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.     

A comprehensive study of the solvent effects on the cycloaddition reaction of diethyl azodicarboxylate and ethyl vinyl ether: Efficient implementation of QM and TD‐DFT study

In this work, quantum chemistry calculations performed to study the kinetics and thermodynamic parameters of [2+2] cycloaddition reaction of diethyl azodicarboxylate and ethyl vinyl ether in eighty‐three solvents and gas phase. The solvent effect on the reaction path and electron density of the C2? N6 critical bond as the reaction coordinate at the TS was investigated. Calculated rate constants in various solvents showed that increase in the activation dipole moment accelerates the reaction. Based on the time‐dependent studies, using a conductor like polarizable continuum model solvation model, the solvent effects on the excitation energies of the reactants and transition states (TSs) and the corresponding chemical shifts were analyzed. Finally, some correlations between the rate constant and quantum reactivity indices such as electrophilicity index, chemical hardness, and electronic chemical potential were investigated. © 2014 Wiley Periodicals, Inc.     

The quantum solvation, adiabatic versus nonadiabatic, and Markovian versus non-Markovian nature of electron-transfer rate processes

In this work, we revisit the electron-transfer rate theory, with particular interests in the distinct quantum solvation effect and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full account for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theor. Comput. Chem. 2006, 5, 685. Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier crossing to tunneling and from barrierless to quantum barrier crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubo's motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.     

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.     

Equilibrium solvation in quadrupolar solvents

We present a microscopic theory of equilibrium solvation in solvents with zero dipole moment and nonzero quadrupole moment (quadrupolar solvents). The theory is formulated in terms of autocorrelation functions of the quadrupolar polarization (structure factors). It can be therefore applied to an arbitrary dense quadrupolar solvent for which the structure factors are defined. We formulate a simple analytical perturbation treatment for the structure factors. The solute is described by coordinates, radii, and partial charges of constituent atoms. The theory is tested on Monte Carlo simulations of solvation in model quadrupolar solvents. It is also applied to the calculation of the activation barrier of electron transfer reactions in a cleft-shaped donor-bridge-acceptor complex dissolved in benzene with the structure factors of quadrupolar polarization obtained from molecular-dynamics simulations.     

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.     

Pendant unit effect on electron tunneling in U-shaped molecules

The electron transfer reactions of three U-shaped donor-bridge-acceptor molecules with different pendant groups have been studied in different solvents as a function of temperature. Analysis of the electron transfer kinetics in nonpolar and weakly polar solvents provides experimental reaction Gibbs energies that are used to parameterize a molecular solvation model. This solvation model is then used to predict energetic parameters in the electron transfer rate constant expression and allow the electronic coupling between the electron donor and electron acceptor groups to be determined from the rate data. The U-shaped molecules differ by alkylation of the aromatic pendant group, which lies in the ‘line-of-sight’ between the donor and acceptor groups. The findings show that the electronic coupling through the pendant group is similar for these molecules.     

Cope elimination: elucidation of solvent effects from QM/MM simulations

The Cope elimination reactions for threo- and erythro-N,N-dimethyl-3-phenyl-2-butylamine oxide have been investigated using QM/MM calculations in water, THF, and DMSO. The aprotic solvents provide up to million-fold rate accelerations. The effects of solvation on the reactants, transition structures, and rates of reaction are elucidated here using two-dimensional potentials of mean force (PMF) derived from free-energy perturbation calculations in Monte Carlo simulations (MC/FEP). The resultant free energies of activation in solution are in close agreement with experiment. Ab initio calculations at the MP2/6-311+G-(2d,p) level using the PCM continuum solvent model were also carried out; however, only the QM/MM methodology was able to reproduce the large rate increases in proceeding from water to the dipolar aprotic solvents. Solute-solvent interaction energies and radial distribution functions are also analyzed and show that poorer solvation of the reactant in the aprotic solvents is primarily responsible for the observed rate enhancements. It is found that the amine oxide oxygen is the acceptor of three hydrogen bonds from water molecules for the reactant but only one to two weaker ones at the transition state. The overall quantitative success of the computations supports the present QM/MM/MC approach, featuring PDDG/PM3 as the QM method.     

Theoretical investigation of electron transfer transition in tetracyanoethylene-contained organic complexes

In this work, the authors use complete active space self-consistent field method to investigate the photoinduced charge-separated states and the electron transfer transition in complexes ethylene-tetracyanoethylene and tetramethylethylene-tetracyanoethylene. Geometries of isolated tetracyanoethylene, ethylene, and tetramethylethylene have been optimized. The ground state and the low-lying excited states of ethylene and tetracyanoethylene have been optimized. The state energies in the gas phase have been obtained and compared with the experimentally observed values. The torsion barrier of tetracyanoethylene has been investigated through the state energy calculation at different conformations. Attention has been particularly paid to the charge-separated states and the electron transfer transition of complexes. The stacked conformations of the donor-acceptor complexes have been chosen for the optimization of the ground and low-lying excited states. Equilibrium solvation has been considered by means of conductor-like screening model both in water and in dichloromethane. It has been found that the donor and tetracyanoethylene remain neutral in complexes in ground state (1)A(1) and in lowest triplet state (3)B(1), but charge separation appears in excited singlet state (1)B(1). Through the correction of nonequilibrium solvation energy based on the spherical cavity approximation, pi-->pi* electron transfer transition energies have been obtained. Compared with the experimental measurements in dichloromethane, the theoretical results in the same solvent are found higher by about 0.5 eV.     

Dynamics of intramolecular electron transfer in dinitrodibenzodioxin radical anions

The activation energy for intramolecular electron transfer in radical anions of 2,7-dinitrodibenzodioxin and 2,8-dinitrodibenzodioxin, obtained by simulation of their temperature-dependent EPR spectra, are well predicted by the values calculated by the two-state Marcus-Hush model from the optical charge-transfer bands using quartic-adjusted energy surfaces. The electronic coupling is higher in the 2,8-dinitrodibenzodioxin (H(ab) = 485 cm(-1)) than in the 2,7-dinitrodibenzodioxin radical anion (H(ab) = 250 cm(-1)), but for each solvent the reorganization energy, taken as the maximum of the optical band, is only slightly higher in the latter. These values are consistent with the fact that the reaction is faster in the 2,8-dinitrodibenzodioxin radical anion isomer, as determined by EPR spectroscopy. The pre-exponential factors obtained combining the EPR-derived rate constants and the activation energies calculated from the optical bands fit well the theoretical (modified) nonadiabatic values in the less viscous solvents. However, for the more viscous solvents, the trend of the pre-exponential values with solvent can only be explained if dynamical solvent effects increasingly influence their value. The influence of solvent dynamics in the 2,8-dinitrodibenzodioxin radical anion starts in the less viscous solvents DMF and DMSO, but in the 2,7-dinitrodibenzodioxin isomer this is only fully evident for the more viscous PhCN and HMPA. The influence of solvent dynamics is higher in the radical with the lowest activation barrier.     

Influence of inter- and intramolecular hydrogen bonding on kemp decarboxylations from QM/MM simulations

The Kemp decarboxylation reaction for benzisoxazole-3-carboxylic acid derivatives has been investigated using QM/MM calculations in protic and dipolar aprotic solvents. Aprotic solvents have been shown to accelerate the rates of reaction by 7-8 orders of magnitude over water; however, the inclusion of an internal hydrogen bond effectively inhibits the reaction with near solvent independence. The effects of solvation and intramolecular hydrogen bonding on the reactants, transition structures, and the rate of reaction are elucidated using two-dimensional potentials of mean force (PMF) derived from free energy perturbation calculations in Monte Carlo simulations (MC/FEP). Free energies of activation in six solvents have been computed to be in close agreement with experiment. Solute-solvent interaction energies show that poorer solvation of the reactant anion in the dipolar aprotic solvents is primarily responsible for the observed rate enhancements over protic media. In addition, a discrepancy for the experimental rate in chloroform has been studied in detail with the conclusion that ion-pairing between the reactant anion and tetramethylguanidinium counterion is responsible for the anomalously slow reaction rate. The overall quantitative success of the computations supports the present QM/MM/MC approach, which features PDDG/PM3 as the QM method.     

Solvent reorganization of electron transitions in viscous solvents

We develop a model of electron transfer reactions at conditions of nonergodicity when the time of solvent relaxation crosses the observation time window set up by the reaction rate. Solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile is studied by molecular dynamics simulations at varying temperatures. 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. 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 the relaxation of the solvent dipolar polarization. An analytical theory proposed to describe this effect agrees well with both the simulations and experimental Stokes shift data. The theory is applied to the analysis of charge-transfer kinetics in a low-temperature glass former. We show that the reorganization energy is substantially lower than its equilibrium value for the low-temperature portion of the data. The theory predicts the possibility of discontinuous changes in the dependence of the electron transfer rate on the free energy gap when the reaction switches between ergodic and nonergodic regimes.     

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 theoretical study on nitration mechanism of benzene and solvent effects

Aromatic nitration is an important and canonical example of electrophilic substitution in organic chemistry. The research on nitration mechanism is also very important for synthesis of explosives since benzene molecule is a basic unit to build up into the energetic material. Besides the electrophilic substitution mechanism, there is an electron transfer mechanism[1,2]. The nitronium ion (NO+ 2), however, is a generally accepted active nitrating agent in the aromatic nitration. Therefore, the …     

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

Realistic modeling of ruthenium-catalyzed transfer hydrogenation

We report the first computational study of a fully atomistic model of the ruthenium-catalyzed transfer hydrogenation of formaldehyde and the reverse reaction in an explicit methanol solution. Using ab initio molecular dynamics techniques, we determined the thermodynamics, mechanism, and electronic structure along the reaction path. To assess the effect of the solvent quantitatively, we make a direct comparison with the gas-phase reaction. We find that the energy profile in solution bears little resemblance to the profile in the gas phase and a distinct solvation barrier is found: the activation barriers in both directions are lowered and the concerted hydride and proton transfer in the gas phase are converted into a sequential mechanism in solution with the substrate appearing as methoxide-like intermediate. Our results indicate that besides the metal-ligand bifunctional mechanism, as proposed by Noyori, also a concerted solvent-mediated mechanism is feasible. Our study gives a new perspective of the active role a solvent can have in transition-metal-catalyzed reactions.     

Uncatalyzed transfer hydrogenation of quinones and related systems: a theoretical mechanistic study

Quantum chemistry calculations have been used to study the uncatalyzed transfer hydrogenation between a range of hydrogen donors and acceptors, in the gas phase and in solution. Our study shows in the first place that in order to obtain reliable condensed-phase transition structures, it is necessary to perform geometry optimization in the presence of a continuum. In addition, the use of a free energy of solvation obtained with the UB3-LYP/6-31+G(d,p)/IEF-PCM/UA0 combination, in conjunction with UMPWB1K/6-311+G(3df,2p)//B3-LYP/6-31+G(d,p) gas-phase energies, gives the best agreement with experimental barriers. In condensed phases, the geometries and energies of the transition structures are found to relate to one another in a manner consistent with the Hammond postulate. There is also a correlation between the barriers and the energies of the radical intermediates in accord with the Bell-Evans-Polanyi principle. We find that in the gas phase, all the transfer-hydrogenation reactions examined proceed via a radical pathway. In condensed phases, some of the reactions follow a radical mechanism regardless of the solvent. However, for some reactions there is a change from a radical mechanism to an ionic mechanism as the solvent becomes more polar. Our calculations indicate that the detection of radical adducts by EPR does not necessarily indicate a predominant radical mechanism, because of the possibility of a concurrent ionic reaction. We also find that the transition structures for these reactions do not necessarily have a strong resemblance to the intermediates, and therefore one should be cautious in utilizing the influence of polar effects on the rate of reaction as a means of determining the mechanism.     

Kinetic and Mechanistic Aspects of Reactivity of the Oxidation of Some Fe(II)–Tris Schiff Base Complexes by Peroxydisulfate: Spectrophotometric Tracer and Solvent Effect on the Reactivity

The kinetics of the oxidation of some Fe(II)–Tris Schiff base complexes by peroxydisulfate was studied spectrophotometrically in the aqueous medium and in the organic–aqua binary mixture. The inspected complexes were derived from the condensation of 2‐acetylpyridine and substituted benzylamines. The oxidation reaction of the studied complexes was followed at 303 K under pseudo–first‐order conditions. It was found that the oxidation reaction by S₂O₈^2? consists of two steps. The first step is the formation of an ion pair from the reactants, and the second step is an electron transfer from the metal center to the peroxydisulfate oxidant, with an associated peroxo bond fissure. A mechanism, based on the experimental results, was proposed, and the rate law was derived. The effect of organic solvent on the reaction rate was studied in the presence of different ratios (v/v) of methanol–water and acetone–water mixtures. Moreover, the changes in the activation barrier from water to water–methanol and water–acetone mixtures were estimated from the kinetic data. The transfer chemical potentials of the initial and transition states from water into mixed solvents were determined from solubility measurements. Solvent effects on the reaction rate were discussed in terms of initial state versus transition state solvation.