View PDF Version
 
DOI: 10.1039/A809492F (Paper) Reference Section for: Phys. Chem. Chem. Phys., 1999, 1, 1091-1098

Probabilities for the F+H2→HF+H reaction by the hyperquantization algorithm: alternative sequential diagonalization schemes

(Note: The full text of this document is currently only available in the PDF Version )

Vincenzo Aquilanti, Simonetta Cavalli, Dario De Fazio, Alessandro Volpi, Antonio Aguilar, Xavier Giménez and José María Lucas

Abstract

This work reports on the performances of the hyperquantization algorithm in the symmetric hyperspherical coordinate representation for the F+H2 reaction. The use of alternative sequential diagonalization schemes has greatly reduced the computing time and memory requirements, making the technique very efficient and competitive for applications to atom–diatom reactions for the entire range of hyperradial variable ρ. The effectiveness of the sequential diagonalization-truncation depends on the topology of the potential energy surface, which varies along different ranges of the hyperradius. The appearance at ρ≈4 a0 of the ridge line on the potential energy surface, which separates the reactant and product valleys, marks the transition between the regions of preferential applicability of two alternative ways to perform sequentially the diagonalization of the fixed-ρ Hamiltonian matrix. Reaction probabilties for total zero angular momentum are reported and compared with previous calculations.

References

  1. D. E. Manolopoulos, J. Chem. Soc., Faraday Trans., 1997, 93, 673 RSC.
  2. V. Aquilanti, S. Cavalli and D. De Fazio, J. Chem. Phys., 1998, 109, 3792 CrossRef CAS.
  3. V. Aquilanti and S. Cavalli, Few-Body Systems, 1992, suppl. 6, p. 573 Search PubMed.
  4. V. Aquilanti, S. Cavalli and G. Grossi, in Advances in Molecular Vibrations and Collision Dynamics, ed. J. M. Bowman, JAI Press, Greenwich, CT, 1994, vol. 219, p. 147 Search PubMed.
  5. V. Aquilanti, S. Cavalli, C. Colelti, D. De Fazio and G. Grossi, in New Methods in Quantum Theory, ed. C. A. Tsipis, V. S. Popov, D. R. Herschbach and J. S. Avery, Kluwer, Dordrecht, 1996, p. 233 Search PubMed.
  6. V. Aquilanti, S. Cavalli, D. De Fazio, A. Volpi, A. Aguilar, X. Gimenez and J. M. Lucas, J. Chem. Phys., 1998, 109, 3805 CrossRef CAS.
  7. Z. Ba[c with combining breve]ic, R. M. Whitnell, D. Brown and J. C. Light, Comput. Phys. Commun., 1988, 51, 35 CrossRef CAS.
  8. R. M. Whitnell and J. C. Light, J. Chem. Phys., 1989, 90, 1774 CrossRef.
  9. S. E. Choi and J. C. Light, J. Chem. Phys., 1983, 90, 2593 CrossRef CAS.
  10. V. Aquilanti, S. Cavalli and G. Grossi, Chem. Phys. Lett., 1984, 110, 43 CrossRef CAS.
  11. V. Aquilanti and S. Cavalli, Chem. Phys. Lett., 1987, 141, 309 CrossRef CAS.
  12. V. Aquilanti, S. Cavalli, G. Grossi, V. Pellizzari, M. Rosi, A. Sgamellotti and F. Tarantelli, Chem. Phys. Lett., 1989, 162, 179 CrossRef CAS.
  13. R. Steckler, D. G. Truhlar and B. C. Garrett, J. Chem. Phys., 1990, 169, 473.
  14. G. A. Parker and R. T. Pack, J. Chem. Phys., 1992, 98, 6883 CrossRef CAS.
  15. F. T. Smith, J. Math. Phys., 1962, 3, 735 CrossRef.
  16. R. C. Whitten and F. T. Smith, J. Math. Phys., 1968, 9, 1103 CrossRef.
  17. J. M. Launay and M. Le Dournef, Chem. Phys. Lett., 1989, 163, 178 CrossRef CAS.
  18. J. M. Launay, Theor. Chem. Acta, 1991, 79, 183 Search PubMed.
  19. B. Lepetit and J. M. Launay, J. Chem. Phys., 1991, 95, 5159 CrossRef CAS.
  20. R. T. Pack and G. A. Parker, J. Chem. Phys., 1987, 87, 3888 CrossRef CAS.
  21. R. B. Johnson, J. Chem. Phys., 1983, 79, 1906 CrossRef CAS.
  22. H. Klar and M. Klar, J. Phys. B: Atom. Mol. Phys., 1980, 13, 1057 Search PubMed.
  23. V. Aquilanti, G. Grossi, A. Laganà, E. Pelikan and H. Klar, Lett. Nuovo Cim., 1984, 41, 541 Search PubMed.
  24. V. Aquilanti and S. Cavalli, J. Chem. Phys., 1986, 85, 1355 CrossRef CAS.
  25. V. Aquilanti and S. Cavalli, J. Chem. Soc., Faraday Trans., 1997, 93, 801 RSC.
  26. R. G. Littlejohn, K. A. Mitchell, V. Aquilanti and S. Cavalli, Phys. Rev. A, 1998, 58, 3705 CrossRef CAS.
  27. R. G. Littlejohn, K. A. Mitchell, M. Reinsch, V. Aquilanti and S. Cavalli, Phys. Rev. A, 1998, 58, 3718 CrossRef CAS.
  28. V. Aquilanti, S. Cavalli, G. G. Grossi and R. W. Anderson, J. Chem. Soc., Faraday Trans., 1990, 86, 1681 RSC.
  29. V. Aquilanti, S. Cavalli and D. De Fazio, J. Phys. Chem., 1995, 99, 15694 CrossRef CAS.
  30. J. M. Alvariño, V. Aquilanti, S. Cavalli, S. Crocchianti, A. Laganà and T. Martinez, J. Chem. Phys., 1997, 107, 3339 CrossRef CAS.
  31. V. Aquilanti, S. Cavalli, G. Grossi and R. W. Anderson, J. Phys. Chem., 1991, 95, 8184 CrossRef CAS.
  32. R. W. Anderson, V. Aquilanti, S. Cavalli and G. Grossi, J. Phys. Chem., 1993, 97, 2443 CrossRef CAS.
  33. C. Lanczos, J. Res. Natl. Bur. Standards, Sect. B, 1950, 45, 255 Search PubMed.
  34. C. Lanczos, J. Res. Natl. Bur. Standards, Sect. B, 1952, 45, 255 Search PubMed.
  35. J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. I Theory, Wiley, New York, 1985 Search PubMed.
  36. J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Vol. II Programs, Wiley, New York, 1985 Search PubMed.
  37. A. R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, NJ, 1960 Search PubMed.
  38. T. Ericsson and A. Ruhe, Math. Comput., 1980, 35, 1251.
  39. Z. Ba[c with combining breve]ic and J. C. Light, J. Chem. Phys., 1986, 85, 4594 CrossRef CAS.
  40. P. Pendergast, Z. Darakhan, E. F. Hayes and D. C. Sorensen, J. Comput. Phys., 1994, 113, 201 CrossRef.
  41. Z. Ba[c with combining breve]ic, J. D. Kress, G. A. Parker and R. T. Pack, J. Chem. Phys., 1990, 92, 2344 CrossRef CAS.
  42. G. H. Golub and C. F. Van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore and London, 1996 Search PubMed.
  43. B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980 Search PubMed.
  44. J. D. Kress, Z. Ba[c with combining breve]ic, G. A. Parker and R. T. Pack, Chem. Phys. Lett., 1989, 157, 485 CrossRef CAS.
  45. B. Lepetit, J. M. Launay and M. Le Dourneuf, Chem. Phys., 1986, 106, 103 CrossRef CAS.
  46. R. T. Pack and G. A. Parker, J. Chem. Phys., 1989, 90, 3511 CrossRef.
  47. D. Secrest, Atom-Molecule Collision theory. A Guide for the Experimentalist, R. B. Bernstein, Plenum, New York, 1979 Search PubMed.
  48. L. D. Thomas, M. H. Alexander, B. R. Johnson, W. A. Lester, Jr., J. C. Light, K. D. McLenithan, G. A. Parker, M. J. Redmon, T. G. Schmalz, D. Secrest and R. B. Walker, J. Comput. Phys., 1981, 41, 407 CAS.
  49. R. G. Gordon, J. Chem. Phys., 1969, 51, 14 CAS.
  50. R. Bellman and R. Kalaba, Proc. Natl. Acad. Sci., 1956, 42, 629.
  51. F. Mrugala and D. Secrest, J. Chem. Phys., 1983, 78, 5954 CrossRef CAS.
  52. J. C. Light and R. B. Walker, J. Chem. Phys., 1976, 65, 4272 CrossRef CAS.
  53. F. Huarte-Larrañaga, X. Giménez and A. Aguilar, J. Chem. Phys., 1998, 109, 5761 CrossRef CAS.
  54. V. Aquilanti, S. Cavalli and M. B. Sevryuk, J. Math. Phys., 1993, 34, 3351 CrossRef.
  55. D. E. Manolopoulos and S. K. Gray, J. Chem. Phys., 1994, 101, 4062 CrossRef.
  56. B. R. Johnson, J. Comp. Phys., 1973, 14, 445 Search PubMed.
  57. D. E. Manolopoulos, J. Chem. Phys., 1986, 85, 6425 CrossRef CAS.
  58. M. H. Alexander and D. E. Manolopoulos, J. Chem. Phys., 1987, 86, 2044 CrossRef CAS.
Click here to see how this site uses Cookies. View our privacy policy here.