Curve Crossing Formulation for Proton Transfer Reactions in Solution

Origin of the multi-phasic quenching dynamics in the BLUF domains across the species

Blue light using flavin (BLUF) photoreceptors respond to light via one of nature's smallest photo-switching domains. Upon photo-activation, the flavin cofactor in the BLUF domain exhibits multi-phasic dynamics, quenched by a proton-coupled electron transfer reaction involving the conserved Tyr and Gln. The dynamic behavior varies drastically across different species, the origin of which remains controversial. Here, we incorporate site-specific fluorinated Trp into three BLUF proteins, i.e., AppA, OaPAC and SyPixD, and characterize the percentages for the Wout, WinNHin and WinNHout conformations using 19F nuclear magnetic resonance spectroscopy. Using femtosecond spectroscopy, we identify that one key WinNHin conformation can introduce a branching one-step proton transfer in AppA and a two-step proton transfer in OaPAC and SyPixD. Correlating the flavin quenching dynamics with the active-site structural heterogeneity, we conclude that the quenching rate is determined by the percentage of WinNHin, which encodes a Tyr-Gln configuration that is not conducive to proton transfer.

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.

Reorganization energy of electron transfer

The theory of electron transfer reactions establishes the conceptual foundation for redox solution chemistry, electrochemistry, and bioenergetics. Electron and proton transfer across the cellular membrane provide all energy of life gained through natural photosynthesis and mitochondrial respiration. Rates of biological charge transfer set kinetic bottlenecks for biological energy storage. The main system-specific parameter determining the activation barrier for a single electron-transfer hop is the reorganization energy of the medium. Both harvesting of light energy in natural and artificial photosynthesis and efficient electron transport in biological energy chains require reduction of the reorganization energy to allow fast transitions. This review article discusses mechanisms by which small values of the reorganization energy are achieved in protein electron transfer and how similar mechanisms can operate in other media, such as nonpolar and ionic liquids. One of the major mechanisms of reorganization energy reduction is through non-Gibbsian (nonergodic) sampling of the medium configurations on the reaction time. A number of alternative mechanisms, such as electrowetting of active sites of proteins, give rise to non-parabolic free energy surfaces of electron transfer. These mechanisms, and nonequilibrium population of donor-acceptor vibrations, lead to a universal phenomenology of separation between the Stokes shift and variance reorganization energies of electron transfer.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

Diradical Generation via Relayed Proton-Coupled Electron Transfer

Diradical generation followed by radical-radical cross-coupling is a powerful synthetic tool, but its detailed mechanism has yet to be established. Herein, we proposed and confirmed a new model named relayed proton-coupled electron transfer (relayed-PCET) for diradical generation, which could open a door for new radical-radical cross-coupling reactions. Quantum mechanics calculations were performed on a selected carbene-mediated diradical cross-coupling reaction model and a designed model, and the exact electronic structural changes during the radical processes have been observed for the first time.

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.

Electron-Induced Proton Transfer

The pathway of activationless proton transfer induced by an electron-transfer reaction is studied theoretically. Long-range electron transfer produces highly nonequilibrium medium polarization that can drive proton transfer through an activationless transition during the process of thermalization, dynamically altering the screening of the electron-proton Coulomb interaction by the medium. The cross electron-proton reorganization energy is the main energy parameter of the theory, which exceeds in magnitude the proton-transfer reorganization energy roughly by the ratio of the electron-transfer to proton-transfer distance. This parameter, which can be either positive or negative, is related to the difference in pK_a values in two electron-transfer states. The relaxation time of the medium is on the (sub)picosecond time scale, which establishes the characteristic time for activationless proton transfer. Microscopic calculations predict substantial retardation of the collective relaxation dynamics compared to the continuum estimates due to the phenomenology analogous to de Gennes narrowing. Nonequilibrium medium configuration promoting proton transfer can be induced by either thermal or photoinduced charge transfer.

Solvent and Temperature Effects on Photoinduced Proton-Coupled Electron Transfer in the Marcus Inverted Region

Concerted proton-coupled electron transfer (PCET) in the Marcus inverted region was recently demonstrated (Science 2019, 364, 471-475). Understanding the requirements for such reactivity is fundamentally important and holds promise as a design principle for solar energy conversion systems. Herein, we investigate the solvent polarity and temperature dependence of photoinduced proton-coupled charge separation (CS) and charge recombination (CR) in anthracene-phenol-pyridine triads: 1 (10-(4-hydroxy-3-(4-methylpyridin-2-yl)benzyl)anthracene-9-carbonitrile) and 2 (10-(4-hydroxy-3-(4-methoxypyridin-2-yl)benzyl)anthracene-9-carbonitrile). Both the CS and CR rate constants increased with increasing polarity in acetonitrile:n-butyronitrile mixtures. The kinetics were semi-quantitatively analyzed where changes in dielectric and refractive index, and thus consequently changes in driving force (-ΔG°) and reorganization energy (λ), were accounted for. The results were further validated by fitting the temperature dependence, from 180 to 298 K, in n-butyronitrile. The analyses support previous computational work where transitions to proton vibrational excited states dominate the CR reaction with a distinct activation free energy (ΔG*CR ∼ 140 meV). However, the solvent continuum model fails to accurately describe the changes in ΔG° and λ with temperature via changes in dielectric constant and refractive index. Satisfactory modeling was obtained using the results of a molecular solvent model [J. Phys. Chem. B 1999, 103, 9130-9140], which predicts that λ decreases with temperature, opposite to that of the continuum model. To further assess the solvent polarity control in the inverted region, the reactions were studied in toluene. Nonpolar solvents decrease both ΔG°CR and λ, slowing CR into the nanosecond time regime for 2 in toluene at 298 K. This demonstrates how PCET in the inverted region may be controlled to potentially use proton-coupled CS states for efficient solar fuel production and photoredox catalysis.

Correlation between Kinetics and Thermodynamics for Excited-State Intramolecular Proton Transfer Reactions

Finding the relation between thermodynamics and kinetics for a reaction is of fundamental importance. Here, the thermodynamics and kinetics correlation of excited-state intramolecular proton transfer (ESIPT) was investigated by the TD-DFT calculation under the CAM-B3LYP/6-311+G** level. We choose the family 2-(2'-aminophyenyl)benzothiazole and its amino derivatives as paradigms, which all possess the NH-type intramolecular hydrogen bond (H-bond), and investigate the corresponding ESIPT reaction. The H-bond strength can be systematically tuned, so both activation energy ΔG^‡ and free energy difference between proton transfer tautomer (T*, product) and normal species (N*, reactant) ΔG_T*-N* can be varied. To minimize the environmental interference such as solvent external H-bond and polarity perturbation, a nonpolar solvent such as cyclohexane is chosen as a bath with a polarizable continuum solvation model for the calculation. As a result, the comprehensive computational approach reveals a linear relationship between ΔG_T*-N* and ΔG^‡, which can be expressed as ΔG^‡ = ΔG₀ + αΔG_T*-N*. The fundamental insight is reminiscent of the Bell-Evans-Polanyi (BEP) principle where α represents the character of the position of the transition state along the proton motion coordinate. In other words, the more exergonic the ESIPT reaction is, the faster the proton transfer rate can be observed. To verify that such a correlation is not a sporadic event, another ESIPT family with an -OH proton, 1-hydroxy-11H-benzo[b]fluoren-11-one and its derivatives, was also investigated and proved to follow the BEP principle as well. Unlike the quantum mechanics description of proton transfer where either proton tunneling is dominant or solute/solvent is coupled in ESIPT, this work demonstrates that reaction kinetics and thermodynamics are strongly correlated within the same class of ESIPT molecules with an intrinsic barrier free from solvent perturbation, being faster with the more exergonic reaction.

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.

Recent progress in approximate quantum dynamics methods for the study of proton-coupled electron transfer reactions

Proton-coupled electron transfer (PCET) reactions are ubiquitous natural processes at the heart of energy conversion reactions in photosynthesis and respiration, DNA repair, and diverse enzymatic reactions. Theoretical formulation and computational method developments have eyed modeling of thermal and photoinduced PCET for the last three decades. The accumulation of these studies, collected in dozens of reviews, accounts, and perspectives, has firmly established the influence of quantum effects, including non-adiabatic electronic transitions, vibrational relaxation, zero-point energy, and proton tunneling, on the rate and mechanism of PCET reactions. Here, we focus on some recently-developed methods, spanning the last eight years, that can quantitatively capture these effects in the PCET context and provide efficient means for their qualitative description in complex systems. The theoretical background of each method and their accuracy with respect to exact results are discussed and the results of relevant PCET simulations based on each method are presented.

Proton-Coupled Electron Transfer Guidelines, Fair and Square

Proton-coupled electron transfer (PCET) reactions are fundamental to energy transformation reactions in natural and artificial systems and are increasingly recognized in areas such as catalysis and synthetic chemistry. The interdependence of proton and electron transfer brings a mechanistic richness of reactivity, including various sequential and concerted mechanisms. Delineating between different PCET mechanisms and understanding why a particular mechanism dominates are crucial for the design and optimization of reactions that use PCET. This Perspective provides practical guidelines for how to discern between sequential and concerted mechanisms based on interpretations of thermodynamic data with temperature-, pressure-, and isotope-dependent kinetics. We present new PCET-zone diagrams that show how a mechanism can switch or even be eliminated by varying the thermodynamic (ΔGPT° and ΔGET°) and coupling strengths for a PCET system. We discuss the appropriateness of asynchronous concerted PCET to rationalize observations in organic reactions, and the distinction between hydrogen atom transfer and other concerted PCET reactions. Contemporary issues and future prospects in PCET research are discussed.

Polariton-Mediated Electron Transfer via Cavity Quantum Electrodynamics

We investigate the polariton-mediated electron transfer reaction in a model system with analytic rate constant theory and direct quantum dynamical simulations. We demonstrate that the photoinduced charge transfer reaction between a bright donor state and dark acceptor state can be significantly enhanced or suppressed by coupling the molecular system to the quantized radiation field inside an optical cavity. This is because the quantum light-matter interaction can influence the effective driving force and electronic couplings between the donor state, which is the hybrid light-matter excitation, and the molecular acceptor state. Under the resonance condition between the photonic and electronic excitations, the effective driving force can be tuned by changing the light-matter coupling strength; for an off-resonant condition, the same effect can be accomplished by changing the molecule-cavity detuning. We further demonstrate that using both the electronic coupling and light-matter coupling helps to extend the effective couplings across the entire system, even for the dark state that carries a zero transition dipole. Theoretically, we find that both the counter-rotating terms and the dipole self-energy in the quantum electrodynamics Hamiltonian are important for obtaining an accurate polariton eigenspectrum as well as the polariton-mediated charge transfer rate constant, especially in the ultrastrong coupling regime.

Hydrogen and proton exchange at carbon. Imbalanced transition state and mechanism crossover

A recent remarkable study of the C-H oxidation of substituted fluorenyl-benzoates together with the transfer of a proton to an internal receiving group by means of electron transfer outer-sphere oxidants, in the noteworthy absence of hydrogen-bonding interactions, is taken as an example to uncover the existence of a mechanism crossover, making the reaction pass from a CPET pathway to a PTET pathway as the driving force of the global reaction decreases. This was also the occasion to stress that considerations based on "imbalanced" or "asynchronous" transition states cannot replace activation/driving force models based on the quantum mechanical treatment of both electrons and transferring protons.

Consecutive Marcus Electron and Proton Transfer in Heme Peroxidase Compound II-Catalysed Oxidation Revealed by Arrhenius Plots

Electron and proton transfer reactions in enzymes are enigmatic and have attracted a great deal of theoretical, experimental, and practical attention. The oxidoreductases provide model systems for testing theoretical predictions, applying experimental techniques to gain insight into catalytic mechanisms, and creating industrially important bio(electro)conversion processes. Most previous and ongoing research on enzymatic electron transfer has exploited a theoretically and practically sound but limited approach that uses a series of structurally similar ("homologous") substrates, measures reaction rate constants and Gibbs free energies of reactions, and analyses trends predicted by electron transfer theory. This approach, proposed half a century ago, is based on a hitherto unproved hypothesis that pre-exponential factors of rate constants are similar for homologous substrates. Here, we propose a novel approach to investigating electron and proton transfer catalysed by oxidoreductases. We demonstrate the validity of this new approach for elucidating the kinetics of oxidation of "non-homologous" substrates catalysed by compound II of Coprinopsis cinerea and Armoracia rusticana peroxidases. This study - using the Marcus theory - demonstrates that reactions are not only limited by electron transfer, but a proton is transferred after the electron transfer event and thus both events control the reaction rate of peroxidase-catalysed oxidation of substrates.

Kinetics of Proton Discharge on Metal Electrodes: Effects of Vibrational Nonadiabaticity and Solvent Dynamics

Proton discharge on metal electrodes, also denoted the Volmer reaction, is a critical step in a wide range of electrochemical processes. This electrochemical proton-coupled electron transfer (PCET) reaction is predominantly electronically adiabatic in aqueous solution and is typically treated as fully adiabatic. Recently, a theoretical model for this PCET reaction was developed to generate the vibronic free energy surfaces as functions of a collective solvent coordinate and the distance of the proton-donating acid from the electrode. Herein a unified formulation is devised to describe such PCET reactions in terms of a curve crossing between two diabatic vibronic states corresponding to the lowest two proton vibrational states, employing an interpolation scheme that spans the adiabatic transition state theory, nonadiabatic Fermi golden rule, and solvent-controlled regimes. In contrast to previous treatments, application of this formulation to the aqueous Volmer reaction highlights the importance of vibrational nonadiabaticity and solvent dynamics. The calculated transfer coefficients and kinetic isotope effects are in reasonable agreement with experimental measurements. These fundamental insights have broad implications for understanding electrochemical processes.

Switching between Stepwise and Concerted Proton-Coupled Electron Transfer Pathways in Tungsten Hydride Activation

Catalytic processes to generate (or oxidize) fuels such as hydrogen are underpinned by multiple proton-coupled electron transfer (PCET) steps that are associated with the formation or activation of metal-hydride bonds. Fully understanding the detailed PCET mechanisms of metal hydride transformations holds promise for the rational design of energy-efficient catalysis. Here we investigate the detailed PCET mechanisms for the activation of the transition metal hydride complex CpW(CO)₂(PMe₃)H (Cp = cyclopentadienyl) using stopped-flow rapid mixing coupled with time-resolved optical spectroscopy. We reveal that all three limiting PCET pathways can be accessed by changing the free energy for elementary proton, electron, and proton-electron transfers through the choice of base and oxidant, with the concerted pathway occurring exclusively as a secondary parallel route. Through detailed kinetics analysis, we define free energy relationships for the kinetics of elementary reaction steps, which provide insight into the factors influencing reaction mechanism. Rate constants for proton transfer processes in the limiting stepwise pathways reveal a large reorganization energy associated with protonation/deprotonation of the metal center (λ = 1.59 eV) and suggest that sluggish proton transfer kinetics hinder access to a concerted route. Rate constants for concerted PCET indicate that the concerted routes are asynchronous. Additionally, through quantification of the relative contributions of parallel stepwise and concerted mechanisms toward net product formation, the influence of various reaction parameters on reactivity are identified. This work underscores the importance of understanding the PCET mechanism for controlling metal hydride reactivity, which could lead to superior catalyst design for fuel production and oxidation.

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.

Escape of anions from geminate recombination in THF due to charge delocalization

Geminate recombination of 24 radical anions (M˙^-) with solvated protons (RH₂⁺) was studied in tetrahydrofuran (THF) with pulse radiolysis. The recombination has two steps: (1) diffusion of M˙^- and RH₂⁺ together to form intimate (contact and solvent separated) ion pairs, driven by Coulomb attraction; (2) annihilation of anions due to proton transfer (PT) from RH₂⁺ to M˙^-. The non-exponential time-dependence of the geminate diffusion was determined. For all molecules protonated on O or N atoms the subsequent PT step is too fast (<0.2 ns) to measure, except for the anion of TCNE which did not undergo proton transfer. PT to C atoms was as slow as 70 ns and was always slow enough to be observable. A possible effect of charge delocalization on the PT rates could not be clearly separated from other factors. For 21 of the 24 molecules studied here, a free ion yield (71.6 ± 6.2 nmol J^-1) comprising ∼29% of the total, was formed. This yield of "Type I" free ions is independent of the PT rate because it arises entirely by escape from the initial distribution of ion pair distances without forming intimate ion pairs. Three anions of oligo(9,9-dihexyl)fluorenes, F_n˙^- (n = 2-4) were able to escape from intimate ion-pairs to form additional yields of "Type II" free ions with escape rate constants near 3 × 10⁶ s^-1. These experiments find no evidence for an inverted region for proton transfer.

Influence of Proton Acceptors on the Proton-Coupled Electron Transfer Reaction Kinetics of a Ruthenium-Tyrosine Complex

A polypyridyl ruthenium complex with fluorinated bipyridine ligands and a covalently bound tyrosine moiety was synthesized, and its photo-induced proton-coupled electron transfer (PCET) reactivity in acetonitrile was investigated with transient absorption spectroscopy. Using flash-quench methodology with methyl viologen as an oxidative quencher, a Ru³⁺ species is generated that is capable of initiating the intramolecular PCET oxidation of the tyrosine moiety. Using a series of substituted pyridine bases, the reaction kinetics were found to vary as a function of proton acceptor concentration and identity, with no significant H/D kinetic isotope effect. Through analysis of the kinetics traces and comparison to a control complex without the tyrosine moiety, PCET reactivity was found to proceed through an equilibrium electron transfer followed by proton transfer (ET-PT) pathway in which irreversible deprotonation of the tyrosine radical cation shifts the ET equilibrium, conferring a base dependence on the reaction. Comprehensive kinetics modeling allowed for deconvolution of complex kinetics and determination of rate constants for each elementary step. Across the five pyridine bases explored, spanning a range of 4.2 pK_a units, a linear free-energy relationship was found for the proton transfer rate constant with a slope of 0.32. These findings highlight the influence that proton transfer driving force exerts on PCET reaction kinetics.

Photochemistry and Photophysics in Silica-Based Materials: Ultrafast and Single Molecule Spectroscopy Observation

Silica-based materials (SBMs) are widely used in catalysis, photonics, and drug delivery. Their pores and cavities act as hosts of diverse guests ranging from classical dyes to drugs and quantum dots, allowing changes in the photochemical behavior of the confined guests. The heterogeneity of the guest populations as well as the confinement provided by these hosts affect the behavior of the formed hybrid materials. As a consequence, the observed reaction dynamics becomes significantly different and complex. Studying their photobehavior requires advanced laser-based spectroscopy and microscopy techniques as well as computational methods. Thanks to the development of ultrafast (spectroscopy and imaging) tools, we are witnessing an increasing interest of the scientific community to explore the intimate photobehavior of these composites. Here, we review the recent theoretical and ultrafast experimental studies of their photodynamics and discuss the results in comparison to those in homogeneous media. The discussion of the confined dynamics includes solvation and intra- and intermolecular proton-, electron-, and energy transfer events of the guest within the SBMs. Several examples of applications in photocatalysis, (photo)sensors, photonics, photovoltaics, and drug delivery demonstrate the vast potential of the SBMs in modern science and technology.

Influence of Solvent Relaxation on Ultrafast Excited-State Proton Transfer to Solvent

A thorough understanding of the microscopic mechanism of excited-state proton transfer (ESPT) and the influence of the solvent environment on its dynamics are of great fundamental interest. We present here a detailed investigation of an ESPT to solvent (DMSO) using time-resolved broadband fluorescence and transient absorption spectroscopies. All excited-state species are resolved spectrally and kinetically using a global target analysis based on the two-step Eigen-Weller model. Reversibility of the initial short-range proton transfer producing excited contact ion pairs (CIP*) is observed unambiguously in fluorescence and must be explicitly considered to obtain the individual rate constants. Close inspection of the early dynamics suggests that the relative populations of the protonated form (ROH*) and CIP* are governed by solvent relaxation that influences the relative energies of the excited states. This constitutes a breakdown of the Eigen-Weller model, although the overall agreement between the data and the analysis using classical rate equations is excellent.

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

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

Decoherence Allows Model Reduction in Nonadiabatic Dynamics Simulations

A nonadiabatic (NA) molecular dynamics (MD) simulation requires calculation of NA coupling matrix elements, the number of which scales as a square of the number of basis states. The basis size can be huge in studies of nanoscale materials, and calculation of the NA couplings can present a significant bottleneck. A quantum-classical approximation, NAMD overestimates coherence in the quantum, electronic subsystem, requiring decoherence correction. Generally, decoherence times decrease with increasing energy separation between pairs of states forming coherent superpositions. Since rapid decoherence stops quantum dynamics, one expects that decoherence-corrected NAMD can eliminate the need for calculation of NA couplings between energetically distant states, notably reducing the computational cost. Considering several types of dynamics in a semiconductor quantum dot, we demonstrate that indeed, decoherence allows one to reduce the number of needed NA coupling matrix elements. If the energy levels are spaced closer than 0.1 eV, one obtains good results while including only three nearest-neighbor couplings, and in some cases even with just the first nearest-neighbor coupling scheme. If the energy levels are spaced by about 0.4 eV, the nearest-neighbor model fails, while three or more nearest-neighbor schemes also provide good results. In comparison, the results of NAMD simulation without decoherence vary continuously with changes in the number of NA couplings. Thus, decoherence effects induced by coupling to a quantum-mechanical environment not only provide the physical mechanism for NAMD trajectory branding and improve the accuracy of NAMD simulations, but also afford significant computational savings.

Solvent dependence of excited-state proton transfer from pyranine-derived photoacids

Steady-state and time-resolved techniques were employed to study the excited-state proton-transfer (ESPT) rate of two newly synthesized 8-hydroxy-1,3,6-pyrenetrisulfonate (pyranine, HPTS) derived photoacids in three protic solvents, water, methanol and ethanol. The ESPT rate constant k(PT) of tris(1,1,1,3,3,3-hexafluoropropan-2-yl)-8-hydroxypyrene-1,3,6-trisulfonate, 1a, whose pK(a)* ~ -4, in water, methanol and ethanol is 3 × 10(11) s(-1), 8 × 10(9) s(-1) and 5 × 10(9) s(-1) respectively. (8-Hydroxy-N1,N3,N6-tris(2-hydroxyethyl)-N1,N3,N6-trimethylpyrene-1,3,6 trisulfonamide, 1b) is a weaker acid than 1a but still a strong photoacid with pK(a)* ~ -1 and the ESPT rate in water, methanol and ethanol is 7 × 10(10) s(-1), 4 × 10(8) s(-1) and 2 × 10(8) s(-1). We qualitatively explain our kinetic results by a Marcus-like free-energy correlation which was found to have a general form suitable for describing proton transfer reactions in both the proton-adiabatic and the proton-non-adiabatic limits.

Fast photoinduced reactions in the condensed phase are nonexponential

Time-resolved measurements of photoinduced reactions reveal that many ultrafast reactions in the femto- to picosecond time scale are nonexponential. In this article we provide several examples of reactions that exhibit a nonexponential rate. We explain the wide range of the nonexponential reaction by the lack of time separation between τ(s), the characteristic fast equilibration time of the population in the reactant potential well, and the longer time τ(e), the characteristic time to cross the energy barrier between the reactant and the product.

Isolating the spectral signature of H3O+ in the smallest droplet of dissociated HCl acid

The smallest droplet of HCl acid, H₃O⁺(H₂O)₃Cl⁻, and its isolated H₃O⁺ infrared signature.

Unveiling the Eigen-Weller ion pair from the excited state proton transfer kinetics of 3-chloro-4-methyl-7-hydroxycoumarin

The prototropic reactions of the first excited singlet state of 3-chloro-4-methylumbelliferone (3Cl4MU), in dioxane:water mixtures (Dx:H2O), were revisited using ps-time-resolved fluorescence techniques. The data response to the dielectric constant of the mixtures revealed the presence of an additional fourth kinetic species, kinetically coupled to the neutral (N*), the tautomeric (T*), and anionic (A(-)*) forms of 3Cl4MU, which is assigned to the elusive geminate (A(-)*···H(+)) ion pair. From the data analysis, all rate constants of the prototropic and diffusion processes involved were separately evaluated. The results showed that, whenever the geminate ionic pair is not kinetically detected, the evaluated values for deprotonation and protonation rate constants can substantially deviate from the real ones, depending on the efficiencies of pair recombination and dissociation. Finally, the results provide convincing kinetic evidence for the Eigen-Weller mechanism (intermediacy of the geminate ionic pair) in a quasi-aqueous medium, which to our knowledge had not yet been given.