Shift of vibrational bands upon isotope substitution in molecules
A.D. Bykov, B.A. Voronin, A.S. Dudaryonok, E.R. Polovtseva
V.E. Zuev Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, Russia
Keywords: isotopic shift of vibrational levels, RayleighSchrodinger perturbation theory, summation of divergent series of perturbation theory
Abstract
Highorder RayleighSchrodinger perturbation theory and series summation by the PadeHermit 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 (O^{16}>O^{18}) substitution. However, the use of the PadeHermit 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.
