Vol. 36, issue 05, article # 1

Bykov A. D., Voronin B. A. Shift of vibrational energy levels of molecules under isotopical substitution. Isotopic series and semi-empirical approach. // Optika Atmosfery i Okeana. 2023. V. 36. No. 05. P. 339–345. DOI: 10.15372/AOO20230501 [in Russian].
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The perturbation theory is applied to calculation of the vibrational energy levels of isotopically substituted molecules. Within the Born–Oppenheimer approximation, the isotopic shifts of energy levels are represented in the form of power series of small parameters, i.e., the relative change in the masses of substituted atoms. The coefficients of the series are functions of the molecular constants of only one modification of the isotopic family of a molecule. This makes it possible, having determined these coefficients either from calculation or on the basis of a semi-empirical approach from experimental data, to calculate isotopic shifts for any isotopologues, including short-lived ones. As an example, the isotopic shifts of the levels of unstable water isotopologues Н2ХО, Х = 13–15 and 19–24, with a half-life of more than 1 ms are calculated. The levels calculated are compared with the results of variational calculations with a high-precision function of the intramolecular potential energy.


isotopic series, H2O isotopologue, vibrational energy level


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