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Chebyshev Propagation and Applications to Scattering Problems

  • Conference paper
Theory of Chemical Reaction Dynamics

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry ((NAII,volume 145))

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Abstract

The Chebyshev operator is a discrete cosine-type propagator that bears many formal similarities with the time propagator. It has some unique and desirable numerical properties that distinguish it as an optimal propagator for a wide variety of quantum mechanical studies of molecular systems. In this contribution, we discuss some recent applications of the Chebyshev propagator to scattering problems, including the calculation of resonances, cumulative reaction probabilities, S-matrix elements, cross-sections, and reaction rates.

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References

  1. R. Kosloff, J. Phys. Chem. 92, 2087 (1988).

    Article  CAS  Google Scholar 

  2. J. Z. H. Zhang, Theory and Application of Quantum Molecular Dynamics. (World Scientific, Singapore, 1999).

    Google Scholar 

  3. C. Leforestier, R. H. Bessling, C. Cerjan, M. D. Feit, R. Friesner, A. Guldberg, A. Hammerich, G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, and R. Kosloff, J. Comput. Phys. 94, 59 (1991).

    Article  Google Scholar 

  4. R. Kosloff, Annu. Rev. Phys. Chem. 45, 145 (1994).

    Article  CAS  Google Scholar 

  5. R. Kosloff, in Numerical Grid Methods and Their Applications to Schrodinger’s Equation, edited by C. Cerjan (Kluwer, Dordrecht, 1993).

    Google Scholar 

  6. J. C. Light and T. Carrington, Adv. Chem. Phys. 114, 263 (2000).

    Google Scholar 

  7. J. P. Boyd, Chebyshev and Fourier Spectral Methods. (Springer-Verlag, Berlin, 1989).

    Google Scholar 

  8. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. (Dover, New York, 1970).

    Google Scholar 

  9. C. Lanczos, Applied Analysis. (Prentice Hall, Englewood Cliffs, 1956).

    Google Scholar 

  10. H. Tal-Ezer and R. Kosloff, J. Chem. Phys. 81, 3967 (1984).

    Article  CAS  Google Scholar 

  11. Y. Huang, D. J. Kouri, and D. K. Hoffman, Chem. Phys. Lett. 225, 37 (1994).

    CAS  Google Scholar 

  12. Y. Huang, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. 101, 10493 (1994).

    CAS  Google Scholar 

  13. W. Zhu, Y. Huang, D. J. Kouri, C. Chandler, and D. K. Hoffman, Chem. Phys. Lett. 217(1,2), 73 (1994).

    CAS  Google Scholar 

  14. R. Chen and H. Guo, J. Chem. Phys. 105, 1311 (1996).

    CAS  Google Scholar 

  15. R. Chen and H. Guo, J. Chem. Phys. 105, 3569 (1996).

    CAS  Google Scholar 

  16. S. K. Gray and G. G. Balint-Kurti, J. Chem. Phys. 108, 950 (1998).

    Article  CAS  Google Scholar 

  17. R. Chen and H. Guo, J. Chem. Phys. 108, 6068 (1998).

    CAS  Google Scholar 

  18. R. Chen and H. Guo, Comput. Phys. Comm. 119, 19 (1999).

    Article  CAS  Google Scholar 

  19. D. Neuhauser, Chem. Phys. Lett. 200, 173 (1992).

    Article  CAS  Google Scholar 

  20. V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 103(8), 2903 (1995).

    Article  CAS  Google Scholar 

  21. V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 102, 7390 (1995).

    CAS  Google Scholar 

  22. Y. Huang, S. S. Iyengar, D. J. Kouri, and D. K. Hoffman, J. Chem. Phys. 105, 927 (1996).

    CAS  Google Scholar 

  23. R. Chen and H. Guo, Chem. Phys. Lett. 261, 605 (1996).

    Article  CAS  Google Scholar 

  24. H.-G. Yu and S. C. Smith, J. Chem. Phys. 107, 9985 (1997).

    Article  CAS  Google Scholar 

  25. V. A. Mandelshtam, in Multiparticle Quantum Scattering with Applications to Nuclear, Atomic and Molecular Physics, edited by D. G. Truhlar and B. Simon (Springer, New York, 1996).

    Google Scholar 

  26. C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950).

    Google Scholar 

  27. J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations. (Birkhauser, Boston, 1985).

    Google Scholar 

  28. S.-W. Huang and T. Carrington, Chem. Phys. Lett. 312, 311 (1999).

    Article  CAS  Google Scholar 

  29. D. Xie, R. Chen, and H. Guo, J. Chem. Phys. 112, 5263 (2000).

    CAS  Google Scholar 

  30. V. A. Mandelshtam and T. Carrington, Phys. Rev. E 65, 028701 (2002).

    Google Scholar 

  31. R. Chen and H. Guo, J. Chem. Phys. 119, 5762 (2003).

    CAS  Google Scholar 

  32. Resonances in Electron-Molecule Scattering, van der Waals Complexes, and Reactive Chemical Dynamics, edited by D. G. Truhlar (ACS, Washington D.C., 1984).

    Google Scholar 

  33. G. Jolicard and E. J. Austin, Chem. Phys. Lett. 121, 106 (1985).

    Article  CAS  Google Scholar 

  34. N. Moiseyev, Isreal J. Chem. 31,311 (1991).

    CAS  Google Scholar 

  35. M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995).

    Article  CAS  Google Scholar 

  36. V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 106, 5085 (1997).

    Article  CAS  Google Scholar 

  37. V. A. Mandelshtam and H. S. Taylor, Phys. Rev. Lett. 78, 3274 (1997).

    Article  CAS  Google Scholar 

  38. V. A. Mandelshtam and H. S. Taylor, J. Chem. Phys. 107, 6756 (1997).

    Article  CAS  Google Scholar 

  39. R. Chen and H. Guo, Chem. Phys. Lett. 279, 252 (1997).

    CAS  Google Scholar 

  40. R. Chen and H. Guo, J. Chem. Phys. 111, 464 (1999).

    CAS  Google Scholar 

  41. G. Li and H. Guo, Chem. Phys. Lett. 336, 143 (2001).

    CAS  Google Scholar 

  42. G. Li and H. Guo, Chem. Phys. Lett. 347, 443 (2001).

    CAS  Google Scholar 

  43. A. Neumaier and V. A. Mandelshtam, Phys. Rev. Lett. 86, 5031 (2001).

    Article  CAS  Google Scholar 

  44. W. H. Miller, J. Chem. Phys. 61,1823 (1974).

    CAS  Google Scholar 

  45. W. H. Miller, S. D. Schwartz, and J. W. Tromp, J. Chem. Phys. 79, 4889 (1983).

    CAS  Google Scholar 

  46. T. Seideman and W. H. Miller, J. Chem. Phys. 96, 4412 (1992).

    Article  CAS  Google Scholar 

  47. T. Seideman and W. H. Miller, J. Chem. Phys. 97, 2499 (1992).

    Article  CAS  Google Scholar 

  48. U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993).

    CAS  Google Scholar 

  49. D. H. Zhang and J. C. Light, J. Chem. Phys. 104, 6184 (1996).

    CAS  Google Scholar 

  50. K. M. Forsythe and S. K. Gray, J. Chem. Phys. 112, 2623 (2000).

    Article  CAS  Google Scholar 

  51. H. O. Karlsson and O. Goscinski, J. Phys. Chem. 105A, 2599 (2001).

    Google Scholar 

  52. S. M. Miller and T. Carrington, Chem. Phys. Lett. 267, 417 (1997).

    Article  CAS  Google Scholar 

  53. S. Garashchuk and D. J. Tannor, J. Chem. Phys. 110, 2761 (1999).

    Article  CAS  Google Scholar 

  54. D. Xie, S. Li, and H. Guo, J. Chem. Phys. 116, 6391 (2002).

    CAS  Google Scholar 

  55. D. J. Tannor and D. E. Weeks, J. Chem. Phys. 98, 3884 (1993).

    Article  CAS  Google Scholar 

  56. D. J. Kouri, Y. Huang, W. Zhu, and D. K. Hoffman, J. Chem. Phys. 100, 3662 (1994).

    Article  CAS  Google Scholar 

  57. S. S. Iyengar, D. J. Kouri, and D. K. Hoffman, Theo. Chem. Acc. 104, 471 (2000).

    CAS  Google Scholar 

  58. V. A. Mandelshtam, J. Chem. Phys. 108, 9999 (1998).

    CAS  Google Scholar 

  59. G.-J. Kroes and D. Neuhauser, J. Chem. Phys. 105, 8690 (1996).

    CAS  Google Scholar 

  60. A. J. H. M. Meijer, E. M. Goldfield, S. K. Gray, and G. G. Balint-Kurti, Chem. Phys. Lett. 293,270 (1998).

    Article  CAS  Google Scholar 

  61. H. Guo, J. Chem. Phys. 108, 2466 (1998).

    CAS  Google Scholar 

  62. H. Guo, Chem. Phys. Lett. 289, 396 (1998).

    Article  CAS  Google Scholar 

  63. S. Y. Lin and H. Guo, J. Chem. Phys. 117, 5183 (2002).

    CAS  Google Scholar 

  64. S. Y. Lin and H. Guo, Chem. Phys. 289, 191 (2003).

    Article  CAS  Google Scholar 

  65. S. Y. Lin and H. Guo, J. Phys. Chem. in press (2003).

    Google Scholar 

  66. R. Chen, G. Ma, and H. Guo, Chem. Phys. Lett. 320, 567 (2000).

    Article  CAS  Google Scholar 

  67. R. Chen, G. Ma, and H. Guo, J. Chem. Phys. 114, 4763 (2001).

    CAS  Google Scholar 

  68. P. McGuire and D. J. Kouri, J. Chem. Phys. 60, 2488 (1974).

    Article  CAS  Google Scholar 

  69. R. T. Pack, J. Chem. Phys. 60, 633 (1974).

    Article  CAS  Google Scholar 

  70. D. Neuhauser, M. Baer, R. S. Judson, and D. J. Kouri, J. Chem. Phys. 93, 312 (1990).

    CAS  Google Scholar 

  71. D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 101, 1146 (1994).

    CAS  Google Scholar 

  72. S. Y. Lin and H. Guo, J. Chem. Phys. (in press).

    Google Scholar 

  73. G. G. Balint-Kurti, A. Gonzalez, E. M. Goldfield, and S. K. Gray, Faraday Disc. 110, 169 (1998).

    Article  CAS  Google Scholar 

  74. S. K. Gray, C. Petrongolo, K. Drukker, and G. C. Schatz, J. Phys. Chem. 103, 9448 (1999).

    CAS  Google Scholar 

  75. B. Bussery-Honvault, P. Honvault, and J.-M. Launay, J. Chem. Phys. 115, 10701 (2001).

    Article  CAS  Google Scholar 

  76. L. Banares, F. J. Aoiz, S. A. Vazquez, T.-S. Ho, and H. Rabitz, Chem. Phys. Lett. 374, 243 (2003).

    CAS  Google Scholar 

  77. S. Y. Lin and H. Guo, J. Phys. Chem. (submitted).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Chemistry, University of New Mexico, Albuquerque, NM, 87131, USA

    H. Guo

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  1. H. Guo
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Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Perugia, Italy

    Antonio Lagana

  2. Institute of Chemistry, Chemical Research Center, Budapest, Hungary

    Gyögy Lendvay

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© 2004 Kluwer Academic Publishers

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Guo, H. (2004). Chebyshev Propagation and Applications to Scattering Problems. In: Lagana, A., Lendvay, G. (eds) Theory of Chemical Reaction Dynamics. NATO Science Series II: Mathematics, Physics and Chemistry, vol 145. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2165-8_9

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