Optics and Spectroscopy

, Volume 107, Issue 2, pp 221–227 | Cite as

On the use of the finite difference method in a calculation of vibration-rotation energies

  • R. I. Ovsyannikov
  • P. Jensen
  • M. Yu. Tretyakov
  • S. N. Yurchenko
Spectroscopy of Atoms and Molecules
  • 62 Downloads

Abstract

The use of the finite difference method to obtain a Taylor series expansion of a potential energy function for a subsequent calculation of the rovibration energies of molecules is considered. A method is proposed that allows the stability of a finite-difference scheme to be increased against the computational inaccuracy upon numerical expansion of a multidimensional potential energy function into a high-order Taylor series. The method is based on the successive elimination of calculated expansion coefficients of a higher order in calculating the lower-order coefficients by the finite difference method. The approach is illustrated for the example of the CO and H2S molecules.

PACS numbers

33.20.Tp 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. R. Bunker and R. Jensen, Molecular Symmetry and Spectroscopy (NRC Research Press, Ottawa, 1998).Google Scholar
  2. 2.
    D. Papoušek and M. R. Aliev, Molecular Rotational-Vibrational Spectra (Elsevier, Amsterdam, 1982).Google Scholar
  3. 3.
    D. Lauvergnat and A. Nauts, J. Chem. Phys. 116, 8560 (2002).CrossRefADSGoogle Scholar
  4. 4.
    S. N. Yurchenko, W. Thiel, and P. Jensen, J. Mol. Spectrosc. 245(2), 126 (2007).CrossRefADSGoogle Scholar
  5. 5.
    N. N. Kalitkin, Numerical Methods (Nauka, Moscow, 1978) [in Russian].Google Scholar
  6. 6.
    N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods (Nauka, Moscow, 2001) [in Russian].Google Scholar
  7. 7.
    K. Nakagawa and M. Akiyama, Chem. Phys. Lett. 190, 91 (1992).CrossRefADSGoogle Scholar
  8. 8.
    O. L. Polyansky, P. Jensen, and J. Tennyson, J. Mol. Spectrosc. 178(2), 184 (1996).CrossRefADSGoogle Scholar
  9. 9.
    L. E. Snyder and T. H. Edwards, J. Mol. Spectrosc. 31, 347 (1969).CrossRefADSGoogle Scholar
  10. 10.
    J.-M. Flaud, C. Camy-Peyret, and J. W. C. Johns, Can. J. Phys. 61, 1462 (1983).ADSGoogle Scholar
  11. 11.
    L. Lechuga-Fossat, J.-M. Flaud, C. Camy-Peyret, and J. W. C. Johns, Can. J. Phys. 62, 1889 (1984).ADSGoogle Scholar
  12. 12.
    W. C. Lane, T. H. Edwards, J. R. Gillis, F. S. Bonomo, and F. J. Murcray, J. Mol. Spectrosc. 111(2), 320 (1985).CrossRefADSGoogle Scholar
  13. 13.
    L. Lechuga-Fossat, J.-M. Flaud, C. Camy-Peyret, P. Arcas, and M. Cuisenier, Mol. Phys. 61(1), 23 (1987).CrossRefADSGoogle Scholar
  14. 14.
    S. P. Belov, K. M. T. Yamada, G. Winnewisser, L. Poteau, R. Bocquet, J. Demaison, O. L. Polyansky, and M. Yu. Tretyakov, J. Mol. Spectrosc. 173(2), 380 (1995).CrossRefADSGoogle Scholar
  15. 15.
    A. D. Bykov, O. V. Naumenko, M. A. Smirnov, L. N. Sinitsa, L. R. Brown, J. Crisp, and D. Crisp, Can. J. Phys. 72, 989 (1994).ADSGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • R. I. Ovsyannikov
    • 1
    • 2
  • P. Jensen
    • 2
  • M. Yu. Tretyakov
    • 1
  • S. N. Yurchenko
    • 3
  1. 1.Institute of Applied PhysicsRussian Academy of SciencesNizhni NovgorodRussia
  2. 2.Bergische Universität WuppertalWuppertalGermany
  3. 3.Technische Universität DresdenDresdenGermany

Personalised recommendations