Exact quantum,quasiclassical forward and reverse reaction probabilities for a colldmear asymmetric model reaction

Detailed quasiclassical and time-independent quantum reaction probabilities are given for a surface on which large discrepancies between quasiclassical and wavepacket results have previously been found. The quasiclassical results are shown to agree relatively reasonably with the oscillation-averaged time-independent quantum ones if the quasiclassical reverse probabilities are chosen in the threshold region.     

Cumulative reaction probabilities and transition state properties: a study of the F + H2 reaction and its deuterated isotopic variants

A comparative quantum mechanical (QM) and quasiclassical trajectory (QCT) study of the cumulative reaction probabilities (CRPs) is presented in this work for the F + H(2) reaction and its isotopic variants for low values of the total angular momentum J. The agreement between the two sets of calculations is very good with the exception of some features whose origin is genuinely QM. The agreement also extends to the CRP resolved in the helicity quantum number k. The most remarkable feature is the steplike structure, which becomes clearly distinct when the CRPs are resolved in odd and even rotational states j. The analysis of these steps shows that each successive increment is due to the opening of the consecutive rovibrational states of the H(2) or D(2) molecule, which, in this case, nearly coincide with those of the transition state. Moreover, the height of each step reflects the number of helicity states compatible with a given J and j values, thus indicating that the various helicity states for a specific j have basically the same contribution to the CRPs at a given total energy. As a consequence, the dependence with k of the reactivity is practically negligible, suggesting very small steric restrictions for any possible orientation of the reactants. This behavior is in marked contrast to that found in the D + H(2) reaction, wherein a strong k dependence was found in the threshold and magnitude of the CRP. The advantages of a combined QCT and QM approaches to the study of CRPs are emphasized in this work.     

Exact quantum dynamics of N(2D) + H2 --> NH + H reaction: cross-sections, rate constants, and dependence on reactant rotation

Using an exact Chebyshev wave packet method, initial state-specified (upsilon(i)=0, j(i)=0,2) integral cross-sections and rate constants are obtained for the title reaction on the latest ab initio potential energy surface. Reaction probabilities up to J=29 are dependent on the reactant rotation and show mild oscillations superimposed on a broad background. Due to a barrier in the entrance channel, the cross sections increase with energy with clear thresholds and the rate constants vary with temperature in the Arrhenius form. The calculated canonical rate constant is in good agreement with the experimental measurements. Our results also indicate that the quasiclassical trajectory method underestimates the rate due to the neglect of tunneling, while the quantum statistical approach overestimates because of the short lifetime of the reaction intermediate.     

A reduced dimensionality quasiclassical and quantum study of the proton transfer reaction H3O(+)+H2O-->H2O+H3O(+)

We report quantum and quasiclassical calculations of proton transfer in the reaction H(3)O(+)+H(2)O in three degrees of freedom, the two OH(+) bond lengths and the OH(+)O angle. The reduced dimensional potential energy surface is obtained from the full dimensional OSS3(p) energy function of H(5)O(2) (+) [L. Ojamae, I. Shavitt, and S. J. Singer, J. Chem. Phys. 109, 5547 (1998)], with an additional long-range correction to reproduce the correct ion-molecule interaction. This surface is used to perform both quasiclassical trajectory and quantum reactive scattering calculations of the zero total angular momentum cumulative reaction probability and cross sections for initial rotational states 0, 1, and 2. Comparison of these quantities are made to assess the importance of quantum effects in this reduced dimensional reaction. Additional quasiclassical cross sections are calculated to obtain the thermal rate constant for the reaction.     

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.     

Quasiclassical determination of reaction probabilities as a function of the total angular momentum

This article presents a quasiclassical trajectory (QCT) method to determine the reaction probability as a function of the total angular momentum J for any given value of the initial rotational angular momentum j. The proposed method is based on a discrete sampling of the total and orbital angular momenta for each trajectory and on the development of equations that have a clear counterpart in the quantum-mechanical (QM) case. The reliability of the method is illustrated by comparing QCT and time-dependent wave-packet QM results for the H+D(2)(upsilon=0,j=4,10) reaction. The small discrepancies between both sets of calculations, when they exist, indicate some genuine quantum effects. In addition, a procedure to extract the reaction probabilities as a function of J when trajectories are calculated in the usual way using a continuous distribution of impact parameters is also described.     

Six-dimensional quasiclassical and quantum dynamics of H2 dissociation on the c(2 × 2)-Ti/Al(100) surface

Based on a slab model of H(2) dissociation on a c(2 × 2) structure with Ti atoms in the first and third layers of Al(100), a six-dimensional (6D) potential energy surface (PES) has been built. In this PES, a molecular adsorption well with a depth of 0.45 eV is present in front of a barrier of height 0.13 eV. Using this PES, H(2) dissociation probabilities are calculated by the classical trajectory (CT), the quasiclassical trajectory (QCT), and the time-dependent wave-packet (TDWP) method. The QCT study shows that trajectories can be trapped by the molecular adsorption well. Higher incident energy can lead to direct H(2) dissociation. Vibrational pre-excitation is the most efficient way to promote direct dissociation without trapping. We find that both rotational and vibrational excitation have efficacies close to 1.0 in the entire range of incident energies investigated, which supports the randomization in the initial conditions making the reaction rate solely dependent on the total (internal and translational) energy. The H(2) dissociation probabilities from quantum dynamics are in reasonable agreement with the QCT results in the energy range 50-200 meV, except for some fluctuations. However, the TDWP results considerably exceed the QCT results in the energy range 200-850 meV. The CT reaction probabilities are too low compared with the quantum dynamical results.     

A comparison of attack angle dependence of exchange channel of reaction H + HS (v = 0, 1; j = 0) on 3A″ and 3A′ surfaces

In this theoretical work, we report quasiclassical dynamics predictions for the attack angle‐dependence exchange processes for the H + HS (v = 0, 1; j = 0) reaction by using the new triplet 3A″ and 3A′ potential energy surfaces, respectively. The calculated quasiclassical reaction probabilities of exchange reaction channel of reaction H(D)′ + H(D)S 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 2.0 eV on 3A″ surfaces. The attack angle dependence reaction probability of the title reactions at J = 0 are calculated, respectively, on the two surfaces. The reaction probability was found to be strongly dependent on the attack angle. It may be ascribe to the significant difference of the effective potential barrier height in the two reactions. Besides, the reaction probabilities of exchange reaction channel of reaction H(D)′ + H(D)S for J = 0, 10, 20, 30, 40 are also predicted on 3A′ surfaces. © 2013 Wiley Periodicals, Inc.     

Cumulative reaction probabilities: A comparison between quasiclassical and quantum mechanical results

This article presents a quasiclassical trajectory (QCT) method for determining the cumulative reaction probability (CRP) as a function of the total energy. The method proposed is based on a discrete sampling using integer values of the total and orbital angular momentum quantum numbers for each trajectory and on the development of equations that have a clear counterpart in the quantum mechanical (QM) case. The calculations comprise cumulative reaction probabilities at a given total angular momentum J, as well as those summed over J. The latter are used to compute QCT rate constants. The method is illustrated by comparing QCT and exact QM results for the H+H2, H+D2, D+H2, and H+HD reactions. The agreement between QCT and QM results is very good, with small discrepancies between the two data sets indicating some genuine quantum effects. The most important of these involves the value of the CRP at low energies which, due to the absence of tunneling, is lower in the QCT calculations, causing the corresponding rate constants to be smaller. The second is the steplike structure that is clearly displayed in the QM CRP for J = 0, which is much smoother in the corresponding QCT results. However, when the QCT density of reactive states, i.e., the derivatives of the QCT CRP with respect to the energy, is calculated, a succession of maxima and minima is obtained which roughly resembles those found in the QM calculations, although the latter are considerably sharper. The analysis of the broad peaks in the QCT density of reactive states indicates that the distributions of collision times associated with the maxima are somewhat broader, with a tail extending to larger collision times, than those associated with the minima. In addition, the QM and QCT dynamics of the isotopic variants mentioned above are compared in the light of their CRPs. Issues such as the compliance of the QCT CRP with the law of microscopic reversibility, as well as the similarity between the CRPs for ortho and para species in the QM and QCT cases, are also addressed.     

Quantum and quasiclassical state-to-state dynamics of the NH + H reaction: competition between abstraction and exchange channels

Quantum and quasiclassical state-to-state dynamics for the NH + H' reaction at high collision energies up to 1.6 eV was studied on an accurate ab initio potential energy surface. Both of the endothermic abstraction (NH + H' → N + HH') and thermoneutral exchange (NH + H' → H + NH') channels were investigated from the same set of wave packets using an efficient coordinate transformation method. It is found that the abstraction represents a minor reaction channel in the energy range studied, primarily due to endothermicity. The cross section for the abstraction reaction increases monotonically with the collision energy, while that for the exchange reaction is relatively energy insensitive. As a result, the thermal rate constant for the abstraction reaction follows the Arrhenius law, where that for the exchange reaction is nearly temperature independent. Finally, it is shown that the quantum mechanical results can be reasonably reproduced by the Gaussian-binning quasiclassical trajectory method and to a lesser extent by a quantum statistical model.     

On the dynamics of the H+ +D2(v=0,j=0)-->HD+D + reaction: a comparison between theory and experiment

The H+ +D2(v=0,j=0)-->HD+D + reaction has been theoretically investigated by means of a time independent exact quantum mechanical approach, a quantum wave packet calculation within an adiabatic centrifugal sudden approximation, a statistical quantum model, and a quasiclassical trajectory calculation. Besides reaction probabilities as a function of collision energy at different values of the total angular momentum, J, special emphasis has been made at two specific collision energies, 0.1 and 0.524 eV. The occurrence of distinctive dynamical behavior at these two energies is analyzed in some detail. An extensive comparison with previous experimental measurements on the Rydberg H atom with D2 molecules has been carried out at the higher collision energy. In particular, the present theoretical results have been employed to perform simulations of the experimental kinetic energy spectra.     

Quantum mechanical scattering calculations on a spline-fitted ab initio surface: the He + H+2 (ν = 0, 1, 2) → HeH+ + H reaction

All-channel time-dependent quantum mechanical reaction probabilities are reported for the collinear He + H⁺₂(ν = 0, 1, 2) → HeH⁺ + H reaction at a total energy of 1.2 eV on previously reported diatomics-in-molecule (DIM) and spline fitted ab initio (SAI) surfaces. These results are in agreement with the previous quasiclassical trajectory results in that there is vibrational enhancement of the reaction probability on the SAI surface but not on the DIM surface. This agreement lends support to our previously drawn conclusion that small differences in the potential-energy surface can lead to substantially different dynamic results.     

Quasiclassical trajectory study of reactive and dissociative processes in H2+H2: comparison with quantum-mechanical calculations

Quasiclassical trajectory calculations have been carried out for H(2)(v(1)=high)+H(2)(v(2)=low) collisions within a three degrees of freedom model where five different geometries of the colliding complex were considered. Within this approach, probabilities for different competitive processes are studied: four center reaction, collision induced dissociation, reactive dissociation, and three-body complex formation. The purpose is to compare in detail with equivalent quantum-mechanical wave packet calculations [Bartolomei et al., J. Chem. Phys 122, 064305 (2005)], especially the behavior of the probabilities near reaction thresholds. Quasiclassical calculations compare quite well with the quantum-mechanical ones for collision induced dissociation as well as for the four center reaction, although quantum effects become very important near thresholds, particularly for lower v(1)'s and for the four center process. Less quantitative agreement is found for reactive dissociation and three-body complex formation. It is found that most quantum effects are due to differences between quantum and classical vibrational distributions of H(2)(v(1)=high). Zero point energy violation has been found in the classical reactive-dissociative probabilities. Extension of these findings to full-dimensional treatments is examined.     

Wave packet and quasiclassical trajectory calculations for the N(D) + H2 reaction and its isotopic variants

The N(²D) + H₂(v = 0, j = 0) reaction and its HD and D₂ isotopic variants have been studied by means of quantum mechanical real wave packet and wave packet with split operator and quasiclassical trajectory methodologies on the potential energy surface of Ho et al. [J. Chem. Phys. 119 (2003) 6]. Total initial state-selected and final state-resolved reaction probabilities and product rotational distributions have been calculated for total angular momentum J = 0 in a broad range of collision energies. The real wave packet results are in very good agreement with the corresponding split operator wave packet calculations. A reasonable overall good agreement has been found between the wave packet and quasiclassical trajectory results. Integral cross-sections and thermal rate constants have been calculated from the wave packet reaction probabilities by means of standard J-shifting, refined J-shifting and uniform J-shifting methods in combination with the centrifugal sudden approximation for J > 0. Comparisons with available exact wave packet, quasiclassical trajectory and experimental results are made and discussed.     

Quantum dynamics study of the K+HF(v=0-2,j=0)-->KF+H reaction and comparison with quasiclassical trajectory results

Extensive quantum real wave packet calculations within the helicity decoupling approximation are used to analyze the influence of the HF vibrational excitation on the K+HF(v=0-2,j=0)-->KF+H reaction. Quantum reaction probabilities P and reaction cross sections sigma are compared with corresponding quasiclassical trajectory (QCT) results. Disregarding threshold regions for v=0 and 1 (v=2 has no threshold), both approaches lead to remarkably similar results, particularly for sigma, validating the use of the QCT method for this system. When moving from v=0 to v=1 there is a large increase in P and sigma, as expected for a late barrier system. For v=2 the reaction becomes exoergic and P approximately 0.95 (with the exception of large total angular momenta where centrifugal barriers play a role). While substantial vibrational enhancement of the reactivity is thus seen, it is still quite less than that inferred from experimental data in the intermediate and high collision energy ranges. The origin of this discrepancy is unclear.     

Quantum study of Eley-Rideal reaction and collision induced desorption of hydrogen atoms on a graphite surface. I. H-chemisorbed case

Collision induced (CI) processes involving hydrogen atoms on a graphite surface are studied quantum mechanically within the rigid, flat surface approximation, using a time-dependent wave packet method. The Eley-Rideal (ER) reaction and collision induced desorption (CID) cross sections are obtained with the help of two propagations which use different sets of coordinates, a "product" and a "reagent" set. Several adsorbate-substrate initial states of the target H atom in the chemisorption well are considered, and CI processes are studied over a wide range of projectile energy. Results show that (i) the Eley-Rideal reaction is the major reactive outcome and (ii) CID cross sections do not exceed 4 A2 and present dynamic thresholds for low values of the target vibrational quantum number. ER cross sections show oscillations at high energies which cannot be reproduced by classical and quasiclassical trajectory calculations. They are related to the vibrational excitation of the reaction products, which is a rather steep decreasing function of the collision energy. This behavior causes a selective population of the low-lying vibrational states and allows the quantization of the product molecular states to manifest itself in a collisional observable. A peak structure in the CID cross section is also observed and is assigned to the selective population of metastable states of the transient molecular hydrogen.     

Quasiclassical trajectory study of the vibrational quenching of hydroxyl radicals through collision with O atoms

The collisional removal of vibrationally excited OH radicals by O atoms is studied by the quasiclassical trajectory method. To evaluate the effect of different topological features on the scattering processes two different global potential energy surfaces, DMBE IV and TU, are used. Results for reactive, exchange, and inelastic scattering probabilities are reported for central collisions (with zero total angular momentum) with a fixed relative translational energy for vibrational levels of OH ranging from nu=1 to v=8. Vibrational state distributions of product molecules are also compared on the two potential energy surfaces. Both surfaces predict higher probabilities for reaction than for exchange or inelastic scattering. The vibrational state distributions of the product diatomic molecules are different on the two surfaces. In particular, the two surfaces give substantially different probabilities for multiquantum OH vibrational relaxation transitions OH(v)+O-->OH(v')+O.     

Ar+ ArH+ Reactive Collisions of Astrophysical Interest: The Case of 36Ar

The reactive collision between ³⁶Ar and the ³⁶ArH⁺ species has been investigated by means of quantum mechanical (QM), quasiclassical trajectories (QCT) and statistical quantum mechanical (SQM) approaches. Reaction probabilities, cross sections as a function of the energy and rate constants in terms of the temperature have been obtained. Cumulative distributions as a function of the collision time and the inspection of selected QCT corresponding to specific dynamical mechanisms have been analysed. Predictions by means of the SQM method are in good agreement with the QM results, thus supporting the complex-forming nature of the process.