Ligand reorganization and activation energies in nonadiabatic electron transfer reactions

The activation energy and ligand reorganization energy for nonadiabatic electron transfer reactions in chemical and biological systems are investigated in this paper. The free energy surfaces and the activation energy are derived exactly in the general case in which the ligand vibration frequencies are not equal. The activation energy is derived by free energy minimization at the transition state. Our formulation leads to the Marcus-Hush [J. Chem. Phys. 24, 979 (1956); 98, 7170 (1994); 28, 962 (1958)] results in the equal-frequency limit and also generalizes the Marcus-Sumi [J. Chem. Phys. 84, 4894 (1986)] model in the context of studying the solvent dynamic effect on electron transfer reactions. It is found that when the ligand vibration frequencies are different, the activation energy derived from the Marcus-Hush formula deviates by 5%-10% from the exact value. If the reduced reorganization energy approximation is introduced in the Marcus-Hush formula, the result is almost exact.     

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.     

Calculation of vibronic couplings for phenoxyl/phenol and benzyl/toluene self-exchange reactions: implications for proton-coupled electron transfer mechanisms

The vibronic couplings for the phenoxyl/phenol and the benzyl/toluene self-exchange reactions are calculated with a semiclassical approach, in which all electrons and the transferring hydrogen nucleus are treated quantum mechanically. In this formulation, the vibronic coupling is the Hamiltonian matrix element between the reactant and product mixed electronic-proton vibrational wavefunctions. The magnitude of the vibronic coupling and its dependence on the proton donor-acceptor distance can significantly impact the rates and kinetic isotope effects, as well as the temperature dependences, of proton-coupled electron transfer reactions. Both of these self-exchange reactions are vibronically nonadiabatic with respect to a solvent environment at room temperature, but the proton tunneling is electronically nonadiabatic for the phenoxyl/phenol reaction and electronically adiabatic for the benzyl/toluene reaction. For the phenoxyl/phenol system, the electrons are unable to rearrange fast enough to follow the proton motion on the electronically adiabatic ground state, and the excited electronic state is involved in the reaction. For the benzyl/toluene system, the electrons can respond virtually instantaneously to the proton motion, and the proton moves on the electronically adiabatic ground state. For both systems, the vibronic coupling decreases exponentially with the proton donor-acceptor distance for the range of distances studied. When the transferring hydrogen is replaced with deuterium, the magnitude of the vibronic coupling decreases and the exponential decay with distance becomes faster. Previous studies designated the phenoxyl/phenol reaction as proton-coupled electron transfer and the benzyl/toluene reaction as hydrogen atom transfer. In addition to providing insights into the fundamental physical differences between these two types of reactions, the present analysis provides a new diagnostic for differentiating between the conventionally defined hydrogen atom transfer and proton-coupled electron transfer reactions.     

Observation of proton-coupled electron transfer by transient absorption spectroscopy in a hydrogen-bonded, porphyrin donor-acceptor assembly

Proton-coupled electron transfer (PCET) kinetics of a Zn(II) porphyrin donor noncovalently bound to a naphthalene-diimide acceptor through an amidinium-carboxylate interface have been investigated by time-resolved spectroscopy. The S1 singlet excited-state of a Zn(II) 2-amidinium-5,10,15,20-tetramesitylporphyrin chloride (ZnP-beta-AmH+) donor is sufficiently energetic (2.04 eV) to reduce a carboxylate-diimide acceptor (DeltaG degrees = -460 mV, THF). Static quenching of the porphyrin fluorescence is observed and time-resolved measurements reveal more than a 3-fold reduction in the S1 lifetime of the porphyrin upon amidinium-carboxylate formation (THF, 298 K). Picosecond transient absorption spectra of the free ZnP-beta-AmH+ in THF reveal the existence of an excited-state isosbestic point between the S1 and T1 states at lambdaprobe = 650 nm, providing an effective 'zero-kinetics' background on which to observe the formation of PCET photoproducts. Distinct rise and decay kinetics are attributed to the build-up and subsequent loss of intermediates resulting from a forward and reverse PCET reaction, respectively (kPCET(fwd) = 9 x 108 s-1 and kPCET(rev) = 14 x 108 s-1). The forward rate constant is nearly 2 orders of magnitude slower than that measured for covalently linked Zn(II) porphyrin-acceptor dyads of comparable driving force and D-A distance, establishing the importance of a proximal proton network in controlling charge transport.     

Spectroscopic determination of proton position in the proton-coupled electron transfer pathways of donor-acceptor supramolecule assemblies

A homologous set of porphyrin derivatives possessing an isocyclic five-membered ring appended with an amidinium functionality has been used to examine proton-coupled electron transfer (PCET) through well-characterized amidine-carboxylic acid interfaces. Conjugation between the porphyrin chromophore and the amidinium interface can be altered by selective reduction of the isocyclic ring of an amidinium-purpurin to produce an amidinium-chlorin. The highly conjugated amidinium-purpurin displays large spectral shifts in the visible region upon alteration of the amidinium/amidine protonation state; no such change is observed for the chlorin homologue. Analysis of the UV-vis absorption and emission profiles of the amidinium-purpurin upon deprotonation allows for the measurement of the porphyrinic-amidinium acidity constant for the ground state (pKa = 9.55 +/- 0.1 in CH3CN) and excited state (pKa)= 10.40 +/- 0.1 in CH3CN). The absorption spectrum of the purpurin also provides a convenient handle for determining the protonation state of assembled interfaces. In this way, the purpurin macrocycle provides a general tool for PCET studies because it can be used to determine the location of a proton within PCET interfaces formed from carboxylic acid electron acceptors including dinitrobenzenes (DNBs) and naphthalenediimide (NI), which have been used extensively in previous PCET studies. An amidine-carboxylic acid interface is observed for electron-rich acceptors, whereas the ionized amidinium-carboxylate interface is observed for electron-poor acceptors. The PCET kinetics for purpurin/chlorin associated to NI are consistent with an amidine-carboxylic acid interface, which is also verified spectrally.     

Voltammetric applications of hydrogen bonding and proton-coupled electron transfer reactions of organic molecules

Proton-coupled electron transfer and hydrogen bonding reactions are ubiquitous requisites for the occurrence of many natural processes and man-made applications. These reactions either involve the direct transfer of charge (in the form of protons and electrons) or contain sufficient electrostatic characteristics to be affected by the application of a potential. Hence, they can be analyzed or initiated by voltammetry, which is itself highly sensitive yet tolerant to a variety of interferences and so can be used under various experimental conditions. The purpose of this review is to highlight the potential of this electrochemical technique for studying important processes such as those involved in energy storage, CO₂ reduction, and sensor applications.     

Solvent reorganization in electron and ion transfer reactions near a smooth electrified surface: a molecular dynamics study

Molecular dynamics simulations of electron and ion transfer reactions near a smooth surface are presented, analyzing the effect of the geometrical constraint of the surface and the interfacial electric field on the relevant solvation properties of both a monovalent negative ion and a neutral atom. The simulations show that, from the solvation point of view, ion adsorption is an uphill process due to the need to shed off the ion's solvation shell and displace water from the surface. Atom adsorption, on the other hand, has only a small barrier, related to the molecularity of the solvent. Both the electrostatic interaction of the ion with the solvent and the ion's solvent reorganization energy (the relevant parameter in the Marcus electron transfer theory) decrease as the surface is approached, whereas these parameters are not sensitive to the distance from the surface for the atom. This is a consequence of the importance of long-range electrostatic interactions for ion solvation and the importance of short-range interactions for atom solvation. The electric field either attracts or repels an ion to or from the surface, but the field has no influence on the solvent reorganization energy. By including the quantum-mechanical electron transfer between the metal surface and the ion/atom in solution in the MD simulation by using a model Hamiltonian, we calculated two-dimensional free energy surfaces for ion adsorption allowing for partial charge transfer, based on a fully molecular picture of ion solvation near the surface.     

Photoinduced intramolecular electron transfer reactions within donor-acceptor linked compounds in solution and within donor-acceptor ion-pairs in crystal

Intramolecular electron transfer (ET) processes within donor-acceptor linked compounds in solution and donor-acceptor ion-pairs in crystal have been investigated by means of laser photolysis kinetic spectroscopy. An excited Ru(II)-moiety of donor-acceptor compounds undergoes intramolecular electron-transfer to either ruthenium(III) ion, rhodium(III) ion or a cobalt(III) ion, followed by back ET to regenerate the original reactant. An Arrhenius plot of the ET rate gave a straight line with an intercept (frequency factor) and a slope (activation energy) for the photoinduced ET and the back ET. Mixed-valence isomer states produced via photoinitiated ET rapidly decayed via back ET. A common and large frequency factor observed for Ru(II)-Rh(III) compounds is accounted for in terms of solvent-relaxation dynamics. For the back ET in the Ru(II)-Co(III) compounds, the frequency factors are reduced because of negative entropy change. ET within donor-acceptor ion-pair of Ru(bpy)₂³ and Co(CN)₃⁶ in crystal took place very rapidly compared with in water.     

Effect of pressure on proton-coupled electron transfer reactions of seven-coordinate iron complexes in aqueous solutions

For the first time, the effect of pressure on proton-coupled electron-transfer reactions of two selected seven-coordinate FeIII/II(H2L)(H2O)2 systems [where H2L = 2,6-diacetylpyridine-bis(semicarbazone) and 2,6-diacetylpyridine-bis(semioxamazide), respectively] was examined. The acid-base equilibria of the different Fe(III/II) systems were investigated by spectrophotometric, potentiometric, and electrochemical titrations. On the basis of the obtained species distributions, the pH intervals in which the different protonated forms of the two studied systems exist were defined. In different pH ranges, a different number of protons (from 0 to 3 protons per electron) can be transferred during the redox process, which affects the change in the overall charge on the complexes. For all the different protonation forms of the studied complexes, the change in the redox potentials with pressure was measured and the redox reaction volume was obtained by high-pressure cyclic voltammetry. The results show that in the case of proton-coupled electron transfer, the reaction volume for the neutralization of protons contributes to the overall reaction volume. A linear correlation between Deltaz2 (change in the square of the charge) and the overall reaction volume of the complexes upon reduction, DeltaVcomplex0, was found. The average value of the intrinsic volume change for the selected seven-coordinate iron complexes was estimated from the intercept of the plot of DeltaVcomplex0 versus Deltaz2 to be 9.2 +/- 0.7 cm3 mol(-1). For the combined redox and protonation processes, the data are discussed in terms of linear correlations between Deltaz2 and the redox and neutralization reaction volumes reported in the literature.     

Synthesis,electronic structure,and electron transfer dynamics of (Aryl)ethynyl-bridged donor-acceptor systems

The ET dynamics of a series of donor-spacer-acceptor (D-Sp-A) systems featuring (porphinato)zinc(II), (aryl)ethynyl bridge, and arene diimide units were investigated by pump-probe transient absorption spectroscopy. Analysis of these data within the context of the Marcus-Levich-Jortner equation suggests that the pi-conjugated (aryl)ethynyl bridge plays an active role in the charge recombination (CR) reactions of these species by augmenting the extent of (porphinato)zinc(II) cation radical electronic delocalization; this increase in cation radical size decreases the reorganization energy associated with the CR reaction and thereby attenuates the extent to which the magnitudes of the CR rate constants are solvent dependent. The symmetries of porphyrin-localized HOMO and HOMO-1, the energy gap between these two orbitals, and D-A distance appear to play key roles in determining whether the (aryl)ethynyl bridge simply mediates electronic superexchange or functions as an integral component of the D and A units.     

Theory and computation of electron transfer reorganization energies with continuum and molecular solvent models

Contemporary continuum-based models of solvation in polar media are surveyed and assessed, with special focus on non-equilibrium solvation. A new hybrid approach combining molecular-level treatment of inertial solvent response, and inclusion of inertialess solvent response at the continuum level, is presented and illustrated in terms of calculated equilibrium solvation free energies for small molecular ions and reorganization free energies for model dumbbell systems.     

Lone pair-pi and pi-pi interactions play an important role in proton-coupled electron transfer reactions

Proton-coupled electron transfer (PCET), a class of formal hydrogen atom transfer (HAT) reactions, is of widespread interest because it is implicated in a broad range of chemical and biochemical processes. PCET is typically differentiated from HAT by the fact that it occurs when a proton and electron are transferred between different sets of molecular orbitals. Previous theoretical work predicted that hydrogen bonding between reactants is a necessary but not sufficient condition for H exchanges to take place by PCET. This implies that HAT is the only mechanism for H exchange between two carbon atoms. In this work, we present computational results that show that the H exchange in the tert-butylperoxyl/phenol couple, a prototypical antioxidant exchange reaction, occurs by PCET and that the transfer of the electron can occur via an oxygen lone pair-ring pi overlap. We then show that the H exchange in a model for the tyrosyl/tyrosine couple, which is implicated in ribonucleotide reductase chemistry, occurs via PCET and that one path for the electron transfer is provided by a strong pi-stacking interaction. Finally, we show that a pi-stacking interaction in the benzyl/toluene couple, a system in which there is no H-bonding, can result in this exchange occurring via PCET to some extent. Collectively, these results indicate that PCET reactions are not unique to systems that can engage in H-bonding and that lone pair-pi and pi-pi interactions in these systems may be more important than previously understood.     

Intra- vs intermolecular photoinduced electron transfer reactions of a macrocyclic donor-acceptor dyad

The synthesis, structural characterization, and photophysical behavior of a 14-membered tetraazamacrocycle with pendant 4-dimethylaminobenzyl (DMAB) and 9-anthracenylmethyl groups is reported (L3, 6-((9-anthracenylmethyl)amino)-trans-6,13-dimethyl-13-((4-dimethylaminobenzyl)amino)-1,4,8,11-tetraazacyclotetradecane). In its free base form, this compound displays rapid intramolecular photoinduced electron transfer (PET) quenching of the anthracene emission, with both the secondary amines and the DMAB group capable of acting as electron donors. When complexed with Zn(II), the characteristic fluorescence of the anthracene chromophore is restored as the former of these pathways is deactivated by coordination. Importantly, it is shown that the DMAB group, which remains uncoordinated and PET active, acts only very weakly to quench emission, by comparison to the behavior of a model Zn complex lacking the pendant DMAB group, [ZnL2]2+ (Chart 1). By contrast, Stern-Volmer analysis of intermolecular quenching of [ZnL2]2+ by N,N-dimethylaniline (DMA) has shown that this reaction is diffusion limited. Hence, the pivotal role of the bridge in influencing intramolecular PET is highlighted.     

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

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

Competition of concatenated and thermally activated medium reorganization in photoinduced electron transfer reactions

Two mechanisms of photoinduced electron-transfer reactions, the classical mechanism of the preliminary thermally activated reorganization of a medium and reactants (at relatively weak electronic interaction between reactant molecules) and the mechanism of intermediate formation of exciplexes by concatenated medium reorganization correlated with charge displacement (at relatively strong electronic interaction between the reactants) are compared.     

Electrochemically induced chemically reversible proton-coupled electron transfer reactions of riboflavin (vitamin B2)

The electrochemical behavior of the naturally occurring vitamin B(2), riboflavin (Fl(ox)), was examined in detail in dimethyl sulfoxide solutions using variable scan rate cyclic voltammetry (ν = 0.1 - 20 V s(-1)) and has been found to undergo a series of proton-coupled electron transfer reactions. At a scan rate of 0.1 V s(-1), riboflavin is initially reduced by one electron to form the radical anion (Fl(rad)(?-)) at E(0)(f) = -1.22 V versus Fc/Fc(+) (E(0)(f) = formal reduction potential and Fc = ferrocene). Fl(rad)(?-) undergoes a homogeneous proton transfer reaction with the starting material (Fl(ox)) to produce Fl(rad)H(?) and Fl(ox)(-), which are both able to undergo further reduction at the electrode surface to form Fl(red)H(-) (E(0)(f) = -1.05 V vs Fc/Fc(+)) and Fl(rad)(?2-) (E(0)(f) = -1.62 V vs Fc/Fc(+)), respectively. At faster voltammetric scan rates, the homogeneous reaction between Fl(rad)(?-) and Fl(ox) begins to be outrun, which leads to the detection of a voltammetric peak at more negative potentials associated with the one-electron reduction of Fl(rad)(?-) to form Fl(red)(2-) (E(0)(f) = -1.98 V vs Fc/Fc(+)). The variable scan rate voltammetric data were modeled quantitatively using digital simulation techniques based on an interconnecting "scheme of squares" mechanism, which enabled the four formal potentials as well as the equilibrium and rate constants associated with four homogeneous reactions to be determined. Extended time-scale controlled potential electrolysis (t > hours) and spectroscopic (EPR and in situ UV-vis) experiments confirmed that the chemical reactions were completely chemically reversible.     

Strategies for switching the mechanism of proton-coupled electron transfer reactions illustrated by mechanistic zone diagrams

The mechanism by which proton-coupled electron transfer (PCET) occurs is of fundamental importance and has great consequences for applications, e.g. in catalysis. However, determination and tuning of the PCET mechanism is often non-trivial. Here, we apply mechanistic zone diagrams to illustrate the competition between concerted and stepwise PCET-mechanisms in the oxidation of 4-methoxyphenol by Ru(bpy)₃³⁺-derivatives in the presence of substituted pyridine bases. These diagrams show the dominating mechanism as a function of driving force for electron and proton transfer (ΔG⁰_ET and ΔG⁰_PT) respectively [Tyburski et al., J. Am. Chem. Soc., 2021, 143, 560]. Within this framework, we demonstrate strategies for mechanistic tuning, namely balancing of ΔG⁰_ET and ΔG⁰_PT, steric hindrance of the proton-transfer coordinate, and isotope substitution. Sterically hindered pyridine bases gave larger reorganization energy for concerted PCET, resulting in a shift towards a step-wise electron first-mechanism in the zone diagrams. For cases when sufficiently strong oxidants are used, substitution of protons for deuterons leads to a switch from concerted electron–proton transfer (CEPT) to an electron transfer limited (ETPT_lim) mechanism. We thereby, for the first time, provide direct experimental evidence, that the vibronic coupling strength affects the switching point between CEPT and ETPT_lim, i.e. at what driving force one or the other mechanism starts dominating. Implications for solar fuel catalysis are discussed.

The mechanism by which proton-coupled electron transfer (PCET) occurs is of fundamental importance and has great consequences for applications, e.g. in catalysis.     

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

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