Tomás González-Lezana

A rigorous test of the statistical model for atom–diatom insertion reactions

The statistical model of atom–diatom insertion reactions is combined with coupled-channel capture theory and used to calculate differential cross sections for the reactions of C(1D), N(2D), O(1D) and S(1D) with H2. In the case of C(1D) and S(1D), the resulting statistical differential cross sections are found to be in excellent agreement with the recent quantum reactive scattering calculations of Honvault and Launay. They are therefore also in good agreement with molecular beam experiments for the S(1D)+H2 reaction, in contrast to the results of earlier calculations based on a less rigorous statistical theory. However, because the exact quantum mechanical differential cross sections for N(2D) and O(1D) exhibit a slight forward–backward asymmetry, the agreement with the statistical model for these reactions is not quite so good. The difference between the two cases can be rationalized in terms of the greater exoergicities of the N(2D) and O(1D) reactions, which lead to broader resonances and hence to short...

Statistical quantum studies on insertion atom–diatom reactions

The study of insertion atom–diatom reactions is usually complicated by the existence of deep potential wells between reactants and products. The large number of bound and resonance states to be properly described makes exact quantum mechanical calculations extremely demanding in terms of numerical effort. In this type of collision, the process proceeds via the formation of an intermediate complex of finite lifetime. The application of statistical quantum methods provides a valid alternative to investigate the dynamics of the reaction. In this work, studies performed with a statistical quantum method recently developed by Rackham et al. on a variety of different reactions are extensively reviewed. The overall dynamics of the processes selected to test this statistical model range from complex-forming mechanisms to a competition between insertion and direct abstraction reaction pathways. This review includes studies of X + H2 reactions, where X is one of the following electronically excited non-metallic atoms: C(1 D), N(2 D), O(1 D) or S(1 D). An ion–diatom collision, the H system (with its isotope variants), is also investigated. Finally, results of the statistical study of the H + O2 reaction are discussed. In all cases, comparison with both exact quantum mechanical calculations and experimental measurements shows that the method provides valid and rigorous information about the underlying dynamics of the reactions under study.

Differential Cross Sections and Product Rotational Polarization in A + BC Reactions Using Wave Packet Methods: H+ + D2 and Li + HF Examples

The state-to-state differential cross sections for some atom + diatom reactions have been calculated using a new wave packet code, MAD-WAVE3, which is described in some detail and uses either reactant or product Jacobi coordinates along the propagation. In order to show the accuracy and efficiency of the coordinate transformation required when using reactant Jacobi coordinates, as recently proposed [ J. Chem. Phys. 2006 , 125 , 054102 ], the method is first applied to the H + D(2) reaction as a benchmark, for which exact time-independent calculations are also performed. It is found that the use of reactant coordinates yields accurate results, with a computational effort slightly lower than that when using product coordinates. The H(+) + D(2) reaction, with the same masses but a much deeper insertion well, is also studied and exhibits a completely different mechanism, a complex-forming one which can be treated by statistical methods. Due to the longer range of the potential, product Jacobi coordinates are more efficient in this case. Differential cross sections for individual final rotational states of the products are obtained based on exact dynamical calculations for some selected total angular momenta, combined with the random phase approximation to save the high computational time required to calculate all partial waves with very long propagations. The results obtained are in excellent agreement with available exact time-independent calculations. Finally, the method is applied to the Li + HF system for which reactant coordinates are very well suited, and quantum differential cross sections are not available. The results are compared with recent quasiclassical simulations and experimental results [J. Chem. Phys. 2005, 122, 244304]. Furthermore, the polarization of the product angular momenta is also analyzed as a function of the scattering angle.

Comparative configurational study for He, Ne, and Ar trimers

Helium trimer bound states are calculated by means of a variational method described in terms of atom pair coordinates and distributed Gaussian basis functions for zero total angular momentum. To show the feasibility of this method, we also apply it to the calculation of the first vibrational levels of the Ar3 and Ne3 clusters. Special emphasis is made on the study of the possible Efimov behavior of the first excited state found in the 4He3 trimer. Geometrical configurations of the ground and first excited states of these rare gas trimers have been exhaustively studied owing to the proper symmetry of the coordinates chosen.

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 statistical quasiclassical trajectory model for atom-diatom insertion reactions.

A statistical model based on the quasiclassical trajectory method is presented in this work for atom-diatom insertion reactions. The basic difference between this and the corresponding statistical quantum model (SQM) 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. In particular, it is shown that conservation of parity can be taken into account in a natural and precise way in the statistical quasiclassical trajectory (SQCT) model. Additionally, the SQCT model complies with the principle of detailed balance and overcomes the problem of the zero point energy in the products. As a test, the model is applied to the H3+ and H+D2 exchange reactions. The excellent agreement between the SQCT and SQM results, especially in the case of the differential cross sections, indicates that the effect of tunneling through the centrifugal barrier is negligible. The effect of ignoring quantum mechanical parity conservation is also investigated.

Quantum reactive scattering with a transmission-free absorbing potential

A recently derived transmission-free absorbing potential is applied to the study of atom-diatom chemical reactions. This absorbing potential only depends on a single parameter--the width of the absorbing region--and its reflection properties are guaranteed to improve as this parameter is increased. Converged results can therefore be obtained very easily, as we illustrate with time-dependent wave packet calculations on the H + H2,F + H2, and H + O2 reactions.

Dynamics of the C(D1)+D2 reaction: A comparison of crossed molecular-beam experiments with quasiclassical trajectory and accurate statistical calculations

In this paper we report a combined experimental and theoretical study on the dynamics of the insertion reaction C((1)D)+D(2) at 15.5 kJ mol(-1) collision energy. Product angular and velocity distributions have been obtained in crossed beam experiments and quasiclassical trajectory (QCT) and rigorous statistical calculations have been performed on the recent and accurate ab initio potential energy surface of Bussery-Honvault, Honvault, and Launay at the energy of the experiment. The molecular-beam results have been simulated using the theoretical calculations. Good agreement between experiment and both QCT and statistical predictions is found.

Quantum approaches for the insertion dynamics of the H++D2 and D++H2 reactive collisions

The H(+)+D(2) and D(+)+H(2) reactive collisions are studied using a recently proposed adiabatic potential energy surface of spectroscopic accuracy. The dynamics is studied using an exact wave packet method on the adiabatic surface at energies below the curve crossing occurring at approximately 1.5 eV above the threshold. It is found that the reaction is very well described by a statistical quantum method for a zero total angular momentum (J) as compared with the exact ones, while for higher J some discrepancies are found. For J >0 different centrifugal sudden approximations are proposed and compared with the exact and statistical quantum treatments. The usual centrifugal sudden approach fails by considering too high reaction barriers and too low reaction probabilities. A new statistically modified centrifugal sudden approach is considered which corrects these two failures to a rather good extent. It is also found that an adiabatic approximation for the helicities provides results in very good agreement with the statistical method, placing the reaction barrier properly. However, both statistical and adiabatic centrifugal treatments overestimate the reaction probabilities. The reaction cross sections thus obtained with the new approaches are in rather good agreement with the exact results. In spite of these deficiencies, the quantum statistical method is well adapted for describing the insertion dynamics, and it is then used to evaluate the differential cross sections.

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.