Vol. 34, issue 04, article # 1

Abstract:

High-order Rayleigh–Schrödinger perturbation theory and series summation by the Padé–Hermit approximants are used to calculate the vibrational energy levels of isotopically substituted molecules. As an example, the levels of water isotopologues are calculated. It is found that the perturbation series diverge in the cases of both hydrogen by deuterium or tritium substitution and "heavy" oxygen atom (¹⁶О–¹⁸О) substitution. However, the use of the Padé–Hermit approximants makes it possible to calculate the isotopic level shifts quite accurately for any isotope substitution, both preserving the symmetry of the molecule and reducing it.

Keywords:

isotopic shift of vibrational levels, Rayleigh–Schrödinger perturbation theory, summation of divergent series of perturbation theory

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