Kramers problem for nonequilibrium current-induced chemical reactions

We discuss the use of tunneling electron current to control and catalyze chemical reactions. Assuming the separation of time scales for electronic and nuclear dynamics we employ Langevin equation for a reaction coordinate. The Langevin equation contains nonconservative current-induced forces and gives nonequilibrium, effective potential energy surface for current-carrying molecular systems. The current-induced forces are computed via Keldysh nonequilibrium Green's functions. Once a nonequilibrium, current-depended potential energy surface is defined, the chemical reaction is modeled as an escape of a Brownian particle from the potential well. We demonstrate that the barrier between the reactant and the product states can be controlled by the bias voltage. When the molecule is asymmetrically coupled to the electrodes, the reaction can be catalyzed or stopped depending on the polarity of the tunneling current.     

A Monte Carlo simulation of free energy relationships for the electron transfer reaction between Fe+ and Fe2+ in water

A free energy barrier ΔF^≠ = 174.2 kJ/mol for the self-exchange electron transfer reaction model Fe⁺/Fe²⁺ in water has been calculated by combining Monte Carlo simulations and the statistical perturbation theory. We have shown that, even for those electron transfer reactions that present a very high free energy barrier of activation, the free energy curve behaves parabolically versus the reaction coordinate, which justifies the quadratic expression for the activation free energy done by Marcus.     

Quantum Monte Carlo study of the reaction: Cl+CH3OH-->CH2OH+HCl

A theoretical study is reported of the Cl+CH3OH-->CH2OH+HCl reaction based on the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo method. Using a DMC trial function constructed as a product of Hartree-Fock and correlation functions, we have computed the barrier height, heat of reaction, atomization energies, and heats of formation of reagents and products. The DMC heat of reaction, atomization energies, and heats of formation are found to agree with experiment to within the error bounds of computation and experiment. M?ller-Plesset second order perturbation theory (MP2) and density functional theory, the latter in the B3LYP generalized gradient approximation, are found to overestimate the experimental heat of reaction. Intrinsic reaction coordinate calculations at the MP2 level of theory demonstrate that the reaction is predominantly direct, i.e., proceeds without formation of intermediates, which is consistent with a recent molecular beam experiment. The reaction barrier as determined from MP2 calculations is found to be 2.24 kcal/mol and by DMC it is computed to be 2.39(49) kcal/mol.     

Ab initio calculations including electron correlation for the minimum energy path of the (1A1) CH2+(1Σ)H2→ (1A1) CH4 insertion reaction

Ab initio calculations on the SCF level and with the inclusion of valence shell electron correlation in the IEPA–PNO (independent electron pair approximation with pair natural orbitals), the PNO–CI (pair-natural-orbital configuration interaction) and the CEPA–PNO (coupled electron pair approximation with pair natural orbitals) schemes with Gaussian lobe functions of “double zeta quality” have been performed for the minimum energy path of the insertion of singlet (¹A₁) methylene to the (¹Σ)H₂ molecule to yield methane. The energy was minimized on the SCF level to all geometrical parameters for various values of the “approximate” reaction coordinate. The energy along the reaction path decreases monotonically without a barrier and the curves representing the total energy of the system as a function of approximate reaction coordinates obtained at different levels of approximations have the same shape. From the physical point of view three phases of the reaction can be distinguished (chemically two steps) with different geometrical arrangements and different internal geometries of the partners.     

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.     

Computer-assisted study on the reaction between pyruvate and ylide in the pathway leading to lactyl–ThDP

In this study the formation of the lactyl-thiamin diphosphate intermediate (L-ThDP) is addressed using density functional theory calculations at X3LYP/6-31++G(d,p) level of theory. The study includes potential energy surface scans, transition state search, and intrinsic reaction coordinate calculations. Reactivity is analyzed in terms of Fukui functions. The results allow to conclude that the reaction leading to the formation of L-ThDP occurs via a concerted mechanism, and during the nucleophilic attack on the pyruvate molecule, the ylide is in its AP form. The calculated activation barrier for the reaction is 19.2?kcal/mol, in agreement with the experimental reported value.     

氧原子与二硫化碳反应的机理

用从头计算法、内禀反应坐标和电子密度拓扑分析方法研究了3P态氧原子与二硫化碳的反应.找到了分别形成CS SO,S OCS和S2 CO三个反应通道上的极小点和过渡态.采用UHF/631G进行几何构型优化,并在UMP2/631G水平上进行能量校正.三个反应通道上的稳定点和过渡态都经内禀反应坐标(IRC)跟踪得以确认,并用电子密度拓扑分析方法考察了反应过程中化学键的变化.计算结果表明,反应过程中所有稳定点和过渡态都具有Cs对称性,即对每个反应通道而言在整个反应过程中分子始终保持在同一平面内.在三个反应通道中,第一个反应通道O CS2→CS SO由于具有较小的活化能而更容易发生,与实验结果相一致.文中对反应机理进行了较详细的讨论.     

RISM-SCF study of the free-energy profile of the Menshutkin-type reaction NH3+CH3Cl→NH3CH3++Cl− in aqueous solution

The free-energy profile for the Menshutkin-type reaction NH₃ + CH₃Cl → NH₃CH₃ ⁺ + Cl⁻ in aqueous solution is studied using the RISM-SCF method. The effect of electron correlation on the free-energy profile is estimated by the RISM-MP2 method at the HF optimized geometries along the reaction coordinate. Solvation was found to have a large influence on the vibrational frequencies at the reactant, transition state and product; these vibrational frequencies are utilized to calculate the zero-point energy correction of the free-energy profile. The computed barrier height and reaction exothermicity are in reasonable agreement with those of experiment and previous calculations. The change of solvation structure along the reaction path is represented by radial distribution functions between solute-solvent atomic sites. The mechanisms of the reaction are discussed from the view points of solute electronic and solvation structures. Received: 26 June 1998/Accepted: 28 August 1998 / Published online: 2 November 1998     

Model studies of hydrogen atom addition and abstraction processes involving ortho-, meta-, and para-benzynes.

H-atom addition and abstraction processes involving ortho-, meta-, and para-benzyne have been investigated by multiconfigurational self-consistent field methods. The H(A) + H(B)...H(C) reaction (where r(BC) is adjusted to mimic the appropriate singlet-triplet energy gap) is shown to effectively model H-atom addition to benzyne. The doublet multiconfiguration wave functions are shown to mix the "singlet" and "triplet" valence bond structures of H(B)...H(C) along the reaction coordinate; however, the extent of mixing is dependent on the singlet-triplet energy gap (DeltaE(ST)) of the H(B)...H(C) diradical. Early in the reaction, the ground-state wave function is essentially the "singlet" VB function, yet it gains significant "triplet" VB character along the reaction coordinate that allows H(A)-H(B) bond formation. Conversely, the wave function of the first excited state is predominantly the "triplet" VB configuration early in the reaction coordinate, but gains "singlet" VB character when the H-atom is close to a radical center. As a result, the potential energy surface (PES) for H-atom addition to triplet H(B)...H(C) diradical is repulsive! The H3 model predicts, in agreement with the actual calculations on benzyne, that the singlet diradical electrons are not coupled strongly enough to give rise to an activation barrier associated with C-H bond formation. Moreover, this model predicts that the PES for H-atom addition to triplet benzyne will be characterized by a repulsive curve early in the reaction coordinate, followed by a potential avoided crossing with the (pi)1(sigma*)1 state of the phenyl radical. In contrast to H-atom addition, large activation barriers characterize the abstraction process in both the singlet ground state and first triplet state. In the ground state, this barrier results from the weakly avoided crossing of the dominant VB configurations in the ground-state singlet (S0) and first excited singlet (S1) because of the large energy gap between S0 and S1 early in the reaction coordinate. Because the S1 state is best described as the combination of the triplet X-H bond and the triplet H(B)...H(C) spin couplings, the activation barrier along the S0 abstraction PES will have much less dependence on the DeltaE(ST) of H(B)...H(C) than previously speculated. For similar reasons, the T1 potential surface is quite comparable to the S0 PES.     

介质阻挡放电等离子体中·OH和HO2·自由基的数值模拟计算

在介质阻挡放电等离子体N2/O2/H2O/HCHO体系中通过解Boltzmann方程, 得到电子能量分布函数, 利用得到的电子能量分布函数计算电子-分子碰撞反应速率常数. 然后把有关的反应速率常数带入速率方程, 计算得到该体系在介质阻挡放电时,·OH、HO2·和电子的浓度随时间的演变以及·OH、HO2·浓度随H2O、O2摩尔分数的变化, 并将模拟结果与实验值进行了对比, 两者符合得较好.     

Simple and exact approach to the electronic polarization effect on the solvation free energy: formulation for quantum-mechanical/molecular-mechanical system and its applications to aqueous solutions

We present a simple and exact numerical approach to compute the free energy contribution δμ in solvation due to the electron density polarization and fluctuation of a quantum-mechanical solute in the quantum-mechanical/molecular-mechanical (QM/MM) simulation combined with the theory of the energy representation (QM/MM-ER). Since the electron density fluctuation is responsible for the many-body QM-MM interactions, the standard version of the energy representation method cannot be applied directly. Instead of decomposing the QM-MM polarization energy into the pairwise additive and non-additive contributions, we take sum of the polarization energies in the QM-MM interaction and adopt it as a new energy coordinate for the method of energy representation. Then, it is demonstrated that the free energy δμ can be exactly formulated in terms of the energy distribution functions for the solution and reference systems with respect to this energy coordinate. The benchmark tests were performed to examine the numerical efficiency of the method with respect to the changes in the individual properties of the solvent and the solute. Explicitly, we computed the solvation free energy of a QM water molecule in ambient and supercritical water, and also the free-energy change associated with the isomerization reaction of glycine from neutral to zwitterionic structure in aqueous solution. In all the systems examined, it was demonstrated that the computed free energy δμ agrees with the experimental value, irrespective of the choice of the reference electron density of the QM solute. The present method was also applied to a prototype reaction of adenosine 5'-triphosphate hydrolysis where the effect of the electron density fluctuation is substantial due to the excess charge. It was demonstrated that the experimental free energy of the reaction has been accurately reproduced with the present approach.     

硅烯与甲醛环加成反应的理论研究

本文用RHF/6-31G^*解析梯度方法研究了单重态硅烯与甲醛环加成反应的机理,用二级微扰方法对各构型的能量进行了相关能校正,并用统计热力学方法和过渡态理论计算了该反应在不同温度下的热力学函数的变化和动力学性质。结果表明,此反应历程由两步组成:1)硅烯与甲醛生成一中间配合物,是一无势垒的放热反应,2)中间配合物异构化为产物,此步势垒经零点能校正后只有51.4kJ·mol^-^1(MP2/6-31G^*//6-31G^*);从热力学和动力学的综合角度考虑,该反应在300～400K温度下进行为宜,如此,反应既有较大的自发趋势和平衡常数,又具有较快的反应速率。     

Friction dependence of reaction rates in simple barrierless reactions

We have investigated the dynamics of simple chemical reactions which proceed without an activation barrier along the reaction coordinate. In the absence of the barrier the solvent friction is the only impediment to the reactive motion. By numerical simulation we show that in the low-friction limit the reaction rate increases as a fractional power of the friction coefficient. The power law dependence is sensitive to the initial conditions of the reactive coordinate. After exhibiting a maximum, the behaviour crosses over to that of inverse friction dependence in the high-friction limit. We have compared our results with earlier approximate analytical treatments and differences are pointed out.     

Intramolecular charge transfer in 4-aminobenzonitriles does not necessarily need the twist

In electron donor/acceptor species such as 4-(dimethylamino)benzonitrile (DMABN), the excitation to the S(2) state is followed by internal conversion to the locally excited (LE) state. Dual fluorescence then becomes possible from both the LE and the twisted intramolecular charge-transfer (TICT) states. A detailed mechanism for the ICT of DMABN and 4-aminobenzonitrile (ABN) is presented in this work. The two emitting S(1) species are adiabatically linked along the amino torsion reaction coordinate. However, the S(2)/S(1) CT-LE radiationless decay occurs via an extended conical intersection "seam" that runs almost parallel to this torsional coordinate. At the lowest energy point on this conical intersection seam, the amino group is untwisted; however, the seam is accessible for a large range of torsional angles. Thus, the S(1) LE-TICT equilibration and dual fluorescence will be controlled by (a) the S(1) torsional reaction path and (b) the position along the amino group twist coordinate where the S(2)/S(1) CT-LE radiationless decay occurs. For DMABN, population of LE and TICT can occur because the two species have similar stabilities. However, in ABN, the equilibrium lies in favor of LE, as a TICT state was found at much higher energy with a low reaction barrier toward LE. This explains why dual fluorescence cannot be observed in ABN. The S(1)-->S(0) deactivation channel accessible from the LE state was also studied.     

锗烯与乙烯环加成反应的理论研究

用RHF/6-31G^*解析梯度方法研究了单重态锗烯与乙烯环加成反应的机理,用二级微扰方法对各构型的能量进行了相关能校正,并用统计热力学方法和过渡态理论计算了该反应在不同温度下的热力学函数的变化和动力学性质。结果表明,此反应历程由两步组成:1)锗烯与乙烯生成了一中间配合物,是一无势垒的放热反应,2)中间配合物异构化为产物锗杂环丙烷,此步势垒经零点能校正后为26.9kJ.mol^-^1(MP2/6-31G^*//6-31G^*);从热力学和动力学的综合角度考虑,该反应在200-300K温度下进行为宜,如此,反应既有较大的自发趋势和平衡常数,又具有较快的反应速率。     

Oriented Electric Fields Accelerate Diels–Alder Reactions and Control the endo/exo Selectivity

Herein we demonstrate that an external electric field (EEF) acts as an accessory catalyst/inhibitor for Diels–Alder (DA) reactions. When the EEF is oriented along the “reaction axis” (the coordinate of approach of the reactants in the reaction path), the barrier of the DA reactions is lowered by a significant amount, equivalent to rate enhancements by 4–6 orders of magnitude. Simply flipping the EEF direction has the opposite effect, and the EEF acts as an inhibitor. Additionally, an EEF oriented perpendicular to the “reaction axis” in the direction of the individual molecule dipoles can change the endo/exo selectivity, favouring one or the other depending on the positive/negative directions of the EEF vis‐à‐vis the individual molecular dipole. At some critical value of the EEF along the “reaction axis”, there is a crossover to a stepwise mechanism that involves a zwitterionic intermediate. The valence bond diagram model is used to comprehend these trends and to derive a selection rule for EEF effects on chemical reactions: an EEF aligned in the direction of the electron flow between the reactants will lower the reaction barrier. It is shown that the exo/endo control by the EEF is not associated with changes in secondary orbital interactions.     

Ultrafast deactivation processes in aminopyridine clusters: excitation energy dependence and isotope effects

Fast excited-state relaxation in H-bonded aminopyridine clusters occurs via hydrogen transfer in the excited state. We used femtosecond pump-probe spectroscopy to characterize the excited-state reaction coordinate. Considerable isotope effects for partially deuterated clusters indicate that H-transfer is the rate-limiting step and validate ab initio calculations in the literature. A nonmonotonous dependence on the excitation energy, however, disagrees with the picture of a simple barrier along the reaction coordinate. An aminopyridine dimer serves as a model for Watson-Crick base pairs, where similar reactions have been predicted by theory.     

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