Quasiclassical Trajectory Approach Research Articles

Energetics and Predissociation Dynamics of Small Water, HCl, and Mixed HCl-Water Clusters.

This Review summarizes recent research on vibrational predissociation (VP) of hydrogen-bonded clusters. Specifically, the focus is on breaking of hydrogen bonds following excitation of an intramolecular vibration of the cluster. VP of the water dimer and trimer, HCl clusters, and mixed HCl-water clusters are the major topics, but related work on hydrogen halide dimers and trimers, ammonia clusters, and mixed dimers with polyatomic units are reviewed for completion and comparison. The theoretical focus is on generating accurate potential energy surfaces (PESs) that can be used in detailed dynamical calculations, mainly using the quasiclassical trajectory approach. These PESs have to extend from the region describing large amplitude motion around the minimum to regions where fragments are formed. The experimental methodology exploits velocity map imaging to generate pair-correlated product translational energy distributions from which accurate bond dissociation energies of dimers and trimers and energy disposal in fragments are obtained. The excellent agreement between theory and experiment on bond dissociation energies, energy disposal in fragments, and the contributions of cooperativity demonstrates that it is now possible, with state-of-the-art experimental and theoretical methods, to make accurate predictions about dynamical and energetic properties of dissociating clusters.

Classical reactive scattering in a quantum spirit: improving the shape of rotational state distributions for indirect reactions in the quantum regime

For indirect triatomic chemical reactions under single-collision conditions, we propose a new implementation of the quasi-classical trajectory (QCT) approach to rotational state distributions, of particular interest in the quantum regime where only a few rotational states are available to the products. This method is directly inspired from the amendments to be introduced in classical phase space theory (PST) in order to make it in exact agreement with quantum PST. The approach is applied to the \(\hbox {D}^{+} + \hbox {H}_2\) and \(\hbox {H}^{+} + \hbox {D}_2\) reactions, and the population of the rotational ground state is found to be in much closer agreement with the exact quantum one than the one obtained by means of standard QCT calculations. The impact on the whole distribution is all the stronger as the number of available states is small. Lastly, the shape of the distribution appears to be controlled to a large extent by three factors, respectively, called parity, edge and rotational shift factors. The method is a complementary alternative to the statistical–dynamical methods, often used to study indirect processes. However, contrary to what is done in these methods, trajectories are not stopped at the entrance of the strong coupling region within our approach, thus expected to lead to reasonable predictions also for indirect processes that are not fully statistical, like those involving an osculating complex.

The dissociative chemisorption of methane on Ni(100) and Ni(111): Classical and quantum studies based on the reaction path Hamiltonian

Electronic structure methods based on density functional theory are used to construct a reaction path Hamiltonian for CH4 dissociation on the Ni(100) and Ni(111) surfaces. Both quantum and quasi-classical trajectory approaches are used to compute dissociative sticking probabilities, including all molecular degrees of freedom and the effects of lattice motion. Both approaches show a large enhancement in sticking when the incident molecule is vibrationally excited, and both can reproduce the mode specificity observed in experiments. However, the quasi-classical calculations significantly overestimate the ground state dissociative sticking at all energies, and the magnitude of the enhancement in sticking with vibrational excitation is much smaller than that computed using the quantum approach or observed in the experiments. The origin of this behavior is an unphysical flow of zero point energy from the nine normal vibrational modes into the reaction coordinate, giving large values for reaction at energies below the activation energy. Perturbative assumptions made in the quantum studies are shown to be accurate at all energies studied.

Quantum wave packet and quasiclassical trajectory studies of the reaction H(2S) + CH(X2Π; v = 0, j = 1) → C(1D) + H2(X1): Coriolis coupling effects and stereodynamics

The quantum mechanics (QM) and quasiclassical trajectory (QCT) calculations have been carried out for the title reaction with the ground minimal allowed rotational state of CH (j = 1) on the 1 (1)A' potential energy surface. For the reaction probability at total angular momentum J = 0, a similar trend of the QM and QCT calculations is observed, and the QM results are larger than the latter almost in the whole considered energy range (0.1-1.5 eV). The QCT integral cross sections are larger than the QM results with centrifugal sudden approximation, while smaller than those from QM method including Coriolis coupling for collision energies bigger than 0.25 eV. The quantum wave-packet computations show that the Coriolis coupling effects get more and more pronounced with increasing of J. In addition to the scalar properties, the stereodynamical properties, such as the average rotational alignment factor <P2 (j'•k)>, the angular distributions P(θr ), P(ϕr ), P(θr ,ϕr ), and the polarization-dependent generalized differential cross sections have been explored in detail by QCT approach.

Investigation of Stereo-dynamic Properties for the Reaction H+HLi by Quasi-classical Trajectory Approach

E-mail: yarmiay@163.comReceived March 26, 2012, Accepted May 24, 2012Quasi-classical trajectory (QCT) calculations of H+HLi reaction have been carried out on a new potentialenergy surface of the ground state reported by Prudente et al. [Chem. Phys. Lett. 2009, 474, 18]. The fourpolarization-dependent differential cross sections have been carried out in the center of mass (CM) frame atvarious collision energies. The reaction probability for the depletion channel has been studied over a widecollision energy range. It has been found that the collision energy decreases remarkably reaction probability,which shows the expected behavior of the title reaction belonging to an exothermic barrierless reaction. Theresults are in good agreement with previous RMP results. The P(θ

Quasi-classical trajectory approach to the influence of the rotational excitation on the stereodynamics of the reaction O+HBrOH+Br

Quasi-classical trajectory method is used to investigate the influence of rotational excitation on the vector properties of the dynamics for the reaction O+HBrOH+Br based on the abinitio potential energy surface. At the collision energy 0.3 eV, we discuss the polarization-dependent differential cross sections (PDDCSs), the distribution P(r) describing k - j correlation, and the distribution P(r) describing k - k- j correlation. The calculated results suggest that the product rotational polarization becomes weaker as the rotational quantum number increases and the products are mainly forward scattered.

Quasi-classical trajectory approach to the O(1D)+HBr→OH+Br reaction stereo-dynamics on X1A′ potential energy surface

The vector properties of reaction O(1D)+HBr→OH+Br on the potential energy surface (PES) of X1A′ ground singlet state are studied by using the quasi-classical trajectory (QCT) theory. The polarization-dependent differential cross sections (PDDCSs), the average rotational alignment factor 〈P2(j′ · k)〉, as well as the distributions reflecting vector correlations are also computed. The analysis of the results shows that the alignment and the orientation distribution of the rotation angular momentum vector of product molecule OH is influenced by both the effect of heavy—light—heavy (HLH) type mass combination and the deep well of PES.

On the role of dynamical barriers in barrierless reactions at low energies: S(1D) + H2

Reaction probabilities as a function of total angular momentum (opacity functions) and the resulting reaction cross sections for the collision of open shell S((1)D) atoms with para-hydrogen have been calculated in the kinetic energy range 0.09-10 meV (1-120 K). The quantum mechanical hyperspherical reactive scattering method and quasi-classical trajectory and statistical quasi-classical trajectory approaches were used. Two different ab initio potential energy surfaces (PESs) have been considered. The widely used reproducing kernel Hilbert space (RKHS) PES by Ho et al. [T.-S. Ho, T. Hollebeek, H. Rabitz, S. D. Chao, R. T. Skodje, A. S. Zyubin, and A. M. Mebel, J. Chem. Phys 116, 4124 (2002)] and the recently published accurate double many-body expansion (DMBE)/complete basis set (CBS) PES by Song and Varandas [Y. Z. Song and A. J. C. Varandas, J. Chem. Phys. 130, 134317 (2009)]. The calculations at low collision energies reveal very different dynamical behaviors on the two PESs. The reactivity on the RKHS PES is found to be considerably larger than that on the DMBE/CBS PES as a result of larger reaction probabilities at low total (here also orbital) angular momentum values and to opacity functions which extend to significantly larger total angular momentum values. The observed differences have their origin in two major distinct topographic features. Although both PESs are essentially barrierless for equilibrium H-H distances, when the H-H bond is compressed the DMBE/CBS PES gives rise to a dynamical barrier which limits the reactivity of the system. This barrier is completely absent in the RHKS PES. In addition, the latter PES exhibits a van der Walls well in the entrance channel which reduces the height of the centrifugal barrier and is able to support resonances. As a result, a significant larger cross section is found on this PES, with marked oscillations attributable to shape resonances and/or to the opening of partial wave contributions. The comparison of the results on both PESs is illustrative of the wealth of the dynamics at low collision energy. It is also illuminating about the difficulties encountered in modeling an all-purpose global potential energy surface.

Energy dependent dynamics of the O(1D) + HCl reaction: A quantum, quasiclassical and statistical study

The dynamics of the reaction O((1)D) + HCl → ClO + H, OH + Cl has been investigated in detail by means of a time-dependent wave packet (TDWP) method in comparison with quasiclassical trajectory (QCT) and statistical approaches on the ground potential energy surface by Martínez et al. [Phys. Chem. Chem. Phys., 2000, 2, 589]. Fully coupled quantum mechanical (QM) reaction probabilities for high values of the total angular momentum (J≤ 50) are reported for the first time. At the low collision energy regime (E(c)≤ 0.4 eV) the TDWP probabilities are well reproduced by the QCT and statistical results for the ClO forming product channel, but for the OH + Cl arrangement, only QCT probabilities are found to agree with the QM values. The good accordance found between the rigorous statistical models and the dynamical QM and QCT calculations for the O + HCl → ClO + H process underpins the assumption that the reaction pathway leading to ClO is predominantly governed by a complex-forming mechanism. In addition, to further test the statistical character of this reaction channel, the laboratory angular distribution and time-of-flight spectra obtained in a crossed molecular beam study by Balucani et al. [Chem. Phys. Lett. 1991, 180, 34] at a collision energy as high as 0.53 eV have been simulated using the state resolved differential cross section obtained with the statistical approaches yielding a satisfactory agreement with the experimental results. For the other channel, O + HCl → OH + Cl, noticeable differences between the statistical results and those found with the QCT calculation suggest that the dynamics of the reaction are controlled by a direct mechanism. The comparison between the QCT and QM-TDWP results in the whole range of collision energies lends credence to the QCT description of the dynamics of this reaction.

Isotope interchange reaction dynamics of the T+OD system

The atomic and molecular reaction dynamics for T+OD have been studied basad on the potential energy function of DTO(1 A1) by Monte Carlo quasi-classical trajectory approach. It is shown that the reaction T+ODDTO with a long-lived complex has a threshold energy at low collision energy, which accords with the potential curve. The interchange reaction increases with collision energy increasing, until the DTO molecules decompose into D, T, and O completely, and these reactions have threshold energyies too. The trajectories and the collision cross-sections of T+OD(0, 0) and D+OT(0, 0) are different due to the isotopic effect of D atom and T atom.

Quasi-classical trajectory approach to the stereo-dynamics of the reaction F + HO → HF + O

Quasi-classical trajectory (QCT) calculations are employed for the reaction F + HO(0,0)→HF + O based on the adiabatic potential energy surface (PES) of the ground 3A″triplet state. The average rotational alignment factor 〈P2(j′·k)〉 as a function of collision energy and the four polarization dependent generalized differential cross sections have been calculated in the center-of-mass (CM) frame, separately. The distribution P(θr) of the angle between k and j′, the distribution P(ϕr) of dihedral angle denoting k-k′-j′ correlation, and the angular distribution P(θr, ϕr) of product rotational vectors in the form of polar plots are calculated as well. The effect of Heavy-Light-Heavy (HLH) mass combination and atom F’s relatively strong absorbability to charges on the alignment and the orientation of product molecule HF rotational angular momentum vectors j′ is revealed.

Asymmetry of molecular reactive collision of the DTO molecules

Based on the potential energy function which considers the nuclear motion and isotopic effect of DTO (X1A1), the atomic and molecular reactive collision for O+DT has been studied by Monte-Carlo quasi-classical trajectory approach. It is shown that the reaction O+DT→DTO with a long-lived complex compound has no threshold energy at low collision energy, which agrees with the potential surface. When the collision energy is higher than 209.2 kJ·mol-1, the interchange reactions will start and then increase until DTO molecules are decomposed completely into D, T, O with the collision energy increasing. The interchange reactions O+DT(0, 0)→OD+T and O+DT (0, 0)→OT+D have corresponding threshold energies. The trajectories and collision section of interchange reactions show asymmetrical distribution which corresponds to the potential surface.

Global dynamics and transition state theories: Comparative study of reaction rate constants for gas‐phase chemical reactions

In this review article, we present a systematic comparison of the theoretical rate constants for a range of bimolecular reactions that are calculated by using three different classes of theoretical methods: quantum dynamics (QD), quasi-classical trajectory (QCT), and transition state theory (TST) approaches. The study shows that the difference of rate constants between TST results and those of the global dynamics methods (QD and QCT) are seen to be related to a number of factors including the number of degrees-of-freedom (DOF), the density of states at transition state (TS), etc. For reactions with more DOF and higher density of states at the TS, it is found that the rate constants from TST calculations are systematically higher than those obtained from global dynamics calculations, indicating large recrossing effect for these systems. The physical insight of this phenomenon is elucidated in the present review.

Dissociative chemisorption of H2 on the Cu(110) surface: A quantum and quasiclassical dynamical study

Six-dimensional quantum dynamical and quasiclassical trajectory (QCT) calculations are reported for the reaction and vibrationally inelastic scattering of (v = 0,1,j = 0) H(2) scattering from Cu(110), and for the reaction and rovibrationally elastic and inelastic scattering of (v = 1,j = 1) H(2) scattering from Cu(110). The dynamics results were obtained using a potential energy surface obtained with density functional theory using the PW91 functional. The reaction probabilities computed with quantum dynamics for (v = 0,1,j = 0) were in excellent agreement with the QCT results obtained earlier for these states, thereby validating the QCT approach to sticking of hydrogen on Cu(110). The vibrational de-excitation probability P(v=1,j = 0 --> v = 0) computed with the QCT method is in remarkably good agreement with the quantum dynamical results for normal incidence energies E(n) between 0.2 and 0.6 eV. The QCT result for the vibrational excitation probability P(v = 0,j = 0 --> v = 1) is likewise accurate for E(n) between 0.8 and 1 eV, but the QCT method overestimates vibrational excitation for lower E(n). The QCT method gives probabilities for rovibrationally (in)elastic scattering, P(v = 1,j = 1 --> v('),j(')), which are in remarkably good agreement with quantum dynamical results. The rotationally averaged, initial vibrational state-selective reaction probability obtained with QCT agrees well with the initial vibrational state-selective reaction probability extracted from molecular beam experiments for v = 1, for the range of collision energies for which the v=1 contribution to the measured total sticking probability dominates. The quantum dynamical probabilities for rovibrationally elastic scattering of (v = 1,j = 1) H(2) from Cu(110) are in good agreement with experiment for E(n) between 0.08 and 0.25 eV.

A detailed quantum mechanical and quasiclassical trajectory study on the dynamics of the H++H2→H2+H+ exchange reaction

The H+ + H2 exchange reaction has been studied theoretically by means of a different variety of methods as an exact time independent quantum mechanical, approximate quantum wave packet, statistical quantum, and quasiclassical trajectory approaches. Total and state-to-state reaction probabilities in terms of the collision energy for different values of the total angular momentum obtained with these methods are compared. The dynamics of the reaction is extensively studied at the collision energy of E(coll)=0.44 eV. Integral and differential cross sections and opacity functions at this collision energy have been calculated. In particular, the fairly good description of the exact quantum results provided by the statistical quantum method suggests that the dynamics of the process is governed by an insertion mechanism with the formation of a long-lived collision complex.

A classical trajectory study of bond dissociation in HONO and HOOH

Dissociations of the O–N bond in trans-HONO and O–O bond in HOOH are studied using the quasiclassical trajectory approach. Despite their similarities, the results are quite different. The method seems to work well for HONO, giving results in accord with experiment. On the other hand, the classical trajectory approximation breaks down for HOOH near the reaction threshold due to the aphysical zero-point energy flow, although it is better for the higher energy states. These results show that the intramolecular couplings are quite different for the two seemingly similar systems.

Potential energy functions and molecular reaction dynamics for LiH, LiO and LiOH

The structures of LiH, LiO and LiOH have been optimized based on the density functional (B3LYP/sdd) method with relativistic effective core potential. The Murrell-Sorbie analytic potential energy functions for LiH and LiO, and the many-body expansion analytic potential energy function for LiOH are derived by using the many-body expansion theory and normal equation fitting methods. The dissociation energies for LiH, LiO and LiOH are calculated from the analytic potential energy functions. Then, the atomic and molecular reaction dynamic processes for the collision of O+LiH(ν=0,j=0) system are investigated with the present potential energy functions by Monte-Carlo quasi-classical trajectory approach. The results show that O+LiH(ν=0,j=0) has no energy threshold, and the dominated product is LiO.

Molecular potential energy function and reaction dynamics for LaH2 (C2V, X̃ 2A1)

The present work has derived an analytical potential energy function for the ground state (C2V, X̃ 2A1) of LaH2. The electronic state and reasonable dissociation limits are correctly determined based on Atomic and Molecular Reaction Statics (AMRS), and then, using a relativistic compact effective potential (RCEP) for La. The equilibrium geometry, dissociation energy and harmonic frequencies for LaH2 have been calculated by ab initio methods. The results show that R(LaH)=2.1945Å, ∠HLaH=124.4° and De(LaH2)=5.599eV, and ν1, ν2 and ν3 are 1216.521, 1087.417 and 2156.957cm−1, respectively. Molecular reaction dynamics for the collision La(2Dg)+H2(X1Σg+,v=j=0) has been studied based on the analytical potential energy function of LaH2(X̃ 2A1) by using the Monte Carlo quasi-classical trajectory approach. The results for the collision process indicate that the main channel is the exchange reaction La(2Dg)+H2(X1Σg+,v=j=0)→LaH(X1Σ+,v′,j′)+H(2Sg) with the product LaH, and without the formation of the complex compound LaH2. The relationship of the reactive cross-section σr with the relative translational energy Et shows that there is a threshold energy of 40kcal/mol. Because of the tremendous difference in the masses of La and H2, these is a direct collision, and the distributions of the products LaH and H2 are along the direction of forward scattering.

Microdynamics study on reaction of atom H and radical NH (X3Σ)

The dynamics of the H + NH→-N + H2, reaction has been investigated by means of the 3-atom model quasiclassical trajectory approach. The LEPS potential energy surface is employed in the study, which is obtained from theab initio results and has an early saddle point in the minimum energy path. The results indicate that the reaction product H2, is mainly scattered backward, and the reaction is found to occur via a direct channel. The product H2, is in a cold excitation of rotational state, but has a hot vibrational excitation. Based on the potential surface and the trajectory analysis, the reaction mechanism has been explained successfully.

Quasiclassical trajectory study of the reaction NH(X3Σ−) + H → N(4S) + H2

AbstractThe dynamics of the NH + H → N + H2 reaction has been investigated by means of the 3D quasiclassical trajectory approach by using the LEPS potential energy surface. The calculated rate coefficient is in good agreement with the experimental value. The reaction was found to occur via a direct channel. The product H2 has a cold excitation of rotational state, but has a reverse distribution of the vibrational state with a peak at v=l. Based on the potential energy surface and the trajectory analysis, the reaction mechanism has been explained successfully.