Quasi-classical Trajectory Method Research Articles

Time-dependent quantum wave packet dynamics of S + OH reaction on its electronic ground state.

Initial state-selected dynamics of the S((3)P) + OH (X(2)Π) → SO (X(3)Σ(-)) + H ((2)S) reaction on its electronic ground potential energy surface (X̃(2)A") is investigated here by a time-dependent wave packet propagation (TDWP) approach. Total reaction probabilities for the three-body rotational angular momentum up to J = 138 are calculated to obtain converged integral reaction cross sections and state-specific rate constants employing the centrifugal sudden (CS) approximation. The convergence of the latter quantities is checked by varying all parameters used in the numerical calculations. The cross section and rate constant results are compared with those available in the literature, calculated with the aid of the quasi-classical trajectory method on the same potential energy surface. Reaction probabilities obtained with the TDWP approach exhibit dense oscillatory structures, implying formation of a metastable quasi-bound complex during the collision process. The effect of rotational and vibrational excitations of reagent OH on the dynamical attributes is also examined. While the rotational excitation of reagent OH decreases the reactivity, its vibrational excitation enhances the same.

Theoretical investigation of the influence of collision energy on the stereodynamics of Li+DF→LiF+D reaction

Calculations on the stereodynamics of the title reaction have been performed using the quasi-classical trajectory (QCT) method on the Aguado-Paniagua2-potential energy surface (AP2-PES) developed by Aguado et al. (J. Chem. Phys. 106 1013 (1997)) [1]. The product angular distributions which describe the vector correlations, P(θr), P(ϕr) and P(θr,ϕr) are presented. The calculated results indicate that the vector properties are sensitive to the change of the collision energy.

Reaction Dynamics of Methane with F, O, Cl, and Br on ab Initio Potential Energy Surfaces

The bimolecular hydrogen abstraction reactions of methane with atoms have become benchmark systems to test and extend our knowledge of polyatomic chemical reactivity. We review the state-of-the-art methodologies for reaction dynamics computations of X + methane [X = F, O((3)P), Cl, Br] reactions, which consist of two key steps: (1) potential energy surface (PES) developments and (2) reaction dynamics computations on the PES using either classical or quantum methods. We briefly describe the permutationally invariant polynomial approach for step 1 and the quasiclassical trajectory method, focusing on the mode-specific polyatomic product analysis and the Gaussian binning (1GB) techniques, and reduced-dimensional quantum models for step 2. High-quality full-dimensional ab initio PESs and dynamical studies of the X + CH4 and CHD3 reactions are reviewed. The computed integral cross-sections, angular, vibrational, and rotational product distributions are compared with available experiments. Both experimental and theoretical findings shed light on the rules of mode-selective polyatomic reactivity.

Stereodynamics investigation of F + HO → HF + O(1D) on the ground singlet potential energy surface by means of the quasi-classical trajectory method

The stereodynamics calculation of F + HO → HF + O(1D) was carried out using the quasi-classical trajectory method on the 11A′ potential energy surface provided by Gomez-Carrasco et al. (Chem. Phys. Lett. 2007, 435, 188). The effect of the collision energy, isotopic substitution, and different initial ro-vibrational states on the reaction is discussed. It is found that for the initial ground state of HO (v = 0, j = 0), the degree of the forward scattering and the product polarizations remarkably change as the collision energy varies. Isotopic effect leads to the increase of alignment and decrease of orientation of product rotational angular momentum. Moreover, the P(θr) distribution and P(φr) distribution change noticeably by varying the initial vibrational number. The initial vibrational excitation plays a more important role in the enhancement of alignment and orientation distribution of j′ for the title reaction. Although the influence of the initial rotational excitation effect on the aligned and oriented distribution of product is not stronger than that of the initial vibrational excitation effect, the initial rotational excitation makes the alignment of the product rotational angular momentum decrease to some extent. The probabilities show that the reactivity of the title reaction strongly depends on the initial vibrational state.

Theoretical Study of Reagent Rotational Excitation Effect on the Stereodynamics of H + LiF→HF+Li Reaction

The reagent rotational excitation effect on the stereodynamics of H+LiF→HF+Li is calculated by means of the quasi-classical trajectory method on the Aguado-Paniagua2-potential energy surface (AP2-PES) constructed by Aguado et al. [J. Chem. Phys. 106, 1013 (1997)]. The angular distributions of vector correlations between products and reactants, P(θr) and P(ϕr) are presented. Meanwhile, the four polarization-dependent generalized differential cross sections are computed. The results indicate that the reagent rotational quantum numbers have impact on the vector properties of the title reaction. In addition, the reaction probability has been calculated as well.

Quasi-classical trajectory study of the isotope effect on the stereodynamics in the reaction H(2S) + CH(X2Π; υ = 0, j = 1) → C(1D) + H2(X1Σg+)

The isotope effect on the stereodynamic properties in the title reaction is investigated by a quasi-classical trajectory (QCT) method on the 11A′ potential energy surface at a collision energy of 23.06 kcal/mol. The angular distributions P(θr), P(φr), P(θr,φr), and the polarization-dependent generalized differential cross sections are calculated, which demonstrate the observable influences on the rotational polarization of the product by the isotopic substitution of H with D.

Reagent vibrational, rotational and isotopic effects on stereodynamics of theH+OCl→OH+Clreaction

The quasi-classical trajectory method has been employed to investigate the initial vibrational and rotational effects of the title reaction on an improved ab initio potential energy surface for the 11A′ state. Meanwhile, isotopic effect has also been studied at collision energy of 19 kcal/mol. The product rotational alignment factor 〈P2(j′ • k)〉, angular distributions of P(ϕr), P(θr) and the generalized polarization dependent differential cross-sections have been calculated. The- results show that the reagent vibrational excitation generally strengthens the product alignment perpendicular to the reagent relative velocity vector k and affects the product scattering preference, and the rotational excitation has the same trend from j = 0 to 2 except for the higher excitation of j = 3. Further, the substitution of atom H with D leads to a stronger product alignment while changes some stereodynamical properties subtly.

Collision energy effect on stereodynamics for Sr+CH3I→SrI+CH3

Based on semiemperical London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES), stereodynamic properties of the reaction Sr+CH3I→SrI+CH3 in different initial reagent collision energies are studied theoretically by using the quasiclassical trajectory method. The results indicate that the collision energy of reagent has considerable influences on the orientations and alignments of angular momentum of products for the title reaction.

Quantum wave-packet and quasiclassical trajectory of reaction S(3P)+HD

In this paper, the S(3P)+HD→SD+H and SH+D reactions are studied by means of quantum wave packet (QMWP) and quasi-classical trajectory (QCT) methods on a new ab initio 3A" potential energy surface. The reactive probabilities, integral cross sections, intra-molecular isotope parameters and product rotational alignment parameters for both reactive channels are calculated for collision energies in a range between 0.8 and 2.2 eV. The results reveal a pronounced isotopic effect. Plots of the potential energy surface and typical reactive trajectories show the evidence of an additional reaction mechanism for the SD+H product channel. This reaction mechanism, together with mass combination, can explain the isotopic effect for the title reaction.

Understanding the effect of vibrational excitation in reaction dynamics: the Ne + H2+(v = 0–17, j = 1) → NeH+ + H, Ne + H+ + H proton transfer and dissociation cross sections

The dependence of the cross section (σ) of the Ne + H2(+)→ NeH(+) + H proton transfer reaction on the vibrational excitation of H2(+), v = 0-17 and j = 1, was analyzed in detail at the collision energies (Ecol) of 0.7 and 1.7 eV, using the quasi-classical trajectory (QCT) method and the PHHJ3 and LZHH potential energy surfaces (PESs), taking advantage of the rich experimental data available for this reaction as a function of H2(+)(v). The efficiency of vibrational excitation to promote the reaction was investigated from the analysis of the σ(QCT) vs. v dependence in terms of the average reaction probability, maximum impact parameter, regions of the (late barrier) PES explored, and taking into account the Ne + H2(+)→ Ne + H(+) + H dissociative channel, which plays a dominant role at high enough total energies. Although the earlier PHHJ3 PES performs rather well, the LZHH PES QCT results show a better agreement with the experiment. On the other hand, some artifacts were found in recently reported QCT calculations (unphysical oscillations in σ(QCT) as a function of v), and the present study shows that special care is needed when carrying out QCT calculations involving highly excited vibrational states.

Dynamics for the reaction O+DCl→OD+Cl

With the quasi-classical trajectory method the stereodynamics of the O+DCl→OD+Cl reaction on the ground potential energy surface is investigated. The characteristic of calculated integral cross-section is consistent with that of the non-energy barrier reaction path on the potential energy surface, which implies that the title reaction is a typical exothermic reaction. The obtained differential reaction cross-section shows that the products tend to both forward and backward scattering, and the forward scattering is stronger than the backward one. So we can infer that the reaction follows the indirect reaction mechanism that has been verified by the randomly abstractive reaction trajectories. The distribution curves of P(θr) and 2(J'· K)> reflect that the degree of rotational alignment of the product OD first increases and then decreases with collision energy increasing. The product rotational angular momentum vector J' is aligned along the y-axis direction but is oriented along the positive direction of y-axis at higher collision energy. With the increase of the collision energy the rotation mechanism of the product molecules transits from the “in-plane” mechanism to the “out-of-plane” mechanism.

Theoretical investigation of vibrational relaxation of highly excited O3 in collisions with HO2

We report calculations of the relaxation process involving highly excited O3 with vibrationally cold HO2. The initial vibrational energies of O3 between 9 and 21 kcal mol−1 are considered. All calculations employ the quasi-classical trajectory method and the realistic double many-body expansion potential energy surface for HO5(2A). Both the traditional histogram boxing and momentum Gaussian binning schemes are utilized in examining the energy transfer process, the latter for the first time in the case of triatomic fragments. The results indicate that it may notable in studying the stratospheric ozone budget.

Quasiclassical trajectory study of energy relaxation process in collision of highly vibrationally excited O2 and ground-state N2

Vibrational relaxation processes in the collision of highly vibrationally excited O2 (v=15–20) and ground-state N2 (v=0) have been studied using a quasiclassical trajectory method. The potential energy surface of the system is obtained using the interpolating moving least-squares method. The energy transfer and the scattering processes in the collision were investigated. We found that vibrational–vibrational (V–V) transfer was dominant under the conditions of our calculations.

Stereodynamics in reaction O(1D) + CH4 → OH + CH3

A theoretical study of the stereodynamics for reaction O(1D) + CH4 → OH + CH3 has been carried out using the quasiclassical trajectory method (QCT) on a potential energy surface structured by Gonzalez et al. The integral cross sections (ICSs), differential cross sections (DCSs) and product rotational angular momentum polarization have been calculated. With the collision energy increasing, the ICS decreases. There is no threshold energy, because no barrier is found on the minimum energy path. The DCS results show that the backward and forward scatterings exist at the same time. With the collision energy increasing, the dominant rotation of the product changes from the right-handed direction to the left-handed direction in planes parallel to the scattering plane. In the isotopic effect study, the decrease of the mass factor weakens the polarization degree of the rotational angular momentum vectors of the products.

Quasi-classical Trajectory Study of F+H2O→HF+OH Reaction: Influence of Barrier Height, Reactant Rotational Excitation, and Isotopic Substitution

The reaction dynamics of the F+H2O/D2O→HF/DF+OH/OD are investigated on an accurate potential energy surface (PES) using a quasi-classical trajectory method. For both isotopomers, the hydrogen/deuterium abstraction reaction is dominated by a direct rebound mechanism over a very low “reactant-like” barrier, which leads to a vibrationally hot HF/DF product with an internally cold OH/OD companion. It is shown that the lowered reaction barrier on this PES, as suggested by high-level ab initio calculations, leads to a much better agreement with the experimental reaction cross section, but has little impact on the product state distributions and mode selectivity. Our results further indicate that rotational excitation of the H2O reactant leads to significant enhancement of the reactivity, suggesting a strong coupling with the reaction coordinate.

Theoretical prediction of the optimal conditions for observing the stereodynamical vector properties of the C(3P) + OH (X2Π) → CO(X1Σ+) + H(2S) reaction

The best optimal initial reactant state and collision energy for observing the stereodynamical vector properties of the title reaction in the ground electronic state X2A′ potential energy surface (PES) [Zanchet et al. 2006 J. Phys. Chem. A 110 12017] are theoretically predicted using the quasi-classical trajectory (QCT) method for the first time. The calculated results reveal that the smallest value of the rotational quantum number j, larger vibrational quantum number v, and the lower strength of collision energy should be selected for offering the most obvious picture about the stereodynamical vector properties. Polarization-dependent differential cross sections and the angular momentum alignment distribution, P(θr) and P(Φr) in the center-of-mass frame, are obtained to gain an insight into the alignment and orientation of the product molecules. The rotational angular momentum vector j′ of CO is aligned to be perpendicular to reagent relative velocity k. The product polarizations align along the y axis, pointing to the positive direction of the y axis. A new method is developed to investigate massive reactions with various initial states and to further study the vector properties of the fundamental reactions in detail.

Theoretical Study of the H+ClO Reaction

We present a theoretical study of the H+OCl system on an accurate ab initio potential energy surface (PES) investigated by Peterson et al.[J. Chem. Phys. 113 (2000) 6186]. Both the exact time-dependent quantum wave packet (TDWP) and quasi-classical trajectory (QCT) methods are employed. The results of reaction probabilities for total angular momentum J = 0 and the integral cross section calculated by the TDWP are in good agreement with the QCT ones. Additionally, the nearly forward-backward symmetric product scattering angular distributions and the weak products' rotational alignment effect obtained by the QCT calculations are attributed to a long-lived intermediate reaction process.

Time-Dependent Wave Packet Quantum Scattering and Quasi-Classical Trajectory Calculations of the H + FCl(v=0,j=0) → HF + Cl/HCl + F Reaction

The dynamics of the title reaction are investigated using both time-dependent wave packet quantum scattering and quasi-classical trajectory (QCT) methods on adiabatic ground 1(2)A' potential energy surface (PES). Compared with the quantum results of reaction probabilities of H + FCl(J=0) → HF + Cl/HCl + F, the QCT method is proven feasible and further employed to produce integral cross sections and rate constants. Significant resonance structures are observed in the reaction probabilities using the quantum method; however, there are some undulations in the calculated QCT integral cross sections for both product channels. A comparison between the quantum mechanical coupled-channel (CC) calculation and centrifugal sudden approximation calculation reveals the very important role of Coriolis coupling effects in the quantum calculation. Comparisons between the calculated thermal rate constants for both reactions and the previous theoretical and experimental results have been done. HCl product formation is favored over the HF product in the reactive system. Finally, the HF products are found to be mainly forward scattering, and the HCl products are mainly backward scattering.

Theoretical studies of dynamics for the reactions H + HBr (v = 0,1; j = 0) and D + DBr (v = 0,1; j = 0)

Theoretical studies of the dynamics of the title reactions have been performed with quasi-classical trajectory (QCT) method on MB3 potential energy surface. The calculated quasi-classical reaction probabilities of two reaction channels of reaction H′+HBr for J=0, 10, 20, 30, 40 are in good agreement with quantum wave packet results over the collision energy range from 0.1 to 2.0eV. The agreement between quasi-classical and quantum wave packet results is remarkably good for the integral cross section of the two reaction channels of reaction H′+HBr. The attack angle dependent reaction probabilities of the title reactions at J=0 have also been calculated. The distribution of the reaction probabilities was found to be strongly dependent on the attack angle. Besides, the integral cross sections of two channels of reaction D′+DBr are predicted in this work. Validity of the QCT calculation has been examined and proved in the comparison with the quantum wave packet calculation.

Influence of early-staged energy barrier on stereodynamics of reaction of LiH(ν=0, j=0)+H→Li + H2

Theoretical studies of stereodynamics for reaction LiH(ν=0, j=0)+H→Li+H2 have been carried out with quasiclassical trajectory method on two potential energy surfaces(PESs) structured as W-PES and P-PES. The main difference of the two PESs is at fixed angle of Li-H-H from 110° to 180°. In this angle range, there is an early-staged energy barrier on the P-PES, but there is no barrier on the W-PES. Some studies have been done to explore the influence of the early-staged energy barrier on this exothermic reaction. Integral cross sections, differential cross sections and product rotational angular momentum of the reaction have been calculated. When Ec 0.48 eV, the dominant influence of barrier is to promote reacting. The angular distribution of the product H2 is extremely forward on both the PESs, because the lifetime of most complexes is short. Totally, the lifetime on the P-PES is longer than that on W-PES for the existence of the barrier. With the collision energy increasing, on the both PESs, the distribution of the direction of the product H2 angular momentum changed, and there is a trend that peak at (90°,270°) gets weaker and peak at (90°,90°) gets stronger. The energy barrier weakens the degree of the rotation alignment of the H2.