Dynamical arrest of electron transfer reorganization in super-cooled water

This paper reports the results of Molecular Dynamics (MD) simulations of the solvent reorganization energy of electron transfer (ET) reactions in low-temperature solvents. Simulations are carried out for a model charge-transfer optical dye (p-nitroaniline) in SPC/E water in a range of temperatures down to the point of solvent ideal glass transition. We show a significant departure of the solvent reorganization energy, measured on a given time window, from its thermodynamic limit obtained by averaging over long simulation trajectories. Our results thus indicate that optical solvatochromism and activation parameters of ET reactions measured in viscous solvents will be significantly affected by the dynamical arrest of nuclear solvation when the experimental time scale becomes comparable to the characteristic relaxation time of the solvent.     

Reorganization energy of electron transfer in viscous solvents above the glass transition

We present a molecular-dynamics study of the solvent reorganization energy of electron transfer in supercooled water. We observe a sharp decrease of the reorganization energy at a temperature identified as the temperature of structural arrest due to cage effect as discussed by the mode coupling theory. Both the heat capacity and dielectric susceptibility of the pure water show sharp drops at about the same temperature. This temperature also marks the onset of the enhancement of translational diffusion relative to rotational relaxation signaling the breakdown of the Stokes-Einstein relation. The change in the reorganization energy at the transition temperature reflects the dynamical arrest of the slow, collective relaxation of the solvent related to Debye relaxation of the solvent dipolar polarization.     

Solvent reorganization entropy of electron transfer in polar solvents

We report the results of molecular dynamics simulations of the solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile at varying temperatures. The simulations confirm the prediction of microscopic solvation theories of a positive reorganization entropy in polar solvents. The results of simulations are analyzed in terms of the splitting of the reorganization entropy into the contributions from the solute-solvent interaction and from the alteration of the solvent structure induced by the solute. These two contributions mutually cancel each other, resulting in the reorganization entropy amounting to only a fraction of each component.     

Activation entropy of electron transfer reactions

We report microscopic calculations of free energies and entropies for intramolecular electron transfer reactions. The calculation algorithm combines the atomistic geometry and charge distribution of a molecular solute obtained from quantum calculations with the microscopic polarization response of a polar solvent expressed in terms of its polarization structure factors. The procedure is tested on a donor–acceptor complex in which ruthenium donor and cobalt acceptor sites are linked by a four-proline polypeptide. The reorganization energies and reaction energy gaps are calculated as a function of temperature by using structure factors obtained from our analytical procedure and from computer simulations. Good agreement between two procedures and with direct computer simulations of the reorganization energy is achieved. The microscopic algorithm is compared to the dielectric continuum calculations. We found that the strong dependence of the reorganization energy on the solvent refractive index predicted by continuum models is not supported by the microscopic theory. Also, the reorganization and overall solvation entropies are substantially larger in the microscopic theory compared to continuum models.     

Computational methods for intramolecular electron transfer in a ferrous-ferric iron complex

The limitations of common theoretical and molecular computational approaches for predicting electron transfer quantities were assessed, using an archetypal bridged ferrous-ferric electron transfer system in aqueous solution. The basis set effect on the magnitude of the electronic coupling matrix element computed using the quasi-diabatic method was carefully examined, and it was found that the error related to a poor basis set could exceed the thermal energy at room temperature. A range of approaches to determining the external (solvent) reorganization energy were also investigated. Significant improvements from the Marcus continuum model can be obtained by including dipolar Born-Kirkwood-Onsager correction. In this regard, we also found that Klamt's Conductor-Like Screening Model (COSMO) yields estimations of the external reorganization energy similar to those obtained with explicit solvent molecular dynamics simulations if the fast-frequency modes are neglected, which makes it an attractive alternative to laborious umbrella sampling simulations. By using the COSMO model, we also confirm that a decrease in curvature of the potential energy surface is a manifestation of the dielectric saturation observed in the first solvation layer. The linearity of solvent response to the charge redistribution was assessed by analyzing the energy gap autocorrelation function as well as the solvent density and dipole moment fluctuations. Molecular dynamics was also used to evaluate the sign and magnitude of the solvent reorganization entropy and to determine its effect on the predicted electron transfer rate. Finally, we present a simple way of estimating the vibration frequency along the reaction coordinate, which also enables prediction of the mass-dependent isotopic signature of electron transfer reactions.     

A Model Electron Transfer Reaction in Confined Aqueous Solution

Liquid water confined within nanometer-sized channels exhibits a strongly reduced local dielectric constant perpendicular to the wall, especially at the interface, and this has been suggested to induce faster electron transfer kinetics at the interface than in the bulk. We study a model electron transfer reaction in aqueous solution confined between graphene sheets with classical molecular dynamics. We show that the solvent reorganization energy is reduced at the interface compared to the bulk, which explains the larger rate constant. However, this facilitated solvent reorganization is due to the partial desolvation by the graphene sheet of the ions involved in the electron transfer and not to a local dielectric constant reduction effect.     

Hopping transport in conductive heterocyclic oligomers: reorganization energies and substituent effects

Molecular scale charge motion in disordered organic materials at ambient temperature occurs via a hopping-type mechanism with rates dictated both by the charge transfer integral and by the reorganization energy due to geometric relaxation. This contribution presents a systematic theoretical analysis of cation internal reorganization energies for a broad family of organic oligoheterocycles-variation of reorganization energy with oligomer chain length, heteroatom identity, and a range of heterocycle substituents provides key information on important structural properties governing internal reorganization energies. At room temperature, the range in reorganization energies induced by substituent variations corresponds to a >10(2)-fold variation in intrinsic hole transfer rate, suggesting that changes in reorganization energy dominate variations in charge-transfer rates for many semiconducting/conducting oligomers.     

Stationary points in the temperature dependence of electron transfer rates

The temperature dependence of the rate of electron transfer is analyzed in the framework of a molecular theory presented recently, characterized by decoupling the total solvent reorganization energy into two contributions featuring reorganizations of permanent dipoles as well as solvent density. The inclusion of the temperature dependence of liquid density reorganization can give rise to a maximum in the Arrhenius coordinates for electron transfer in the inverted region and for exothermic reactions with small activation barriers as well.     

Proton-coupled electron transfer in soybean lipoxygenase

The proton-coupled electron transfer reaction catalyzed by soybean lipoxygenase-1 is studied with a multistate continuum theory that represents the transferring hydrogen nucleus as a quantum mechanical wave function. The inner-sphere reorganization energy of the iron cofactor is calculated with density functional theory, and the outer-sphere reorganization energy of the protein is calculated with the frequency-resolved cavity model for conformations obtained with docking simulations. Both classical and quantum mechanical treatments of the proton donor-acceptor vibrational motion are presented. The temperature dependence of the calculated rates and kinetic isotope effects is in agreement with the experimental data. The weak temperature dependence of the rates is due to the relatively small free energy barrier arising from a balance between the reorganization energy and the reaction free energy. The unusually high deuterium kinetic isotope effect of 81 is due to the small overlap of the reactant and product proton vibrational wave functions and the dominance of the lowest energy reactant and product vibronic states in the tunneling process. The temperature dependence of the kinetic isotope effect is strongly influenced by the proton donor-acceptor distance with the dominant contribution to the overall rate. This dominant proton donor-acceptor distance is significantly smaller than the equilibrium donor-acceptor distance and is determined by a balance between the larger coupling and the smaller Boltzmann probability as the distance decreases. Thus, the proton donor-acceptor vibrational motion plays a vital role in decreasing the dominant donor-acceptor distance relative to its equilibrium value to facilitate the proton-coupled electron transfer reaction.     

Nonadiabatic proton-coupled electron transfer reactions: impact of donor-acceptor vibrations, reorganization energies, and couplings on dynamics and rates

Fundamental aspects of proton-coupled electron transfer (PCET) reactions in solution are analyzed with molecular dynamics simulations for a series of model systems. The analysis addresses the impact of the solvent reorganization energy, the proton donor-acceptor mode vibrational frequency, and the distance dependence of the nonadiabatic coupling on the dynamics of the reaction and the magnitude of the rate. The rate for nonadiabatic PCET is expressed in terms of a time-dependent probability flux correlation function. The time dependence of the probability flux correlation function is determined mainly by the solvent reorganization energy and is not significantly influenced by the proton donor-acceptor frequency or the distance dependence of the nonadiabatic coupling. The magnitude of the PCET rate becomes greater as the solvent reorganization energy decreases, the proton donor-acceptor frequency decreases, and the distance dependence of the nonadiabatic coupling increases. The approximations underlying a previously derived analytical PCET rate expression are also investigated. The short-time approximation for the solvent is valid for these types of systems. In addition, solvent damping effects on the proton donor-acceptor motion are not significant on the time scale of the probability flux. The rates calculated from the molecular dynamics simulations agree well with those calculated from the analytical rate expression.     

Solvent Reorganization Energy and Electronic Coupling for Intramolecular Electron Transfer in Biphenyl-Acceptor Anion Radicals

A novel algorithm was designed and implemented to realize the numerical calculation of the solvent reorganization energy for electron transfer reactions, on the basis of nonequilibrium solvation theory and the dielectric polarizable continuum model. Applying the procedure to the well-investigated intramolecular electron transfer in biphenyl-androstane-naphthyl and biphenyl-androstane-phenanthryl systems, the numerical results of solvent reorganization energy were determined to be around 60 kJ/mol, in good agreement with experimental datKoopman's theorem was adopted for the calculation of the electron transfer coupling element, associated with the linear reaction coordinate approximation. The values for this quantity obtained are acceptable when compared with experimental results.     

Photoinduced intramolecular charge transfer in push-pull polyenes: effects of solvation, electron-donor group, and polyenic chain length

Subpicosecond absorption spectroscopy is used to characterize the primary photoinduced processes in a class of push-pull polyenes bearing a julolidine end group as the electron donor and a diethylthiobarbituric acid end group as the electron acceptor. The excited-state decay time and relaxation pathway have been studied for four polyenes of increasing chain length (n = 2-5 double bonds) in aprotic solvents of different solvation time, polarity, and viscosity. Intramolecular charge transfer (ICT) leading to a transient state of cyanine-like structure (fully conjugated with no bond length alternation) is observed in all polar solvents at a solvent dependent rate, but the reaction is not observed in cyclohexane, a nonpolar solvent. In polar solvents, the reaction time increases with the average solvation time but remains slightly larger, except in the viscous solvent triacetin. These facts are interpreted as an indication that both solvent reorganization and internal restructuring are involved in the ICT-state formation. The observed photodynamics resemble those we previously found for another class of polyenes bearing a dibutylaniline group as the donor, including a similar charge-transfer rate in spite of the larger electron donor character of the julolidine group. This observation brings further support to the proposal that an intramolecular coordinate is involved in the charge-transfer reaction, possibly a torsional motion of the donor end group. On the other hand, relaxation of the ICT state leads to cis-trans isomerization or crossing to the triplet state, depending on the length of the polyenic chain. In dioxane, tetrahydrofuran, and triacetin, the ICT state of the shorter chains (n = 2, 3) relaxes to the isomer with a viscosity-dependent rate, while that of the longer ones (n = 4, 5) leads to the triplet state with a viscosity-independent rate, as expected. In acetonitrile, the ICT-state lifetime is generally much shorter. A change from photoisomerization to intersystem crossing at n = 4 is also proposed in this solvent, but the formation of a photoproduct at n = 2 is not clear. In cyclohexane, where the ICT state is not formed, the relaxation pathway of the initially excited state is found to lead to an isomer for n = 2. As in polar solvents, a change to intersystem crossing at n = 4 is proposed. The direct relaxation to the ground state found at n = 3 for the series bearing a dibutylaniline group is not observed with the julolidine group. The results clearly illustrate that photoinduced reaction trajectories in push-pull polyenes are controlled by the static and dynamic properties of the solvent, the chemical nature and size of the end groups, and the conjugated-chain length and flexibility.     

Protein-water electrostatics and principles of bioenergetics

Despite its diversity, life universally relies on a simple basic mechanism of energy transfer in its energy chains-hopping electron transport between centers of electron localization on hydrated proteins and redox cofactors. Since many such hops connect the point of energy input with a catalytic site where energy is stored in chemical bonds, the question of energy losses in (nearly activationless) electron hops, i.e., energetic efficiency, becomes central for the understanding of the energetics of life. We show here that standard considerations based on rules of Gibbs thermodynamics are not sufficient, and the dynamics of the protein and the protein-water interface need to be involved. The rate of electronic transitions is primarily sensitive to the electrostatic potential at the center of electron localization. Numerical simulations show that the statistics of the electrostatic potential produced by hydration water are strongly non-Gaussian, with the breadth of the electrostatic noise far exceeding the expectations of the linear response. This phenomenon, which dramatically alters the energetic balance of a charge-transfer chain, is attributed to the formation of ferroelectric domains in the protein's hydration shell. These dynamically emerging and dissipating domains make the shell enveloping the protein highly polar, as gauged by the variance of the shell dipole which correlates with the variance of the protein dipole. The Stokes-shift dynamics of redox-active proteins are dominated by a slow component with the relaxation time of 100-500 ps. This slow relaxation mode is frozen on the time-scale of fast reactions, such as bacterial charge separation, resulting in a dramatically reduced reorganization free energy of fast electronic transitions. The electron transfer activation barrier becomes a function of the corresponding rate, self-consistently calculated from a non-ergodic version of the transition-state theory. The peculiar structure of the protein-water interface thus provides natural systems with two "non's"-non-Gaussian statistics and non-ergodic kinetics-to tune the efficiency of the redox energy transfer. Both act to reduce the amount of free energy released as heat in electronic transitions. These mechanisms are shown to increase the energetic efficiency of protein electron transfer by up to an order of magnitude compared to the "standard picture" based on canonical free energies and the linear response approximation. In other words, the protein-water tandem allows both the formation of a ferroelectric mesophase in the hydration shell and an efficient control of the energetics by manipulating the relaxation times.     

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.     

二氯二氰基苯醌及其阴离子自交换电子转移反应的理论研究

基于非平衡溶剂化能的约束平衡方法和溶剂重组能的新表达式, 实现了电子转移反应溶剂重组能的数值解, 研究了二氯二氰基苯醌(DDQ)及其阴离子体系DDQ-之间的自交换电子转移反应. 考虑了DDQ与DDQ-分子以平行方式形成受体-给体络合物时的两种构型. 引入线性反应坐标, 计算了该反应在不同溶剂中的溶剂重组能. 基于两态变分模型得到了反应的电子耦合矩阵元. 根据电子转移动力学模型, 计算了该自交换电子转移反应的速率常数.     

Ultrafast electron-transfer and solvent adiabaticity effects in viologen charge-transfer complexes

We report ultrafast electron transfer (ET) in charge-transfer complexes that shows solvent relaxation effects consistent with adiabatic crossover models of nonadiabatic ET. The complexes of either dimethyl viologen (MV) or diheptyl viologen (HV) with 4,4'-biphenol (BP) (MVBP or HVBP complexes) have identical charge-transfer spectra and kinetics in ethylene glycol with approximately 900 fs ET decay. We assign this decay time as largely due to adiabatic control of a predicted approximately 40 fs nonadiabatic ET. The MVBP decay in methanol of 470 fs is reduced in mixtures having low (2-20%) concentrations of acetonitrile to as short as 330 fs; these effects are associated with faster relaxation time in methanol and its mixtures. In contrast, HVBP has much longer ET decay in methanol (730 fs) and mixture effects that only reduce its decay to 550 fs. We identify the heptyl substituent as creating major perturbations to solvent relaxation times in the methanol solvation shell of HVBP. These charge-transfer systems have reasonably well-defined geometry with weak electronic coupling where the electronic transitions are not dependent on intramolecular motions. We used a nonadiabatic ET model with several models for adiabatic crossover predictions to discuss the small variation of energy gap with solvent and the ET rates derived from adiabatic solvent control. A time correlation model of solvent relaxation was used to define the solvent relaxation times for this case of approximately zero-barrier ET.     

Energetics and kinetics of primary charge separation in bacterial photosynthesis

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.     

A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region

A phenomenological model of electron transfer reactions in solvents undergoing glass transition is discussed. The reaction constant cuts off slow polarization modes from the spectrum of nuclear thermal motions active on the observation time scale. The arrest of nuclear solvation in turn affects the reaction activation barrier making it dependent on the rate. The resultant rate constant is sought from a self-consistent equation. The model describes well the sharp change in the solvent Stokes shift of optical lines in the glass-transition region. It is also applied to describe the temperature dependence of primary charge separation and reduction of primary pair in photosynthetic reaction centers. The model shows that a weak dependence of the primary charge separation rate on temperature can be explained by dynamical arrest of nuclear solvation on the picosecond time scale of electron transfer. For reduction of primary pair by cytochrome, the model yields a sharp turnover of the reaction kinetics at the transition temperature when nuclear solvation freezes in.     

Dynamics of proton transfer and vibrational relaxation in dilute hydrofluoric acid

The molecular mechanisms in both vibrational relaxation and proton transfer (PT) associated with infrared (IR)-induced PT in a dilute hydrofluoric acid solution at ambient temperature are studied by molecular dynamics (MD) simulations with the multistate empirical valence bond model. To investigate the solvation dynamics, a collective solvent coordinate and its perpendicular bath modes are defined from the diabatic energy gap and their motions are examined by the generalized Langevin equation (GLE) formalism. The GLE analysis using the equilibrium MD simulation shows that the major solvent reorganizations in the PT are represented by the libration and hindered translation. In particular, the libration gives the stronger coupling to the solvent reorganization and the faster relaxation. The nonequilibrium MD simulation demonstrated that both the HF stretching vibration and the solvent reorganization relax on a similar time scale and thus compete in the PT. It also supported the "presolvation mechanism" for the PT in this system.     

Solvent dynamics in a model system

We report herein a study of the solvent reorganization process in an electron transfer reaction. The calculations are based on a model consisting of 26 or 62 solvent particles. Molecular dynamics simulations are performed to calculate the electric field fluctuations during the orientational and translational motion of the solvent molecules. The changes in the electric fields at various points near the reacting sites in the system are evaluated as a function of time. From these electric fields, electric field time correlation functions are calculated. The main conclusion in this work is that it requires nearly 3 ps for the model solvent to reorient during the charge transfer. These results suggest ways of incorporating solvent dynamics based on molecular models into theoretical studies of electron transfer rates in condensed media.