论化学反应动力学中的稳态假设

对单分子气相反应undemann机理提出了一个不用稳态假设的动力学新表述，并指出经典表述中的稳态假设是主观硬性加上的，缺少了一个条件。当反应气体压强变小时，经典表述中虽然应用稳态假设，但实际上是高活性中间产物的近似，并不真正存在稳态。稳态假设的适用性有两种不同的近似本质，一是平衡态近似或真稳态，另一是高活性中间产物近似，应予分辨。过去文献中往往把两者混在一起，这会导致得不到一般性结论，或所得一般性结论会有错误。文中也讨论了在复杂反应中真稳态的存在，而平衡态和真稳态的建立，都需经过一个初期瞬间过程，而高活性中间产物近似没有初期瞬间过程，因为不是一个形成稳态的过程。     

A New Formulation of the Lindemann Mechanism of Unimolecular Reactions

A new formulation of the Lindemann mechanism of unimolecular reactions in gaseous phase is presented, without the use of steady state hypothesis. It is hereby shown that the nature of applicability of steady state hypothesis in the regime of high reactant gas pressure is different from that in the regime of low gas pressure. In the former case it is an equilibrium approximation, while in the latter case it is a highly reactive intermediate approximation in no connection with a steady state. Furthermore for the latter case it is shown that in the classical formulation of Lindemann mecbRnism the use of steady state hypothesis is an ad hoc assumption. A highly reactive intermediate in the sense that its concentration is very small during the whole course of reaction is a necessary condition for the applicability of very reactive intermediate approximation. When the two distinctive nature of the applicability of steady state hypothesis is mlxed-up, wrong or useless conclusion may be arrived at. The only possible case of realizing a true steady state in a complex reaction is pointed out.     

Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches.     

Efficient first-principles electronic dynamics

An efficient first-principles electronic dynamics method is introduced in this article. The approach we put forth relies on incrementally constructing a time-dependent Fock∕Kohn-Sham matrix using active space density screening method that reduces the cost of computing two-electron repulsion integrals. An adaptive stepsize control algorithm is developed to optimize the efficiency of the electronic dynamics while maintaining good energy conservation. A selected set of model dipolar push-pull chromophore molecules are tested and compared with the conventional method of direct formation of the Fock∕Kohn-Sham matrix. While both methods considered herein take on identical dynamical simulation pathways for the molecules tested, the active space density screening algorithm becomes much more computationally efficient. The adaptive stepsize control algorithm, when used in conjunction with the dynamically active space method, yields a factor of ～3 speed-up in computational cost as observed in electronic dynamics using the time dependent density functional theory. The total computational cost scales nearly linear with increasing size of the molecular system.     

Effective potential theory of atom–diatom scattering in the presence of “intermediate” reactive channels

A field-theoretical formalism is applied to the problem of atom–diatom scattering, in the presence of “intermediate” reactive channels. This leads to an integral equation formulation for elastic processes and to a numerical quadrature problem for inelastic vibro–rotational transitions. The key quantity of the theory is represented by an effective potential that contains full information on the dynamics of the process. A closed equation is obtained for this quantity, along with an approximation scheme of the second order in the system interaction potential. A diagrammatic technique is introduced and the physical interpretation of the approximate form of the effective potential considered.     

Diagrammatic kinetic theory for a lattice model of a liquid. II. Comparison of theory and simulation results

We compare the predictions of the mean field, the two site multiple scattering, and the simple mode coupling approximation developed in the previous paper for the dynamics of a tagged particle in an excluded volume lattice gas with the results of computer simulations. The tagged particle has a transition rate of gamma while the background particles have transition rates of alphagamma. We consider the tracer diffusion coefficient and the incoherent intermediate scattering function (IISF) for low, intermediate, and high concentrations of particles and for simple square and cubic lattices. In general, the approximate kinetic theories are more accurate in predicting simulations results at low concentrations, high dimensions, and large alpha. For the tracer diffusion coefficient, the mean field approximation is the least accurate, the two site multiple scattering approximation is more accurate, and the simple mode coupling approximation is the most accurate; all three approximate theories overestimate the simulation results. For the IISF, the mean field approximation is quantitatively accurate in the limit of small concentration and large alpha but in general decays too quickly. The two site multiple scattering approximation is quantitatively accurate at low and intermediate concentrations for large wave vectors; it is always more accurate than the mean field approximation and always decays more quickly than the simulation results. The simple mode coupling approximation is the most accurate of the three approximations in most cases and especially so for small wave vectors, high concentration, and small alpha; unfortunately, its predictions are not quantitatively accurate in these highly nonmean field regimes. We discuss the implications of these results for developing diagrammatic kinetic theories.     

Systematic stepsize variation: Efficient method for searching conformational space of polypeptides

A new and efficient method for overcoming the multiple minima problem of polypeptides, the systematic stepsize variation (SSV) method, is presented. The SSV is based on the assumption that energy barriers can be passed over by sufficiently large rotations about rotatable bonds: randomly chosen dihedral angles are updated starting with a small stepsize (i.e., magnitude of rotation). A new structure is accepted only if it possesses a lower energy than the precedent one. Local minima are passed over by increasing the stepsize systematically. When no new structures are found any longer, the simulation is continued with the starting structure, but other trajectories will be followed due to the random order in updating the torsional angles. First, the method is tested with Met-enkephalin, a peptide with a known global minimum structure; in all runs the latter is found at least once. The global minimum conformations obtained in the simulations show deviations of ±0.0004 kcal/mol from the reference structure and, consequently, are perfectly superposable. For comparison, Metropolis Monte Carlo simulated annealing (MMC-SA) is performed. To estimate the efficiency of the algorithm depending on the complexity of the optimization problem, homopolymers of Ala and Gly of different lengths are simulated, with both the SSV and the MMC-SA method. The comparative simulations clearly reveal the higher efficiency of SSV compared with MMC-SA. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1470–1481, 1998     

NMR diffusometry with beds of nanoporous host particles: an assessment of mass transfer in compartmented two-phase systems

Molecular diffusion in a bed of zeolite crystallites is mimicked by dynamic Monte Carlo simulation of a particle hopping on a two-dimensional square lattice. The resulting probability distribution of molecular propagation (the "mean propagator") is used for a rigorous determination of the resulting dependencies of diffusion measurement by pulsed field gradient NMR. In the limiting cases of intracrystalline, restricted, and long-range diffusion, these dependencies are found to coincide with the well-known relations resulting from the application of a simplifying exchange model (the "two-region" approximation). The intensity of transport resistances on the boundary between the intra- and intercrystalline spaces, i.e., on the compartment boundaries, is only accessible in the intermediate case, i.e., for observation times comparable with the mean lifetimes within the different compartments. In this case, significant differences between the results of the rigorous treatment and the "two-region" approximation may occur.     

A new study on the kinetics of Stöber synthesis by in-situ liquid 29Si NMR

Liquid-state ²⁹Si NMR was used to investigate the hydrolysis and condensation kinetics of ammonia-catalyzed tetraethoxysilane (TEOS) in methanol system. The reactive rate constants were calculated by applying first-order reaction approximation and the steady state approximation theory. The reaction orders with respect to TEOS, ammonia and water were derived, as well as the activation energies and the Arrhenius constants. It was found that the formation of intermediate species Si(OH)(OEt)₃ was the rate-limiting step and its reaction rate equation was r _TEOS=7.41×10⁻³[TEOS][NH₃]^0.333[H₂O]^0.227. Higher reactive temperature benefited the hydrolysis of TEOS. The results presented here indicated quantificationally that the formation of colloidal SiO₂ particles was controlled by the initial hydrolysis of TEOS.     

Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE–2009)

In this article, we solve numerically singularly perturbed non-linear autonomous initial-value problems (IVPs) by using a non-standard algorithm on a variable stepsize implementation. On a recent article (Ramos et al. in J Math Chem, To appear) we had used nonuniform meshes for resolving the difficulties arising from the steep gradient of the solution in the initial layer. The present method is intended for solving the nonlinear problem using a nonuniform mesh originated by a suitable strategy provided for changing the stepsize. Numerical experiments are carried out to verify the efficiency and accuracy of the method, showing that the new procedure leads to better results than in (Ramos et al. in J Math Chem, To appear).     

燃烧反应动力学研究进展

化学反应动力学是燃烧过程分析的重要工具。燃烧微观反应过程、复杂反应机理、燃烧实验测量和湍流燃烧数值模拟等方面的研究工作已经取得了长足进步。本文主要介绍燃烧反应动力学研究方法,包括电子结构方法、燃烧反应热力学和速率常数的计算方法、燃烧详细机理构建和简化、反应力场分子模拟以及燃烧中间体测量、燃料点火延迟和光谱诊断等方面的研究现状。燃烧反应动力学具有很强的应用背景,燃烧过程化学物种的反应速率计算是湍流燃烧数值模拟的一个中心任务。由于燃烧反应网络的高度复杂性,我们对燃烧机理的认识还远不清楚。化学反应和湍流相互作用研究的深入、燃烧反应动力学和计算流体力学的协同发展,将对新燃料设计、燃烧数值模拟、发动机内流道流场结构的准确描述产生深远影响。     

DFT evidence for a stepwise mechanism in the O-neophyl rearrangement of 1,1-diarylalkoxyl radicals

Hybrid DFT calculations of the potential energy surface (PES) relative to the O-neophyl rearrangement of a series of ring-substituted 1,1-diarylalkoxyl radicals have been carried out at the UB3LYP/6-31G(d) level of theory. On the basis of the computational data, the rearrangement can be described as a consecutive reaction of the type a <--/--> b --> c (see above graphic), and the steady-state approximation could be applied in all cases to the intermediate b. The first-order rearrangement rate constants [kobs = k1k2/(k-1 + k2)] were thus obtained from the computed activation free-energies and were compared with the experimental rate constants measured previously in MeCN solution by laser flash photolysis. An excellent agreement is observed along the two series, which strongly supports the hypothesis that the O-neophyl rearrangement of 1,1-diarylalkoxyl radicals proceeds through the formation of the reactive 1-oxaspiro [2,5]octadienyl radical intermediate. This is in contrast to previous hypotheses that involve either a long-lived intermediate or the absence of this intermediate along the reaction path. The calculated rearrangement free-energies decrease upon going from the methoxy-substituted radical (Delta G degrees = -16.4 kcal x mol-1) to the nitro-substituted one (Delta G degrees = -21.8 kcal x mol-1), which follows a trend that is similar to the one observed for the CAr-O bond dissociation enthalpies (BDEs) of ring-substituted anisoles. This evidence indicates that in the O-neophyl rearrangement the effect of ring substituents on the strength of the newly formed CAr-O bond plays an important role.     

Nature of the chemical bond in protonated methane

Protonated methane, CH(5)(+), is a key reactive intermediate in hydrocarbon chemistry and a borderline case for chemical structure theory, being the simplest example of hypercoordinated carbon. Early quantum mechanical calculations predicted that the properties of this species could not be associated with only one structure, because it presents serious limitations of the Born-Oppenheimer approximation. However, ab initio molecular dynamics and diffusion Monte Carlo calculations showed that the most populated structure could be pictured as a CH(3) tripod linked to a H(2) moiety. Despite this controversy, a model for the chemical bonds involved in this ion still lacks. Here we present a modern valence bond model for the electronic structure of CH(5)(+). The chemical bond scheme derived directly from our calculations pictures this ion as H(3)C...H(2)(+). The fluxionality can be seen as the result of a proton transfer between C-H bonds. A new insight on the vibrational bands at approximately 2400 and approximately 2700 cm(-1) is suggested. Our results show that the chemical bond model can be profitably applied to such intriguing systems.     

Potential oscillations in galvanostatic electrooxidation of formic acid on platinum: a mathematical modeling and simulation

We have modeled temporal potential oscillations during the electrooxidation of formic acid on platinum on the basis of the experimental results obtained by time-resolved surface-enhanced infrared absorption spectroscopy (J. Phys. Chem. B 2005, 109, 23509). The model was constructed within the framework of the so-called dual-path mechanism; a direct path via a reactive intermediate and an indirect path via strongly bonded CO formed by dehydration of formic acid. The model differs from earlier ones in the intermediate in the direct path. The reactive intermediate in this model is formate, and the oxidation of formate to CO2 is rate-determining. The reaction rate of the latter process is represented by a second-order rate equation. Simulations using this model well reproduce the experimentally observed oscillation patterns and the temporal changes in the coverages of the adsorbed formate and CO. Most properties of the voltammetric behavior of formic acid, including the potential dependence of adsorbate coverages and a negative differential resistance, are also reproduced.     

流体系统模拟中邻区列表算法的优化理论

分子动力学模拟中邻区列表算法的效率依赖于其参数的选择. 作者提供了一种选择最优化参数的计算方法, 通过分别使用自由粒子近似和扩散近似对所需模拟的时间进行计算, 再对两种近似计算进行比较. 结果表明, 在密度较低或者皮肤半径较小的情况下需要采用自由粒子近似, 而当密度较高或者皮肤半径较大的情况下则需要采用扩散近似. 该方法的结果与Lennard-Jones流体系统的模拟结果符合得很好.     

Olefin oxygenation by the hydroperoxide adduct of a nonheme manganese(IV) complex: epoxidations by a metallo-peracid produces gentle selective oxidations

The reactive intermediates and mechanisms of oxygenation of olefins by manganese complexes were investigated by treating olefins with newly synthesized [MnIV(Me2EBC)(OH)2](PF6)2 in the presence and absence of peroxide and by studying its catalytic epoxidation reaction in normal aqueous solution and, individually, with isotopically labeled H218O, 18O2, and H218O2. The manganese oxo species is not the reactive intermediate for the oxygen transfer process mediated by this manganese complex. A novel manganese(IV) peroxide intermediate, MnIV(Me2EBC)(O)(OOH)+, was captured by mass spectrometry and is proposed as the intermediate that oxygenates olefins in this catalytic system.     

An adaptive stepsize method for the chemical Langevin equation

Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes.     

Free-energy landscape of nucleation with an intermediate metastable phase studied using capillarity approximation

Capillarity approximation is used to study the free-energy landscape of nucleation when an intermediate metastable phase exists. The critical nucleus that corresponds to the saddle point of the free-energy landscape as well as the whole free-energy landscape can be studied using this capillarity approximation, and various scenarios of nucleation and growth can be elucidated. In this study, we consider a model in which a stable solid phase nucleates within a metastable vapor phase when an intermediate metastable liquid phase exists. We predict that a composite critical nucleus that consists of a solid core and a liquid wetting layer as well as pure liquid and pure solid critical nuclei can exist depending not only on the supersaturation of the liquid phase relative to that of the vapor phase but also on the wetting behavior of the liquid surrounding the solid. The existence of liquid critical nucleus indicates that the phase transformation from metastable vapor to stable solid occurs via the intermediate metastable liquid phase, which is quite similar to the scenario of nucleation observed in proteins and colloidal systems. By studying the minimum-free-energy path on the free-energy landscape, we can study the evolution of the composition of solid and liquid within nuclei which is not limited to the critical nucleus.     

How much can an intermediate state influence competing reactive pathways?

A molecule undergoing reaction may form a short-lived intermediate. Under certain conditions, the rate at which the reaction proceeds toward the product state via the intermediate may exceed that of a simple, direct path. The competition of two alternative reactive pathways is analyzed here in terms of a stochastic model. The approach allows one to diagnose this competition as a function of the energy of the intermediate relative to the barrier heights of the potential surface and values of the reactive vibrational modes. The result has applications to a variety of problems in chemical physics, ranging from the "lock-and-key" mechanism for the enzymatic activity to control of temporal evolution of complex systems by optimal laser fields.     

The palladium catalyzed asymmetric addition of oxindoles and allenes: an atom-economical versatile method for the construction of chiral indole alkaloids

The Pd-catalyzed asymmetric allylic alkylation (AAA) is one of the most useful and versatile methods for asymmetric synthesis known in organometallic chemistry. Development of this reaction over the past 30 years has typically relied on the use of an allylic electrophile bearing an appropriate leaving group to access the reactive Pd(π-allyl) intermediate that goes on to the desired coupling product after attack by the nucleophile present in the reaction. Our group has been interested in developing alternative approaches to access the reactive Pd(π-allyl) intermediate that does not require the use of an activated electrophile, which ultimately generates a stoichiometric byproduct in the reaction that is derived from the leftover leaving group. Along these lines, we have demonstrated that allenes can be used to generate the reactive Pd(π-allyl) intermediate in the presence of an acid cocatalyst, and this system is compatible with nucleophiles to allow for formation of formal AAA products by Pd-catalyzed additions to allenes. This article describes our work regarding the use of oxindoles as carbon-based nucleophiles in a Pd-catalyzed asymmetric addition of oxindoles to allenes (Pd-catalyzed hydrocarbonation of allenes). By using the chiral standard Trost ligand (L1) and 3-aryloxindoles as nucleophiles, this hydrocarbonation reaction provides products with two vicinal stereocenters, with one being quaternary, in excellent chemo-, regio-, diastereo-, and enantioselectivities in high chemical yields.