A method of precise determination of the eigenvalues of energies of the molecular Hamiltonian based on high-order perturbation theory has been developed and implemented for a diatomic molecule. The proposed method makes it possible not only to obtain the energy values, but also to estimate the accuracy of their prediction and the applicability limits for the employed model. Numerical calculations have been performed for the extended Morse oscillator with corrections for the potential functions up to the sixth power of the Morse coordinate. The results obtained are compared with the results of calculation for the model of the truncated Hamiltonian matrix. The possibilities of application of the method are analyzed compared to other approaches to the determination of the potential functions for polyatomic molecules.
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References
J. M. L. Martin, T. J. Lee, P. R. Taylor, and J. P. Francois, J. Chem. Phys., 103, 2589–2602 (1995).
J. M. L. Martin, T. J. Lee, and P. R. Taylor, Chem. Phys. Lett., 205, 535–542 (1993).
J. M. L. Martin, T. J. Lee, and P. R. Taylor, J. Chem. Phys., 97, 8361–8371 (1992).
R. Koos, M. Gronovski, and P. Botschwina, J. Chem. Phys., 128, 154305 (2008).
H. Xinchuan, W. D. Schwenke, and T. J. Lee, J. Quant. Spectrosc. Radiat. Transf., 230, 222–246 (2019).
H. Xinchuan, W. D. Schwenke, and T. J. Lee, J. Quant. Spectrosc. Radiat. Transf., 225, 327–336 (2019).
H. H. Nielsen, Rev. Mod. Phys., 23, 90–136 (1951).
G. Amat, H. H. Nielsen, and G. Tarrago, Rotation-Vibration of Polyatomic Molecules, M. Dekker, Inc., New York (1971).
D. Papousek and M. R. Aliev, Molecular Vibrational-Rotational Spectra, Elsevier, Amsterdam (1982).
F. Jorgensen, Mol. Phys., 29, 1137–1164 (1975).
F. Jorgensen, T. Pedersen, and A. Chedin, Mol. Phys., 30, 1377–1395 (1975).
A. E. Cheglokov, O. N. Ulenikov, A. S. Zhilyakov, et al., J. Phys. B, 22, 997–1015 (1989).
A. Messiah, Quantum Mechanics, Vols. 1 and 2 [Russian translation], L. D. Faddeev, ed., Nauka, Moscow (1978).
L. D. Landau and F. M. Lifshits, Theoretical Physics: Textbook for High Schools in 10 Volumes, V. III. Quantum Mechanics (Nonrelativistic Theory) [in Russian], Nauka, Moscow (1989).
A. S. Davydov, Quantum Mechanics [in Russian], Nauka, Moscow (1973).
P. M. Morse, Phys. Rev., 34, 57–58 (1929).
Yu. S. Efremov, Opt. Spectrosc., 44, 198–201 (1978).
A. Bordoni and N. Manini, Quant. Chem., 107, 782–797 (2007).
P. Spirko, P. Jensen, P. R. Bunker, and A. Cejchan, J. Mol. Spectrosc., 112, 183–202 (1985).
P. Niay, P. Bernage, and G. Guelachvili, in: Congrès de Spectroscopie Moleculaire à Haute Resolution, Tours (1979).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 172–177, September, 2020.
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Bekhtereva, E.S., Gromova, O.V., Glushkov, P.A. et al. On the Method of Correct Determination of Eigenvalues of a Truncated Hamiltonian Matrix on the Example of a Morse Oscillator. Russ Phys J 63, 1639–1645 (2021). https://doi.org/10.1007/s11182-021-02216-6
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DOI: https://doi.org/10.1007/s11182-021-02216-6