电子转移溶剂重组能计算的自洽反应场新方法

基于非平衡溶剂化理论, 推导了用于非平衡溶剂化能数值计算的类导体屏蔽模型(COSMO)的相关公式. 在此基础上, 修改了HONDO99中COSMO模块, 并用以估算了[(CH₂)₂C]+—(CH₂)_n—C(CH₂)₂(n＝1～13)体系中的电子转移溶剂重组能. 结果表明, 溶剂重组能值与电子转移距离的倒数有很好的线性关系. 根据溶剂重组能数值解结果, 用新的双球模型给出了合理的给受体球半径.     

Thermodynamics for nonequilibrium solvation and numerical evaluation of solvent reorganization energy

This work presents a thermodynamic method for treating nonequilibrium solvation. By imposing an extra electric field onto the nonequilibrium solvation system, a virtual constrained equilibrium state is prepared. In this way, the free energy difference between the real nonequilibrium state and the con-strained equilibrium one is simply the potential energy of the nonequilibrium polarization in the extra electronic field, according to thermodynamics. Further, new expressions of nonequilibrium solvation energy and solvent reorganization energy have been formulated. Analysis shows that the present formulations will give a value of reorganization energy about one half of the traditional Marcus theory in polar solvents, thus the explanation on why the traditional theory tends to overestimate this quantity has been found out. For the purpose of numerical determination of solvent reorganization energy, we have modified Gamess program on the basis of 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 have been found to be in good agreement with the experimental fittings.     

Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment

Computer simulations of biological electron transfer reactions are reviewed with a focus on the calculation of reaction free energy (driving force) and reorganization free energy. Then a mixed quantum mechanical/molecular mechanical (QM/MM) approach is described which is designed for computation of these quantities for pure electron transfer reactions with large donor-acceptor separation distances. The method is applied to intra-protein electron transfer in Ru(bpy)(2)(im)His33 cytochrome c and the results compared to experimental data. Several modeling aspects which are important for successful calculation of free energies with QM/MM are discussed in detail.     

电子转移反应O~2+O~2^.^-→O~2^.^-+O~2的从头算研究

利用abinitio方法,在UHF,UMP2及不同基组3-21G,6-31G^*,6-311+G^*和UMP2(full)/6-311+G^*水平上,研究了O~2/O~2^.^-自交换电子转移反应。优化了电子转移前后反应物和产物的结构,研究了体系能量的变化,计算了自交换电子转移反应的内重组能。对UHF方法和UMP2方法的计算结果进行了比较,并与实验结果进行了对照。结果表明UHF方法由于没有考虑组态相互作用,计算结果存在较大偏差,UMP2(full)/6-311+G^*水平上的计算结果与实验值吻合较好。在UMP2(full)/6-311+G^*水平上计算了气相自交换电子转移反应速率常数。在优化了电子转移复合物结构的基础上考虑了溶剂效应的影响,计算了水溶液中的溶剂重组能。研究结果表明O~2/O~2^.^-体系电子转移反应的活化能主要来源于溶剂重组能的贡献。最后计算了该反应在水溶液中的反应速率常数。理论计算结果与实验值吻合得很好。     

Continuous medium theory for nonequilibrium solvation: IV. Solvent reorganization energy of electron transfer based on conductor-like screening model

In this work the authors present some evidences of defects in the popular continuous medium theories for nonequilibrium solvation. Particular attention has been paid to the incorrect reversible work approach. After convincing reasoning, the nonequilibrium free energy has been formulated to an expression different from the traditional ones. In a series of recent works by the authors, new formulations and some analytical application models for ultrafast processes were developed. Here, the authors extend the new theory to the cases of discrete bound charge distributions and present the correct form of the nonequilibrium solvation energy in such cases. A numerical solution method is applied to the evaluation of solvent reorganization energy of electron transfer. The test calculation for biphenyl-cyclohexane-naphthalene anion system achieves excellent agreement with the experimental fitting. The central importance presented in this work is the very simple and a consistent form of nonequilibrium free energy for both continuous and discrete charge distributions, based on which the new models can be established.     

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.     

Scaling for Experimental Inner-Sphere Reorganization Energy of Hydrated Ions via Accurate Potential Function

Reported here are several new calculation methods for the inner-sphere reorganization energy of hydrated metal ions involved in electron transfer processes.It is based on the self-exchange model of reorganization and utilizes the more exact potential functions between central metal ion and the inner-sphere ligands.The parameters involved are determined via the spectroscopic and thermodynamic data.The predictions of the inner-sphere reorganization energies from those models agree well with the photoemission experimental results.     

溶剂-导体界面电子转移溶剂重组能的球-界面模型

在连续介质理论基础上, 根据热力学基本原理, 用一个外加电场Eex将非平衡态2[Enon2, Dnon2]变成约束平衡态[E*2, D*2], 推导出了正确普适的溶剂重组能公式. 基于球-界面近似, 推导出了正确的溶剂-导体界面电子转移溶剂重组能公式. 和Marcus的公式相比, 本文的结果多了(εs-εop)/(εop(εs-1))因子. 对极性溶剂, 预测的溶剂重组能约为Marcus模型所得结果的一半. 以C343(Coumarin 343)-TiO2体系为算例, 计算了溶剂重组能并与实验值进行了比较.     

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.     

Application of the Marcus theory to description of the kinetics of reduction processes of organic cations

The calculation of the rate constants for the processes in the reduction of diazonium, tropylium, verdazylium, and pyrylium cations by various organic electron donors, using the equations of the Marcus theory with allowance for the reorganization energy of only the outer coordination sphere, leads to values which are one to seven orders of magnitude higher than the experimental values. By quantum-chemical calculations it was shown that the reduction of diazonium and tropylium cations to the corresponding radicals is accompanied by a substantial change in the structure of the reagents. This leads to high values for the reorganization energy of the inner coordination sphere of the cations, which must be taken into account during calculation of the rate constants. The differences in the rate constants of the processes of direct electron transfer from the electron donors to the organic cations and the recombination of these reagents depend on the dissociation energy of the bond of the cation with the donor leading to the electron transfer products.     

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.     

Excited singlet (S1)-state interactions of Nile red with aromatic amines

Both steady-state (SS) and time-resolved (TR) studies show that the fluorescence of the dye Nile red (NR) is quenched by various aromatic amines (ArA). Bimolecular quenching constants (kq) from both SS and TR measurements are observed to match well, indicating that the interaction is dynamic in nature. The quenching interaction in the present systems has been attributed to electron transfer (ET) from ArA to excited NR, based on the variations in the kq values with the oxidation potentials of the amines. The kq values calculated within the framework of Marcus' outer-sphere ET theory at different free-energy changes (deltaG0) of the ET reactions match well with the experimental ones, supporting the ET mechanism in the systems studied. The reorganization energy (lambda) estimated from the correlation of the experimental and the calculated kq values is quite similar to the solvent reorganization energy (lambda(s)), calculated on the basis of the solvent dielectric continuum model along with the assumption that the reactants are the effective spheres. Although a modest error is involved in this lambda(s) calculation, the similarity in lambda and lambda(s) values suggests that the solvent reorganization plays a dominant role in governing the ET dynamics in the present systems.     

A modified two-sphere model for solvent reorganization energy in electron transfer

In this work, the solvent reorganization energy is formulated within the framework of classical thermodynamics, by adding some external charges to construct a constrained equilibrium state. The derivation clearly shows that the reorganization energy is exactly the polarization cost for the inertial part of the polarization. We perform our derivation just within the framework of the first law of thermodynamics, and the final form of the reorganization energy is completely the same as that we gave in our recent work by defining a nonequilibrium solvation free energy. With the two-sphere model approximation, our solvent reorganization energy is derived as λ(0) = Δq(2)/2[1/r(D) + 1/r(A) - 2/d][(ε(-1)(op) - ε(-1)(s))/(1 - ε(-1)(s))]. This amends Marcus' model by a factor of (ε(-1)(op) - ε(-1)(s))/(1 - ε(-1)(s)), which is coupled with the solvent polarity. Making use of the modified expression of solvent reorganization energy, two recently reported electron transfer processes are investigated in representative solvents. The results show that our formula can well reproduce the experimental observations.     

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.     

Theoretical Study on Electron Transfer Matrix Element in Oxidation of α—Amino Carbon—Centered Radical by O2

As a successive work of our previous paper,^1the electron transfer matrix element(Vrp)in the oxidation of the simplified model molecule of α-amino carbon-centered radical by O2 has been investigated with ab initio calculation at the level of UHF/6-31 G**.Based on the optimized geometries of the reactgant and the ion-pair complex obtained previously,the reaction heat and the iuner reorganization energy have been obtained by constructing the potential energy curves of reactant and product states considering the solvent effect with the conductor-like screening model(COSMO).The solvent reorganization energy has been estimated using Lippert-Mataga relationship.The calculated results show that the value of Vrp is several times larger than that of RT,which means that the model reaction is an adiabatic one.Theoretical investigation indicates that the solvent effect on the direct electron transfer (ET) process of oxidation of α-amino carbon-centered radical by oxygen is remarkable.     

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

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

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.     

Influence of Nonlocal Effects on Kinetic Parameters of Heterogeneous Charge Transfer Reactions

The influence of the spatial dispersion of the solvent and of the effect of the electrical field penetration into a metal on the free energy of the solvent reorganization and the activation free energy for heterogeneous charge transfer reactions is studied. The calculations are based on the exactly solved model of a sharp metal/electrolyte interface, the model of a Born sphere for the ion, and the three-mode approximation for the dielectric function of the solvent. In the sharp-interface model, in the case of a mirror reflection, a relationship for the dielectric tensor of a heterogeneous system comprising two contacting media with a plane interface is obtained, along with an expression for the potential created by a point charge. This expression formally coincides with the expression derived earlier by Vorotyntsev and Kornyshev, but it contains true bulk dielectric functions of contacting media. In the model of the Born sphere for the ion and the three-mode approximation for the dielectric function of the solvent, an expression for the potential of image forces, which determines the dependence of the solvent reorganization energy on the distance from the reacting ion to the electrode, is obtained. It is shown that both the reorganization energy and the activation free energy decrease with decreasing distance from the ion to the electrode. The calculation results are compared with estimates of the reorganization energy obtained from experimental data for the reaction Fe³⁺/Fe²⁺ and the reaction of the hydronium ion discharge.     

Cyclopropyl conjugation and ketyl anions: when do things begin to fall apart?

Results pertaining to the electrochemical reduction of 1,2-diacetylcyclopropane (5), 1-acetyl-2-phenylcyclopropane (6), 1-acetyl-2-benzoylcyclopropane (7), and 1,2-dibenzoylcyclopropane (8) are reported. While 6*- exists as a discrete species, the barrier to ring opening is very small (<1 kcal/mol) and the rate constant for ring opening is >10(7) s(-1). For 7 and 8, the additional resonance stabilization afforded by the benzoyl moieties results in significantly lower rate constants for ring opening, on the order of 10(5)-10(6) s(-1). Electron transfer to 8 serves to initiate an unexpected vinylcyclopropane --> cyclopentene type rearrangement, which occurs via a radical ion chain mechanism. The results for reduction of 5 are less clear-cut: The experimental results suggest that the reduction is unexceptional, with a symmetry coefficient alpha 相似文献   

Theoretical Study of the Inner/sphere Reorganization Energy and Activation Energy of Self/exchange Electron Transfer Reaction for M(H2O)26+/3+ (M=V, Cr, Mn, Fe and Co) Systems

通过建立电子转移过程的活化模型和重组模型, 提出了用量子化学从头算方法研究电子转移过程内层重组能和活化能的新方法. 在UMP26/311G水平上获得了5对过渡金属水合离子体系M(H