State-to-state quantum dynamics of the H + HBr reaction: competition between the abstraction and exchange reactions

Quantum state-to-state dynamics for the H + HBr(υ(i) = 0, j(i) =0) reaction was studied on an accurate ab intio potential energy surface for the electronic ground state of BrH(2). Both the H + HBr → H(2) + Br abstraction reaction and the H' + HBr → H'Br + H exchange reaction were investigated up to a collision energy of 2.0 eV. It was found that the abstraction channel is dominant at lower collision energies, while the exchange channel becomes dominant at higher collision energies. The total integral cross section of the abstraction reaction at a collision energy of 1.6 eV was found to be 1.37 A?(2), which is larger than a recent quantum mechanical result (1.06 A?(2)) and still significantly smaller than the experimental value (3 ± 1 A?(2)). Meanwhile, similar to the previous theoretical study, our calculations also predicted much hotter product rotational state distributions than those from the experimental study. This suggests that further experimental investigations are highly desirable to elucidate the dynamic properties of the title reactions.     

Ab initio potential energy surface of CH and reaction dynamics of H + CH+

This work presents a new ground state potential energy surface (PES) for CH. The potential is tested using quasi classical trajectory (QCT) and quantum reactive scattering methods for the H + CH(+) reaction. Cross sections and rate coefficients for all reaction channels up to 300 K are calculated. The abstraction rate coefficients follow the expected slightly decreasing behaviour above 90 K, but have a positive gradient with lower temperatures. The inelastic collision and exchange reaction rate constants are increasing monotonically with temperature. The rate coefficients of the exchange reaction differ significantly between QCT and quantum reactive scattering, due to intrinsic shortcomings of the QCT final state distributions.     

A time-dependent quantum dynamical study of the H + HBr reaction

Time-dependent wave packet calculations were carried out to study the exchange and abstraction processes in the title reaction on the Kurosaki-Takayanagi potential energy surface (Kurosaki, Y.; Takayanagi, T. J. Chem. Phys. 2003, 119, 7838). Total reaction probabilities and integral cross sections were calculated for the reactant HBr initially in the ground state, first rotationally excited state, and first vibrationally excited state for both the exchange and abstraction reactions. At low collision energy, only the abstraction reaction occurs because of its low barrier height. Once the collision energy exceeds the barrier height of the exchange reaction, the exchange process quickly becomes the dominant process presumably due to its larger acceptance cone. It is found that initial vibrational excitation of HBr enhances both processes, while initial rotational excitation of HBr from j(0) = 0 to 1 has essentially no effect on both processes. For the abstraction reaction, the theoretical cross section at E(c) = 1.6 eV is 1.06 A(2), which is smaller than the experimental result of 3 +/- 1 A(2) by a factor of 2-3. On the other hand, the theoretical rate constant is larger than the experimental results by about a factor of 2 in the temperature region between 220 and 550 K. It is also found that the present quantum rate constant is larger than the TST result by a factor of 2 at 200 K. However, the agreement between the present quantum rate constant and the TST result improves as the temperature increases.     

Real wave packet and quasiclassical trajectory studies of the H+ + LiH reaction

Time-dependent real wave packet (RWP) and quasiclassical trajectory (QCT) calculations have been carried out to study the H(+) + LiH reaction on the ab initio potential-energy surface of Martinazzo et al. [J. Chem. Phys., 2003, 119, 11241]. Total initial state-selected and final state-resolved reaction probabilities for the two possible reaction channels, H(2)(+) + Li and LiH + H(+), have been calculated for total angular momentum J=0 at a broad range of collision energies. Integral cross sections and thermal rate coefficients have been calculated using the QCT method and from the corresponding J=0 RWP reaction probabilities by means of a capture model. The calculated thermal rate coefficients are found to be nearly independent of temperature in the 100-500 K interval with a value of approximately 10(-9) cm(3) s(-1), which is in good agreement with estimates used in evolutionary models of early-Universe lithium chemistry. The RWP results are found to be in good agreement overall with the corresponding QCT calculations.     

A full dimensional time-dependent wave packet study for the H4 four-center, collision induced dissociation, and single exchange reactions: reaction probabilities for J=0

A time-dependent initial state selected wave packet method has been developed to study the H2(v(1)=10-11,j1=0)+H2'(v2=0,j2=0)-->HH'+HH' four-center (4C) reaction, and two other competing reactions: the H2+H2'-->H+H+H2' collision induced dissociation (CID) and the H2+H2'-->H+HH'+H' single exchange (SE) reaction, in full six dimensions. Initial state-specific total reaction probabilities for these three competing reactions are presented for total angular momentum J=0 and the effects of reagent vibration on reactions are examined. It is found that (a) the CID process is the dominant process over the whole energy range considered in this study, but the 4C and SE processes also have non-negligible probabilities; (b) the SE process has a lower threshold energy than the 4C process, but the SE probability increases slower than the 4C probability as collision energy increases; (c) the vibrational excitation of H2(v1) is much more efficient than translational motion for promoting these processes, in particular to the CID process.     

Cross sections and low temperature rate coefficients for the H + CH+ reaction: a quasiclassical trajectory study

The H + CH(+) reaction is studied by quasiclassical trajectory (QCT) calculations, along with phase space theory (PST) and quantum rigid rotor calculations, employing a global single-valued potential energy surface recently derived by our group. We report QCT total cross sections for each of the three channels, for low collision energies and different reactant rotational quantum numbers. At the lowest collision energies, all cross sections exhibit a capture-like behaviour, as expected from a barrierless reaction. At higher energies, there are important dynamical effects coming from the opening of new channels in the inelastic and reactive exchange collisions. The inelastic cross sections turn out to largely increase, while the reactive abstraction cross sections are declining faster than predicted by the capture theory. A large value of the reactant rotational quantum number tends to suppress these dynamical effects. The QCT rate coefficients are reported for a temperature range from 1-700 K. Below 20 K, the abstraction and exchange QCT rate coefficients are almost constant, as predicted by the capture theory. Above this temperature, the abstraction rate coefficient declines, while the exchange and inelastic rate coefficients are increasing, due to the opening of new channels. A good agreement is observed between the experimental abstraction rate coefficient and the QCT and PST ones. The QCT inelastic results are also compared with those obtained from rigid rotor close coupling (CCRR) calculations in order to check the ability of this approach to provide a reliable estimate of the inelastic rate coefficients for a reactive system without a barrier. The laws of variation as a function of temperature are found to be very similar and the curves are parallel above 20 K. However, reaction is not allowed in the rigid rotor approximation, therefore the CCRR results are about twice as large as their QCT counterparts.     

Accurate time-dependent wave packet study of the Li + H₂⁺ reaction and its isotopic variants

The dynamics and kinetics of the Li + H?? reaction and its isotopic variants (D?? and T??) have been studied by using a time-dependent wave packet (TDWP) coupled-channel (CC) method on the ab initio potential energy surface (PES) of Martinazzo et al. [J. Chem. Phys. 2003, 119, 21]. Total initial v = 0, j = 0 state-selected reaction probabilities for the Li + H?? reaction and its isotopic variants have been calculated from the threshold up to 1 eV for total angular momenta J from 0 to 90. Integral cross sections have been evaluated from the reaction probabilities at collision energies from threshold (≈0.2 eV) up to 1.0 eV collision. The calculated rate constants as a function of temperature show an Arrhenius type behavior in the 200 ≤ T ≤ 1000 K temperature interval. It has been found to be a considerable large intermolecular kinetic isotope effect. The TDWP-CC results are in overall good agreement with those obtained applying the TDWP Centrifugal-Sudden (CS) approximation, showing that the CS approximation is rather accurate for the title reaction.     

Capture and dissociation in the complex-forming CH + H2 → CH2 + H, CH + H2 reactions

The rate coefficients for the capture process CH + H(2)→ CH(3) and the reactions CH + H(2)→ CH(2) + H (abstraction), CH + H(2) (exchange) have been calculated in the 200-800 K temperature range, using the quasiclassical trajectory (QCT) method and the most recent global potential energy surface. The reactions, which are of interest in combustion and in astrochemistry, proceed via the formation of long-lived CH(3) collision complexes, and the three H atoms become equivalent. QCT rate coefficients for capture are in quite good agreement with experiments. However, an important zero point energy (ZPE) leakage problem occurs in the QCT calculations for the abstraction, exchange and inelastic exit channels. To account for this issue, a pragmatic but accurate approach has been applied, leading to a good agreement with experimental abstraction rate coefficients. Exchange rate coefficients have also been calculated using this approach. Finally, calculations employing QCT capture/phase space theory (PST) models have been carried out, leading to similar values for the abstraction rate coefficients as the QCT and previous quantum mechanical capture/PST methods. This suggests that QCT capture/PST models are a good alternative to the QCT method for this and similar systems.     

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.     

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.     

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.     

准经典轨线研究Li+HF(ν=0, j=0)→LiF+H反应动力学

基于Aguado等人拟合的APW势能面(PES), 运用准经典轨线(QCT)方法, 对反应Li+HF(ν=0, j=0)→LiF+H的动力学性质进行了计算. 主要研究了不同碰撞能条件下的反应截面、转动取向、产物散射角分布和竞争反应模式等. 结果表明, 该反应存在直接提取型和间接插入型两种反应模式, 在低能量下反应以间接插入反应模式为主, 能量大于200 meV时则以直接提取反应为主.     

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.     

Time-dependent wave packet quantum and quasi-classical trajectory study of He + H₂⁺, D₂⁺ → HeH⁺ + H, HeD⁺ + D reaction on an accurate FCI potential energy surface

The quantum scattering dynamics and quasi-classical trajectory (QCT) calculations have been carried out for the title reaction on an accurate potential energy surface (PES) computed using the full configuration interaction (FCI). On the basis of the PES, the integral cross-sections of He + H?? (v = 0-3, j = 1) → HeH? + H reaction have been calculated, and the results are generally agreed with the experimental cross-sections obtained by Tang et al. [J. Chem. Phys. 2005, 122, 164301] after taking into account the experimental uncertainties, which proves the reliability of implementing dynamics calculations on the FCI PES. The reaction probability of He + D?? (v = 0-2, j = 0) → HeD? + D reactions for total angular momentum J = 0 and the integral cross-section (ICS) have been calculated. The significant quantum effect has been explored by the comparison between the QCT reaction probabilities (or ICS) and the quantum mechanical (QM) reaction probabilities (or ICS), which may be attributed to the deep well in the PES of this light atoms system. Furthermore, the role of Coriolis coupling (CC) effects has also been found not important by the comparison between the CC calculation and the centrifugal sudden (CS) approximation calculation, except that the CC total cross-sections for the v = 1 and 2 states show the collision energy-dependent behaviors in the low-energy area, which are different from those based on the CS calculation.     

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.     

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 pulsed-field ionization photoelectron secondary ion coincidence study of the H2+ (X,upsilon+=0-15,N+=1)+He proton transfer reaction

The endothermic proton transfer reaction, H2+(upsilon+)+He-->HeH+ + H(DeltaE=0.806 eV), is investigated over a broad range of reactant vibrational levels using high-resolution vacuum ultraviolet to prepare reactant ions either through excitation of autoionization resonances, or using the pulsed-field ionization-photoelectron-secondary ion coincidence (PFI-PESICO) approach. In the former case, the translational energy dependence of the integral reaction cross sections are measured for upsilon+=0-3 with high signal-to-noise using the guided-ion beam technique. PFI-PESICO cross sections are reported for upsilon+=1-15 and upsilon+=0-12 at center-of-mass collision energies of 0.6 and 3.1 eV, respectively. All ion reactant states selected by the PFI-PESICO scheme are in the N+=1 rotational level. The experimental cross sections are complemented with quasiclassical trajectory (QCT) calculations performed on the ab initio potential energy surface provided by Palmieri et al. [Mol. Phys. 98, 1839 (2000)]. The QCT cross sections are significantly lower than the experimental results near threshold, consistent with important contributions due to resonances observed in quantum scattering studies. At total energies above 2 eV, the QCT calculations are in excellent agreement with the present results. PFI-PESICO time-of-flight (TOF) measurements are also reported for upsilon+=3 and 4 at a collision energy of 0.6 eV. The velocity inverted TOF spectra are consistent with the prevalence of a spectator-stripping mechanism.     

Molecular beam scattering studies of the reaction D + H2 (v = 0) and D + H2 (v = 1) → HD + H

The reaction D + H₂ → HD + H has been investigated in two molecular beam scattering experiments. Angular and time-of-flight distributions have been measured for the initial vibrational ground state (v = 0) at a most probable collision energy of E_cm = 1.5 eV and for the first vibrational excited state (v = 1) at E_cm = 0.28 eV with the same apparatus. Results for the ground-state experiment are compared with quasiclassical trajectory calculations(QCT) on the LSTH-hypersurface transformed into the laboratory system and averaged over the apparatus distributions. The agreement isquite satisfactory. At this high collision energy the HD products are no longer scattered in a backward direction but in a wide angular region concentrated about θ = 90° in the center-of-mass system. The absolute reactive cross section has been determined and the agreement with the theoretical value from QCT calculations is within the experimental error. The high sensitivity of the experiment to different properties of the doubly differential cross section has also been demonstrated. A preliminary evaluation of the experiment with initial vibrational excitation (v = 1) shows that the HD-product molecules are preferably backward scattered and the change of internal energy is small supporting the concept of a reaction which is adiabatic with respect to the internal degrees of freedom.