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.     

Ab initio characterization of electron transfer coupling in photoinduced systems: generalized Mulliken-Hush with configuration-interaction singles

To calculate electronic couplings for photoinduced electron transfer (ET) reactions, we propose and test the use of ab initio quantum chemistry calculation for excited states with the generalized Mulliken-Hush (GMH) method. Configuration-interaction singles (CIS) is proposed to model the locally excited (LE) and charge-transfer (CT) states. When the CT state couples with other high lying LE states, affecting coupling values, the image charge approximation (ICA), as a simple solvent model, can lower the energy of the CT state and decouple the undesired high-lying local excitations. We found that coupling strength is weakly dependent on many details of the solvent model, indicating the validity of the Condon approximation. Therefore, a trustworthy value can be obtained via this CIS-GMH scheme, with ICA used as a tool to improve and monitor the quality of the results. Systems we tested included a series of rigid, sigma-linked donor-bridge-acceptor compounds where "through-bond" coupling has been previously investigated, and a pair of molecules where "through-space" coupling was experimentally demonstrated. The calculated results agree well with experimentally inferred values in the coupling magnitudes (for both systems studied) and in the exponential distance dependence (for the through-bond series). Our results indicate that this new scheme can properly account for ET coupling arising from both through-bond and through-space mechanisms.     

A Smplified Method for the Computation of Correlation Effects on the Band Structure of Semiconductors

We present a simplified computational scheme in order to calculate the effects of electron correlations on the energy bands of diamond and silicon. By adopting a quasiparticle picture we compute first the relaxation and polarization effects around an electron set into a conduction-band Wannier orbital. This is done by allowing the valence orbitals to relax within a self-consistent field (SCF) calculation. The diagonal matrix element of the Hamiltonian leads to a shift of the center of gravity of the conduction band while the off-diagonal matrix elements result in a small reduction of the conduction-electron bandwidth. This calculation is supplemented by the computation of the loss of ground-state correlations due to the blocked Wannier orbital into which the added electron has been placed. The same procedure applies to the removal of an electron, i.e., to the valence bands. But the latter have been calculated previously in some detail and previous results are used to estimate the energy gap in the two materials. The numerical data reported here show that the methods works, in principle, but that some extension of the scheme is also necessary to obtain fully satisfactory results.Dedicated to J.-P. Malrieu on the occasion of his 60th birthday     

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 .     

Single particle versus ensemble average: from power-law intermittency of a single quantum dot to quasistretched exponential fluorescence decay of an ensemble

Light-induced diffusion-controlled electron transfer is proposed as an underlying mechanism for the intermittency (power law and breakdown) of a single quantum dot and ensemble-averaged fluorescence decay. The intensity decay can be approximated to a stretched exponential expression. The physical links to the free energy gap, reorganization energy, electronic coupling, and diffusion correlation times are discussed. A procedure is described for extracting these molecular-based parameters from experiments and is demonstrated with examples using existing data.     

Coupling matrix element of electron self-exchange reactions in solution

On the basis of the common feature among the electron transfer process and the ion hydration process as well as the relevant experimental kinetic data of electron transfer reaction,a new accurate hydration potential function scheme for the determination of electron transfer coupling matrix element is presented.The coupling matrix element between two hydrated ions of the reacting system in solution is calculated.The results and the applicability of this scheme are discussed.     

Condensed-phase relaxation of multilevel quantum systems. I. An exactly solvable model

An analytically solvable model of multilevel condensed-phase quantum dynamics relevant to vibrational relaxation and electron transfer is presented. Exact solutions are derived for the reduced system density matrix dynamics of a degenerate N-level quantum system characterized by nearest-neighbor hopping and off-diagonal coupling (which is linear in the bath coordinates) to a harmonic oscillator bath. We demonstrate that for N> 2 the long-time steady-state system site occupation probabilities are not the same for all sites; that is, they are distributed in a non-Boltzmann manner, which depends on the initial conditions and the number of levels in the system. Although the system-bath Hamiltonian considered here is restricted in form, the availability of an exact solution enables us to study the model in all regions of an extensive parameter space.     

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.     

Electronic coupling calculation and pathway analysis of electron transfer reaction using ab initio fragment-based method. I. FMO-LCMO approach

By making use of an ab initio fragment-based electronic structure method, fragment molecular orbital-linear combination of MOs of the fragments (FMO-LCMO), developed by Tsuneyuki et al. [Chem. Phys. Lett. 476, 104 (2009)], we propose a novel approach to describe long-distance electron transfer (ET) in large system. The FMO-LCMO method produces one-electron Hamiltonian of whole system using the output of the FMO calculation with computational cost much lower than conventional all-electron calculations. Diagonalizing the FMO-LCMO Hamiltonian matrix, the molecular orbitals (MOs) of the whole system can be described by the LCMOs. In our approach, electronic coupling T(DA) of ET is calculated from the energy splitting of the frontier MOs of whole system or perturbation method in terms of the FMO-LCMO Hamiltonian matrix. Moreover, taking into account only the valence MOs of the fragments, we can considerably reduce computational cost to evaluate T(DA). Our approach was tested on four different kinds of model ET systems with non-covalent stacks of methane, non-covalent stacks of benzene, trans-alkanes, and alanine polypeptides as their bridge molecules, respectively. As a result, it reproduced reasonable T(DA) for all cases compared to the reference all-electron calculations. Furthermore, the tunneling pathway at fragment-based resolution was obtained from the tunneling current method with the FMO-LCMO Hamiltonian matrix.     

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.     

Adiabatic electrochemical electron-transfer reactions involving frequency changes of inner-sphere modes

A Hamiltonian model is formulated for electrochemical electron-transfer reactions involving frequency changes of the inner-sphere modes. The adiabatic free energy surface is calculated and it is shown that this nonlinear coupling leads to a transfer coefficient different from 1/2, and that the transfer coefficient can no longer be identified with the electron occupation probability in the transition state saddle point, as in the linear coupling case.     

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…     

Complete basis set, Gaussian, and hybrid density functional theory evaluation of the proton affinities of water and ammonia

An ab inito computation of reorganization energy for the electron transfer (ET) reactions between metal–benzene and metal ion–benzene complexes is presented. The geometry optimization of the metal–benzene complexes was performed. The metal atoms (or metal ions)– benzene molecule separation distances computed using an ab initio method were found to agree with earlier reported results. Values of reorganization energies using George-Griffith Marcus (GGM) method (the contribution from only diagonal elements of force constant matrix) and Hessian matrix method (including the contribution from both diagonal and off-diagonal elements) were computed. Results of reorganization energy show that the GGM method gives much lower values compared to those obtained using the Hessian method, suggesting that the coupling interactions between different vibrational modes are important to the inner-sphere reorganization energy for the ET reactions in gaseous phase.     

How to choose one-dimensional basis functions so that a very efficient multidimensional basis may be extracted from a direct product of the one-dimensional functions: energy levels of coupled systems with as many as 16 coordinates

In this paper we propose a scheme for choosing basis functions for quantum dynamics calculations. Direct product bases are frequently used. The number of direct product functions required to converge a spectrum, compute a rate constant, etc., is so large that direct product calculations are impossible for molecules or reacting systems with more than four atoms. It is common to extract a smaller working basis from a huge direct product basis by removing some of the product functions. We advocate a build and prune strategy of this type. The one-dimensional (1D) functions from which we build the direct product basis are chosen to satisfy two conditions: (1) they nearly diagonalize the full Hamiltonian matrix; (2) they minimize off-diagonal matrix elements that couple basis functions with diagonal elements close to those of the energy levels we wish to compute. By imposing these conditions we increase the number of product functions that can be removed from the multidimensional basis without degrading the accuracy of computed energy levels. Two basic types of 1D basis functions are in common use: eigenfunctions of 1D Hamiltonians and discrete variable representation (DVR) functions. Both have advantages and disadvantages. The 1D functions we propose are intermediate between the 1D eigenfunction functions and the DVR functions. If the coupling is very weak, they are very nearly 1D eigenfunction functions. As the strength of the coupling is increased they resemble more closely DVR functions. We assess the usefulness of our basis by applying it to model 6D, 8D, and 16D Hamiltonians with various coupling strengths. We find approximately linear scaling.     

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 .     

The dynamical correlation in spacer-mediated electron transfer couplings

The dynamical correlation effect in electron transfer (ET) coupling was studied in this work, for cases where electrons tunnel through a many-electron environment. The ET couplings for three different bridge-mediated model systems were calculated: (I) trans-alkyl chains [H2C-(CH2)n-CH2, n = 2-10], (II) two isomers of trans-1,4-dimethylenecyclohexane, and (III) two ethylenes spaced by a saturated ethane molecule. The couplings were calculated as half energy gaps of the two lowest adiabatic states. The dynamical correlation was included with spin-flip (SF) and ionization potential or electron affinity coupled-cluster singles and doubles (SF-CCSD and IP/EA-CCSD) and a DeltaCCSD scheme. The direct coupling (DC) scheme is also used as a way to obtain a solution with nondynamical correlation, since DC uses approximated eigenstates that are symmetry-restoring linear combinations of two symmetry-broken unrestricted Hartree-Fock configurations. For all cases tested except for one, results from the DC scheme closely follow the CCSD data, indicating that the dual-configuration solutions can be a good approximation of wave functions with nondynamical correlation included, but there exist exceptions. Comparing the DC results with SF-CCSD and IP or EA-CCSD data, we concluded that the dynamical correlation effect is small for most of the cases we tested.     

Revealing the roles of Hamiltonian coupling in bound-state quantum systems

A Hamiltonian coupling identification (HCI) technique is introduced to reveal the independent and cooperative roles of Hamiltonian matrix elements in determining the bound-state energies of quantum systems. The HCI technique operates by encoding each Hamiltonian matrix element with a unique modulation signal, producing a nonlinear signature in the energy eigenvalues that may be decoded to reveal the contributing coupling structure in the Hamiltonian. The HCI technique is capable of exploring the roles of Hamiltonian coupling structure within and beyond the convergence limits of standard perturbation theory expansions. The flexibility residing in the encoding and decoding processes may be exploited to tailor the analysis to meet the desired degree of sought-after information about the Hamiltonian coupling structure. HCI, based on a Fourier encoding and decoding scheme, is illustrated by extracting information on the role of coupling interactions in the potential matrix elements of several simple model systems.     

Electronic Structure Characteristics of ESIPT and TICT Fluorescence Emissions and Calculations of Emitting Energies

A scheme of time-dependent density functional theory (TDDFT) combined with the single-excitation configuration interaction (CIS) approach was employed to investigate the first excited singlet state (S₁) for eight salicylanilide derivatives and analogues, which have similar structural formulas. The results showed that fluorescence-emitting mechanisms of these molecules were in two distinct manners (excited-state intramolecular proton transfer (ESIPT) and twisted intramolecular charge transfer (TICT)), which agreed with the well-known experiments. For ESIPT compounds with inconspicuous charge transfer (CT) during electron transition, pure functionals without Hartree-Fock (HF) exchange energy, such as OLYP and BLYP, were suitable to calculate emitting energies. For TICT compounds with large CT during electron transition, hybrid functionals with about 37% HF exchange energy, such as mPW1B95 and MPW1K, performed well. On condition that the exchange-correlation (XC) functionals were chosen properly according to the rules above, reliable emitting energies for salicylanilide derivatives and analogues could be obtained at the TDDFT/6-31G(d)//CIS/3-21G(d) level. The average accuracy reached about 0.2 eV. For the salicylanilides with both proton transfer (PT) and CT reaction channels, only one channel occurred actually according to the principle of energy minimum. This actual reaction decided proper XC functionals, whereas the reaction that did not occur actually was trivial. Eight appendent compounds were calculated to prove that this successful scheme is expected to be suitable for other ESIPT and TICT compounds.     

ESIPT和TICT荧光发射的电子结构特征及发射能计算

采用含时密度泛函理论(TDDFT)与单激发组态相互作用(CIS)相结合的计算方案对八种结构相似的水杨酰苯胺衍生物及其类似物第一激发单重态(S1)进行考察, 证实它们的荧光发射分属分子内质子转移(ESIPT)和分子扭转-电荷转移(TICT)两种不同机制且结论与已知实验事实相符. ESIPT发光的化合物在电子跃迁前后无明显的电荷转移发生, 发射能计算的适用泛函是OLYP和BLYP等无Hartree-Fock(HF)交换成分的纯泛函; TICT发光的化合物在电子跃迁前后发生明显的电荷转移, 其适用泛函为含约37% HF交换成分的混合型泛函(例如mPW1B95和MPW1K). 按上述原则来选择适用泛函, 即可在TDDFT/6-31G(d)//CIS/3-21G(d)理论水平上正确预测水杨酰苯胺衍生物和类似物的发射能, 平均精度可达0.2 eV. 兼具质子转移与电荷转移双反应通道的化合物, 两者的竞争遵从能量最小原理, 结果使荧光发射仅选择其中一个通道进行. 泛函的选择只与实际发生的反应有关, 与并未实际发生的反应通道无关. 附加的八个算例进一步表明, 此成功的计算方案可望推广应用于其它类型的ESIPT和TICT荧光有机物.     

Calculation of the Stark effect of neon I usingjl coupled wave functions

A method to calculate the Stark shifts and splittings in noble gases is described and results for neon I are presented. The energy values in a static homogeneous electric field are found by diagonalizing the energy matrix numerically. This matrix consists of the energy values of the free atom taken from experiment and of off-diagonal matrix elements of the electric field operator. The latter are computed using wave functions consisting of a radial function of the excited electron found by numerical integration, and of a two-particle (core+electron) spin-orbital part represented by rigorousjl coupling. As an example, the splitting of the levels 6s to 6p is shown and is explained in terms of atomic level positions, the relative size of matrix elements and of selection rules. A nomenclature for the high field Stark effect is developed in accord with group theory.