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Manuscript Title: Quantum calculations of transport properties in molecular gases.
Authors: F.A. Gianturco, S. Serna, A.V. Storozhev
Program title: SBECROSS
Catalogue identifier: ADFB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 103(1997)251
Programming language: Fortran.
Computer: IBM RS/6000.
Operating system: AIX 2.3.
RAM: 8M words
Word size: 64
Keywords: Inelastic, Molecular, Scattering, Rotational excitations, In collisions, Generalized, Non-equilibrium, Properties in molecular, Gases, Interactions in atom Molecule mixtures, Elastic, Fluid dynamics.
Classification: 12, 16.7.

Nature of problem:
The generalized cross sections involved in the calculation of transport properties are obtained for atom-diatom gaseous mixtures within the range of applicability of the WCUB theory.

Solution method:
The S-matrix describing the atom-diatom collisions in the gas at a given energy are read from external files and recoupled to obtain energy dependent cross sections. These S-matrices must have been previously computed by using the MOLSCAT [2] code or any other one with the same output format. This is performed for a set of energies which correspond to the pivots of a Chebyshev polynomial interpolation [3]. The final Boltzmann averaging over the energy is then computed by using a standard Simpson quadrature [3].

Restrictions:
The current version of the program evaluates the effective cross sections in the first perturbative order of the Wang-Chang and Uhlenbeck theory [4] for atom-diatom mixtures in the rigid rotor approximation. Although the angular recoupling involved in the calculation of the effective cross sections can be rather expensive, the bottleneck is usually the computation of the quantum S-matrices. The exact, close- coupling description of the collision becomes prohibitive at high energies, thus making it necessary to employ dynamical approximations to reduce the complexity of the problem. The program also has been designed to process S-matrices computed within the coupled-states (CS) decoupling scheme.

Unusual features:
Most of the dimensions in the program are defined by parameter statements. Several control statements have been included in the Fortran code in order to avoid the use of any array out of its allocated memory.

Running time:
The most time-consuming section of the program is the evaluation of the 3j, 6j and 9j coefficients needed to recouple the S-matrices. This means that the running time will depend mainly on the number of rotational open channels existing at each collision energy, the number of partial waves for which the S-matrix has been computed and the number of effective cross sections required. In addition, the amount of angular recoupling is different for each cross section. In a typical calculation involving the seven cross sections described in the main text, the running time may vary from a few seconds at low energies up to more than one hour at very high energies. The test run took 5 seconds.

References:
[1] For a review of the current status of the study of the transport properties, see V. Vesovic, W.A. Wakeham, Int. Rev. in Phys. Chem. 11, 161, (1992).
[2] J.M. Huston, S. Green, 1986 MOLSCAT Computer Code, distributed by Collaborative Computational Project No. 6 of the Science and Engineering Research Council U.K., version 8.
[3] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes, Cambridge University Press (1986).
[4] G.C. Maitland, M. Rigby, E.B. Smith, W. Wakeham, Intermolecular Forces, Oxford University Press (1981).