Method for studying diatomic rovibrational spectra at a given vibrational state

  • Yi Zhang
  • WeiGuo SunEmail author
  • Jia Fu
  • QunChao Fan
  • Jie Ma
  • LianTuan Xiao
  • SuoTang Jia


An algebraic method for rotational energies at a given vibrational state (AMr(v)) is proposed in this study in order to obtain unknown high-lying rovibrational energies. Applications of this method to the ground electronic state X1Σ+ of CO and the excited state C1Σ+ of 39K7Li molecules show the following: (1) the AMr(v) can give the rational upper limit \(\overline J \) of a rotational quantum number of a diatomic electronic state; (2) the full AMr(v) rovibrational energies {EυJ}υ} of given vibrational states not only reproduce all known experimental data excellently but also predict precisely the values of all high-lying rovibrational energies, which may not be available experimentally.


rovibrational energies diatomic systems algebraic method 

Supplementary material

11433_2018_9311_MOESM1_ESM.pdf (4.7 mb)
A novel method to study the diatomic rovibrational spectra at given vibrational state


  1. 1.
    C. Puzzarini, M. P. de Lara-Castells, R. Tarroni, P. Palmieri, and J. Domaison, Phys. Chem. Chem. Phys. 1, 3955 (1999).CrossRefGoogle Scholar
  2. 2.
    R. Wynar, R. S. Freeland, D. J. Han, C. Ryu, and D. J. Heinzen, Science 287, 1016 (2000).CrossRefGoogle Scholar
  3. 3.
    D. Demille, and E. R. Hudson, Nat. Phys. 4, 911 (2008).CrossRefGoogle Scholar
  4. 4.
    B. Xiao, S. Kado, S. Kajita, and D. Yamasaki, Plasma Phys. Control. Fusion 46, 653 (2004).CrossRefGoogle Scholar
  5. 5.
    M. Mladenovic, Spectrochim. Acta Part A-Mol. Biomol. Spectr. 58, 809 (2002).CrossRefGoogle Scholar
  6. 6.
    T. J. Martínez, M. Ben-Nun, and R. D. Levine, J. Phys. Chem. A 101, 6389 (1997).CrossRefGoogle Scholar
  7. 7.
    P. D. Kleiber, J. Cooper, K. Burnett, C. V. Kunasz, and M. G. Raymer, Phys. Rev. A 27, 291 (1983).CrossRefGoogle Scholar
  8. 8.
    P. Staanum, A. Pashov, H. Knöckel, and E. Tiemann, Phys. Rev. A 75, 042513 (2007).CrossRefGoogle Scholar
  9. 9.
    V. Bednarska, I. Jackowska, W. Jastrzebski, and P. Kowalczyk, J. Mol. Spectr. 189, 244 (1998).CrossRefGoogle Scholar
  10. 10.
    G. Lazarov, A. M. Lyyra, and L. Li, J. Mol. Spectr. 205, 73 (2001).CrossRefGoogle Scholar
  11. 11.
    J. T. Kim, H. Wang, J. T. Bahns, and W. C. Stwalley, J. Mol. Spectr. 181, 389 (1997).CrossRefGoogle Scholar
  12. 12.
    M. Korek, and H. Kobeissi, Can. J. Chem. 71, 313 (1993).CrossRefGoogle Scholar
  13. 13.
    M. Korek, and H. Kobeissi, J. Comput. Chem. 13, 1103 (1992).CrossRefGoogle Scholar
  14. 14.
    J. A. Coxon, and P. G. Hajigeorgiou, J. Chem. Phys. 132, 094105 (2010).CrossRefGoogle Scholar
  15. 15.
    M. Korek, and A. R. Allouche, Chem. Phys. 189, 33 (2001).Google Scholar
  16. 16.
    A. Shayesteh, R. J. Le Roy, T. D. Varberg, and P. F. Bernath, J. Mol. Spectr. 237, 87 (2006).CrossRefGoogle Scholar
  17. 17.
    W. Sun, Y. Zhang, Q. Fan, H. Feng, J. Fu, H. Li, J. Ma, L. Xiao, and S. Jia, Spectrochim. Acta Part A-Mol. Biomol. Spectr. 132, 32 (2014).CrossRefGoogle Scholar
  18. 18.
    J. L. Dunham, Phys. Rev. 41, 721 (1932).CrossRefGoogle Scholar
  19. 19.
    G. Herzberg, and S. Mrozowski, Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules (D. Van Nostrand Company, New York, 1950), p. 273.Google Scholar
  20. 20.
    W. Sun, S. Hou, H. Feng, and W. Ren, J. Mol. Spectr. 215, 93 (2002).CrossRefGoogle Scholar
  21. 21.
    Y. Zhang, W. Sun, J. Fu, Q. Fan, J. Ma, L. Xiao, S. Jia, H. Feng, and H. Li, J. Quant. Spectr. Radiat. Transfer 120, 81 (2013).CrossRefGoogle Scholar
  22. 22.
    Y. Zhang, W. Sun, J. Fu, Q. Fan, J. Ma, L. Xiao, S. Jia, H. Feng, and H. Li, Spectrochim. Acta Part A-Mol. Biomol. Spectr. 117, 442 (2014).CrossRefGoogle Scholar
  23. 23.
    K. Xu, Advanced Atomic and Molecular Physics (Science Press, Beijing, 2011), p. 150.Google Scholar
  24. 24.
    A. P. Mishra, B. J. Shetty, and R. J. Kshirsagar, J. Mol. Spectr. 232, 296 (2005).CrossRefGoogle Scholar
  25. 25.
    A. Grochola, P. Kowalczyk, W. Jastrzebski, P. Crozet, and A. J. Ross, Acta Phys. Pol. A 102, 729 (2002).CrossRefGoogle Scholar
  26. 26.
    Y. F. Liu, Y. Jia, D. H. Shi, and J. F. Sun, J. Quant. Spectr. Radiat. Transfer 112, 2296 (2011).CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yi Zhang
    • 1
  • WeiGuo Sun
    • 2
    • 3
    Email author
  • Jia Fu
    • 2
  • QunChao Fan
    • 2
  • Jie Ma
    • 4
  • LianTuan Xiao
    • 4
  • SuoTang Jia
    • 4
  1. 1.College of Advanced Interdisciplinary StudiesNational University of Defense TechnologyChangshaChina
  2. 2.School of Science, Research Center for Advanced ComputationXihua UniversityChengduChina
  3. 3.Institute of Atomic and Molecular PhysicsSichuan UniversityChengduChina
  4. 4.State key Laboratory of Quantum Optics and Quantum Optics Devices, Laser Spectroscopy LaboratoryShanxi UniversityTaiyuanChina

Personalised recommendations