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.     

Electron transfer at different electrode materials: Metals,semiconductors, and graphene

Electron transfer reactions are the most important processes at electrochemical interfaces. They are determined by the interplay between the interaction of the reactant with the solvent and the electronic levels of the electrode surface. Theoretical treatments only based on Density Functional Theory calculations are not sufficient. This review emphasizes mainly the effect of the electronic structure of the electrode material on electron transfer under different kinetic regimes. Our goal is to understand experimental results in the framework of a theory valid for arbitrary strengths of electronic coupling.     

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.     

Electronic coupling matrix elements from charge constrained density functional theory calculations using a plane wave basis set

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q(-)) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, (<|H(ab)|(2)>)(1/2)=6.7 mH, is significantly higher than the value obtained for the minimum energy structure, |H(ab)|=3.8 mH. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q(-) in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.     

Non-Condon电子转移速率理论与含时波包方法

随着电子转移理论在化学、材料科学、生物医学等领域的广泛应用,人们针对不同体系提出了多种电子转移理论模型。本文主要总结了近年来我们在non-Condon电子转移理论以及含时波包方法等方面的相关工作。首先阐述包含non-Condon效应的电子转移速率理论并用于二噻吩四硫富瓦烯有机半导体迁移率的计算。而后介绍了包含量子相干效应的含时波包方法,并初步用于研究二聚芴分子三三态能量转移过程。另外,本文还阐述了如何采用量子化学计算获得电子转移速率的结构参数。     

Model study of coherent quantum dynamics of hole states in functionalized semiconductor nanostructures

Functionalization of semiconductor nanocrystals can be achieved by anchoring organic ligands to the surface dangling bonds. The resulting surface complexes often introduce electronic states in the semiconductor band gap. These interband states sensitize the host material for photoabsorption at frequencies characteristic of the molecular adsorbates, leading to the well-known process of photoexcitation and subsequent femtosecond interfacial electron transfer. This paper investigates the relaxation dynamics of hole states, energetically localized deep in the semiconductor band gap, after the ultrafast electron-hole pair separation due to interfacial electron transfer. Mixed quantum-classical methods, based on mean-field nuclear dynamics approximated by ab initio density functional theory molecular dynamics simulations, reveal superexchange hole tunneling between adjacent adsorbate molecules in a model study of functionalized TiO2-anatase nanostructures. It is shown that electronic coherences can persist for hundreds of picoseconds under cryogenic and vacuum conditions, despite the partial intrinsic decoherence induced by thermal ionic motion, providing results of broad theoretical and experimental interest.     

Theoretical study of ultrafast heterogeneous electron transfer reactions at dye-semiconductor interfaces: coumarin 343 at titanium oxide

A theoretical study of photoinduced heterogeneous electron transfer in the dye-semiconductor system coumarin 343-TiO(2) is presented. The study is based on a generic model for heterogeneous electron transfer reactions, which takes into account the coupling of the electronic states to the nuclear degrees of freedom of coumarin 343 as well as to the surrounding solvent. The quantum dynamics of the electron injection process is simulated employing the recently proposed multilayer formulation of the multiconfiguration time-dependent Hartree method. The results reveal an ultrafast injection dynamics of the electron from the photoexcited donor state into the conduction band of the semiconductor. Furthermore, the mutual influence of electronic injection dynamics and nuclear motion is analyzed in some detail. The analysis shows that--depending on the time scale of nuclear motion--electronic vibrational coupling can result in electron transfer driven by coherent vibrational motion or vibrational motion induced by ultrafast electron transfer.     

构型对芳基桥体分子内电子转移矩阵元影响的理论研究

在HF/6-31G水平上,研究了有机化合物二甲氧基-4-甲苯-四甲苯基桥体-二甲氧基-4-甲苯正离子间的电子转移.用线性反应坐标确定电子转移的过渡态,用两态变分法计算了电子转移矩阵元V_AB,在考虑非平衡态溶剂化效应下,计算了电子转移速率常数.改变桥体与氧化还原中心的二面角,计算了相应的电子转移矩阵元.通过电子结构分析,将电子转移矩阵元分为通过空间的直接耦合和通过键的耦合,提出了将后者进一步分为通过σ键和π键的耦合.得出通过π键的耦合与二面角余弦的平方成正比的结论.     

Effects of Configurational Fluctuation on Electronic Coupling for Charge Transfer Dynamics

We advance a theory for the effects of bridge configurational fluctuations on the electronic coupling for electron transfer reactions in donor-bridge-acceptor systems. The theory of radiationless transitions was applied for activationless electron transfer, where the nuclear Franck–Condon constraints are minimized, with the initial vibronic state interacting directly with the final vibronic manifold, without the need for thermal activation. Invoking the assumption of energy-independent coupling, the time-dependent initial state population probability was analyzed in terms of a cumulant expansion. Two limiting situations were distinguished, i.e. the fast configurational fluctuation limit, where the electron transfer rate is given in terms of the configurational average of me squared electronic coupling, and the slow configurational fluctuation limit, where the dynamics is determined by a configurational averaging over a static distribution of electron transfer probability densities. The correlation times for configurational fluctuations of the electronic coupling will be obtained from the analysis of molecular dynamics, in conjunction with quantum mechanical calculations of the electronic coupling, to establish the appropriate limit for electron transfer dynamics.     

Acetyl group orientation modulates the electronic ground-state asymmetry of the special pair in purple bacterial reaction centers

Recent experimental data point to an asymmetric ground-state electronic distribution in the special pair (P) of purple bacterial reaction centers, which acts as the primary electron donor in photosynthesis. We have performed a density functional theory investigation on an extended model including the bacteriochlorophyll dimer and a few relevant surrounding residues to explore the origin of this asymmetry. We find strong evidence that the ground-state electron density in P is intrinsically asymmetric due to protein-induced distortions of the porphyrin rings, with excess electron charge on the P(M) bacteriochlorophyll cofactor. Moreover, the electron charge asymmetry is strongly modulated by the specific orientation of the C3(1) acetyl group, which is hydrogen bonded to His168. The electronic excitation has a significant charge transfer character inducing a displacement of electron charge from P(L) to P(M), in agreement with experimental data in the excited state. These results are relevant for the understanding of the unidirectional electron transfer path in photosynthesis.     

DNA double-helix-mediated long-range electron transfer

A theoretical analysis based upon large-scale self-consistent Hartree-Fock calculations at a semiempirical quantum theory level (CNDO/S) is performed to investigate long-range electron transfer in a donor-DNA-acceptor molecule, where the donor and acceptor moieties are tethered to the DNA. The π-stacked base pairs are found to dominate the long-range electronic coupling. Despite the π-electron mediated coupling, the exponential distance decay constant of the electron transfer rate is ∼ 1.2–1.6 Å⁻¹, values typical of electron transfer proteins. The calculated long-range electron transfer rate of the order of 10⁶ s⁻¹ for a metal-to-metal distance of 21 Å is found to be in agreement with kinetic measurements by Meade and Kayyem. Based on the current analysis, the π-electrons dominate the long-range electronic coupling interactions in DNA, but they do not lead to one-dimensional molecular wire-like properties. © 1996 John Wiley & Sons, Inc.     

Quantum effect of intramolecular high-frequency vibrational modes on diffusion-controlled electron transfer rate: from the weak to the strong electronic coupling regions

The Sumi-Marcus theory is extended by introducing two approaches to investigate electron transfer reactions from weak-to-strong electronic coupling regime. One of these approaches is the quantum R-matrix theory, useful for dealing with the intramolecular vibrational motions in the whole electronic coupling domain. The other is the split operator approach that is employed to solve the reaction-diffusion equation. The approaches are then applied to electron transfer in the Marcus inverted regime to investigate the nuclear tunneling effect on the long time rate and the survival probabilities. The numerical results illustrate that the adiabatic suppression obtained from the R-matrix approach is much smaller than that from the Landau-Zener theory whereas it cannot be predicted by the perturbation theory. The jointed effects of the electronic coupling and solvent relaxation time on the rates are also explored.     

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.     

Electron transfer versus proton transfer in gas-phase ion/ion reactions of polyprotonated peptides

The ion/ion reactions of several dozen reagent anions with triply protonated cations of the model peptide KGAILKGAILR have been examined to evaluate predictions of a Landau-Zener-based model for the likelihood for electron transfer. Evidence for electron transfer was provided by the appearance of fragment ions unique to electron transfer or electron capture dissociation. Proton transfer and electron transfer are competitive processes for any combination of anionic and cationic reactants. For reagent anions in reactions with protonated peptides, proton transfer is usually significantly more exothermic than electron transfer. If charge transfer occurs at relatively long distances, electron transfer should, therefore, be favored on kinetic grounds because the reactant and product channels cross at greater distances, provided conditions are favorable for electron transfer at the crossing point. The results are consistent with a model based on Landau-Zener theory that indicates both thermodynamic and geometric criteria apply for electron transfer involving polyatomic anions. Both the model and the data suggest that electron affinities associated with the anionic reagents greater than about 60-70 kcal/mol minimize the likelihood that electron transfer will be observed. Provided the electron affinity is not too high, the Franck-Condon factors associated with the anion and its corresponding neutral must not be too low. When one or the other of these criteria is not met, proton transfer tends to occur essentially exclusively. Experiments involving ion/ion attachment products also suggest that a significant barrier exists to the isomerization between chemical complexes that, if formed, lead to either proton transfer or electron transfer.     

Computing the superexchange electronic factor of electron transfer theory using a grid‐based numerical method

We report a method for calculating the electronic factor in the superexchange rate equation of electron transfer theory; this method is a basis set independent, grid‐based numerical technique that utilizes fast Fourier transforms (FFTs) and a Lanczos recursion in a pseudospectral framework and is used to treat a three‐dimensional one‐electron model of the electronic factor. We compare eigenvalues calculated from the current method to eigenvalues from the literature for both one‐dimensional (1D) and three‐dimensional (3D) model problems and find that the current method provides excellent accuracy and efficiency. With respect to the superexchange electronic factor, we use model potentials to calculate the tunneling matrix elements with the present method to illustrate how the method can be used to address current issues in superexchange. In particular, we show how this method is useful in evaluating the effect of the bridge potential on the superexchange electronic factor when using repulsive‐core pseudopotentials to represent the bridge. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1262–1273, 2000     

The femtosecond dynamics of electron transfer in a modified photosynthesis reaction center: Quantum, classical, and kinetic analyses

The dynamics of electron transfer in a modified photosynthesis reaction center in which electron transfer from the bridge to the acceptor is blocked is considered. A microscopic model of the process is suggested. Within this model, the diabatic electronic states of the donor and bridge are described by one-dimensional displaced harmonic oscillators. The dynamics of the population of electronic states is calculated by the quantum method of wave packets and classical and kinetic modeling. The suggested model is used to study the qualitative dependence of the dynamics of electron transfer on the nonadiabatic interaction potential. The parameters of the model are determined by comparing the experimental and calculated absorption spectra of the product of electron transfer. It is shown that kinetic models can be used to approximately describe the dynamics of electron transfer in reaction centers. The boundaries of the applicability of the kinetic method are considered.     

Molecular modeling of 3,4-pyridinedicarbonitrile dye sensitizer for solar cells using quantum chemical calculations

The geometries, electronic structures, polarizabilities, and hyperpolarizabilities of organic dye sensitizer 3,4-pyridinedicarbonitrile was studied based on Hartree–Fock (HF) and density functional theory (DFT) using the hybrid functional B3LYP. Ultraviolet–visible (UV–Vis) spectrum was investigated by time dependent DFT (TD-DFT). Features of the electronic absorption spectrum in the visible and near-UV regions were assigned based on TD-DFT calculations. The absorption bands are assigned to π → π1 transitions. Calculated results suggest that the three lowest energy excited states are due to photoinduced electron transfer processes. The interfacial electron transfer between semiconductor TiO₂ electrode and 3,4-pyridinedicarbonitrile is due to electron injection process from excited dye to the semiconductor’s conduction band. The role of cyanine in 3,4-pyridinedicarbonitrile in geometries, electronic structures, and spectral properties were analyzed.     

有机染料敏化剂JK16和JK17的几何结构、电子结构及相关性质

运用密度泛函理论中的杂化泛函B3LYP研究了高效太阳能电池新型染料敏化剂JK16和JK17的几何结构、电子结构、极化率和超极化率, 并用含时密度泛函理论(TDDFT)研究了电子吸收谱. 基于含时密度泛函理论计算结果和实验结果的定性符合, 指认了在可见和近紫外区的吸收属于π→π*跃迁. 计算结果还表明JK16和JK17激发能最低的三个跃迁都与光诱导电荷转移过程有关, 而且二-二甲基芴氨基苯并噻吩基团对光电转换过程的敏化起主要作用, 发生于染料敏化剂JK16、JK17和TiO2界面之间的电荷转移是由染料分子激发态向半导体导带的电子注入过程. 此外, 通过对JK16和JK17的比较, 分析了亚乙烯基对几何结构、电子结构和谱学特性的影响.     

Exploring dynamical electron theory beyond the Born-Oppenheimer framework: from chemical reactivity to non-adiabatically coupled electronic and nuclear wavepackets on-the-fly under laser field

Chemical theory and its application to dynamical electrons in molecules under intense electromagnetic fields is explored, in which we take an explicit account of nuclear nonadiabatic (kinematic) interactions along with simultaneous coupling with intense optical interactions. All the electronic wavefunctions studied here are necessarily time-dependent, and thereby beyond stationary state quantum chemistry based on the Born-Oppenheimer framework. As a general and tractable alternative framework with which to track the electronic and nuclear simultaneous dynamics, we propose an on-the-fly method to calculate the electron and nuclear wavepackets coupled along the branching non-Born-Oppenheimer paths, through which their bifurcations, strong quantum entanglement between nuclear electronic motions, and coherence and decoherence among the phases associated with them are properly represented. Some illustrative numerical examples are also reported, which are aimed at our final goals; real time tracking of nonadiabatic electronic states, chemical dynamics in densely degenerate electronic states coupled with nuclear motions and manipulation and/or creation of new electronic states in terms of intense lasers, and so on. Other examples are also presented as to how the electron wavepacket dynamics can be used to analyze chemical reactions, shedding a new light on some typical and conventional chemical reactions such as proton transfer followed by tautomerization.