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


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.

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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

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