Skip to main content
SpringerLink
Log in

Multiparameter model functions in problems of approximating ab initio potentials and spectroscopic data of diatomic molecules

  • Spectroscopy of Atoms and Molecules
  • Published:
Optics and Spectroscopy Aims and scope Submit manuscript

Abstract

A new multiparameter function of the generalized Morse long-range potential is presented. All earlier similar constructions turn out to be particular cases of this new function. The operation technique for this function is described. Using realistic test examples (ab initio potentials of the K2 molecule and “experimental” spectroscopic data calculated by them), the possibilities of this function are compared with those of the most developed form of the piecewise continuous model potential in problems of direct optimization modeling of potential functions and in problems of optimization modeling of experimental data aiming at determining potentials. A conclusion is drawn that, although the two classes of functions lead, in general, to comparable results in quality, the piecewise continuous approximant permits one to achieve a better reproduction of the modeled data in some cases. Using the available collection of experimental data, parameters of the piecewise continuous approximant were determined for the potentials of the 1 g (33Π g ) and a 3Σ + u states of the Cs2 molecule, for which we previously constructed potentials in the form of a generalized Morse function (J. Chem. Phys. 135, 024303 (2011)).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. D. Landau and E. M. Lifshits, Quantum Mechanics: Nonrelativistic Theory (Nauka, Moscow, 1989).

    Google Scholar 

  2. S. Flügge, Practical Quantum Mechanics (Springer, Berlin, 1971), Vol. 1.

    Book  Google Scholar 

  3. I. G. Kaplan, Introduction to the Theory of Molecular Interactions (Nauka, Moscow, 1982).

    Google Scholar 

  4. J. L. Dunham, Phys. Rev. 41, 721 (1932).

    Article  ADS  Google Scholar 

  5. G. Simmons, R. G. Parr, and J. M. Finlan, J. Chem. Phys. 59, 3229 (1973).

    Article  ADS  Google Scholar 

  6. J. M. Finlan and G. Simmons, J. Mol. Spectrosc. 57, 1 (1975).

    Article  ADS  Google Scholar 

  7. J. F. Ogilvie, Proc. Roy. Soc. (London) Ser. A 378, 287 (1981).

    Article  ADS  Google Scholar 

  8. A. A. Šurkus, R. J. Rakauskas, and A. B. Bolotin, Chem. Phys. Lett. 105, 291 (1984).

    Article  ADS  Google Scholar 

  9. M. Molski, J. Mol. Spectrosc. 193, 244 (1999).

    Article  ADS  Google Scholar 

  10. C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knöckel, and E. Tiemann, Phys. Rev. A: 63, 012710 (2000).

    Article  ADS  Google Scholar 

  11. J. S. Wright, J. Chem. Soc. Faraday Trans. 84, 219 (1988).

    Article  Google Scholar 

  12. R. Rydberg, Z. Phys. 73, 376 (1932).

    Article  ADS  Google Scholar 

  13. R. Rydberg, Z. Phys. 80, 514 (1933).

    Article  ADS  Google Scholar 

  14. O. Klein, Z. Phys. 76, 226 (1932).

    Article  ADS  MATH  Google Scholar 

  15. A. L. G. Rees, Proc. Phys. Soc. (London) 59, 998 (1947).

    Article  ADS  MATH  Google Scholar 

  16. W. C. Stwalley and H. Wang, J. Mol. Spectrosc. 195, 194 (1999).

    Article  ADS  Google Scholar 

  17. C. Strauss, T. Takekoshi, F. Lang, K. Winkler, R. Grimm, J. H. Denschlag, and E. Tieman, Phys. Rev. A: 82, 052514 (2010).

    Article  ADS  Google Scholar 

  18. P. G. Hajigeorgiou and R. J. Le Roy, J. Chem. Phys. 112, 3949 (2000).

    Article  ADS  Google Scholar 

  19. R. J. Le Roy, Y. Huang, and C. Jary, J. Chem. Phys. 125, 164310 (2006).

    Article  ADS  Google Scholar 

  20. R. J. Le Roy and R. D. E. Henderson, Mol. Phys. 105, 663 (2007).

    Article  ADS  Google Scholar 

  21. V. B. Sovkov, V. S. Ivanov, L. Li, Z. Chen, and S. Magnier, J. Mol. Spectrosc. 236, 35 (2006).

    Article  ADS  Google Scholar 

  22. F. Xie, V. B. Sovkov, A. M. Lyyra, D. Li, S. Ingram, J. Bai, V. S. Ivanov, S. Magnier, and L. Li, J. Chem. Phys. 130, 051102 (2009).

    Article  ADS  Google Scholar 

  23. B. Besser, V. B. Sovkov, J. Bai, E. H. Ahmed, C. C. Tsai, F. Xie, L. Li, V. S. Ivanov, and A. M. Lyyra, J. Chem. Phys. 131, 094505 (2009).

    Article  ADS  Google Scholar 

  24. F. Xie, L. Li, D. Li, V. B. Sovkov, K. V. Minaev, V. S. Ivanov, A. M. Lyyra, and S. Magnier, J. Chem. Phys. 135, 024303 (2011).

    Article  ADS  Google Scholar 

  25. A. Pashov, O. Docenko, M. Tamanis, R. Ferber, H. Knöckel, and E. Tieman, Phys. Rev. A: 76, 022511 (2007).

    Article  ADS  Google Scholar 

  26. B. M. Smirnov and M. I. Chibisov, Zh. Eksp. Teor. Fiz. 48, 939 (1965).

    Google Scholar 

  27. U. Wolf and E. Tiemann, Chem. Phys. Lett. 139, 191 (1987).

    Article  ADS  Google Scholar 

  28. E. Tiemann, Mol. Phys. 65, 359 (1988).

    Article  ADS  Google Scholar 

  29. A. Pashov, W. Jastrz bsi, and P. Kowalczyk, Comput. Phys. Commun. 128, 622 (2000).

    Article  ADS  MATH  Google Scholar 

  30. A. Pashov, W. Jastrz bski, and P. Kowalczyk, J. Chem. Phys. 113, 6624 (2000).

    Article  ADS  Google Scholar 

  31. A. Pashov, W. Jastrz bski, and P. Kowalczyk, J. Mol. Spectrosc. 203, 264 (2000).

    Article  ADS  Google Scholar 

  32. M. Molski and J. Konarski, Int. J. Quantum Chem. 90, 183 (2002).

    Article  Google Scholar 

  33. S. Magnier and P. Millié, Phys. Rev. A: 54, 204 (1996).

    Article  ADS  Google Scholar 

  34. V. B. Sovkov, V. S. Ivanov, D. Li, F. Xie, and L. Li, Opt. Spectrosc. 103(5), 723 (2007).

    Article  ADS  Google Scholar 

  35. L. Li and R. W. Field, J. Phys. Chem. 87, 3020 (1983).

    Article  Google Scholar 

  36. L. Li and A. M. Lyyra, Spectrochim. Acta, Part A 55, 2147 (1999).

    Article  ADS  Google Scholar 

  37. E. Ahmed, A. M. Lyyra, L. Li, V. S. Ivanov, V. B. Sovkov, and S. Magnier, J. Mol. Spectrosc. 229, 122 (2005).

    Article  ADS  Google Scholar 

  38. E. Ahmed, A. M. Lyyra, F. Xie, D. Li, Y. Chu, L. Li, V. S. Ivanov, V. B. Sovkov, and S. Magnier, J. Mol. Spectrosc. 234, 41 (2005).

    Article  ADS  Google Scholar 

  39. F. Xie, D. Li, Y. Chu, L. Li, S. Magnier, V. B. Sovkov, and V. S. Ivanov, J. Phys. Chem. A 110, 11260 (2006).

    Article  Google Scholar 

  40. D. Li, F. Xie, Y. Chu, L. Li, S. Magnier, V. B. Sovkov, and V. S. Ivanov, Chem. Phys. 332, 10 (2007).

    Article  ADS  Google Scholar 

  41. D. Li, F. Xie, L. Li, V. B. Sovkov, V. S. Ivanov, E. Ahmed, A. M. Lyyra, J. Huennekens, and S. Magnier, J. Chem. Phys. 126, 194314 (2007).

    Article  ADS  Google Scholar 

  42. S. Sainis, Ph. D. Thesis (Yale University, 2005).

  43. T. Bergeman and D. de Mille, Private Communication (2008).

  44. D. Li, F. Xie, L. Li, S. Magnier, V. B. Sovkov, and V. S. Ivanov, Chem. Phys. Lett. 441, 39 (2007).

    Article  ADS  Google Scholar 

  45. P. J. Leo, C. J. Williams, and P. S. Julienne, Phys. Rev. Lett. 85, 2721 (2000).

    Article  ADS  Google Scholar 

  46. S. H. Patil and K. T. Tang, J. Chem. Phys. 106, 2298 (1997).

    Article  ADS  Google Scholar 

  47. N. Vanhaecke, C. Lisdat, B. T’Jampens, D. Comparat, A. Crubellier, and P. Pillet, Eur. Phys. J. D 28, 351 (2004).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, 198504, Russia

    V. B. Sovkov, V. S. Ivanov, K. V. Minaev & M. S. Aleksandrov

Authors
  1. V. B. Sovkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. S. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. V. Minaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. S. Aleksandrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. B. Sovkov.

Additional information

Original Russian Text © V.B. Sovkov, V.S. Ivanov, K.V. Minaev, M.S. Aleksandrov, 2013, published in Optika i Spektroskopiya, 2013, Vol. 114, No. 2, pp. 185–195.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sovkov, V.B., Ivanov, V.S., Minaev, K.V. et al. Multiparameter model functions in problems of approximating ab initio potentials and spectroscopic data of diatomic molecules. Opt. Spectrosc. 114, 167–176 (2013). https://doi.org/10.1134/S0030400X13020288

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0030400X13020288

Keywords

Search

Navigation