Real wavepacket code for ABC+DAB+CD reactive scattering

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Abstract

We discuss a six-dimensional, time-dependent real wavepacket (RWP) code designed to obtain reaction probabilities for ABC(vI) + D  AB + CD four-atom reactions, where vI is a collective index for the initial quantum state of the triatomic molecule. The code provides exact results for total angular momentum J=0, and invokes the helicity decoupling (or centrifugal sudden) approximation for J>0. Our new RWP code has been extensively checked by considering the benchmark H + H2O  H2 + OH abstraction reaction.

Program summary

Program title: ABC + D RWP Code

Catalogue identifier: AECD_v1_0

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECD_v1_0.html

Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 808 025

No. of bytes in distributed program, including test data, etc.: 4 840 859

Distribution format: tar.gz

Programming language: Fortran 77

Computer: Tested on Intel Xeon 2.8 GHz; AMD Opteron 244 1.8 GHz. Should run on any architecture providing a Fortran 77 compiler.

Operating system: Linux

RAM: Problem dependent

Classification: 16.8, 16.12

Nature of problem: Determination of dynamic properties (reaction probabilities and cross sections) for ABC + D  AB + CD four-atom reactions.

Solution method: Propagation of the real part of a wavepacket under the action of a modified Hamiltonian on a grid using several techniques such as dispersion fitted finite difference and potential optimized DVR.

Restrictions: Use of the helicity decoupling or centrifugal sudden approximation, which neglects the Coriolis coupling terms.

Running time: Hours to days, depending on the problem under study and computational resources. The test example takes between 15 and 30 hours depending on the environment used. The example is made up of several programs and can therefore be split into shorter time periods.

Introduction

An accurate description of the chemical reaction dynamics that occurs when atoms and molecules collide requires, in principle, a quantum mechanical treatment. Either time-independent or time-dependent quantum approaches are possible. The main advantages of the time-dependent approach, the subject of this paper, are that a single calculation provides the dynamic properties for a range of collision energies and the microscopic reaction mechanisms involved can be characterized in a rather straightforward way.

Rigorous quantum mechanical approaches are computationally challenging and still limited to relatively small system sizes. In this context, the time-dependent real wavepacket (RWP) method [1] becomes relevant, since just the real part of the wavepacket is propagated. Both computation time and computer memory are thus reduced relative to the propagation of a complex-valued wavepacket. Furthermore, as with standard wavepacket calculations [2], this type of calculation can be done efficiently due to the incorporation of numerical methods such as fast Fourier transforms (FFTs) [2], discrete variable representations (DVRs) [3], and related finite-difference approaches such as dispersion fitted finite differences (DFFDs) [4].

The RWP method has been successfully applied to investigate numerous A + BC → AB + C triatomic reactions, see, e.g., Refs. [5], [6], [7], [8], [9], [10], [11]. While fully coupled total angular momentum J>0 calculations are possible, many of such studies have employed the helicity-decoupling (HD) approximation, which is also called the centrifugal sudden approximation [12], [13], and J-shifting techniques [14]. These approximations considerably reduce the effort associated with estimating observables such as cross sections and rate constants that involve summations over many total angular momenta. HD-RWP calculations have also been reported for several AB + CD → ABC + D tetratomic reactions, including the OH + H2 [15], OH + D2 [16], OH + CO [17], and CH + H2 [18] systems. Owing to the computational challenges of such calculations, several parallel-computing strategies for carrying out RWP calculations have also been developed [19], [20], [21]. Many of the triatomic and tetratomic systems studied have been quite challenging due to the presence of deep potential wells, for example. Nonetheless, the results obtained, and comparisons with experiment and other calculations where available, show that the HD-RWP approach is capable of providing accurate, useful quantum dynamics information.

It is interesting to note that there have been relatively few full-dimensional, rigorous quantum dynamics studies of ABC + D → AB + CD reactions [22], [23], [24], [25], [26], [27]. In this work we develop a HD-RWP code to deal with this type of reaction. The code complements our previously developed AB + CD code [15], thus providing the capability to carry out RWP calculations on any four-atom bimolecular reactive system. To test the goodness of this code, we apply it to the simplest atom–triatom system for which several 5D [23], [24] and rigorous quantum dynamics calculations in full dimensionality (6D) [22], [25], [26], [27] are available, i.e., the H + H2O benchmark system and its isotopic variants. Since our concern here is to demonstrate the validity of our ABC + D code, we consider the H + H2O → H2 + OH abstraction reaction on one of the simplest available potential energy surfaces, the Walch–Dunning–Schatz–Elgersma (WDSE) potential energy surface [28], [29], [30] slightly modified by Clary [31].

Section 2 outlines the general features of the ABC + D RWP code, Section 3 presents its application on the H + H2O → H2 + OH abstraction reaction, and in Section 4 some brief concluding remarks are given.

Section snippets

ABC + D real wavepacket code

The ABC + D time-dependent HD-RWP code utilizes the basic structure of a previously developed diatom–diatom or AB + CD RWP code [15]. The main differences involve the definition of the coordinate system, the transformation from body-fixed (BF) Jacobi coordinates to Cartesian coordinates, and the determination of the ABC quantum states for the initial wavepacket.

Application to the H + H2O → H2 + OH abstraction reaction

The H + H2O → H2 + OH abstraction reaction is one of the simplest and relevant atom–triatom reactions and has been the subject of several reduced dimension and full-dimensional (6D) quantum dynamics calculations.

Concluding remarks

We developed and validated a HD-RWP code to obtain dynamical properties for atom–triatom, ABC + D, reactions. This code complements our AB + CD code and thus allows RWP calculations to be carried out on a wide variety of tetratomic systems.

To validate the RWP code we studied the H + H2O → H2 + OH abstraction reaction, since it is the “simplest” relevant atom–triatom reaction for which several quantum dynamics calculations in full dimension are available. While there can be some minor

Acknowledgements

The work at Barcelona was supported by the Spanish Ministry of Education and Science (Project No. CTQ2005-09334-C02-01), by the “Generalitat de Catalunya” (Autonomous Government of Catalonia, Grant No. 2005SGR 00175), and by CESCA (Supercomputing Center of Catalonia). The work at Argonne National Laboratory was supported by the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, U.S. Department of Energy, under Contract No. DE-AC02-06CH11357. One of the

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