Vol. 36, issue 05, article # 1

Abstract:

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 Н₂^ХО, 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.

Keywords:

isotopic series, H2O isotopologue, vibrational energy level

References:

1. Schwenke D.W. First principles prediction of isotopic shifts in Н₂О // J. Chem. Phys. 2003. V. 118. P. 6898. DOI: 10.1063/1.1561053.
2. Chesnokov E.N., Gorelik S.R., Gritsan N.P. Calculations of the isotopic shifts of fundamental frequencies for dihaloid silanes // Vib. Spectrosc. 2003. V. 32. P. 241–248.
3. Loëte M., Richard C., Boudon V. Isotopic relations for tetrahedral and octahedral molecules // J. Mol. Structure. 2020. V. 1206. P. 127729. DOI: 10.1016/j.molstruc.2020.127729.hal-03030693.
4. Khriachtchev L., Lundell J., Pettersson M., Tanskanen H., Rasanen M. Anomalous isotopic effect on vibrational properties of HXeOH // J. Chem. Phys. 2002. V. 116, N 12. P. 4758–4761.
5. Bykov A.D., Makushkin Yu.S., Ulenikov O.N. Izotopozameshchenie v mnogoatomnyh molekulah. Novosibirsk: Nauka, 1985. 157 p.
6. Bykov A.D., Makushkin Yu.S., Ulenikov O.N. On isotope effects in polyatomic molecules: Some comments on the method // J. Mol. Spectrosc. 1981. V. 85. P. 462–479.
7. Bykov A.D., Makushkin Yu.S., Ulenikov O.N. On the displacements of the centers of vibration-rotation bands under isotope substitution in polyatomic molecules // J. Mol. Spectrosc. 1982. V. 93, N 1. P. 46–54.
8. Bykov A.D., Makushkin Yu.S., Ulenikov O.N. On the displacements of the centers of vibration-rotation lines under isotope substitution in polyatomic molecules // J. Mol. Phys. 1984. V. 51, N 4. P. 907–918.
9. Fowler P.W. Perturbation calculation of isotope shifts in molecular properties // Mol. Phys. 1983. V. 48, N 1. P. 153–160.
10. Bykov A.D., Voronin B.A., Dudarenok A.S., Polovtseva E.R. Sdvig kolebatel'nyh polos pri izotopozameshchenii v molekulah // Optika atmosf. i okeana. 2021. V. 34, N 4. P. 237–244. DOI: 10.15372/AOO20210401.
11. Krasnoshchekov S.V., Dobrolyubov E.O., Chan S. Fundamental'nyj analiz singulyarnyh i rezonansnyh yavlenij v kolebatel'nyh poliadah molekuly diftorsililena // Opt. i spektroskop. 2020. V. 128, N 12. P. 1795–1805.
12. Krasnoshchekov S.V., Isayeva E.V., Stepanov N.F. Criteria for first- and second-order vibrational resonances and correct evaluation of the Darling–Dennison resonance coefficients using the canonical Van Vleck perturbation theory // J. Chem. Phys. 2014. V. 141, N 23. DOI: 10.1063/1.4903927.
13. Krasnoshchekov S.V., Dobrolyubov E.O., Syzgantseva M.A., Palvelev R.V. Rigorous vibrational Fermi resonance criterion revealed: Two different approaches yield the same result // Mol. Phys. 2020. V. 118, N 11. P. e1743887. DOI: 10.1080/00268976.2020.1743887.
14. Krasnoshchekov S.V., Dobrolyubov E.O., Chang X. Hypoorous acid (HOF): A molecule with a rare 1–21 vibrational resonance and (8, 3, 2) polyad structure revealed by Pade-Hermite resummation of divergent Raleigh–Schrödinger perturbation theory series // J. Quant. Spectrosc. Radiat. Transfer. 2021. V. 268. P. 107620-1–107620-15. DOI: 10.1016/j.jqsrt.2021.107620.
15. Babich L.P. Grozovye nejtrony // Uspekhi fiz. nauk. 2019. V. 189. P. 1044–1069. DOI: 10.3367/UFNr.2018.12.038501.
16. Ortega P.G. Isotope production in thunderstorms // J. Atmos. Sol.-Terr. Phys. 2020. V. 208. P. 105349. DOI: 10.1016/j.jastp.2020.105349.
17. Nemoto K., Maksimchuk A., Banerjee S., Flippo K., Mourou G., Umstadter D., Bychenkov V.Yu. Laser-triggered ion acceleration and table top isotope production // Appl. Phys. Lett. 2001. V. 78, N 5. P. 595–597.
18. Žohar A., Snoj L. On the dose fields due to activated cooling water in nuclear facilities // Prog. Nucl. Energy. 2019. V. 117, N 103042. P. 1–14. DOI: 10.1016/J.PNUCENE.2019.103042.
19. Chernov V.I., Goncharova N.M., Goldberg V.E., Dudnikova E.A., Zelchan R.V., Medvedeva A.A., Sinilkin I.G., Bragina O.D., Avgustinovich A.V., Goldberg A.V., Ermolenko R.V., Popova N.O., Simolina E.I., Vysotskaya V.V. The value of PET/CT in the diagnosis, studding and monitoring of colorectal cancer // Siberian J. Oncology. 2019. V. 18, N 4. P. 67–77. DOI: 10.21294/1814-4861-2019-18-4-67-77.
20. Tennyson J., Kostin M.A., Barletta P., Harris G.J., Polyansky O.L., Ramanlal J., Zobov N.F. DVR3D: A program suite for the calculation of rotation-vibration spectra of triatomic molecules // Comput. Phys. Commun. 2004. V. 163. P. 85–116.
21. Bubukina I.I., Zobov N.F., Polyansky O.L., Shirin S.V., Yurchenko S.N. Optimized semiempirical potential energy surface for H₂¹⁶O up to 26000 cm^-1 // Opt. Spectrosc. 2011. V. 110, N 2. P. 160–166.
22. Tennyson J., Bernath P.F., Brown L.R., Campargue A., Carleer M.R., Császár A.G., Gamache R.R., Hodges J.T., Jenouvrier A., Naumenko O.V., Polyansky O.L., Rothman L.S., Toth R.A., Vandaele A.C., Zobov N.F., Daumont L., Fazliev A.Z., Furtenbacher T., Gordon I.E., Mikhailenko S.N., Shirin S.V. IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I–Energy levels and transition wavenumbers for H₂¹⁷O and H₂¹⁸O // J. Quant. Spectrosc. Radiat. Transfer. 2009. V. 110. P. 573–596.
23. Meng Wang, Audi G., Kondev F.G., Huang W.J., Naimi S., Xing Xu. The AME2016 atomic mass evaluation (II). Tables, graphs and references // Chinese Phys. C. 2017. V. 41, N 3. P. 030003.