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.     

A dynamical study of the Si(+) + H(2)O reaction

A dynamical study of the Si(+) + H(2)O reaction has been carried out by means of a quasiclassical trajectory method that decomposes the reaction into a capture step, for which an accurate analytical potential is employed, and an unimolecular step, in which the evolution of the collision complex is studied through a direct dynamics BHandHLYP/6-31G(d,p) method. The capture rate coefficient has been computed for thermal conditions corresponding to temperatures ranging from 50 to 1000 K. It is concluded that the main reason why the reaction rate is about 10 times smaller than the capture rate (at T = 298 K) is the topology of the potential energy surface of the ground state. It is also concluded that the ratio between the rates of product and reactant generation from the collision complex decreases quite steeply with increasing temperature, and therefore, the reaction rate decreases even more sharply. Exciting the stretching normal modes of water substantially increases that ratio, and moderate rotational excitation does not appear to have a relevant effect. The collision complex is always initially SiOH(2)(+), but in some trajectories, it becomes HSiOH(+), which generates the products, although the former species is the main intermediate.     

Chemical reaction dynamics of Rydberg atoms with neutral molecules: a comparison of molecular-beam and classical trajectory results for the H(n)+D2-->HD+D(n') reaction

Recent molecular-beam experiments have probed the dynamics of the Rydberg-atom reaction, H(n)+D2-->HD+D(n) at low collision energies. It was discovered that the rotationally resolved product distribution was remarkably similar to a much more limited data set obtained at a single scattering angle for the ion-molecule reaction H++D2-->D++HD. The equivalence of these two problems would be consistent with the Fermi-independent-collider model (electron acting as a spectator) and would provide an important new avenue for the study of ion-molecule reactions. In this work, we employ a classical trajectory calculation on the ion-molecule reaction to facilitate a more extensive comparison between the two systems. The trajectory simulations tend to confirm the equivalence of the ion+molecule dynamics to that for the Rydberg-atom+molecule system. The theory reproduces the close relationship of the two experimental observations made previously. However, some differences between the Rydberg-atom experiments and the trajectory simulations are seen when comparisons are made to a broader data set. In particular, the angular distribution of the differential cross section exhibits more asymmetry in the experiment than in the theory. The potential breakdown of the classical model is discussed. The role of the "spectator" Rydberg electron is addressed and several crucial issues for future theoretical work are brought out.     

A quantum wave packet dynamics study of the N(2D) + H2 reaction

We report a dynamics study of the reaction N((2)D) + H(2) (v=0, j=0-5) --> NH + H using the time-dependent quantum wave packet method and a recently reported single-sheeted double many-body expansion potential energy surface for NH(2)(1(2)A' ') which has been modeled from accurate ab initio multireference configuration-interaction calculations. The calculated probabilities for (v=0, j=0-5) are shown to display resonance structures, a feature also visible to some extent in the calculated total cross sections for (v=0, j=0). A comparison between the calculated centrifugal-sudden and coupled-channel reaction probabilities validate the former approximation for the title system. Rate constants calculated using a uniform J-shifting scheme and averaged over a Boltzmann distribution of rotational states are shown to be in good agreement with the available experimental values. Comparisons with other theoretical results are also made.     

Cross sections of the O+ + H2 --> OH+ + H ion-molecule reaction and isotopic variants (D2, HD): quasiclassical trajectory study and comparison with experiments

A dynamics study [cross section and microscopic mechanism versus collision energy (E(T))] of the reaction O+ + H2 --> OH+ + H, which plays an important role in Earth's ionosphere and interstellar chemistry, was conducted using the quasiclassical trajectory method, employing an analytical potential energy surface (PES) recently derived by our group [R. Martinez et al., J. Chem. Phys. 120, 4705 (2004)]. Experimental excitation functions for the title reaction, as well as its isotopic variants with D2 and HD, were near-quantitatively reproduced in the calculations in the very broad collision energy range explored (E(T) = 0.01-6.0 eV). Intramolecular and intermolecular isotopic effects were also examined, yielding data in good agreement with experimental results. The reaction occurs via two microscopic mechanisms (direct and nondirect abstraction). The results were satisfactorily interpreted based on the reaction probability and the maximum impact parameter dependences with E(T), and considering the influence of the collinear [OHH]+ absolute minimum of the PES on the evolution from reactants to products. The agreement between theory and experiment suggests that the reaction mainly occurs through the lowest energy PES and nonadiabatic processes are not very important in the wide collision energy range analyzed. Hence, the PES used to describe this reaction is suitable for both kinetics and dynamics studies.     

Stringent test of the statistical quasiclassical trajectory model for the H+3 exchange reaction: a comparison with rigorous statistical quantum mechanical results

A complete formulation of a statistical quasiclassical trajectory (SQCT) model is presented in this work along with a detailed comparison with results obtained with the statistical quantum mechanical (SQM) model for the H+ +D2 and H+ +H2 reactions. The basic difference between the SQCT and the SQM models lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar and both comply with the principle of detailed balance and conservation of parity. Reaction probabilities, and integral and differential cross sections (DCS's) for these reactions at different levels of product's state resolution and from various initial states are shown and discussed. The agreement is in most cases excellent and indicates that the effect of tunneling through the centrifugal barrier is negligible. Some differences are found, however, between state resolved observables calculated by the SQCT and the SQM methods which makes use of the centrifugal sudden (coupled states) approximation (SQM-CS). When this approximation is removed and the full close coupling treatment is used in the SQM model (SQM-CC), an almost perfect agreement is achieved. This shows that the SQCT is sensitive enough to show the relatively small inaccuracies resulting from the decoupling inherent to the CS approximation. In addition, the effect of ignoring the parity conservation is thoroughly examined. This effect is in general minor except in particular cases such as the DCS from initial rotational state j=0. It is shown, however, that in order to reproduce the sharp forward and backward peaks the conservation of parity has to be taken into account.     

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 surface hopping quasiclassical trajectory study of the H2+ + H2 and (H2 + D2)+ systems

In this work we use a complete surface hopping quasiclassical trajectory method to determine cross sections for the reactions H₂⁺ + H₂ → H₃⁺ + H and the isotopic variants (H₂⁺ + D₂ and D₂⁺ + H₂). Initial translational energies ranged between 0.5 and 6 eV. The vibrational quantum number (v⁺) of the charged diatom is either 0 or 3. Comparing these results with our previous results with a partial treatment of surface hopping, we find essentially no change for v⁺ = 0 and reductions in cross sections of up to 30% for v⁺ = 3 trajectories.     

Renner-Teller quantum dynamics of the N(2D) + H2-->NH + H reaction

We present the Born-Oppenheimer (BO) and Renner-Teller (RT) quantum dynamics of the reaction (14)N((2)D)+(1)H(2)(X (1)Sigma(g) (+))-->NH(X (3)Sigma(-))+H((2)S), considering the NH(2) electronic states X (2)B(1) and A (2)A(1). These states correlate to the same (2)Pi(u) linear species, are coupled by RT nonadiabatic effects, and give NH(X (3)Sigma(-))+H and NH(a (1)Delta)+H, respectively. We develop the Hamiltonian matrix elements in the R embedding of the Jacobi coordinates and in the adiabatic electronic representation, using the permutation-inversion symmetry, and taking into account the nuclear-spin statistics. Collision observables are calculated via the real wave-packet (WP) and flux methods, using the potential-energy surfaces of Santoro et al. [J. Phys. Chem. A 106, 8276 (2002)]. WP snapshots show that the reaction proceeds via an insertion mechanism, and that the RT-WP avoids the A (2)A(1) potential barrier, jumping from the excited to the ground surface and giving mainly the NH(X (3)Sigma(-)) products. X (2)B(1) BO probabilities and cross sections show large tunnel effects and are approximately four to ten times larger than the A (2)A(1) ones. This implies a BO rate-constant ratio k(X (2)B(1))k(A (2)A(1)) approximately 10(5) at 300 K, i.e., a negligible BO formation of NH(a (1)Delta). When H(2) is rotationally excited, RT couplings reduce slightly the X (2)B(1) reaction observables, but enhance strongly the A (2)A(1) reactivity. These couplings are important at all collision energies, reduce the collision threshold, and increase remarkably reaction probabilities and cross sections. The RT k(A (2)A(1)) is thus approximately 3.3 order of magnitude larger than the BO value, and degeneracy-averaged, initial-state-resolved rate constants increase by approximately 13% and by approximately 47% at 300 and 500 K, respectively. Owing to an overestimation of the X (2)B(1) potential barrier, the calculated thermal rate is too low with respect to that observed, but we obtain a good agreement by shifting down the calculated cross section.     

The classical Wigner method with an effective quantum force: application to the collinear H + H2 reaction

To improve the classical Wigner (CW) model, we recently proposed the classical Wigner model with an effective quantum force (CWEQF). The results of the CWEQF model are more accurate than those of the CW model. Still the simplicity of the CW model is retained. The quantum force was obtained by defining a characteristic distance η(0) between two Feynman paths that enter the expression for the flux-flux correlation function. η(0) was considered independent of the position along the reaction path. The CWEQF leads to a lowering of the effective potential barrier. Here we develop the method to use position dependent η(0) values. The method is also generalized to two dimensions. Applications are carried out on one-dimensional model problems and the two-dimensional H + H(2) collinear reaction.     

A quantum scattering study of collinear state-testate reaction probabilities for the F + H2(v) → HF(v') + H system

A new quantum scattering approach (linear combination of arrangement channels-scattering wavefunction, LCAC-SW) proposed by Deng and his co-workers is used to calculate collinear state-to-state reaction probabilities for the F + H₂(v) → HF(v') + H system. Several interesting problems such M threshold energy, compound states and enhance by translational energy of the reactants and the vibration excitation of products are discussed and they are compared with other theoretical investigations reported in the literature. It is shown that the LCAC-SW approach is the successful one of quantum scattering methods.     

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.     

Time-dependent quantum study of the kinetics of the H(2S) + FO(2II) OH(2II) + F(2P) reaction

Quantum mechanical wave packet calculations are carried out for the H((2)S) + FO((2)II) --> OH((2)II) + F((2)P) reaction on the adiabatic potential energy surface of the ground (3)A' triplet state. The state-to-state and state-to-all reaction probabilities for total angular momentum J = 0 have been calculated. The probabilities for J > 0 have been estimated from the J = 0 results by using J-shifting approximation based on a capture model. Then, the integral cross sections and initial state-selected rate constants have been calculated. The calculations show that the initial state-selected reaction probabilities are dominated by many sharp peaks. The reaction cross section does not manifest any sharp oscillations and the initial state-selected rate constants are sensitive to the temperature.     

A comparison of two-dimensional and three-dimensional trajectory calculations in thermal HBr2 and H2Br systems

Two-dimensional (2D) and three-dimensional (3D) quasiclassical trajectory calculations on H + Br₂ at 300°K and H + HBr at 1000°K are reported. Angular scattering, energy disposal, and impact parameter distributions for reactive collisions are compared after removal of phase-space factors (dimensionality bias) as a means of examining the similarities and differences in the dynamic bias in 2D and 3D. Qualitatively, for all reactive processes studied, the 3D trajectory calculated distributions are reproduced by the phase-space adjusted 2D trajectory data. Thus the surprisal of these angular scattering, energy disposal, and impact parameter distributions is dimensionally invariant, and the same dynamic bias appears in 2D and 3D. A systematic method for converting 2D reaction probabilities and maximum reactive impact parameters into 3D rate coefficients is presented. We find that trajectory calculated 3D rate coefficients may in general differ markedly from those derived from 2D trajectory data. In particular, the surprisal associated with rate coefficients depends on dimensionality for the H + HBr → H₂ + Br reaction, but is invariant for the H′ + HBr → H′Br + Br and H + Br₂ → HBr + Br reactions.     

Integral and state-to-state cross sections for the reaction D + H2(νf) → HD(νf) + H: A quantum mechanical study within the infinite order sudden approximation

In this paper are presented quantum mechanical t-initial and t-average cross sections and rate constants for the reactions D + H₂(ν₁ = 0, 1) → HD(ν_f = 0, 1) + H. The calculations were done employing the infinite order sudden approximation. It was found that the t-average total cross sections overlap very nicely with the available classical cross sections. As for rate constants a reasonably good fit was found with available experimental 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.     

Seven-dimensional quantum dynamics study of the H+NH3-->H2+NH2 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H+NH3-->H2+NH2 reaction using a seven-dimensional model and an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values. The total reaction probabilities are calculated for the initial ground and seven excited states of NH3 with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants are calculated for the temperature range 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the total reaction probabilities are overall very small, (b) the symmetric and asymmetric NH stretch excitations enhance the reaction significantly and almost all of the excited energy deposited was used to reduce the reaction threshold, (c) the excitation of the umbrella and bending motion have a smaller contribution to the enhancement of reactivity, (d) the main contribution to the thermal rate constants is thought to come from the ground state at low temperatures and from the stretch excited states at high temperatures, and (e) the calculated thermal rate constants are three to ten times smaller than the experimental data and transition state theory results.     

Quasi-classical trajectory calculations on the H + O2 reaction

Quasi-classical trajectory calculations have been performed on the H + O₂ system. Significant reaction probabilities are obtained when the initial energy is in rotation or vibration, or a combination of the two, but not when the initial energy is in translation. The opacity function shows a bimodal dependence on the impact parameter, with a small peak at 0.9 Å < b < 1.5 Å and a very prominent peak at 2.5 Å < b < 3.3 Å. The product scattering angles and product energy distributions also depend on b and to a limited extent on the initial energy distribution. The observations can be largely interpreted in terms of the nature of the motion on the potential energy surface, while the effects of rotational energy on the reaction follow qualitatively from statistical phase-space theory.