Classical trajectory study of the dynamics of the reaction of Cl atoms with ethane

We present an electronic-structure and dynamics study of the Cl + C2H6 --> HCl + C2H5 reaction. The stationary points of the ground-state potential energy surface have been characterized using various electronic-structure methods and basis sets. Our best calculations, CCSD(T) extrapolated to the complete basis limit, using geometries and harmonic frequencies obtained at the MP2/aug-cc-pVTZ level, are in agreement with the experimental reaction energy. Ab initio information has been used to reparameterize a semiempirical Hamiltonian so that the predictions of the improved Hamiltonian agree with the higher-level calculations in key regions of the potential energy surface. The improved semiempirical Hamiltonian is then used to propagate quasiclassical trajectories. Computed kinetic energy release and scattering angle distributions at a collision energy of approximately 5.5 kcal mol(-1) are in reasonable agreement with experiments, but no evidence was found for the low translational energy HCl products scattered in the backward hemisphere reported in recent experiments.     

Dynamics of bimolecular reactions of vibrationally highly excited molecules: quasiclassical trajectory studies

Excitation functions from quasiclassical trajectory calculations on the H + H2O --> OH + H2, H + HF --> F + H2, and H + H'F --> H' + HF reactions indicate a different behavior at low and high vibrational excitation of the breaking bond. When the reactant tri- or diatomic molecule is in vibrational ground state or in a low vibrationally excited state, all these reactions are activated; i.e., there is a nonzero threshold energy below which there is no reaction. In contrast, at high-stretch excited-states capture-type behavior is observed; i.e., with decreasing translational energy the reactive cross-section diverges. The latter induces extreme vibrational enhancement of the thermal rate consistent with the experiments. The results indicate that the speed-up observed at high vibrational excitation is beyond the applicability of Polanyi's rules in their common form; instead, it can be interpreted in terms of an attractive potential acting on the attacking H atom when it approaches the reactant with a stretched X-H bond.     

Quasiclassical trajectory calculations to evaluate a kinematic constraint on internal energy in suprathreshold collision energy abstraction reactions

Experimentally observed product quantum state distributions across a wide range of abstraction reactions at suprathreshold collision energies have shown a strong bias against product internal energy. Only a fraction, sometimes quite a small fraction, of the energetically accessible product quantum states are populated. Picconatto et al. [J. Chem. Phys. 114, 1663 (2001)] noted a simple mathematical relationship between the highest-energy rovibrational states observed and the kinematics of the reaction system. They proposed a reaction model based on reaction kinematics that quantitatively explains this behavior. The model is in excellent agreement with measured quantum state distributions. The assumptions of the model invoke detailed characteristics of reactive trajectories at suprathreshold collision energies. Here we test those assumptions using quasiclassical trajectory calculations for the abstraction reactions H+HCl-->H2+Cl, D+HCl-->HD+Cl, and H+DCl-->HD+Cl. Trajectories were run on a potential-energy surface calculated with a London-Eyring-Polyani-Sato function with a localized 3-center term (LEPS-3C) previously shown to accurately reproduce experimentally observed product state distributions for the H+HCl abstraction reaction. The trajectories sample collision energies near threshold and also substantially above it. Although the trajectories demonstrate some aspects of the model, they show that it is not valid. However, the inadequacy of the proposed model does not invalidate the apparent kinematic basis of the observed energy constraint. The present results show that there must be some other molecular behavior rooted in the reaction kinematics that is the explanation and the source of the constraint.     

On the rate and activation energy of the Br + Br2 ataom-exchange reaction

The Br + Br₂ atom-exchange reaction has been studied using quasiclassical trajectories and a semi-empirical potential-energy surface with shallow, long-range wells. The computed reaction rate coefficient is in good agreement with experiment. The computed reaction activation energy is ? 1 kcal/mole.     

Quasiclassical trajectory study of the reaction H+CH4(nu3 = 0,1)-->CH3+H2 using a new ab initio potential energy surface

Detailed quasiclassical trajectory calculations of the reaction H+CH4(nu3 = 0,1)-->CH3 + H2 using a slightly updated version of a recent ab initio-based CH5 potential energy surface [X. Zhang et al., J. Chem. Phys. 124, 021104 (2006)] are reported. The reaction cross sections are calculated at initial relative translational energies of 1.52, 1.85, and 2.20 eV in order to make direct comparison with experiment. The relative reaction cross section enhancement ratio due to the excitation of the C-H antisymmetric stretch varies from 2.2 to 3.0 over this energy range, in good agreement with the experimental result of 3.0 +/- 1.5 [J. P. Camden et al., J. Chem. Phys. 123, 134301 (2005)]. The laboratory-frame speed and center-of-mass angular distributions of CH3 are calculated as are the vibrational and rotational distributions of H2 and CH3. We confirm that this reaction occurs with a combination of stripping and rebound mechanisms by presenting the impact parameter dependence of these distributions and also by direct examination of trajectories.     

Energy dependence of the roaming atom pathway in formaldehyde decomposition

Recently, a new mechanism of formaldehyde decomposition leading to molecular products CO and H(2) has been discovered, termed the "roaming atom" mechanism. Formaldehyde decomposition from the ground state via the roaming atom mechanism leads to rotationally cold CO and vibrationally hot H(2), whereas formaldehyde decomposition through the conventional molecular channel leads to rotationally hot CO and vibrationally cold H(2). This discovery has shown that it is possible to have multiple pathways for a reaction leading to the same products with dramatically different product state distributions. Detailed investigations of the dynamics of these two pathways have been reported recently. This paper focuses on an investigation of the energy dependence of the roaming atom mechanism up to 1500 cm(-1) above the threshold of the radical channel, H(2)CO-->H+HCO. The influence of excitation energy on the roaming atom and molecular elimination pathways is reported, and the branching fraction between the roaming atom channel and molecular channel is obtained using high-resolution dc slice imaging and photofragment excitation spectroscopy. From the branching fractions and the reaction rates of the radical channel, the overall competition between all three dissociation channels is estimated. These results are compared with recent quasiclassical trajectory calculations on a global H(2)CO potential energy surface.     

A state-to-state dynamical study of the Br + H(2) reaction: comparison of quantum and classical trajectory results

We present a detailed theoretical investigation of the dynamics corresponding to the strongly endothermic Br + H(2) (v = 0-1, j = 0) → H + HBr reaction in the 0.85 to 1.9 eV total energy range. State-averaged and state-to-state results obtained through time-independent wave packet (TIWP) and time-independent quantum mechanical (TIQM) calculations and quasiclassical trajectories (QCT) are compared and analyzed. The agreement in the results obtained with both quantum mechanical results is very good overall. However, although QCT calculations reproduce the general features, their agreement with the QM results is sometimes only qualitative. The analysis of the mechanism based on state-averaged results turns out to be deceptive and conveys an oversimplified picture of the reaction consistent with a direct-rebound mechanism. Consideration of state-to-state processes, in contrast, unveils the existence of multiple mechanisms that give rise to a succession of maxima in the differential cross section (DCS). Such mechanisms correlate with different sets of partial waves and display similar collision times when analyzed through the time-dependent DCS.     

Quasiclassical trajectory study of colinear Cl− + HBr → HCl + Br−

Energy distributions in the products of the ion-molecule reaction Cl^? + HBr → HC1 + Br^? have been studied using quasiclassical trajectories on a semi-empirical collinear potential energy surface. Vibrational energy is favored in the products. While some trajectories are long-lived, the kinematic factor of the light central atom prevents effective energy redistribution.     

Classical S matrix: Application of the Bessel uniform approximation to a chemical reaction

The Bessel uniform approximation developed by Stine and Marcus is applied to the collinear H + H₂ reaction on Diestler's potential energy surface no. 3 to which we have previously applied other orders of approximation of classical S matrix theory. It appears that an accurate treatment of this system by classical S matrix theory requires interference of real and complex trajectories. Calculations were also performed on two other potential energy surfaces in order to more clearly understand the interrelationships of previous semiclassical and quasiclassical studies of this reaction.     

Cl+C2H6→HCl+C2H5反应的准经典轨线研究

用三原子模型的准经典轨线方法研究了Ｃｌ与Ｃ２Ｈ６（ｖ＝０，ｊ）的反应。计算结果表明，反应产物ＨＣｌ的角度分布基本上为各向同性，其振动分布处于基态，与实验结果相一致。对反应轨线的研究表明，该反应为一直接反应，而且反应碰撞在低及高的碰撞参数下的机理不一样，在低碰撞参数下反应碰撞是直接完成的，产物ＨＣｌ以向后散射为主，转动基本上是冷的，但比高碰撞参数下的热。在高的碰撞参数下则生成短寿命的碰撞复合物，产物     

Dynamics of the D+ + H2 and H+ + D2 reactions: a detailed comparison between theory and experiment

An extensive set of experimental measurements on the dynamics of the H(+) + D(2) and D(+) + H(2) ion-molecule reactions is compared with the results of quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical quasiclassical trajectory (SQCT) calculations. The dynamical observables considered include specific rate coefficients as a function of the translational energy, E(T), thermal rate coefficients in the 100-500 K temperature range. In addition, kinetic energy spectra (KES) of the D(+) ions reactively scattered in H(+) + D(2) collisions are also presented for translational energies between 0.4 eV and 2.0 eV. For the two reactions, the best global agreement between experiment and theory over the whole energy range corresponds to the QCT calculations using a gaussian binning (GB) procedure, which gives more weight to trajectories whose product vibrational action is closer to the actual integer QM values. The QM calculations also perform well, although somewhat worse over the more limited range of translational energies where they are available (E(T) < 0.6 eV and E(T) < 0.2 eV for the H(+) + D(2) and D(+) + H(2) reactions, respectively). The worst agreement is obtained with the SQCT method, which is only adequate for low translational energies. The comparison between theory and experiment also suggests that the most reliable rate coefficient measurements are those obtained with the merged beams technique. It is worth noting that none of the theoretical approaches can account satisfactorily for the experimental specific rate coefficients of H(+) + D(2) for E(T)≤ 0.2 eV although there is a considerable scatter in the existing measurements. On the whole, the best agreement with the experimental laboratory KES is obtained with the simulations carried out using the state resolved differential cross sections (DCSs) calculated with the QCT-GB method, which seems to account for most of the observed features. In contrast, the simulations with the SQCT data predict kinetic energy spectra (KES) considerably cooler than those experimentally determined.     

Quasiclassical trajectory study of formaldehyde unimolecular dissociation: H(2)CO-->H2 + CO, H + HCO

We report quasiclassical trajectory calculations of the dynamics of the two reaction channels of formaldehyde dissociation on a global ab initio potential energy surface: the molecular channel H(2)CO-->H(2) + CO and the radical H(2)CO-->H + HCO. For the molecular channel, it is confirmed that above the threshold of the radical channel a second, intramolecular hydrogen abstraction pathway is opened to produce CO with low rotation and vibrationally hot H(2). The low-j(CO) and high-nu(H(2) ) products from the second pathway increase with the total energy. The competition between the molecular and radical pathways is also studied. It shows that the branching ratio of the molecular products decreases with increasing energy, while the branching ratio of the radical products increases. The results agree well with very recent velocity-map imaging experiments of Suits and co-workers and solves a mystery first posed by Moore and co-workers. For the radical channel, we present the translational energy distributions and HCO rotation distributions at various energies. There is mixed agreement with the experiments of Wittig and co-workers, and this provides an indirect confirmation of their speculation that the triplet surface plays a role in the formation of the radical products.     

Theoretical study of the F + NH3 and F + ND3 reactions: mechanism and comparison with experiment

We study the barrierless and highly exothermic F + NH(3) and F + ND(3) abstraction reactions using quasiclassical trajectory calculations based on an analytical potential energy surface developed in our research group. The calculations correctly reproduce the experimental evidence that the vibrational fraction deposited into the DF product for the F + ND(3) reaction is greater than into HF for the F + NH(3) reaction and that the vibrational distribution is inverted in the HF(v') and the DF(v') products. Of special interest is that recent crossed-beam experiments reported by Yang and co-workers at 4.5 kcal mol(-1) are reproduced for both reactions, with a mainly forward symmetry associated with direct trajectories, and a small sideways-backward symmetry contribution associated with "nearly trapped" trajectories due to a "yo-yo" mechanism, different from the previously suggested mechanism of a long-lived complex.     

辛准经典轨迹法研究Cl+H2反应

用辛准经典轨迹法模拟了Cl+H2反应在mBW2势能面上的动力学行为。研究了各种初始条件下的反应碰撞截面,产物的能量分配,角度分布和态分布。另外,我们还比较了反应物的三种能量形式(平动能,转动能和振动能)对反庆的有效性。     

A classical mechanical study of the LiFH system

A three dimensional and collinear quasiclassical study of the Li + HF → LiF + H reaction is performed on the Zeiri—Shapiro semi-empirical potential energy surface. The results are compared to a recent experimental study. In agreement with experiment ≈43% of available energy is channeled to the internal (vibrational and rotational) mode of the LiF product, most of which, we show, ends up as rotation (≈33%) and only the remaining 10% as vibration. The differential cross section is shown to peak in the forward—backward directions as also observed experimentally. The calculated cross section is more backward peaked than the experimental one. The accuracy of the quasiclassical method for this system is assessed by comparison of collinear results with available quantal calculations. It is shown that the average product vibrational distributions are adequately given by the quasiclassical method. The results are analyzed using periodic-orbit-dividing surfaces which predict correctly the onset of the various dynamic barriers.     

Direct dynamics trajectory study of vibrational effects: can polanyi rules be generalized to a polyatomic system?

We present an ab initio direct dynamics trajectory study of the hydrogen abstraction reaction: H2CO+ + CD4 --> H2COD+ + CD3, with methane excited in two different distortion modes (nu4 and nu2). The trajectory simulations were able to reproduce experimental results and for the first time show how vibrational enhancement originates in reaction of small polyatomic species. Roughly equal contributions from two vibrational enhancement mechanisms were found. The "distortion" mechanism correlates the vibrational effects with vibration-induced reactant distortions, and the "velocity" mechanism correlates vibrational effects with vibrational velocities of the constituent atoms. This reaction has a reactant-like transition state and, thus, would correspond to an "early" barrier system in the context of the well-known Polanyi rules for predicting effects of vibration and collision energy. Straightforward application of these rules would predict that vibration should be ineffective in driving reaction, in disagreement with both experiment and trajectory results. Using the trajectories for guidance, we were able to construct a two-dimensional cut through the reaction potential energy surface that does suggest a predictive, Polanyi-type rule.     

Collision-induced dissociation in (He, H2(+)(v = 0-2; j = 0-3)) system: a time-dependent quantum mechanical investigation

The collision-induced process He + H(2)(+)(v = 0-2; j = 0-3) → He + H + H(+) has been investigated using a time-dependent quantum mechanical wave packet approach, within the centrifugal sudden approximation. The exchange reaction He + H(2)(+) → HeH(+) + H, which has a lower threshold, dominates over the dissociation process over the entire energy range considered in this study. The reaction cross section for both the exchange and dissociation channels and the branching ratio between the two channels have been computed on the McLaughlin-Thompson-Joseph-Sathyamurthy potential-energy surface and compared with the available experimental and quasiclassical trajectory results.     

Can quasiclassical trajectory calculations reproduce the extreme kinetic isotope effect observed in the muonic isotopologues of the H + H2 reaction?

Rate coefficients for the mass extreme isotopologues of the H + H(2) reaction, namely, Mu + H(2), where Mu is muonium, and Heμ + H(2), where Heμ is a He atom in which one of the electrons has been replaced by a negative muon, have been calculated in the 200-1000 K temperature range by means of accurate quantum mechanical (QM) and quasiclassical trajectory (QCT) calculations and compared with the experimental and theoretical results recently reported by Fleming et al. [Science 331, 448 (2011)]. The QCT calculations can reproduce the experimental and QM rate coefficients and kinetic isotope effect (KIE), k(Mu)(T)/k(Heμ)(T), if the Gaussian binning procedure (QCT-GB)--weighting the trajectories according to their proximity to the right quantal vibrational action--is applied. The analysis of the results shows that the large zero point energy of the MuH product is the key factor for the large KIE observed.