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.     

Triplet-triplet energy-transfer coupling: theory and calculation

Triplet-triplet (TT) energy transfer requires two molecular fragments to exchange electrons that carry different spin and energy. In this paper, we analyze and report values of the electronic coupling strengths for TT energy transfer. Two different methods were proposed and tested: (1) Directly calculating the off-diagonal Hamiltonian matrix element. This direct coupling scheme was generalized from the one used for electron transfer coupling, where two spin-localized unrestricted Hartree-Fock wave functions are used as the zero-order reactant and product states, and the off-diagonal Hamiltonian matrix elements are calculated directly. (2) From energy gaps derived from configuration-interaction-singles (CIS) scheme. Both methods yielded very similar results for the systems tested. For TT coupling between a pair of face-to-face ethylene molecules, the exponential attenuation factor is 2.59 A(-1)(CIS6-311+G(**)), which is about twice as large as typical values for electron transfer. With a series of fully stacked polyene pairs, we found that the TT coupling magnitudes and attenuation rates are very similar irrespective of their molecular size. If the polyenes were partially stacked, TT couplings were much reduced, and they decay more rapidly with distance than those of full-stacked systems. Our results showed that the TT coupling arises mainly from the region of close contact between the donor and acceptor frontier orbitals, and the exponential decay of the coupling with separation depends on the details of the molecular contacts. With our calculated results, nanosecond or picosecond time scales for TT energy-transfer rates are possible.     

Ab initio MO study for electron transfer matrix element in hydrogen-bonded system

The electronic coupling matrix element of electron transfer between donor and acceptor connected with hydrogen bonds has been studied in a model system. The calculated matrix element depends largely on the relative rotational conformation of the electron-donor and electron-acceptor sites and a simple orbital analysis has been presented. Along the approximate proton transfer coordinate, the energy potential is a double well and the matrix element has a single maximum at the center of the double well.     

Intramolecular energy-transfer processes in a bis(porphyrin)-ruthenium(II) bis(2,2':6',2'-terpyridine) molecular array

A molecular triad has been synthesized comprising two free-base porphyrin terminals linked to a central ruthenium(II) bis(2,2':6',2'-terpyridine) subunit via meso-phenylene groups. Illumination into the ruthenium(II) complex is accompanied by rapid intramolecular energy transfer from the metal-to-ligand, charge-transfer (MLCT) triplet to the lowest-energy pi-pi* triplet state localized on one of the porphyrin subunits. Transfer takes place from a vibrationally excited level which lowers the activation energy. The electronic coupling matrix element for this process is 73 cm(-1). Selective illumination into the lowest-energy singlet excited state (S1) localized on the porphyrin leads to fast singlet-triplet energy transfer that populates the MLCT triplet state with high efficiency. This latter process occurs via Dexter-type electron exchange at room temperature, but the activation energy is high and the reaction is prohibited at low temperature. For this latter process, the electronic coupling matrix element is only 8 cm(-1).     

黄金规则用于N_3~- N_3体系电子转移的研究

基于 B3P86/6 311＋ G优化的 N3与 N－ 3分子几何 ,确定了 N3＋ N－ 3基态电子转移体系的六种不同的耦合机理 ,及各种形式耦合络合物的几何性质、活化能、稳定化能、耦合矩阵元和态密度 ,并利用黄金规则计算了电子转移速率 ,讨论了各耦合方式对电子转移速率的影响 .     

黄金规则用于N-3＋N3体系电子转移的研究

基于B3P86/6 311＋G优化的N3与N－3分子几何,确定了N3＋N－3基态电子转移体系 的六种不同的耦合机理,及各种形式耦合络合物的几何性质、活化能、稳定化能、耦合矩阵 元和态密度,并利用黄金规则计算了电子转移速率,讨论了各耦合方式对电子转移速率的影响 .     

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。     

Electron Transfer Reaction between M-C_6H_6 and M~ -C_6H_6 Complexes in the Gas Phase: Density Functional Theory Study

Significant progress has been made in understanding the nature of the transition state andthe paths for electron transfer, especially the influences of environmental factors and themolecular properties on the electron transfer rate. These classical and semi-classical, aswell as quantum-mechanical theory, have been very successful in rationalizing severalstructure-reactivity relationships and in predicting novel features of reactivity. Thesemodels established some links between the electron tra…     

Studying and switching electron transfer: from the ensemble to the single molecule

We report here on the systematic investigation of photoinduced intramolecular electron transfer (IET) in a series of donor-bridge-acceptor molecules as a means of understanding electron transport through the bridge. Perylenebisimide chromophores connected by various oligophenylene bridges are studied because their electron-transfer behavior can readily be monitored by following changes in the fluorescence intensity. We find dramatic switching of the IET behavior as the solvent polarity (dielectric constant) is increased. By combining steady-state and time-resolved fluorescence spectroscopy in a variety of solvents at multiple temperatures with standard theories of electron transfer, we determine parameters governing the IET behavior of these dimers, such as the electronic coupling through the bridges. We also deploy available ab initio quantum chemical methods to calculate the through-space component of the electronic coupling matrix element. Single-molecule investigations of the electron-transfer behavior also show that IET can be switched reversibly by a similar mechanism in an isolated individual molecule.     

Electron transfer in self-assembled orthogonal structures

Two new molecular dyads, comprising pyrromethene (bodipy) and 2,2':6',2"-terpyridine (terpy) subunits, have been synthesized and fully characterized. Absorption and fluorescence spectral profiles are dominated by contributions from the bodipy unit. Zinc(II) cations bind to the vacant terpy ligand to form both 1:1 and 1:2 (cation:ligand) complexes, as evidenced by X-ray structural data, NMR and spectrophotometric titrations. Attachment of the cations is accompanied by a substantial decrease in fluorescence from the bodipy chromophore due to intramolecular electron transfer across the orthogonal structure. At low temperature, nuclear tunneling occurs and the rate of electron transfer is essentially activationless. However, activated electron transfer is seen at higher temperatures and allows calculation of the corresponding reorganization energy and electronic coupling matrix element. In both cases, charge recombination is faster than charge separation.     

Influence of redoxinert counterions on photoinduced intermolecular electron transfer rates in dichloromethane

Rate constants k_q of the fluorescence quenching of 9,10-dicyanoanthracene by bromide and chloride ions and of 9-cyanoanthracene by bromide ions were determined in the low polar solvent dichloromethane with a series of tetra-alkylammonium counterions. Cation size dependent electron transfer rate constants k_et were derived from k_q, and were fitted to a nonadiabatic electron transfer model equation. Because of ion pair formation in dichloromethane electrostatic interactions of the redoxinert countercations during electron transfer were considered. Accordingly, the position of the countercation within the precursor complex had to be described.

The electronic coupling matrix element derived by fitting of the experimental data is in satisfactory agreement with results of simple quantum chemical calculations.     

Electronic structure contributions to electron-transfer reactivity in iron-sulfur active sites: 3. Kinetics of electron transfer

The kinetics of electron transfer for rubredoxins are examined using density functional methods to determine the electronic structure characteristics that influence and allow for fast electron self-exchange in these electron-transport proteins. Potential energy surfaces for [FeX(4)](2-,1-) models confirm that the inner-sphere reorganization energy is inherently small for tetrathiolates ( approximately 0.1 eV), as evidenced by the only small changes in the equilibrium Fe-S bond distance during redox (Deltar(redox) approximately 0.05 A). It is concluded that electronic relaxation and covalency in the reduced state allow for this small in this case relative to other redox couples, such as the tetrachloride. Using a large computational model to include the protein medium surrounding the [Fe(SCys)(4)](2-,1-) active site in Desulfovibrio vulgaris Rubredoxin, the electronic coupling matrix element for electron self-exchange is defined for direct active-site contact (H0(DA)). Simple Beratan-Onuchic model is used to extend coupling over the complete surface of the protein to provide an understanding of probable electron-transfer pathways. Regions of similar coupling properties are grouped together to define a surface coupling map, which reveals that very efficient self-exchange occurs only within 4 sigma-bonds of the active site. Longer-range electron transfer cannot support the fast rates of electron self-exchange observed experimentally. Pathways directly through the two surface cysteinate ligands dominate, but surface-accessible amides hydrogen-bonded to the cysteinates also contribute significantly to the rate of electron self-exchange.     

Calculation of vibronic couplings for phenoxyl/phenol and benzyl/toluene self-exchange reactions: implications for proton-coupled electron transfer mechanisms

The vibronic couplings for the phenoxyl/phenol and the benzyl/toluene self-exchange reactions are calculated with a semiclassical approach, in which all electrons and the transferring hydrogen nucleus are treated quantum mechanically. In this formulation, the vibronic coupling is the Hamiltonian matrix element between the reactant and product mixed electronic-proton vibrational wavefunctions. The magnitude of the vibronic coupling and its dependence on the proton donor-acceptor distance can significantly impact the rates and kinetic isotope effects, as well as the temperature dependences, of proton-coupled electron transfer reactions. Both of these self-exchange reactions are vibronically nonadiabatic with respect to a solvent environment at room temperature, but the proton tunneling is electronically nonadiabatic for the phenoxyl/phenol reaction and electronically adiabatic for the benzyl/toluene reaction. For the phenoxyl/phenol system, the electrons are unable to rearrange fast enough to follow the proton motion on the electronically adiabatic ground state, and the excited electronic state is involved in the reaction. For the benzyl/toluene system, the electrons can respond virtually instantaneously to the proton motion, and the proton moves on the electronically adiabatic ground state. For both systems, the vibronic coupling decreases exponentially with the proton donor-acceptor distance for the range of distances studied. When the transferring hydrogen is replaced with deuterium, the magnitude of the vibronic coupling decreases and the exponential decay with distance becomes faster. Previous studies designated the phenoxyl/phenol reaction as proton-coupled electron transfer and the benzyl/toluene reaction as hydrogen atom transfer. In addition to providing insights into the fundamental physical differences between these two types of reactions, the present analysis provides a new diagnostic for differentiating between the conventionally defined hydrogen atom transfer and proton-coupled electron transfer reactions.     

Face-to-face pacman-type porphyrin-fullerene dyads: design, synthesis, charge-transfer interactions, and photophysical studies

Pacman-type face-to-face zinc-porphyrin-fullerene dyads have been newly synthesized and studied. Owing to the close proximity of the donor and acceptor entities, strong pi-pi intramolecular interactions between the porphyrin and fullerene entities resulted in modulating the spectral and electrochemical properties of the dyads. New absorption and emission bands that correspond to the charge-transfer interactions were observed in the near-IR region. Time-resolved transient absorption studies revealed efficient photoinduced electron transfer from the singlet excited porphyrin to the fullerene entity. The rate constants for photoinduced electron transfer are analyzed in terms of the Marcus theory of electron transfer, which afforded a large electron coupling matrix element (V=140 cm(-1)) for the face-to-face dyads. As a consequence of the large charge-recombination driving force in the Marcus inverted region, a relatively long lifetime of the charge-separated state has been achieved.     

Generalized spherical functions in the theory of many-electron atoms

A new method for finding non-relativistic and relativistic wave-functions of an electron moving in the field of a nuclear charge in the jj coupling scheme is proposed. It is based on the usage of generalized spherical functions. The mathematical apparatus necessary to find the expressions for matrix elements of the non-relativistic and relativistic energy or electron transition operators is developed. The formulas obtained for these matrix elements are more convenient than those usually used in jj coupling scheme; only their radial integrals and some phase multipliers depend on orbital quantum numbers.     

Studies on the Mechanism for the Bimolecular Metathesis Reaction CH3 + HCI ⇔︁ CH4 + CI

The geometry optimization of the transition state, the precursor complex and the successor complex was performed at the 6–311G* basis set level. From the analysis of the vibrational frequency of the precursor complex, transition state, successor complex and the isolated state, the reaction mechanism was derived which was complicated with the bond‐rupture electron transfer theory. The atom H in molecule HCI attacks the atom C, forming a transition state via the precursor complex and the electron‐transfer happens in precursor complex. And the active energy, electronic coupling matrix element, the reorganization energy, and the reaction rate are obtained.     

Photoinduced electron transfer and geminate recombination in liquids on short time scales: Experiments and theory

The coupled processes of intermolecular photoinduced forward electron transfer and geminate recombination between the (hole) donor (Rhodamine 3B) and (hole) acceptors (N,N-dimethylaniline) are studied in three molecular liquids: acetonitrile, butyronitrile, and benzonitrile. Two color pump-probe experiments on time scales from approximately 100 fs to hundreds of picoseconds give information about the depletion of the donor excited state due to forward electron transfer and the survival kinetics of the radicals produced by forward electron transfer. The data are analyzed with a model presented previously that includes distance dependent forward and back electron transfer rates, donor and acceptor diffusion, solvent structure, and the hydrodynamic effect in a mean-field theory of through solvent electron transfer. The forward electron transfer is in the normal regime, and the Marcus equation for the distance dependence of the transfer rate is used. The forward electron transfer data for several concentrations in the three solvents are fitted to the theory with a single adjustable parameter, the electronic coupling matrix element Jf at contact. Within experimental error all concentrations in all three solvents are fitted with the same value of Jf. The geminate recombination (back transfer) is in the inverted region, and semiclassical treatment developed by Jortner [J. Chem. Phys. 64, 4860 (1976)] is used to describe the distance dependence of the back electron transfer. The data are fitted with the single adjustable parameter Jb. It is found that the value of Jb decreases as the solvent viscosity increases. Possible explanations are discussed.     

金属原子（离子）-苯配合物的电子转移反应

用密度泛函理论（ＤＦＴ／ＢＬＹＰ）在６－３１Ｇ基组水平上研究了金属原子－苯与离子－苯配合物的气相电子转移过程,得到了Ｍ（Ｌｉ,Ｎａ,Ｍｇ）－Ｃ６Ｈ６和Ｍ＾＋－Ｃ６Ｈ６络合物以及它们之间电子转移过程的先驱络合物的最优几何构型和电子结构。同时,利用线性坐标确定了过滤态的结构,结果表明：ＤＦＴ方法计算得到的单体,即原子（离子）－苯的构型,同ＭＰ２结果较为一致。先驱络合物具有Ｃ６ν对称性,给体与受体间距离     

Co(H_2O)_6~(2 /3 )体系电子转移反应动力学的理论研究

电子转移过程在化学、生命科学、材料科学等领域普遍存在,几十年来一直受到国际学术界的广泛关注,是当前化学研究的前沿课题之一[1－6].过渡金属络合物间的电子转移是一类重要的电子转移过程,其动力学行为是理论和实验研究的热点[7－12].根据过渡态理论,这类自交换反应速率可表示为ket=κeZeffexp(－ΔE/RT)(1)其中,Zeff为核频率因子,对于溶液中的双分子反应其值约为1011dm3·mol－1·s－1[11];ΔE是活化能;κe称为电子因子,对于绝热反应κe=1.显然,活化能和电子因子是影响电子转移速率的两个关键因素.根据络合物的结构特点,一…