电子转移过程的理论——1992年诺贝尔化学奖

1992年10月14日瑞典皇家科学院宣布1992年诺贝尔化学奖授予美国加州理工学院Rudolph A. Marcus教授,以表彰1956—1965年期间他在“电子转移过程理论”方面所做出的重要贡献。电子转移过程可发生于众多的体系之中,如:在溶液中或在胶体中的有机化合物分子;在不同界面如金属/液体界面、半导体/液体以及液体/液体界面的电子转移过程,还有生命体系     

γ-二氧化锰/K~3[Fe(CN)_6]溶液界面的电子转移反转区

Marcus电子转移理论的主要成果之一是预言了电子转移反应反转区的存在.从实验上验证Marcus反转区仍是一个热点问题.通过对γ-MnO_2/K_3[Fe(CN)_6]溶液界面平带电位、极化曲线的测量,计算了在极化条件下,γ-MnO_2导带的电子直接转移到溶液中氧化态物种[Fe(CN)_6]~(3-)空电子能级上的速率常数k_(et),logk_(et)对外加电位作图,观察到了Marcus反转区.从理论上也论证了在半导体/溶液界面上的直接电子转移反转区的存在.     

γ-二氧化锰/K3[Fe(CN)6]溶液界面的电子转移反转区

Marcus电子转移理论的主要成果之一是预言了电子转移反应反转区的存在.从实验上 验证Marcus反转区仍是一个热点问题.通过对γ-MnO2/K3[Fe(CN)6]溶液界面平带电位、极 化曲线的测量,计算了在极化条件下,γ-MnO2导带的电子直接转移到溶液中氧化态物种[F e(CN)6]3-空电子能级上的速率常数ket,logket对外加电位作图,观察到了Marcus反转区. 从理论上也论证了在半导体/溶液界面上的直接电子转移反转区的存在.     

吩噻嗪与四甲基哌啶氧铵正离子的电子转移反应动力学研究

以Marcus半经典电子转移理论为基本框架, 改进了重组能的计算方法, 建立了一套研究自交换和交叉电子转移反应的理论方案。用密度泛函理论和半经验分子轨道理论具体研究了四甲基哌啶氧铵正离子与吩噻嗪在乙腈溶液中的交叉电子转移反应以及相应的2个自交换反应的动力学性质, 计算了反应的活化能、重组能、耦合矩阵元等有关参数,获得了和实验结果相一致的电子转移速率常数。     

γ-二氧化锰电极/溶液界面电子转移动力学

以 [Fe( CN) 6]3- 为受体 ,用大范围分析法 ( global analysis)研究了 γ-二氧化锰电极 /溶液界面的电子转移反应。结果表明 :二氧化锰电极的电子转移速率常数随过电位的变化关系较复杂 ,出现两个反转区 ,与经典的 Marcus电子转移理论不相符合。但 Yuri G.Boroda等人对半导体电极 /溶液界面提出的模型能够很好地解释本文的实验结果 ,表明其电子转移反应是分两步进行的。     

溶液中M(H2O)26+/3+(M=V, Cr, Mn, Fe, Co)自交换电子转移体系内层重组能和活化能的理论研究

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(H2O)26+/3+(M= V, Cr, Mn, Fe, Co)自交换反应的内层重组能和活化能, 获得了与Marcus电子转移理论相一致的结果.     

溶液中M（H2O）6^2＋／3＋（M=V,Cr,Mn,Fe,Co）自交换电子转移体系内层重组能和活

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UMP2／6－311G水平上获得了5对过渡金属水合离子体系M（H2O）6^2 /3 (M=V,Cr,Mn,Fe,Co)自交换反应的内层重组能和活化能,获得了与Marcus电子转移理论相一致的结果。     

氰基苯阴离子与CO2间的内球电子转移

用半经验AM1方法以及从头算方法在3-21G和6－31G*基组水平上研究了从氰基苯阴离子到CO2的电子转移过程．结果表明，对于先驱物(precursor),三种计算方法得出的给体、受体间的距离分别为0.2728nm(AM1)、0.2479nm（UHF/3-21G）和0.2769nm(UHF/6-31G*)．在这样短的距离内给体的HOMO与受体的LUMO轨道具有相当程度的重叠，应产生较强的相互作用，说明此反应是内球电子转移反应，从而解释了此类体系的电子转移反应不符合Marcus理论的原因．计算给出先驱物的束缚能为0.19eV(AM1)和0.26eV(6-31G*)     

四氰基乙烯-四甲基乙烯体系光诱导电子转移双势阱的从头算研 究

以两态模型为基础,用从头算方法,在DZP[所有原子带极化函数的Dunning(9s,5p)/(3s,2p)]基组水平上对四氰基乙烯与四甲基乙烯间的电子转移进行理论计算。通过孤立给体和受体的几何构型优化,计算了给体的电离能和受体的电子亲和能。计算表明,在光诱导电荷分离之后的返回电子转移处于高放热的Marcus反转区。通过碰撞配合物的结构优化和电荷分离处理,在线性反应坐标近似下得到四甲基乙烯-四氰基乙烯配合物电荷分离反应的双势阱,进而获得反应热,键重组能,以及跃迁能。     

联苯负离子自由基与萘分子间长程电子转移的从头算研究

分离处理π σ π体系中的给体 ,受体和σ桥体 ,在HF/4 31G和HF/DZP水平上优化了联苯 ,联苯负离子自由基 ,萘和萘负离子自由基的几何构型 ,计算了分子间电子转移的内重组能 .取线性反应坐标R =0 .5 ,在STO 3G水平上用变分原理和分子轨道跃迁能方法 ,计算了π σ π体系自交换反应的电子转移矩阵元 .对交叉反应体系 ,沿线性反应坐标搜寻最小轨道能级分裂Δmin,确定了电子转移矩阵元和过渡态构型 .用Marcus双球模型计算液相电子转移的溶剂重组能 ,结合半经典模型计算了几种以联苯负离子自由基为给体 ,联苯和萘为受体的π σ π体系分子内电子转移速率常数 .     

Photoinduced electron transfer in hydrogen bonded donor--acceptor systems. Free energy and distance dependence studies and an analysis of the role of diffusion.

The free energy dependence of electron transfer in a few small-molecule donor--acceptor systems having hydrogen-bonding appendages was studied to evaluate the role of diffusion in masking the inverted region in bimolecular PET reactions. A small fraction of the probe molecules associate and this led to the simultaneous observation of unimolecular and diffusion-mediated quenching of the probe fluorescence. Free energy dependence studies showed that the unimolecular electron transfer obeys Marcus behavior and the diffusion-mediated electron transfer obeys Rehm--Weller behavior. The absence of an inverted region in bimolecular PET reactions is thus attributed to diffusion. The results of the free energy dependence studies suggest that distance dependence of electron transfer plays a role in masking the inverted region. To ascertain this aspect we have carried out a study of the distance dependence of electron transfer in the hydrogen-bonded donor--acceptor systems. For a system in the normal region an exponential rate decrease was observed. For a system in the inverted region it was observed that the rate depends very feebly on distance. Thus distance dependence studies did not confirm the prediction of enhanced rates at larger distances in the inverted region.     

Photo-induced intermolecular electron transfer from electron donating solvents to Coumarin dyes in bile salt aggregates: role of diffusion in electron transfer reaction

The photo-induced electron transfer between Coumarin dyes and aromatic amines has been investigated using steady state and time-resolved fluorescence quenching studies. We have observed a Marcus type inversion in the electron transfer rate in correlation of quenching constant to the free energy change occurred during reaction. To justify the "inverted region" obtained in the correlation of quenching constant versus free energy curve, we have performed anisotropy measurement and estimated the several diffusional parameters. The translational diffusion coefficients exhibit a similar picture like electron transfer rate constant when it is plotted against free energy. Thus we argued that the diffusion has played an important role in the electron transfer kinetics.     

The new theory of electron transfer. Thermodynamic potential profiles in the inverted and superverted regions

In a previous paper (S Fletcher, J Solid State Electrochem 11:965, 2007) a non-Marcus theory of electron transfer was developed, with results applicable to the normal region of thermodynamic driving forces. In the present paper, the theory is extended to highly exergonic reactions (the inverted region) and to highly endergonic reactions (the superverted region). The results are presented mathematically and in the form of Gibbs energy profiles plotted against a charge fluctuation reaction coordinate. The new theory utilizes the concept of donor and acceptor “supermolecules,” which consist of conventional donor and acceptor species plus their associated ionic atmospheres. The key findings are as follows. (1) In the inverted region, donor supermolecules are positively charged both before and after the electron transfer event. (2) In the normal region, donor supermolecules change polarity from negative to positive during the electron transfer event. (3) In the superverted region, the donor supermolecule is negatively charged both before and after the electron transfer event. This overall pattern of events makes it possible for polar solvents to catalyse electron transfer in the inverted and superverted regions. Because this new effect is predicted only by the present theory and not by the Marcus theory, it provides a clear means of distinguishing between them.     

New perspective of electron transfer chemistry

A new perspective of electron transfer chemistry is described for fine control of electron transfer reactions including back electron transfer in the charge separated state of artificial photosynthetic compounds and its synthetic application. Fundamental electron transfer properties of suitable components of efficient electron transfer systems are described in light of the Marcus theory of electron transfer, in particular focusing on the Marcus inverted region, and they are applied to design multi-step electron transfer systems which can well mimic the function of a photosynthetic reaction center. Both intermolecular and intramolecular electron transfer processes are finely controlled by complexation of radical anions, produced in the electron transfer, with metal ions which act as Lewis acids. Quantitative measures to determine the Lewis acidity of a variety of metal ions are given in relation to the promoting effects of metal ions on the electron transfer reactions. The mechanistic viability of metal ion catalysis in electron transfer reactions is demonstrated by a variety of examples of chemical transformations involving metal ion-promoted electron transfer processes as the rate-determining steps, which are made possible by complexation of radical anions with metal ions.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Photoinduced electron transfer reaction in polymer-surfactant aggregates: Photoinduced electron transfer between N,N-dimethylaniline and 7-amino coumarin dyes

Photoinduced electron transfer between coumarin dyes and N,N-dimethylaniline has been investigated by using steady state and picosecond time resolved fluorescence spectroscopy in sodium dodecyl sulphate (SDS) micelles and PVP-polyvinyl pyrrolidone (SDS) polymer-surfactant aggregates. A slower rate of electron transfer is observed in PVP-SDS aggregates than in polymer-free SDS micelles. A Marcus type inversion is observed in the correlation of free energy change in comparison with the electron transfer rate. The careful investigation reveals that C-151 deviates from the normal Marcus inverted region compared to its analogs C-152 and C-481 due to slower rotational relaxation and smaller translational diffusion coefficient.     

Direct calculation of electron transfer parameters through constrained density functional theory

It is shown that constrained density functional theory (DFT) can be used to access diabatic potential energy surfaces in the Marcus theory of electron transfer, thus providing a means to directly calculate the driving force and the inner-sphere reorganization energy. We present in this report an analytic expression for the forces in constrained DFT and their implementation in geometry optimization, a prerequisite for the calculation of electron transfer parameters. The method is then applied to study the symmetric mixed-valence complex tetrathiafulvalene-diquinone radical anion, which is observed experimentally to be a Robin-Day class II compound but found by DFT to be in class III. Constrained DFT avoids this pitfall of over-delocalization and provides a way to find the charge-localized structure. In another application, driving forces and inner-sphere reorganization energies are calculated for the charge recombination (CR) reactions in formanilide-anthraquinone (FA-AQ) and ferrocene-formanilide-anthraquinone (Fc-FA-AQ). While the two compounds have similar reorganization energies, the driving force in FA-AQ is 1 eV larger than in Fc-FA-AQ, in agreement with experimental observations and supporting the experimental conclusion that the anomalously long-lived FA-AQ charge-separated state arises because the electron transfer is in the Marcus inverted region.     

Transition state barriers in multidimensional Marcus theory

Multidimensional Marcus theory is the extension of traditional Marcus theory to systems in which multiple particles are transferred. Rather than the intersecting parabolas of Marcus theory, multidimensional Marcus theory involves the intersection of paraboloids. In this paper, we examine the conditions under which a full multidimensional treatment of these paraboloids is necessary and when it is possible to use a simpler one-dimensional formalism. In particular, we examine transition state barrier energies, which are essential parameters in many reaction rate equations, and which depend on the formalism used. We find, based on both analytic calculations and numerical simulation, that the reduced one-dimensional treatment yields excellent agreement with the exact, multidimensional results over a wide variety of conditions for one particular choice of the single collective reaction coordinate. We also outline a procedure for calculating accurate multidimensional transition state barrier energies and apply it to a two-dimensional model of proton-coupled electron transfer.