电子转移的外电场效应──苯分子与苯正离子自由基间电子转移的从头算研究

基于半经典电子转移理论,结合量子化学计算,在HF/DZP水平上,研究外电场作用下平行的苯分子-苯正离子自由基体系(C₆H₄)₂⁺的分子内电子转移问题.在给体和受体几何构型优化的基础上,用线性反应坐标确定电子转移过渡态,分别用两态变分方法和基于Koopmans定理的分子轨道跃迁能方法计算电子转移矩阵元V_AB,讨论了V_AB对给体和受体中心距d的指数衰减关系.取中心距为0.6nm,研究了外电场对反应热的影响,计算得到在不同外电场强度下分子内气相电子转移的速率常数k.     

Sampling the proton transfer reaction coordinate in mixed quantum-classical molecular dynamics simulations

An umbrella sampling approach based on the vibrational energy gap is presented and examined for exploring the reaction coordinate for a proton transfer (PT) reaction. The technique exploits the fact that for a PT reaction the energy gap between the vibrational ground and excited states of the transferring proton reaches a minimum at the transition state. Umbrella sampling is used within mixed quantum-classical simulations to identify the transition state configurations and explore the reaction free energy curve and vibrationally nonadiabatic coupling. The method is illustrated by application to a model phenol-amine proton transfer reaction complex in a nanoconfined solvent. The results from this new umbrella sampling approach are consistent with those obtained from previous umbrella sampling calculations based on a collective solvent coordinate. This sampling approach further provides insight into the vibrationally nonadiabatic coupling for the proton transfer reaction and has potential for simulating vibrational spectra of PT reaction complexes in solution.     

Monte Carlo simulations of heterogeneous electron transfer: New challenges

We report results of MC simulations of electron transfer across a metal electrode/electrolyte solution interface. The model presumes the Landau–Zener theory and a random walk on a two-dimensional lattice formed by crossing parabolic reaction free energy surfaces along the solvent coordinate. Emphasis is put on investigating the activationless discharge regime; the bridge-assisted electron transfer is also partially addressed. We have calculated effective electronic transmission coefficient as a function of the electrode overpotential and temperature in a wide range of orbital overlap. The dependence of the transmission coefficient on the electronic density of states is analyzed as well.     

Chemical bonding in excited states: Energy transfer and charge redistribution from a real space perspective

This work provides a novel interpretation of elementary processes of photophysical relevance from the standpoint of the electron density using simple model reactions. These include excited states of H₂ taken as a prototype for a covalent bond, excimer formation of He₂ to analyze non‐covalent interactions, charge transfer by an avoided crossing of electronic states in LiF and conical interesections involved in the intramolecular scrambling in C₂H₄. The changes of the atomic and interaction energy components along the potential energy profiles are described by the interacting quantum atoms approach and the quantum theory of atoms in molecules. Additionally, the topological analysis of one‐ and two‐electron density functions is used to explore basic reaction mechanisms involving excited and degenerate states in connection with the virial theorem. This real space approach allows to describe these processes in a unified way, showing its versatility and utility in the study of chemical systems in excited states. © 2017 Wiley Periodicals, Inc.     

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.     

Electric field induced electron transfer at the adsorbate-surface interface. Effect of the type of metal surface

The ab initio two-state model for electron transfer induced by an external electric field has been applied to the chloride oxidation on Cu, Rh, Pd, Ag, Pt and Au (001) surface models. The two electronic states involved in the model represent physical situations where the electron transferred from the chloride anion to the metal surface lies either on the halide or on the metal substrate. The model assumes that electron transfer takes place when these two states become degenerate and this is achieved by applying an external electric field. Two different situations representing either ultrahigh vacuum or electrochemical conditions have been considered. For the former the present study shows that electric field necessary to achieve degeneracy of the two electronic states is directly related to the metal surface work function whereas for the latter, it is found to be rather insensitive to the metal surface.     

Generalized electronic diabatic approach to structural similarity and the Hammond postulate

We revisit the notion of structural similarity along a reaction path within the context of a generalized electronic diabatic (GED) molecular model. In this approach, a reaction involving two closed‐shell stable species is described as the evolution of a quantum state that superimposes at least three diabatic electronic species (reactant, product, and an open‐shell transition state) coupled by an external electromagnetic field. Reactant and product amplitudes in this general state are also modulated by changing the geometry of a system of classical positive charges interacting with the electrons. By mapping these amplitudes over nuclear configurational space, we can follow the total quantum state along a reaction coordinate and establish its similarity to each of the diabatic species. As a result, chemical processes, and useful notions such as those of energy barriers and the Hammond postulate, emerge as consequence of Franck–Condon‐like transitions between quantum states. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A quantum theory of chemical processes and reaction rates based on diabatic electronic functions coupled in an external field

The method discussed in this work provides a theoretical framework where simple chemical reactions resemble any other standard quantum process, i.e., a transition in quantum state mediated by the electromagnetic field. In our approach, quantum states are represented as a superposition of electronic diabatic basis functions, whose amplitudes can be modulated by the field and by the external control of nuclear configurations. Using a one-dimensional three-state model system, we show how chemical structure and dynamics can be represented in terms of these control parameters, and propose an algorithm to compute the reaction probabilities. Our analysis of effective energy barriers generalizes previous ideas on structural similarity between reactant, and product, and transition states using the geometry of conventional reaction paths. In the present context, exceptions to empirical rules such as the Hammond postulate appear as effects induced by the environment that supplies the external field acting on the quantum system.     

Electron transfer in a radical ion pair: quantum calculations of the solvent reorganization energy

Results are presented for an investigation of intermolecular electron transfer (ET) in solution by means of quantum calculations. The two molecules that are involved in the ET reaction form a solvent-separated radical ion pair. The solvent plays an important role in the ET between the two molecules. In particular, it can give rise to specific solute-solvent interactions with the solutes. An example of specific interactions is the formation of a hydrogen bond between a protic solvent and one of the molecules involved in the ET. We address the study of this system by means of quantum calculations on the solutes immersed in a continuum solvent. However, when the solvent can give rise to hydrogen bond formation with the negatively charged ion after ET, we explicitly consider solvent molecules in the solute cavity, determining the hydrogen bond energetic contribution to the overall interaction energy. Solute-solvent pair distribution functions, showing the different arrangement of solvent molecules before and after ET in the first solvation shell, are reported. We provide results of the solvent reorganization energy from quantum calculations for both the two isolated fragments and the ion pair in solution. Results are in agreement with available experimental data.     

Triplet-doublet electronic energy transfer from benzophenone to the ketyl radical: viscosity and magnetic field effects

The influence of solvent viscosity and an external magnetic field on the rate constant of electronic energy transfer from triplet bonzophenone to the ketyl radical is studied; it is concluded that the transfer is mediated by electron exchange.     

Theoretical study of electric field‐induced intramolecular electron transfer in donor–acceptor pairs via the rigid space and their suitability as molecular electronic devices

The geometries of two reaction systems have been optimized under the constraint of C_2ν symmetry, using the UHF/6‐31G method. The potential energy surfaces (PES) of the two systems in different external electric field have been constructed using a linear reaction coordinate. It is concluded that the reorganization energies and electron transfer matrix elements for both systems are almost independent of the external electric field. However, the standard Gibbs energy difference changes remarkably with the change of the external electric field. Hence, the applied electric field leads to the variation of rate constant of electron transfer reaction. The threshold field, where the electron transfer becomes barrier free, is obtained to be 0.0015 a.u. for the anion system 1, and 0.00097 a.u. for the anion system 2. The threshold field for modified system 1, in which the hydrogen atoms linking to benzene rings are replaced by fluorine atom, is 0.0018 a.u. The calculations show that the best way to adjust the threshold field is to adjust the dipole moment of the reaction system by changing the length of the bridge. As the rate constant in field‐free case is taken into account, neither reaction systems could be used as molecular electronic device. But if the bridge consists of three or four HCTDs, the rate constant and threshold field will satisfy the practical demand. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

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.     

Photoalkylation of 10-alkylacridinium ion via a charge-shift type of photoinduced electron transfer controlled by solvent polarity

A charge-shift type of photoinduced electron-transfer reactions from various electron donors to the singlet excited state of 10-decylacridinium cation (DeAcrH+) in a nonpolar solvent (benzene) is found to be as efficient as those of 10-methylacridinium cation (MeAcrH+) and DeAcrH+ in a polar solvent (acetonitrile). Irradiation of the absorption bands of MeAcrH+ in acetonitrile solution containing tetraalkyltin compounds (R(4)Sn) results in the efficient and selective reduction of MeAcrH+ to yield the 10-methyl-9-alkyl-9,10-dihydroacridine (AcrHR). The same type of reaction proceeds in benzene when MeAcrH+ is replaced by DeAcrH+ which is soluble in benzene. The photoalkylation of R'AcrH+ (R' = Me and De) also proceeds in acetonitrile and benzene using 4-tert-butyl-1-benzyl-1,4-dihydronicotinamide (Bu(t)BNAH) instead of R(4)Sn, yielding MeAcrHBu(t). The quantum yield determinations, the fluorescence quenching of R'AcrH+ by electron donors, and direct detection of the reaction intermediates by means of laser flash photolysis experiments indicate that the photoalkylation of R'AcrH+ in benzene as well as in acetonitrile proceeds via photoinduced electron transfer from the alkylating agents (R(4)Sn and Bu(t)BNAH) to the singlet excited states of R'AcrH+. The limiting quantum yields are determined by the competition between the back electron-transfer process and the bond-cleavage process in the radical pair produced by the photoinduced electron transfer. The rates of back electron transfer have been shown to be controlled by the solvent polarity which affects the solvent reorganization energy of the back electron transfer. When the free energy change of the back electron transfer (DeltaG(0)(bet)) in a polar solvent is in the Marcus inverted region, the rate of back electron transfer decreases with decreasing the solvent polarity, leading to the larger limiting quantum yield for the photoalkylation reaction. In contrast, the opposite trend is obtained when the DeltaG(0)(bet) value is in the normal region: the limiting quantum yield decreases with decreasing the solvent polarity.     

Photoinduced intramolecular charge transfer (ICT) reaction in trans-methyl p-(dimethylamino) cinnamate: A combined fluorescence measurement and quantum chemical calculations

The photophysical behaviour of trans-methyl p-(dimethylamino) cinnamate (t-MDMAC) donor–acceptor system has been investigated by steady-state absorption and emission spectroscopy and quantum chemical calculations. The molecule t-MDMAC shows an emission from the locally excited state in non-polar solvents. In addition to weak local emission, a strong solvent dependent red shifted fluorescence in polar aprotic solvents is attributed to highly polar intramolecular charge transfer state. However, the formation of hydrogen-bonded clusters with polar protic solvents has been suggested from a linear correlation between the observed red shifted fluorescence band maxima with hydrogen bonding parameters (). Calculations by ab initio and density functional theory show that the lone pair electron at nitrogen center is out of plane of the benzene ring in the global minimum ground state structure. In the gas phase, a potential energy surface along the twist coordinate at the donor (–NMe₂) and acceptor (–CH = CHCOOMe) sites shows stabilization of S₁ state and destabilization S₂ and S₀ states. A similar potential energy calculation along the twist coordinate in acetonitrile solvent using non-equilibrium polarized continuum model also shows more stabilization of S₁ state relative to other states and supports solvent dependent red shifted emission properties. In all types of calculations it is found that the nitrogen lone pair is delocalized over the benzene ring in the global minimum ground state and is localized on the nitrogen centre at the 90° twisted configuration. The S₁ energy state stabilization along the twist coordinate at the donor site and localized nitrogen lone pair at the perpendicular configuration support well the observed dual fluorescence in terms of proposed twisted intramolecular charge transfer (TICT) model.     

Solution reaction space Hamiltonian based on an electrostatic potential representation of solvent dynamics

Quantum chemical solvation models usually rely on the equilibrium solvation condition and is thus not immediately applicable to the study of nonequilibrium solvation dynamics, particularly those associated with chemical reactions. Here we address this problem by considering an effective Hamiltonian for solution-phase reactions based on an electrostatic potential (ESP) representation of solvent dynamics. In this approach a general ESP field of solvent is employed as collective solvent coordinate, and an effective Hamiltonian is constructed by treating both solute geometry and solvent ESP as dynamical variables. A harmonic bath is then attached onto the ESP variables in order to account for the stochastic nature of solvent dynamics. As an illustration we apply the above method to the proton transfer of a substituted phenol-amine complex in a polar solvent. The effective Hamiltonian is constructed by means of the reference interaction site model self-consistent field method (i.e., a type of quantum chemical solvation model), and a mixed quantum/classical simulation is performed in the space of solute geometry and solvent ESP. The results suggest that important dynamical features of proton transfer in solution can be captured by the present approach, including spontaneous fluctuations of solvent ESP that drives the proton from reactant to product potential wells.     

Microscopic modelling of the reduction of a Zn(II) aqua-complex on metal electrodes

The mechanism of the Zn(II) reduction from acid aqueous solution at a metal electrode surface has been elucidated at a microscopic level. The Anderson–Newns model was employed in order to construct the adiabatic potential energy surfaces along the solvent coordinate for several reactions as a function of the electrode–reactant distance and the overpotential. A quantum chemical approach was employed to treat the coupling of the reactant to the metal electrode within a cluster model. The reduction of a [Zn(H₂O)₆]²⁺ complex was found to proceed in the adiabatic regime, the transfer of the first electron being rate-determining. Main attention is focused on effects of a qualitative nature, which are discussed in the light of available experimental data. The electrode charge excess and distance of maximal approach were found to affect significantly the Frank–Condon barriers of the reaction. An experimentally observed dependence of the rate constant of Zn(II) reduction upon the electrode material has been interpreted.     

Proton transfer in a polar solvent from ring polymer reaction rate theory

We have used the ring polymer molecular dynamics method to study the Azzouz-Borgis model for proton transfer between phenol (AH) and trimethylamine (B) in liquid methyl chloride. When the A-H distance is used as the reaction coordinate, the ring polymer trajectories are found to exhibit multiple recrossings of the transition state dividing surface and to give a rate coefficient that is smaller than the quantum transition state theory value by an order of magnitude. This is to be expected on kinematic grounds for a heavy-light-heavy reaction when the light atom transfer coordinate is used as the reaction coordinate, and it clearly precludes the use of transition state theory with this reaction coordinate. As has been shown previously for this problem, a solvent polarization coordinate defined in terms of the expectation value of the proton transfer distance in the ground adiabatic quantum state provides a better reaction coordinate with less recrossing. These results are discussed in light of the wide body of earlier theoretical work on the Azzouz-Borgis model and the considerable range of previously reported values for its proton and deuteron transfer rate coefficients.     

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.     

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.