-\beta r/2), where r is the donor-acceptor distance and \beta ranges from 0.9 to 1.4 Å⁻¹ in protein environments due to through-bond superexchange. Reorganization energy \lambda typically approximates 1 eV for intraprotein ET, encompassing inner-sphere vibrational and outer-sphere solvent contributions that minimize structural changes post-transfer. Representative examples include self-exchange reactions of low-spin iron complexes, such as [\ce{Fe(bpy)3}]^{2+/3+} (bpy = 2,2'-bipyridine), which proceed via outer-sphere mechanisms with bimolecular rate constants around $3 \times 10^8 M⁻¹ s⁻¹ at 25°C, reflecting modest \lambda (~0.8 eV) and strong orbital overlap.^[44] Rates for such self-exchanges generally span 10⁸ to 10¹² M⁻¹ s⁻¹ for optimized systems with delocalized orbitals, far exceeding diffusion limits in rigid media. The Marcus inverted region, where rates diminish despite more favorable \Delta G^\circ (when |\Delta G^\circ| > \lambda), was experimentally confirmed by Closs and coworkers in the 1980s using photoinduced ET in rigid organic donor-acceptor pairs separated by 10-15 Å; these observations showed no pH dependence, highlighting the absence of proton linkage.^[45]

Pure proton transfer

Pure proton transfer (PT) refers to the movement of a proton (H⁺) between donor and acceptor sites without concomitant electron transfer, often occurring through hydrogen-bonded networks such as water chains. In aqueous environments, this process typically proceeds via the Grotthuss mechanism, where protons undergo structural diffusion by hopping from one water molecule to another or via quasi-concerted transfers over short distances (2-3 molecules) facilitated by proton wires—temporary chains of hydrogen-bonded water molecules. Tunneling can also contribute, particularly at low temperatures or in constrained geometries, allowing protons to permeate energy barriers quantum mechanically.^[46] The kinetics of pure PT are extremely rapid, with rate constants in bulk water ranging from 10⁹ to 10¹² s⁻¹ for hopping events, driven by the high mobility of hydrated protons (H₃O⁺). These rates reflect diffusion-controlled processes, as demonstrated in early relaxation spectrometry studies. The thermodynamics are governed by pKₐ differences between donor and acceptor, with the free energy change given by ΔG = 2.303 RT ΔpKₐ, where favorable transfers (ΔpKₐ < 0) proceed exergonically and dominate equilibrium. Ultrafast PT, on the order of picoseconds or faster, was first quantified by Manfred Eigen in 1964 using temperature-jump methods, revealing rates up to 10¹¹ M⁻¹ s⁻¹ for simple protolytic reactions in water.^[47] Representative examples include acid-base equilibria, such as the deprotonation of ammonium ion (NH₄⁺) to ammonia (NH₃) in aqueous solution: NH₄⁺ + H₂O ⇌ NH₃ + H₃O⁺, a reversible PT with equilibrium favoring the side of the weaker acid/base pair based on pKₐ values (pKₐ(NH₄⁺) ≈ 9.25). In biological contexts, PT occurs in enzymes like carbonic anhydrase II, where a proton is shuttled from the zinc-bound water to bulk solvent via a hydrogen-bonded water network involving His64, achieving transfer rates up to 10⁶ s⁻¹ to support CO₂ hydration catalysis.^[48] Quantum effects, particularly tunneling, enhance PT rates in hydrogen-bonded systems by allowing protons to bypass classical barriers. The tunneling probability can be approximated using the WKB method for a simple barrier as

P = \exp\left( -\frac{2 \sqrt{2m V} \, d}{\hbar} \right),

where m is the proton mass, V is the barrier height, d is the barrier width, and \hbar is the reduced Planck's constant; this form highlights the exponential sensitivity to barrier parameters, with tunneling becoming significant for light protons over thin, low barriers (d ≈ 0.1-0.5 Å).^[49] A notable application is proton conductivity in ice, where ordered hydrogen-bond networks form proton wires enabling hopping relays despite limited molecular diffusion, resulting in anomalously high proton mobility (diffusion coefficient ~10⁻⁵ cm²/s at 0°C) compared to other ions. Eigen's 1964 studies confirmed tunneling contributions in such solid-state systems, underscoring the ultrafast nature of PT even in rigid lattices.

PCET

Proton-coupled electron transfer (PCET) in extended biological systems, such as lipid bilayers and cellular membranes, involves the coordinated symport or antiport of electrons and protons, enabling vectorial transport across the membrane barrier. In respiratory complexes embedded in the inner mitochondrial or bacterial plasma membrane, electron transfer from donors like NADH to acceptors like oxygen or quinone is tightly linked to the translocation of protons from the matrix or cytoplasm to the intermembrane space or periplasm, respectively. This process generates a proton motive force (PMF) that powers ATP synthesis and other cellular functions, distinguishing it from uncoupled electron or proton movements by its obligatory linkage and directionality.^[24]^[20] Key examples include mitochondrial uncoupling protein 1 (UCP1), which facilitates proton re-entry into the mitochondrial matrix, dissipating the PMF produced by upstream PCET in respiratory complexes to generate heat in brown adipose tissue rather than ATP. In bacterial systems, electrogenic transporters such as the NADH:ubiquinone oxidoreductase (Complex I homolog) couple electron inflow from NADH to outward proton pumping, maintaining membrane potential and supporting anaerobic or microaerobic respiration. These transporters ensure efficient energy conservation by minimizing dissipative leaks.^[50]^[24] The mechanism of vectorial PCET relies on conformational changes in the protein complexes that channel electrons through redox cofactors while simultaneously relocating protons via dedicated pathways, driven by the transmembrane electrochemical gradient with a membrane potential (Δψ) of approximately 150 mV. Slip rates, representing decoupled proton or electron movements, are typically below 1%, as evidenced by high coupling efficiencies in isolated complexes under physiological conditions. Quantitative measurements, such as the stoichiometry of 2 H⁺ pumped per 2 e⁻ in Complex IV (cytochrome c oxidase), have been confirmed using patch-clamp techniques on mitoplasts to directly monitor charge fluxes.^[51]^[52]^[53] This phenomenon was first systematically elucidated in the 1970s through Peter Mitchell's chemiosmotic theory, which proposed that electron transport drives proton extrusion to create the PMF, a concept validated by experiments on submitochondrial particles and awarded the 1978 Nobel Prize in Chemistry. In bacteria, the PMF generated by such PCET powers efflux pumps like NorA, contributing to multidrug antibiotic resistance by actively expelling drugs from the cytoplasm.^[54]^[55]

References

[1]
Introduction: Proton-Coupled Electron Transfer | Chemical Reviews
Initially, proton-coupled electron transfer (PCET) was defined as a specific type of reaction in which an electron and proton transfer in a single kinetic step.
[2]
Proton-Coupled Electron Transfer: Moving Together and Charging ...
The electron and proton can be transferred between the same sites or between different sites, and they can be transferred in the same direction or in different ...
[3]
Proton-Coupled Electron Transfer in Biology - NIH
Proton-coupled electron transfer (PCET) underpins energy conversion in biology. PCET may occur with the unidirectional or bidirectional transfer of a proton ...
[4]
Proton-Coupled Electron Transfer Guidelines, Fair and Square
Jan 6, 2021 · Proton-coupled electron transfer (PCET) reactions are fundamental to energy transformation reactions in natural and artificial systems and ...Introduction · Why Are Electron Transfer and... · Theories of Electron and...
[5]
Theory of Proton-Coupled Electron Transfer in Energy Conversion ...
In this theory, PCET reactions are described in terms of nonadiabatic transitions between the reactant and product electron-proton vibronic states.
[6]
Proton-Coupled Electron Transfer | Chemical Reviews
The coupling of electron and proton transfer influences both energetics and mechanism. It allows for the buildup of multiple redox equivalents needed to carry ...
[7]
Proton-Coupled Electron Transfer - PMC - NIH
The term PCET has come to be used more broadly to describe reactions and half reactions in which both electrons and protons are transferred without regard to ...
[8]
https://pubs.acs.org/doi/10.1021/ic00146a001
[9]
Concerted and Stepwise Proton-Coupled Electron Transfer for ...
Apr 13, 2022 · Here, we present PCET rate constants for W derivatives with oxidized Ru- and Zn-porphyrin photosensitizers, extracted from laser flash-quench studies.Introduction · Results and Discussion · Conclusions · Supporting Information
[10]
PROTON-COUPLED ELECTRON TRANSFER: A Reaction ...
Jun 1, 2004 · Proton-coupled electron transfer (PCET) reactions involve the concerted transfer of an electron and a proton. Such reactions play an important role in many ...
[11]
Theory of Coupled Electron and Proton Transfer Reactions
Two types of coupled reactions can be distinguished. In concerted electron and proton transfer reactions, both the ET and PT transitions occur in one step.
[12]
Efficient electron transfer across hydrogen bond interfaces by proton ...
Apr 4, 2019 · For the D–HB–A systems, we are able to measure the ET rate constants by analysis of ν(NH) band broadening in the IR spectra, a method used for ...
[13]
Mechanism for Proton-Coupled Electron-Transfer Reactions
R. I. Cukier. A Theory for the Rate Constant of a Dissociative Proton-Coupled Electron-Transfer Reaction. The Journal of Physical Chemistry A 1999, 103 (30) ...Missing: expression | Show results with:expression
[14]
Quinone/hydroquinone-functionalized biointerfaces for biological ...
Aug 27, 2013 · Quinones / hydroquinones (Q/HQ) are a class of prototypical redox molecules that play a variety of vital roles in biology, particularly in ...<|control11|><|separator|>
[15]
Proton-coupled electron transfer between [Ru(bpy)2(py)OH2]2+ and ...
Proton-coupled electron transfer between [Ru(bpy)2(py)OH2]2+ and [Ru(bpy)2(py)O]2+. A solvent isotope effect (kH2O/kD2O) of 16.1.
[16]
Proton-Coupled Electron Transfer in a Series of Ruthenium-Linked ...
Photoinitiated proton-coupled electron transfer (PCET) kinetics has been investigated in a series of four modified tyrosines linked to a ruthenium ...
[17]
Biochemistry and Theory of Proton-Coupled Electron Transfer
Apr 1, 2014 · Cukier's first description of PCET (187, 386) reactions was based on the breakdown of the Condon approximation for the electronic coupling ...
[18]
Long-range proton-coupled electron transfer in biological energy ...
Apr 11, 2018 · Biological energy conversion is driven by efficient enzymes that capture, store and transfer protons and electrons across large distances.
[19]
Proton-Coupled Electron Transfer in Photosystem II - NIH
Electron transfer is initiated through the photooxidation of a chlorophyll molecule. The electron is transferred to a quinone, QA, which acts as a one electron ...
[20]
Charge separation in Photosystem II: A comparative and ...
This occurs with a quantum yield close to 90% and more than half of the energy of the red photon [6] is conserved in the charge separated state.2. Photosystem Ii... · 4. Charge Separation In... · 9.1. Q Redox Switching
[21]
Mechanism of proton-coupled quinone reduction in Photosystem II
Photosystem II uses light to drive water oxidation and plastoquinone (PQ) reduction. PQ reduction involves two PQ cofactors, QA and QB, working in series.
[22]
Energetics and Dynamics of Proton-Coupled Electron Transfer in the ...
Mar 15, 2019 · Complex I functions as an initial electron acceptor in aerobic respiratory chains that reduces quinone and pumps protons across a biological membrane.
[23]
Proton-coupled electron transfer and the role of water molecules in ...
Feb 2, 2015 · Cytochrome c oxidase in the inner membrane of mitochondria and the plasma membrane of bacteria catalyzes the reduction of oxygen to water, and ...
[24]
Proton-coupled electron transfer at the Qo-site of the bc1 complex ...
A coupled proton and electron transfer occurs along this H-bond. This brief review discusses the information available on the nature of this reaction from ...<|control11|><|separator|>
[25]
A leigh syndrome mutation perturbs long-range energy coupling in ...
We show that the mutation drastically perturbs proton translocation and electron transfer activities to the same extent, despite the remarkable 140 Å distance.
[26]
MitoCore: a curated constraint-based model for simulating human ...
Nov 25, 2017 · Summary of the major active pathways of central metabolism in the flux balance analysis ... proton coupled mitochondrial transport steps or the ΔΨ ...
[27]
Optimizing electron and proton transfer in water splitting dye ...
We have found that ruthenium polypyridyl dye molecules coupled to IrO2 clusters via malonate linkages can sensitize porous TiO2 electrodes, and that the low ...
[28]
Strategies to Enhance the Rate of Proton‐Coupled Electron Transfer ...
Each PCET step is initiated by photoinduced electron transfer from a light-absorbing dye to an anode, usually TiO2. Subsequently, bidirectional PCET takes place ...
[29]
The Mechanism of Homogeneous CO2 Reduction by Ni(cyclam ...
Homogeneous CO2 reduction catalyzed by [NiI(cyclam)]+ (cyclam = 1,4,8,11-tetraazacyclotetradecane) exhibits high efficiency and selectivity yielding CO only ...
[30]
For CO 2 Reduction, Hydrogen-Bond Donors Do the Trick
Mar 12, 2018 · (2) The pendant N–H groups appear to be poised to assist CO2 binding through hydrogen-bonding interactions; this binding motif has been observed ...<|separator|>
[31]
Proton-coupled multi-electron transfer and its relevance for artificial ...
Feb 27, 2019 · Porphyrin–quinone dyads are typical examples, and they resemble in their function the role of the P680/QA couple in bacterial photosynthesis ...
[32]
Proton-coupled electron transfer: the mechanistic underpinning for ...
... square scheme (Mayer 2004). For the case of amino acid ... Cukier R.I. Proton-coupled electron transfer through an asymmetric hydrogen-bonded interface.
[33]
Bulk-to-Surface Proton-Coupled Electron Transfer Reactivity of the ...
Nov 3, 2018 · This reaction occurred by PCET to give the corresponding phenol and the original, oxidized MOF. The high level of charging, and the independence ...
[34]
Concerted Proton-Electron Transfers: Fundamentals and Recent ...
Figure 1 shows how proton transfer and electron transfer may be associated along either stepwise or concerted pathways. In the first case, electron transfer may ...<|separator|>
[35]
Electrocatalytic CO2 reduction by a cobalt porphyrin mini-enzyme
A synthetic mini-enzyme with a cobalt porphyrin active site, is developed as a biomolecular catalyst for electrocatalytic CO 2 reduction in water.
[36]
Concerted Proton−Electron Transfers: Electrochemical and Related ...
Mar 16, 2010 · CPET is reserved for PCET reactions in which electron and proton transfers are concerted. The most perturbing aspect of this lack of ...
[37]
[PDF] Henry Taube - Nobel Lecture
Thus the Franck-Condon barrier to electron transfer arising from inner sphere reorganization is small, and facile transfer by an outer sphere mechanism is ...
[38]
On the Theory of Electron‐Transfer Reactions. VI. Unified Treatment ...
A unified theory of homogeneous and electrochemical electron‐transfer rates is developed using statistical mechanics.
[39]
a case study on electron self-exchange reactions of transition metal ...
Nov 1, 2023 · Rate constants for thirteen electron self-exchange reactions ... [Fe(bpy)3]3+/2+, 2/1, 3 × 108, 8.5, 57 and 58. [Co(bpy)3]3+/2+, 1/4 (1/2) ...
[40]
Intramolecular Long-Distance Electron Transfer in Organic Molecules
Theoretical predictions of an "inverted region," where increasing the driving force of the reaction will decrease its rate, have begun to be experimentally ...
[41]
Proton transfer through the water gossamer - PMC - NIH
The diffusion of protons through water is understood within the framework of the Grotthuss mechanism, which requires that they undergo structural diffusion ...
[42]
[PDF] Manfred Eigen - Nobel Lecture
The method proved even more successful in measuring the rates of protolytic reactions. The kinetics of proton transfer have been studied exhaustively with.
[43]
Solvent-Mediated Proton Transfer in Catalysis by Carbonic Anhydrase
Proton transfer in catalysis by carbonic anhydrase provides a useful model for the study of the properties of such proton translocations.Introduction · Mapping Out Proton Transfer... · Properties of Proton Transfer...
[44]
Nuclear Quantum Effects in Proton or Hydrogen Transfer
One of the fascinating consequences of quantum mechanics is the phenomenon of tunneling: crossing an energy barrier without energy investment.
[45]
Structural mechanisms of mitochondrial uncoupling protein 1 ...
UCP1 dissipates the protonmotive force across the inner mitochondrial membrane, which is activated by free fatty acids and inhibited by purine nucleotides.
[46]
Mammalian Complex I Pumps 4 Protons per 2 Electrons at High and ...
The correct stoichiometry for complex I is 4H + /2e − in mouse and human cells at high and physiological proton motive force.
[47]
Experimental discrimination between proton leak and redox slip ...
There is no measurable contribution from redox-slip reactions in the proton pumps caused by high protonmotive force. Neither is there any contribution from ...
[48]
The mechanism of proton pumping by cytochrome c oxidase - PMC
Cytochrome c oxidase catalyzes the reduction of oxygen to water that is accompanied by pumping of four protons across the mitochondrial or bacterial membrane.
[49]
Patch-clamp technique to study mitochondrial membrane biophysics
Jun 22, 2023 · Patch-clamp technique is a powerful method for studying mitochondrial ion transport in real time and under native conditions.Missing: IV 2e-
[50]
Press release: The 1978 Nobel Prize in Chemistry - NobelPrize.org
In addition, this concept of biological power transmission by protonmotive force (or 'proticity', as Mitchell has recently began to call it in an analogy ...
[51]
Proton-coupled transport mechanism of the efflux pump NorA - Nature
May 27, 2024 · Efflux pump antiporters confer drug resistance to bacteria by coupling proton import with the expulsion of antibiotics from the cytoplasm.