Adiabatic to Diabatic Transformation and Nuclear Dynamics on Diabatic Hamiltonian Constructed by Using Ab Initio Potential Energy Surfaces and Non-adiabatic Coupling Terms for Excited States of Sodium Trimer

  • Amit Kumar Paul
  • Somrita Ray
  • Satrajit Adhikari
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 23)


The non-adiabatic coupling terms (NACTs) among the electronic states 22 E and 12 A 1 of Na3 system demonstrate the numerical validity of so called “Curl Condition” and thus such states closely form a sub-Hilbert space. For this subspace, we employ the NAC terms to solve the “Adiabatic–Diabatic Transformation (ADT)” equations to obtain the functional form of the transformation angles and pave the way to construct the continuous and single valued diabatic potential energy surface matrix. Nuclear dynamics has been carried out on those diabatic surfaces to reproduce the experimental spectrum for system B of Na3 cluster and thereby, to explore the numerical validity of the theoretical development on beyond Born–Oppenheimer approach for adiabatic to diabatic transformation.


Conical Intersection Adiabatic Representation Diabatic Representation Diabatic Surface Complex Phase Factor 
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  1. 1.
    Born M, Oppenheimer JR (1927) Ann Phys (Leipzig) 84:457Google Scholar
  2. 2.
    Born M. Huang K (1954) Dynamical theory of crystal lattices. Oxford University Press, New YorkGoogle Scholar
  3. 3.
    Baer M, Niedner-Schatteburg G, Toennies JP (1989) J Chem Phys 91:4169; Baer M, Liao C-L, Xu R, Flesch GD, Nourbaksh S, Ng CY (1990) J Chem Phys 93:4845; Last I, Gilibert M, Baer M (1997) J Chem Phys 107:1451Google Scholar
  4. 4.
    Aguilon F, Sizun M, Sidis V, Billing GD, Markovic N (1996) J Chem Phys 104:4530; Sizun M, Aguilon F, Sidis V, Zenevich V, Billing GD, Markovic N (1996) Chem Phys 209:327; Grimbert D, Sidis V, Cobut V (1998) J Chem Phys 108:6331Google Scholar
  5. 5.
    Longuet-Higgins HC (1961) Adv Spectrosc (NY) 2:429Google Scholar
  6. 6.
    Longuet-Higgins HC (1975) Proc R Soc Lond Ser A 344:147CrossRefGoogle Scholar
  7. 7.
    Child MS (2002) Adv Chem Phys 124:1; Manolopoulos DE, Child MS (1999) Phys Rev Lett 82:2223Google Scholar
  8. 8.
    Herzberg G, Longuet-Higgins HC (1963) Discuss Faraday Soc 35:77CrossRefGoogle Scholar
  9. 9.
    Baer M (1975) Chem Phys Lett 35:112CrossRefGoogle Scholar
  10. 10.
    Baer M (2002) Phys Rep 358:75CrossRefGoogle Scholar
  11. 11.
    Mead CA, Truhlar DG (1979) J Chem Phys 70:2284CrossRefGoogle Scholar
  12. 12.
    Hellmann H (1937) Einfuhrang in die Quantenchemie. Franz Deutiche, Leipzig, Germany; Feynman R (1939) Phys Rev 56:340Google Scholar
  13. 13.
    Epstein ST (1954) Am J Phys 22:613CrossRefGoogle Scholar
  14. 14.
    Baer M, Billing GD (2002) The role of degenerate states in chemistry. Advances in chemical physics, vol 124. Wiley, New YorkGoogle Scholar
  15. 15.
    Baer M, Englman R (1992) Mol Phys 75:293CrossRefGoogle Scholar
  16. 16.
    Varandas AJC, Xu ZR (2000) J Chem Phys 112:2121CrossRefGoogle Scholar
  17. 17.
    Baer R, Charutz D, Kosloff R, Baer M (1996) J Chem Phys 105:9141CrossRefGoogle Scholar
  18. 18.
    Baer M (2006) Beyond Born-Oppenheimer: conical intersections and electronic nonadiabatic coupling terms. Wiley, HobokenCrossRefGoogle Scholar
  19. 19.
    Sarkar B, Adhikari S (2006) J Chem Phys 124:074101CrossRefGoogle Scholar
  20. 20.
    Sarkar B, Adhikari S (2007) Indian J Phys 81(9):925Google Scholar
  21. 21.
    Sarkar B, Adhikari S (2009) Int J Quan Chem 109:650CrossRefGoogle Scholar
  22. 22.
    Sarkar B, Adhikari S (2008) J Phys Chem A 112:9868CrossRefGoogle Scholar
  23. 23.
    Cocchini F, Upton TH, Andreoni W (1988) J Chem Phys 88:6068CrossRefGoogle Scholar
  24. 24.
    Paul AK, Sardar S, Sarkar B, Adhikari S (2009) J Chem Phys 131:124312; Paul AK, Sarkar B, Adhikari S (2010) In: Chaudhuri RK, Mekkaden MV, Raveendran AV, Narayanan AS (eds) Recent advances in spectroscopy. Astrophysics and space science proceedings. Springer, Berlin, p 63Google Scholar
  25. 25.
    Top ZH, Baer M (1977) J Chem Phys 66:1363CrossRefGoogle Scholar
  26. 26.
    Delacrétaz G, Wöste L (1985) Surf Sci 156:770CrossRefGoogle Scholar
  27. 27.
    Ernst WE, Golonzka O (2004) Phys Scr T112:27CrossRefGoogle Scholar
  28. 28.
    Meiswinkel R, Köppel H (1990) Chem Phys 144:117CrossRefGoogle Scholar
  29. 29.
    Mayer M, Cederbaum LS, Köppel H (1996) J Chem Phys 104:8932CrossRefGoogle Scholar
  30. 30.
    Alijah A, Baer M (2000) J Phys Chem A 104:389CrossRefGoogle Scholar
  31. 31.
    Werner H-J, Knowles PJ et al (2009) MOLPRO, Version 2009.1, a package of ab initio programsGoogle Scholar
  32. 32.
    Zwanziger JW, Grantt ER (1987) J Chem Phys 87:2954CrossRefGoogle Scholar
  33. 33.
    Sadygov RG, Yarkony DR (1999) J Chem Phys 110:3639CrossRefGoogle Scholar
  34. 34.
    Koizumi H, Bersuker IB (1999) Phys Rev Letts 83:3009CrossRefGoogle Scholar
  35. 35.
    Paul AK, Ray S, Mukhopadhyay D, Adhikari S (2011) Chem Phys Letts. doi:10.1016/j.cplett.2011.03.087Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Amit Kumar Paul
    • 1
  • Somrita Ray
    • 1
  • Satrajit Adhikari
    • 1
  1. 1.Indian Association for the Cultivation of ScienceKolkataIndia

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