Calculation of multiple initial state selected reaction probabilities from Chebyshev flux-flux correlation functions: influence of reactant internal excitations on H + H2O → OH + H2

A Chebyshev-based flux-flux correlation function approach is introduced for calculating multiple initial state selected reaction probabilities for bimolecular reactions. Based on the quantum transition-state theory, this approach propagates, with the exact Chebyshev propagator, transition-state wave packets towards the reactant asymptote. It is accurate and efficient if many initial state selected reaction probabilities are needed. This approach is applied to the title reaction to elucidate the influence of the H(2)O ro-vibrational states on its reactivity. Results from several potential energy surfaces are compared.     

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H(2)(ν, j) → HD(ν', j') + H reaction for J = 0.     

A transition state view on reactive scattering: initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction studied in full dimensionality

Initial state-selected reaction probabilities for the H+CH(4)→H(2)+CH(3) reaction are computed for vanishing total angular momentum by full-dimensional calculations employing the multiconfigurational time-dependent Hartree approach. An ensemble of wave packets completely describing reactivity for total energies up to 0.58 eV is constructed in the transition state region by diagonalization of the thermal flux operator. These wave packets are then propagated into the reactant asymptotic region to obtain the initial state-selected reaction probabilities. Reaction probabilities for reactants in all rotational states of the vibrational 1A(1), 1F(2), and 1E levels of methane are presented. Vibrational excitation is found to decrease reactivity when reaction probabilities at equivalent total energies are compared but to increase reaction probabilities when the comparison is done at the basis of equivalent collision energies. Only a fraction of the initial vibrational energy can be utilized to promote the reaction. The effect of rotational excitation on the reactivity differs depending on the initial vibrational state of methane. For the 1A(1) and 1F(2) vibrational states of methane, rotational excitation decreases the reaction probability even when comparing reaction probabilities at equivalent collision energies. In contrast, rotational energy is even more efficient than translational energy in increasing the reaction probability when the reaction starts from the 1E vibrational state of methane. All findings can be explained employing a transition state based interpretation of the reaction process.     

A minimum-reaction-flux solution to master-equation models of protein folding

Master equations are widely used for modeling protein folding. Here an approximate solution to such master equations is presented. The approach used may be viewed as a discrete variational transition-state theory. The folding rate constant kf is approximated by the outgoing reaction flux J, when the unfolded set of macrostates assumes an equilibrium distribution. Correspondingly the unfolding rate constant ku is calculated as Jpu(1-pu), where pu is the equilibrium fraction of the unfolded state. The dividing surface between the unfolded and folded states is chosen to minimize the reaction flux J. This minimum-reaction-flux surface plays the role of the transition-state ensemble and identifies rate-limiting steps. Test against exact results of master-equation models of Zwanzig [Proc. Natl. Acad. Sci. USA 92, 9801 (1995)] and Munoz et al. [Proc. Natl. Acad. Sci. USA 95, 5872 (1998)] shows that the minimum-reaction-flux solution works well. Macrostates separated by the minimum-reaction-flux surface show a gap in p(fold) values. The approach presented here significantly simplifies the solution of master-equation models and, at the same time, directly yields insight into folding mechanisms.     

Transition-state theory rate calculations with a recrossing-free moving dividing surface

Two different methods for transition-state theory (TST) rate calculations are presented that use the recently developed notions of the moving dividing surface and the associated moving separatrices: one is based on the flux-over-population approach and the other on the calculation of the reactive flux. The flux-over-population rate can be calculated in two ways by averaging the flux first over the noise and then over the initial conditions or vice versa. The former entails the calculation of reaction probabilities and is closely related to previous TST rate derivations. The latter results in an expression for the transmission factor as the noise average of a stochastic variable that is given explicitly as a function of the moving separatrices. Both the reactive-flux and flux-over-population methods suggest possible new ways of calculating approximate rates in anharmonic systems. In particular, numerical simulations of harmonic and anharmonic systems have been used to calculate reaction rates based on the reactive flux calculation using the fixed and moving dividing surfaces so as to illustrate the computational advantages of the latter.     

Semiclassical nonadiabatic dynamics based on quantum trajectories for the O(3P,1D) + H2 system

The O(3P,1D) + H2 --> OH + H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J = 0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states.     

Path-integral virial estimator for reaction-rate calculation based on the quantum instanton approximation

The quantum instanton approximation is a type of quantum transition-state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low-order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat-capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial (-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.     

HO+CH4→H2O+CH3反应的偏分势能面与散射共振态理论研究

用ab initio方法构建了该体系的偏分势能面, 并用其研究了该体系中散射共振态的形成机理, 估算了第一共振态寿命.     

Theoretical Studies on the Abstraction Reaction of Atomic O（^3p） with Si2H6

The hydrogen abstraction reaction of O(^3P) with Si2H6 has been studied theoretially. Two transition states of ^3A″ and ^3A′ symmetries have been located for this abstraction reaction. Geometries have been optimized at the UMP2 leve with 6-311G (d) basis set. G3MP2 has been used for the final single-point energy calculation. The rate constants have been calculated over a wide temperature range of 200-3000K using canonical variational transition-state sheory (CVT) with small curvature tunneling effect(SCT). The calculated CVT/SCT rate constants match well with the experimental value.     

Theoretical study of hydrogen abstraction and sulfur insertion in the reaction H2S + S

The reaction of H2S + S has been characterized at the multireference configuration interaction level with the geometries optimized using the aug-cc-pVTZ basis set and the single-point energy calculated using the aug-cc-pV(Q+d)Z basis set. As in the analogous reaction of H2 + S, the presence of an intersystem crossing enables products (SH + SH) to be formed on the singlet surface through S insertion, which bypasses the triplet barrier (19.1 kJ mol-1 relative to SH + SH) of the H abstraction route. This provides theoretical evidence for SH + SH formation without barrier beyond endothermicity at sufficiently low temperatures. The H abstraction route, however, is expected to be competitive at higher temperatures due to a much higher Arrhenius pre-exponential factor (6.9 x 10(14) cm3 mol-1 s-1 derived from TST calculation) than that of S insertion channel (3.7 x 10(13) cm3 mol-1 s-1, derived by a least-squares fit to the measurements). With a slightly higher transition-state barrier than that of the H abstraction channel, the production of S2 + H2 is less favored due to proceeding via intersystem crossing and insertion. While the formation of HSS + H is energetically unfavorable relative to SH + SH, recombination channels producing H2SS or the more stable HSSH are expected to occur under collisional stabilization conditions at high pressures.     

New ab initio potential energy surface and quantum dynamics of the reaction H(2S) + NH(X3Σ-) → N(4S) + H2

A new global potential energy surface is reported for the ground state ((4)A(")) of the reaction H((2)S) + NH(X(3)Σ(-)) → N((4)S) + H(2) from a set of accurate ab initio data, which were computed using the multi-reference configuration interaction with a basis set of aug-cc-pV5Z. The many-body expansion and neural network methods have been used to construct the new potential energy surface. The topographical features of the new global potential energy surface are presented. The predicted barrier height is lower than previous theoretical estimates and the heat of reaction with zero-point energy is closer to experimental results. The quantum reactive scattering dynamics calculation was carried out over a range of collision energies (0-1.0 eV) on the new potential energy surface. The reaction probabilities, integral cross-section, and rate constants for the title reaction were calculated. The calculated rate constants are in excellent agreement with the available experimental results.     

一个新的用于反应散射计算的L^2平动基函数集合

本文通过构造新的L^2平动基函数集合改进了Shima-Baer方法.新集合中不再含有任何人工可调参数,取而代之的是反应体系的分子特性常数.由于在平动基函数中含有在非经典区域内的高度衰减因子,从而大大提高了反应几率对平动基函数展开的收敛速度.对共线交换反应H+H~2→H~2+H的计算结果表果,对平均基函数展开的收敛速度已接近包含畸变势的计算结果.改进后的Shima-Baer方法计算量明显降低.     

H原子和(CH3)2SiH2抽提反应的理论研究

采用UMP2/6-31G(d)理论水平优化了H原子和(CH3)2SiH2抽提反应势能面上的所有驻点,并在此水平基础上进行了内禀反应坐标(IRC)的计算,得到该反应的反应途径(MEP)。应用变分过渡态理论及最小能量途径半经典绝热基态隧道效应校正(MEPSAG)、小曲率半经典绝热基态隧道效应校正(SCSAG)等方法对上述反应进行了动力学研究,期望从理论上提供一套温度范围较宽、精度较高的动力学数据,为阐明反应机理和解释实验结果提供理论依据。     

A full dimensional, nine-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction

A full dimensional, nine-degree-of-freedom (9DOF), time-dependent quantum dynamics wave packet approach is presented for the study of the H2+C2H-->H+C2H2 reaction system. This is the first full dimensional quantum dynamics study for a diatom-triatom reaction system. The effects of the initial vibrational and rotational excitations of the reactants on the reactivity of this reaction are investigated. This study shows that vibrational excitations of H2 enhance the reactivity; whereas, the vibrational excitations of C2H only have a small effect on the reaction probability. In addition, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. Comparison of the ground state reaction probabilities of the 9DOF and 8DOF shows the reaction probability from the full dimensional calculation is larger, with more prominent resonance features.     

D+HCN反应的SVRT含时波包理论研究

基于Horst的势能面,用SVRT(SemirigidVibratingRotorTarget)方法对D+HCN反应进行了含时波包动力学研究,计算得到了不同初始振转态的总反应几率和积分反应截面,采用UniformJ-shifting方法得到该反应的热速率常数.计算结果与H+HCN反应进行了比和讨论.     

Nonadiabatic reactant-product decoupling calculation for the F(2P(1/2)) + H2 reaction

In this paper we present a theoretical study using time-dependent nonadiabatic reactant-product decoupling method for the state-to-state reactive scattering calculation of F((2)P(1/2))+H(2) (nu=j=0) reaction on the Alexander-Stark-Werner potential energy surface. In this nonadiabatic state-to-state calculation, the full wave function is partitioned into reactant component and a sum of all product components. The reactant and product components of the wave function are solved independently. For the excited state reaction, the state-to-state reaction probabilities for J=0.5 are calculated. Comparing the state-to-state reaction probabilities, it is found that the vibrational population of the HF product is dominated by vibrational levels nu=2 and 3. The rotation specific reaction probabilities of HF product in j=1 and 2 are larger than those in other rotational levels. As the rotation quantum number j increases, the positions of the peak in the rotational reaction probability of HF product in nu=3 shift to higher collision energy.     

Quantum study of the N+N(2) exchange reaction: state-to-state reaction probabilities, initial state selected probabilities, Feshbach resonances, and product distributions

We report a detailed three-dimensional time-dependent quantum dynamics study of the state-to-state N+N(2) exchange scattering in the 2.1-3.2 eV range using a recently developed ab initio potential energy surface (PES). The reactive flux arrives at the dividing surface in the asymptotic product region in a series of six packets, instead of a single packet. Further study shows that these features arise from the "Lake Eyring" region of the PES, a region with a shallow well between two transition states. Trappings due to Feshbach resonances are found to be the major cause of the time delay. A detailed analysis of the Feshbach resonance features is carried out using an L(2) calculation of the metastable states in the "Lake Eyring" region. Strong resonance features are found in the state-to-state and initial state selected reaction probabilities. The metastable states with bending motions and/or bending coupled with stretching motions are found to be the predominant source of the resonance structure. Initial state selected reaction probabilities further indicate that the lifetimes of the metastable states with bending motions in the "Lake Eyring" region are longer than those of states with stretching motions and thus dominate the reactive resonances. Resonance structures are also visible in some of the integral cross sections and should provide a means for future experimental observation of the resonance behavior. A study of the final rotational distributions shows that, for the energy range studied here, the final products are distributed toward high-rotational states. Final vibrational distributions at the temperatures 2000 and 10,000 K are also reported.     

Constraints at the transition state of the D + H2 reaction: quantum bottlenecks vs. stereodynamics

This article presents a quasiclassical trajectory method for the calculation of cumulative reaction probabilities by sampling of the helicity quantum number of the reagents (k). The method is applied to the D + H(2) reaction at various total angular momentum (J) values, and the helicity-resolved quasiclassical cumulative reaction probabilities are compared to their quantum mechanical counterparts. The agreement between the two sets of results is fairly good. In particular, k-dependent, J-independent reaction thresholds found with quantum methods are reproduced by the quasiclassical calculations. The shift of these thresholds with increasing k, which has been previously attributed to the quantum bottleneck states taking part in the reaction, is revisited and discussed also in terms of the reaction stereodynamics.     

Calculation of the Canonical Rate Constant for the Nonadiabatic Trapping Model Based on Unified Statistical Theory:A Test on The Exchange Reaction H_2 H

IntroductionTheunifiedstatisticaltheory(UST)proposedbyMiller'isappropriatefordescribingdirectcomPlexreachonmechanismsand,especially,thenonadiabahctraPPingmodel.ThelatterisunrelatedtotheInindriaonthepotenhalenergysurface(PES),butrelatedtomulh-dividingsurfaces.ThedetenninahonofdividingsuifacescorrespondingtotherelahveInindriaorrelativemaxdriaofthefluxintegral(N(E,S))playsthecentralroleinUST.ThedividingsurfacesaregenerallyandrigorouslydefmedbyandcrocanonicalvariahonalmethodofN(E,S)onthee…     

3D Generalized langevin equation approach to gas–surface reactive scattering: model H+H→H2/Si(100)-(2×1)

Classical trajectory calculation has been performed for the H+H→H₂/Si(100)-(2×1) reaction by the 3D Generalized Langevin Equation (GLE) approach. The implementation of the 3D GLE approach to the H+H→H₂/Si(100)-(2×1) reaction is presented. Reaction probabilities are calculated for given surface temperatures and given collision energies. We also calculated vibrational and rotational distributions of product H₂ molecules from the reaction. About 80% of the product hydrogen molecules are in the ground vibrational state and the remaining 20% of the products are in the excited states. The rotational state shows non-Boltzmann distribution which can be seen in the direct collision process. Vibrational and Rotational distributions are strongly related to the impact parameter. The vibrational distribution is correlated with the x-component of the impact parameter and reflects the dimer nature of the silicon (2×1) surface. Details of the dynamics involving vibrational and rotational transitions are discussed.