Dynamical arrest of electron transfer in liquid crystalline solvents

We argue that electron transfer reactions in slowly relaxing solvents proceed in the nonergodic regime, making the reaction activation barrier strongly dependent on the solvent dynamics. For typical dielectric relaxation times of polar nematics, electron transfer reactions in the subnanosecond time scale fall into nonergodic regime in which nuclear solvation energies entering the activation barrier are significantly lower than their thermodynamic values. The transition from isotropic to nematic phase results in weak discontinuities of the solvation energies at the transition point and the appearance of solvation anisotropy weakening with increasing solute size. The theory is applied to analyze experimental kinetic data for the electron transfer kinetics in the isotropic phase of 5CB liquid crystalline solvent. We predict that the energy gap law of electron transfer reactions in slowly relaxing solvents is characterized by regions of fast change of the rate at points where the reaction switches between the ergodic and nonergodic regimes. The dependence of the rate on the donor-acceptor separation may also be affected in a way of producing low values for the exponential falloff parameter.     

Electron transfer NO 2 + +NO→N02+NO+ in aromatic nitration

A simple model for computing the electron transfer rate constant of a cross-reaction has been proposed in the framework of semiclassical theory and employed to investigate the electron transfer system NO ₂ ⁺ /NO. The encounter complex of electron transfer NO ₂ ⁺ +NO→N0₂+NO⁺ has been optimized at the level of UHF/6-31G. In the construction of diabatic potential energy surfaces the linear coordinate was used and the kinetic quantities, such as the activation energies and the electron transfer matrix elements, have been obtained. For comparison, the related selfexchange reactlon systems NO ₂ ⁺ /NO₂ and NO⁺/NO were kinetically investigated. The calculated activation energies for the electron transfer reactions of systems NO ₂ ⁺ /NO, NO ₂ ⁺ /NO₂, and NO⁺/NO are 81.4, 128.8, and 39.8 kJ.mol^-1, respectively. With the solvent effect taken into account, the contribution of solvent reorganization to the activation energy has been estimated according to the geometric parameters of the transition states. The obtained rate constants show that the activity of NO ₂ ⁺ as an oxidizing reagent in the aromatic nitration will be greatly decreased due to a high activation barrier contributed mainly from the change of bond angle ONO.     

Photochemical Reactions and Photoinduced Electron‐Transfer Processes in Liquids,Frozen Solutions,and Proteins as Studied by Multifrequency Time‐Resolved EPR Spectroscopy

In this overview, modern multifrequency EPR spectroscopy, in particular at high magnetic fields, is shown to provide detailed information about structure, motional dynamics, and spin chemistry of transient radicals and radical pairs occurring in photochemical reactions. Examples discussed comprise photochemical reactions in liquid solution and light‐initiated electron transfer processes both in biomimetic donor–acceptor model systems in frozen solution or liquid crystals and in natural photosynthetic‐reaction‐center protein complexes. The transient paramagnetic states exhibit characteristic electron polarization (CIDEP) effects. They contain valuable information about structure and dynamics of the transient reaction intermediates. Moreover, they are exploited for signal enhancement. Continuous‐wave (cw) and pulsed versions of time‐resolved high‐field EPR spectroscopy, such as cw‐transient‐EPR (TREPR) and pulsed‐electron‐spin‐echo (ESE) experiments, are compared with respect to their advantages and limitations for the specific system under study. For example, W‐band (95‐GHz) TREPR spectroscopy in conjunction with a continuous‐flow system for light‐generated short‐lived transient spin‐polarized radicals of organic photoinitiators in solution was performed with a time resolution of 10 ns. The increased Boltzmann polarization at high fields even allows detection of transient radicals without CIDEP effects. This enables one to determine initial radical polarization contributions as well as radical‐addition reaction constants. Another example of the power of combined X‐band and W‐band TREPR spectroscopy is given for the complex electron‐transfer and spin dynamics of covalently linked porphyrin–quinone as well as Watson–Crick base‐paired porphyrin–dinitrobenzene donor–acceptor biomimetic model systems. Furthermore, W‐band ESE experiments on the spin‐correlated coupled radical pair in reaction centers of the purple photosynthetic bacterium Rb. sphaeroides reveal details of distance and orientation of the pair partners in their charge‐separated transient state. The results are compared with those of the ground‐state P₈₆₅Q_A. The high orientation selectivity of high‐field EPR provides single‐crystal‐like information even from disordered frozen‐solution samples. The examples given demonstrate that high‐field EPR adds substantially to the capability of ‘classical’ spectroscopic and diffraction techniques for determining structure–dynamics–function relations of biochemical systems, since transient intermediates can be observed in real time in their working states on biologically relevant time scales.     

钐(II)类卡宾CH3SmCH2I与乙烯环丙烷化反应及溶剂化效应的理论研究

用密度泛函B3LYP方法研究了过渡金属钐类卡宾与乙烯的环丙烷化反应的机理. 对钐类卡宾试剂CH₃SmCH₂I和CH₂CH₂反应的反应物、中间体、过渡态和产物构型的全部结构几何参数进行了优化, 并计算了THF溶液的溶剂化效应, 用内禀反应坐标(IRC)计算和频率分析方法, 对过渡态进行了验证. 结果表明: CH₃SmCH₂I与CH₂CH₂环丙烷化反应按亚甲基转移机理(通道A)和卡宾金属化机理(通道B)都可以进行, 与锂类卡宾的反应机理相同, 通道A比通道B反应的势垒降低了14.65 kJ/mol. 溶剂化效应使通道B比通道A的反应势垒大幅度提高, 更有利于反应沿通道A进行, 而不利于通道B.     

A Monte Carlo simulation of free energy relationships for the electron transfer reaction between Fe+ and Fe2+ in water

A free energy barrier ΔF^≠ = 174.2 kJ/mol for the self-exchange electron transfer reaction model Fe⁺/Fe²⁺ in water has been calculated by combining Monte Carlo simulations and the statistical perturbation theory. We have shown that, even for those electron transfer reactions that present a very high free energy barrier of activation, the free energy curve behaves parabolically versus the reaction coordinate, which justifies the quadratic expression for the activation free energy done by Marcus.     

Reaction dynamics of the transfer of stored electrons on TiO2 nanoparticles: A stopped flow study

The dynamics of the transfer of electrons from TiO₂ nanoparticles to a variety of electron acceptors have been investigated employing a simple and facile stopped flow technique. Prior to the kinetic experiments nanosized TiO₂ particles are loaded with electrons by UV (A) photolysis in the presence of methanol as a hole scavenger. As a model for possible electron transfer reactions the reduction of dissolved O₂ and H₂O₂ by stored TiO₂ electrons has been successfully studied.     

How difficult are anion-molecule SNAr reactions of unactivated arenes in the gas phase,dimethyl sulfoxide,and methanol solvents?

Nucleophilic substitution on the aromatic ring (S_NAr) is a very important reaction for organic transformations. This kind of reaction is usually difficult to take place, requiring organometallic catalysis or activation of the ring by electron withdrawing groups to turn the nucleophilic attack possible. In this work, the relative importance of intrinsic gas phase barrier and the solvent effect on several S_NAr reactions using theoretical calculations were investigated. The reactions of the anions OH^?, CN^?, and CH₃O^? and the enolates CH₃COCH₂^? and CH₃COCHCOCH₃^? with bromobenzene and (o, m, p)-methoxy bromobenzene in methanol and dimethyl sulfoxide as solvents were considered. The OH^? and CH₃O^? ions are highly reactive in the gas phase. However, the solvent effect induces a high activation barrier in solution, turning the reaction difficult, although feasible. The CN^? and CH₃COCHCOCH₃^? ions have high activation barriers even in the gas phase. The interesting CH₃COCH₂^? ion has a moderate barrier in the gas phase, although the free energy barrier in DMSO solution reaches 33 kcal mol^?1. Our analysis suggests that decreasing the solvent effect, arylation of enolates with unactivated arenes could become possible.

     

Solvent effects on simple electron transfer reactions: A comparison of results for homogeneous and heterogeneous systems

Solvent effects on the rate constants for both homogeneous and heterogeneous electron transfer reactions have been analyzed on the basis of current models which consider the role of dynamic relaxation processes in determining the magnitude of the pre-exponential factor. A statistical method for separating the effects of the solvent longitudinal relaxation time τ_L from those of the solvent permittivity parameter γ is described and applied to 15 sets of experimental data for which results are available in at least four solvents. The degree to which the explained variation in the logarithm of the rate constant could be attributed to either of these effects varied all the way from 0 to 100% depending on the degree of reaction adiabaticity and the relative sizes of the inner and outer sphere components of the Gibbs energy of activation. Data for the limiting cases in which there is no τ_l dependence in the pre-exponential factor or in which the pre-exponential factor is proportional to τ_L⁻¹ were analyzed further to obtain the size-distance parameter and the components of the pre-exponential factor relevant to the encounter pre-equilibrium model. These parameters have been discussed with respect to current developments in electron transfer theory. Problems in estimating the longitudinal relaxation time in the solvent, required for the analysis, are also considered.     

A Semi-Empirical Model of the Energy Barrier of Proton Transfer Reactions

The energy barrier in proton transfer reactions is described by a Johnston-type equation (1) (n = order of bond to be broken). The barrier model is discussed in terms of free energies. The V_i values are free energies of ionic cleavage in aqueous solution of the X? H and Y? H bonds; they are computed from eqns. (4c) and (4d). The values of p₁ and p₂ affect curvature (absence or presence of maximum) and symmetry of the barrier. It is postulated that pi is a typical constant of the reacting bond and can be transferred from one transition state to another. With the aid of eqn. (1) and its first derivative, values of pi and n_m (bond order at maximum of barrier) can be based on quantities determined experimentally, Δ≠ and ΔG. For O? H bonds, pi ≈ 1.0. For C? H bonds pi is larger than 1.0 and depends on the structure of the carbanionic moiety (influence of resonance and inductive effects). As there cannot be a maximum if p₁ = p₂ = 1.0, the suggested model of the barrier leads to a better understanding why proton transfer must be ‘fast’ in some reactions and ‘slow’ in others. The computed values of n_m may be utilized to gain some insight into the nature of the transition states; they supply a basis for the discussion of primary hydrogen isotope effects.     

Monte Carlo simulation of the diabatic free energy curves for a dissociative electron transfer reaction in a polar solvent

In the present work we have carried out a Monte Carlo simulation of a dissociative electron transfer reaction in a polar solvent. In particular, we have chosen as a very simple model the electrochemical reduction of hydrogen fluoride to give a hydrogen atom and a fluoride anion in a dipolar solvent. From a classical point of view, the electron transfer occurs at the intersection region S* of the diabatic potential hypersurfaces H_pp and H_ss, corresponding to the precursor and successor complexes, respectively. We have evaluated both diabatic surfaces using potential functions that have been built up with ab initio methods by us. For each of the obtained configurations the parameter ΔE = H_ss – H_pp has been calculated. This parameter is then used as the reaction coordinate for obtaining the diabatic free energy curves of the reaction. Because the activation energy is high, a suitable mapping potential along with the statistical perturbation theory is employed to force the system to evolve toward the intersection region S*. A total of 68,340,000 configurations have been generated. The main conclusion of this article is that Marcus' relationship seems to fail for this kind of inner-sphere processes. © 1992 by John Wiley & Sons, Inc.     

Polarizable solute in polarizable and flexible solvents: simulation study of electron transfer reaction systems

A polarizable solute model, based on the empirical valence bond approach, is developed and applied to electron transfer (ET) reactions in polarizable and flexible water solvents. The polarization effect is investigated in comparison with a nonpolarizable solute and solvent model. With free energy curves constructed by a molecular dynamics simulation, the activation energy barrier and the reorganization energy related to ET processes are investigated. The present simulation results show that the activation energy barrier becomes larger in the polarizable model than in the nonpolarizable model and that this makes the ET rate slower than that with the nonpolarizable model. It is shown that the effect of the electronic energy difference of solute molecule on free energy profiles is remarkable and that, corresponding to this effect, the reorganization energy is significantly modified. These results indicate that the process of solvent polarization by the polarized solute to enhance the solute-solvent interaction is a key factor and that treating the polarization of both solute and solvent at the same time is essential. Also, the polarization effect on the diffusive motion of the solute molecule in the polarization solvent is studied. The polarized solute molecule shows slower diffusive motion compared with that in the nonpolarizable model.     

Structural Relaxation in Amorphous Solids Studied by Thermal Analysis Methods

Structural relaxation for simple and more complex thermal histories is described by a phenomenological model based on a non-exponential relaxation function, the reduced-time concept and the nonlinear structural contribution to the relaxation time. The history, development of experimental techniques and data analysis is described. It is shown that the volume and enthalpy relaxation response can conveniently be compared on the basis of a fictive relaxation rate, R _f. A simple equation relating R _f and the parameters of the phenomenological model is given. The calculated data for moderate departures from equilibrium are in good agreement with our experiments and data previously reported in the literature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Modified electron transfer model for excitation functions of the type M + RX → MX + R and M+ + RX− (M = alkali,R = alkyl group,X = halogen) and M′ + N2O → MO* + N2 (M′= Ba OR Sm)

A one-dimensional model is described for the excitation functions of reactions that are initiated by an electron transfer at close range. The process is governed by a barrier in the entrance channel, the abortive reflection of trajectories at higher energies and by the competition of an adiabatic and a diabatic channel for the reactive flux. The model is fitted to measured cross sections for the (K.Rb)+CH₃I, K+C₂H₅Br and (Ba.Sm)÷ N₂O reactions and the electron transfer cross section for K+CH₃I → K⁺ + CH₃I^- is successfully predicted from the fitting parameters of the reactive channel.     

The theory of electron transfer reactions: what may be missing?

Molecular dynamics simulations are presented for condensed-phase electron transfer (ET) systems where the electronic polarizability of both the solvent and the solute is incorporated. The solute polarizability is allowed to change with electronic transition. The results display notable deviation from the standard free energy parabolas of traditional ET theories. A new three-parameter ET model is applied, and the theory is shown to accurately model the free energy surfaces. This paper presents conclusive evidence that the traditional theory for the free energy barrier of ET reactions requires modification.     

Peroxyl Radical Reactions in Water Solution: A Gym for Proton‐Coupled Electron‐Transfer Theories

The reactions of alkylperoxyl radicals with phenols have remained difficult to investigate in water. We describe herein a simple and reliable method based on the inhibited autoxidation of water/THF mixtures, which we calibrated against pulse radiolysis. With this method we measured the rate constants k_inh for the reactions of 2‐tetrahydrofuranylperoxyl radicals with reference compounds: urate, ascorbate, ferrocenes, 2,2,5,7,8‐pentamethyl‐6‐chromanol, Trolox, 6‐hydroxy‐2,5,7,8‐tetramethylchroman‐2‐acetic acid, 2,6‐di‐tert‐butyl‐4‐methoxyphenol, 4‐methoxyphenol, catechol and 3,5‐di‐tert‐butylcatechol. The role of pH was investigated: the value of k_inh for Trolox and 4‐methoxyphenol increased 11‐ and 50‐fold from pH 2.1 to 12, respectively, which indicate the occurrence of a SPLET‐like mechanism. H(D) kinetic isotope effects combined with pH and solvent effects suggest that different types of proton‐coupled electron transfer (PCET) mechanisms are involved in water: less electron‐rich phenols react at low pH by concerted electron‐proton transfer (EPT) to the peroxyl radical, whereas more electron‐rich phenols and phenoxide anions react by multi‐site EPT in which water acts as proton relay.     

Theoretical study of homogeneous electron self-exchange in polar aromatic molecules: the role of the reactant structure

The solvent reorganization energies λ₀ of the electron self-exchange reaction between neutral molecules (nitrobenzene, its five para-substituted derivatives and benzonitrile) and the corresponding radical anions are discussed in terms of the Kirkwood approach combined with a semi-empirical calculation of the reactant structure (AM1 and intermediate neglect of differential overlap (INDO) methods). The theoretical values of λ₀ are compared with the experimental reorganization energies λ calculated from the Marcus equation and the homogeneous rate constants k_ex. It is found that the values of λ₀ obtained using the INDO method are approximately equal to the experimental λ, whereas the AM1 method gives poor results for para-substituted nitrobenzenes. The linear correlation of log k_ex with a_N² where a_N is a nitrogen coupling constant, established for para-substituted nitrobenzenes is interpreted. A simple criterion for slow electron transfer of an arbitrary flat polar arene is formulated in terms of the reactant structure and the model of the “specifying group” suggested earlier by some of the authors.     

Proton-coupled electron transfer in solution, proteins, and electrochemistry

Recent advances in the theoretical treatment of proton-coupled electron transfer (PCET) reactions are reviewed. These reactions play an important role in a wide range of biological processes, as well as in fuel cells, solar cells, chemical sensors, and electrochemical devices. A unified theoretical framework has been developed to describe both sequential and concerted PCET, as well as hydrogen atom transfer (HAT). A quantitative diagnostic has been proposed to differentiate between HAT and PCET in terms of the degree of electronic nonadiabaticity, where HAT corresponds to electronically adiabatic proton transfer and PCET corresponds to electronically nonadiabatic proton transfer. In both cases, the overall reaction is typically vibronically nonadiabatic. A series of rate constant expressions have been derived in various limits by describing the PCET reactions in terms of nonadiabatic transitions between electron-proton vibronic states. These expressions account for the solvent response to both electron and proton transfer and the effects of the proton donor-acceptor vibrational motion. The solvent and protein environment can be represented by a dielectric continuum or described with explicit molecular dynamics. These theoretical treatments have been applied to numerous PCET reactions in solution and proteins. Expressions for heterogeneous rate constants and current densities for electrochemical PCET have also been derived and applied to model systems.