Abstract
Several aspects involved in the theoretical formulation and the practical calculation of reactive cross sections, for atom-diatom systems, are reviewed and discussed, focusing on the time-independent hyperspherical-propagative approach. The general trends of the formalism, that allows a complete scattering calculation for a reactive process, is presented first. Then, the discussion is divided into four additional parts. The first one briefly discusses the coordinate and reference frame problem, showing how the democratic version of the hyperspherical coordinates provides a solution for the cumbersome transition between rearrangement channels. The second part deals with the details of the systematic expansion of the nuclear wavefunction, on a conveniently chosen basis set for the internal (angular) coordinates, performed at fixed values of the remaining (scattering or hyperradial) coordinate. The third part deals with the approach to solving the resulting set of coupled second-order differential equations, the propagative method, which obtains (the logarithmic derivative transform of) the hyperradial solution for a number of increasing discrete values of the hyperradial independent variable. Finally, the fourth part discusses the extraction of the asymptotic information and the calculation for reaction probabilities and integral cross sections. Some examples illustrate each stage into which the calculation process is divided.
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References
J. Z. H. Zhang: Theory and application of quantum molecular dynamics (World Scientific, Singapore, 1999).
Faraday Discussions of the Chemical Society: “Chemical Reaction Theory”, 110 (1998).
Phys. Chem. Chem. Phys. Special Issue: “Chemical Reaction Theory”, 1 (1999).
W. H. Miller, Adv. Chem. Phys. 25, 69 (1974).
J. M. Launay and M. LeDourneuf, in Physics of Electronic and Atomic Collisions “Proceedings of the ICPEAC XVII, Brisbane, July 1991,Section 15” (IOP Publishing, Bristol, 1992) p. 549.
C. L. Russel and D. E. Manolopoulos, J. Chem. Phys. 110, 177 (1999).
Y. C. Zhang, L. X. Zhan, Q. G. Zhang, W. Zhu and J. Z. H. Zhang, Chem. Phys. Lett. 300, 27 (1999).
F. Huarte-Larrañaga, X. Gimenez, J. M. Lucas, A. Aguilar and J.-M. Launay, Phys. Chem. Chem. Phys. 1, 1125 (1999).
J. Z. H. Zhang, J. Chem. Phys. 94, 6047 (1991).
R. B. Gerber, V. Buch and M. A. Ratner, J. Chem. Phys. 77, 3022 (1982); N. Makri and W.H. Miller, J. Chem. Phys. 87, 5781 (1987); H.-D. Meyer, U. Manthe and L.S. Cederbaum, Chem. Phys. Lett. 165, 73 (1990).
U. Manthe, T. Seideman and W. H. Miller, J. Chem. Phys. 99, 10078 (1993); J. Chem. Phys. 101, 4759 (1994).
M. Mladenovic, M. Zhao, D. G. Truhlar, D. W. Schwenke, Y. Sun and D. J. Kouri, J. Phys. Chem. 92, 7035 (1988); J. Z. H. Zhang and W. H. Miller, J. Chem. Phys. 94, 7785 (1990); D. E. Manolopoulos, M. D’Mello and R. E. Wyatt, J. Chem. Phys. 93, 403 (1990); M. Baer, D. Neuhauser and Y. Oreg, J. Chem. Soc. Faraday Trans. 86, 1721 (1990).
A. Kupperman and P. G. Hipes, J. Chem. Phys. 84, 5962 (1986); J. Linderberg, Int. J. Quantum Chem. Symp. 19, 467 (1986); G. A. Parker, R. T Pack, B. J. Archer and R. B. Walker, Chem. Phys. Lett. 137, 564 (1987); G. C. Schatz, Chem. Phys. Lett. 150, 92 (1988); J.-M. Launay and M. LeDourneuf, Chem. Phys. Lett. 163, 178 (1989).
J. C. Light, I. P. Hamilton and J. V. Lill, J. Chem. Phys. 82, 1400 (1985).
D. Neuhauser, J. Chem. Phys. 100, 9272 (1994); H. W. Jang and J. C. Light, J. Chem. Phys. 102, 3262 (1995); D. K. Hoffman, Y. Huang, W. Zhu and D. J. Kouri, J. Chem. Phys. 101, 1242 (1994); V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 102, 7390 (1995).
R. Kosloff and D. Kosloff, J. Comput. Phys. 63, 363 (1986); D. Neuhauser and M. Baer, J. Chem. Phys. 90, 4351 (1989); J. Z. H. Zhang, Chem. Phys. Lett. 160, 417 (1989).
D. Neuhauser and M. Baer, J. Chem. Phys. 91, 4651 (1989).
T. Seideman and W. H. Miller, J. Chem. Phys. 96, 4412 (1992).
M. Baer, L Last and H.-J. Loesch, J. Chem. Phys. 101, 9648 (1994).
F. Huarte-Larrañaga, X. Gimenez, A. Aguilar and M. Baer, Chem. Phys. Lett. 291, 346 (1998); F. Huarte-Larrañaga, X. Gimenez and A. Aguilar, J Chem. Phys. 109, 5761 (1998); ibid, Faraday Discuss. 110, 236 (1998); F. Huarte-Larrañaga, X. Gimenez, J.M. Lucas and A. Aguilar, J. Chem. Phys. 111, 1979 (1999).
F. T. Smith, J. Math. Phys. 3, 735 (1962); R. C. Whitten and F. T. Smith, ibid 9, 1103 (1968); R. C. Whitten, ibid 10, 1631 (1969).
B. R. Johnson, J. Chem. Phys. 73, 5051 (1980); 79, 1906, 1916 (1983).
R. T Pack, Chem. Phys. Lett. 108, 333 (1984); R. T Pack and G. A. Parker, J. Chem. Phys. 87, 3888 (1987).
J.-M. Launay and M. LeDourneuf, in ref. 13.
V. Aquilanti, S. Cavalli and D. de Fazio, 109, 3792 (1998); V. Aquilanti, S. Cavalli, D. de Fazio, A. Volpi, A. Aguilar, X. Gimenez and J.M. Lucas, J. Chem. Phys. 109, 3805 (1998).
G. A. Parker, A. Laganá, S. Crocchianti and R. T Pack, J. Chem. Phys. 102, 1238 (1995).
M. E. Rose, Elementary theory of angular momentum (Wiley, New York, 1957); R. N. Zara, Angular Momentum: Understanding the Spatial Aspects of Chemistry and Physics (Wiley, New York, 1988).
J. R. Taylor, Scattering Theory: The Quantum Theory of Non-relativistic Collisions (Wiley, New York, 1972).
R. G. Newton Scattering theory of waves and particles (Springer-Verlag, New York, 1982).
J.-M. Launay, in Dynamical Processes in Molecular Physics, G. Delgado-Barrio (Ed.) (IOP, Bristol, 1993).
G. C. Schatz and A. Kuppermann, J. Chem. Phys. 85, 4642, 4668 (1976).
W. H. Miller, J. Chem. Phys. 50, 407 (1969).
G. A. Parker, contribution to this volume.
R. Kosloff, in Dynamics of Molecules and Chemical Reactions, R. E. Wyatt and J. Z. H. Zhang, eds. (Marcel Dekker, New York, 1996).
. Dynamics of Molecules and Chemical Reactions, R. E. Wyatt and J. Z. H. Zhang, eds. (Marcel Dekker, New York, 1996).
G. A. Parker and R. T Pack, J. Chem. Phys. 98, 6883 (1993).
D. T. Colbert and W. H. Miller, J. Chem. Phys. 96, 1982 (1992).
V. Aquilanti, S. Cavalli and D. de Fazio, J. Phys. Chem. 99, 15694 (1995).
V. Aquilanti, private communication.
A. Ohsaki and H. Nakamura, Phys. Rep. 187, 1 (1990).
V. Aquilanti, S. Cavalli and G. Grossi, Chem. Phys. Lett. 110, 43 (1984); V. Aquilanti and S. Cavalli, ibid 141, 309 (1987); V. Aquilanti, S. Cavalli, G. Grossi, V. Pellizzari, M. Rossi, A. Sgamellotti and F. Tarantelli, ibid 162, 179 (1989).
F. Mrugala and D. Secrest, J. Chem. Phys. 78, 5954 (1983).
W. H. Press et al. Numerical Recipes (Cambridge Univ. Press, Cambridge, 1992).
J. C. Light and R. B. Walker, J. Chem. Phys. 65, 4272 (1976).
R. E. Gellman and R. E. Kalaba, Proc. Natl. Acad. Sci. 42, 629 (1956).
D. E. Manolopoulos, J. Chem. Phys. 85, 6425 (1986).
M. H. Alexander and D. E. Manolopoulos, J. Chem. Phys. 86, 2044 (1987).
D. E. Manolopoulos (unpublished work).
G. A. Parker, R. T Pack and A. Laganá, Chem. Phys. Lett. 202, 75 (1993).
J. D. Kress, R. B. Walker, E. F. Hayes and P. Pendergast, J. Chem. Phys. 100, 2728 (1994).
J. Manz and J. Römelt, Chem. Phys. Lett. 77, 172 (1981).
F. Huarte-Larrañaga, X. Gimenez, J. M. Lucas, A. Aguilar and J.-M. Launay (in preparation).
F. Huarte-Larrañaga. Contribution to the present volume.
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Bolloni, A., Huarte-Larrañaga, F., Gimenez, X. (2000). The exact Computation of Reactive Cross Sections for Atom-Diatom Systems. The Hyperspherical Propagative Approach. In: Laganà, A., Riganelli, A. (eds) Reaction and Molecular Dynamics. Lecture Notes in Chemistry, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57051-3_16
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DOI: https://doi.org/10.1007/978-3-642-57051-3_16
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