Vol. 36, issue 07, article # 2

Protasevich A. E., Nikitin A. V. Kinetic energy operator for linear A2B2 type molecules in polyspherical non-orthogonal internal coordinates. // Optika Atmosfery i Okeana. 2023. V. 36. No. 07. P. 534–540. DOI: 10.15372/AOO20230702 [in Russian].
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The form of the vibrational-rotational operator of kinetic energy for linear symmetric molecules of the A2B2 type in polyspherical non-orthogonal internal (bond lengths and angles between bonds) coordinates is obtained. Non-orthogonal coordinates have advantages in calculating the wave functions of heavy linear molecules, for example, C2F2, C2Cl2, and also simplify the calculation of the intensity of the lines of the vibrational-rotational spectra of molecules of this type. This work is a continuation of the previous work [1], in which the form of the kinetic energy operator in orthogonal coordinates was obtained. To verify the obtained expressions, the lower vibrational-rotational energy levels of the acetylene molecule were calculated.


linear molecules, acetylene, kinetic energy operator, non-orthogonal coordinates, polyspherical coordinates


1. Protasevich A.E., Nikitin A.V. Operator kineticheskoi energii dlya lineinykh simmetrichnykh molekul tipa A2B2 v polisfericheskikh ortogonal'nykh koordinatakh // Optika atmosf. i okeana. 2021. V. 34, N 11. P. 860–864; Protasevich A.E., Nikitin A.V. Kinetic energy operator of linear symmetric molecules of the A2B2 type in polyspherical orthogonal coordinates region // Atmos. Ocean. Opt. 2022. V. 35, N 1. P. 14–18.
2. Corwell S.M., Handy N.C. The derivation of vibration-rotation kinetic energy operators in internal coordinates. II // Mol. Phys. 1997. V. 92, N 2. P. 317–330.
3. Urru A., Kozin I.N., Mulas G., Braams B.J., Tennyson J. Ro-vibrational spectra of C2H2 based on vibrational nuclear motion calculations // Mol. Phys. 2010. V. 108, N 15. P. 1973–1990.
4. Mladenović M. Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. II. Nonorthogonal descriptions of internal molecular geometry // J. Chem. Phys. 2000. V. 112, N 3. P. 1082–1095.
5. Mladenović M. Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. I. Orthogonal representations // J. Chem. Phys. 2000. V. 112, N 3. P. 1070–1081.
6. Varshalovich D.A., Moskalev A.N., Khersonskii V.K. Kvantovaya teoriya uglovogo momenta. L.: Nauka, 1975. 439 p.
7. Nikitin A.V., Protasevich A.E., Rodina A.A., Rey M., Tjati A., Tyuterev V.G. Ro-vibrational levels and their (ef) splitting of acetylene molecule calculated from new potential energy surfaces // J. Quant. Spectrosc. Radiat. Transfer. 2022. V. 292. P. 108349.
8. Chubb K.L., Joseph M., Franklin J., Choudhury N., Furtenbacher T., Császár A.G., Gaspard G., Oguoko P., Kelly A., Yurchenko S.N., Tennyson J., Sousa-Silva C. MARVEL analysis of the measured high-resolution rovibrational spectra of C2H2 // J. Quant. Spectrosc. Radiat. Transfer. 2018. V. 204. P. 42–55.
9. Herman M., Campargue A., El Idrissi M.I., Vander Auwera J. Vibrational Spectroscopic Database on Acetylene, X1Sg+ (12C2H2, 12C2D2 and 13C2H2) // J. Phys. Chem. Ref. Data 2003. V. 32, N 3. P. 921–1361.
10. Lyulin O.M., Perevalov V.I. ASD-1000: High-resolution, high-temperature acetylene spectroscopic databank // J. Quant. Spectrosc. Radiat. Transfer. 2017. V. 201. P. 94–103.
11. Chubb K.L., Yachmenev A., Tennyson J., Yurchenko S.N. Treating linear molecule HCCH in calculations of rotation-vibration spectra // J. Chem. Phys. 2018. V. 149, N 1. P. 014101.
12. Mellor T.M. Molecular frames for a symmetry-adapted rotational basis set // Mol. Phys. 2022. V. 120. P. e2118638.