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

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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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Correspondence to R. I. Ovsyannikov.

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Original Russian Text © R.I. Ovsyannikov, P. Jensen, M.Yu. Tretyakov, S.N. Yurchenko, 2009, published in Optika i Spektroskopiya, 2009, Vol. 107, No. 2, pp. 236–243.

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Ovsyannikov, R.I., Jensen, P., Tretyakov, M.Y. et al. On the use of the finite difference method in a calculation of vibration-rotation energies. Opt. Spectrosc. 107, 221–227 (2009). https://doi.org/10.1134/S0030400X09080104

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PACS numbers

  • 33.20.Tp