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Van der Waals coefficients for alkali metal clusters and their size dependence

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Abstract

In this paper we employ the hydrodynamic formulation of time-dependent density functional theory to obtain the van der Waals coefficientsC 6 andC 8 of alkali metal clusters of various sizes including very large clusters. Such calculations become computationally very demanding in the orbital-based Kohn-Sham formalism, but are quite simple in the hydrodynamic approach. We show that for interactions between the clusters of the same sizes,C 6 andC 8 scale as the sixth and the eighth power of the cluster radius, respectively, and approach their classically predicted values for the large size clusters.

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References

  1. D Langbein, Theory of van der Waals attraction, in:Springer tracts in modern physics (Springer, Berlin, 1974) vol. 72

    Google Scholar 

  2. A S Amadon and W H Marlow,Phys. Rev. A43, 5483 (1991)

    ADS  Google Scholar 

  3. O Gunnarsson, S Satpathy, O Jepsen and O K Anderson,Phys. Rev. Lett. 67, 3002 (1991)

    Article  ADS  Google Scholar 

  4. Ph Lambin, A A Lucas and J-P Vigneron,Phys. Rev. B46, 1794 (1992)

    ADS  Google Scholar 

  5. J M Pacheco and W Ekardt,Phys. Rev. Lett. 68, 3694 (1992)

    Article  ADS  Google Scholar 

  6. J M Pacheco and W Ekardt,Mod. Phys. Lett. B7, 573 (1993)

    ADS  Google Scholar 

  7. A Banerjee and M K Harbola,J. Chem. Phys. 117, 7845 (2002)

    Article  ADS  Google Scholar 

  8. E K U Gross, J F Dobson and M Petersilka, Density functional theory, in:Topics in current chemistry edited by R F Nalewajski (Springer, Berlin, 1996) vol. 181

    Google Scholar 

  9. A Banerjee and M K Harbola,J. Chem. Phys. 113, 5614 (2000)

    Article  ADS  Google Scholar 

  10. M K Harbola and A Banerjee,J. Theoret. Comp. Chem. 2, 301 (2003)

    Article  Google Scholar 

  11. R M Dreizler and E K U Gross,Density functional theory: An approach to many-body problem (Springer-Verlag, Berlin, 1990)

    MATH  Google Scholar 

  12. R G Parr and W Yang,Density functional theory of atoms and molecules (Oxford, New York, 1989)

    Google Scholar 

  13. J P Perdew,Phys. Rev. Lett. 55, 1665 (1985);55, 2370(E) (1985)

    Article  ADS  Google Scholar 

  14. A D Becke,Phys. Rev. A38, 3098 (1988)

    ADS  Google Scholar 

  15. J P Perdew and Y Wang,Phys. Rev. B33, 8800 (1986)

    ADS  Google Scholar 

  16. J P Perdew, inElectronic structure of solids edited by P Ziesche and H Eschrig (Akademic-Verlag, Berlin, 1991)

    Google Scholar 

  17. Y Andersson, D C Langreth and B I Lundqvist,Phys. Rev. Lett. 76, 102 (1996)

    Article  ADS  Google Scholar 

  18. J F Dobson and B P Dinte,Phys. Rev. Lett. 76, 1780 (1996)

    Article  ADS  Google Scholar 

  19. W Kohn and D Makarov,Phys. Rev. Lett. 80, 4153 (1998)

    Article  ADS  Google Scholar 

  20. I G Kaplan,Theory of molecular interactions (Elsevier, Amsterdam, 1986)

    Google Scholar 

  21. A J Stone,The theory of intermolecular forces (Clarendon, Oxford, 1996)

    Google Scholar 

  22. A Dalgarno,Adv. Chem. Phys. 12, 143 (1967)

    Article  Google Scholar 

  23. A D Buckingham, P W Fowler and J M Hutson,Chem. Rev. 88, 963 (1988)

    Article  Google Scholar 

  24. C Fvon Weizsacker,Z. Phys. 96, 431 (1935)

    Article  ADS  Google Scholar 

  25. M K Harbola,Phys. Rev. A48, 2696 (1993)

    ADS  Google Scholar 

  26. A Banerjee and M K Harbola,Euro. Phys. J. D1, 265 (1998)

    ADS  Google Scholar 

  27. P A M Dirac,Proc. Cambridge Philos. Soc. 26, 376 (1930)

    Article  MATH  Google Scholar 

  28. O Gunnarsson and B I Lundquist,Phys. Rev. B13, 4274 (1976)

    ADS  Google Scholar 

  29. M Brack,Phys. Rev. B39, 3533 (1989)

    ADS  Google Scholar 

  30. M Brack,Rev. Mod. Phys. 65, 677 (1993) and references therein

    Article  ADS  Google Scholar 

  31. M Seidl, K-H Meiwes-Broer and M Brack,J. Chem. Phys. 95, 1295 (1991)

    Article  ADS  Google Scholar 

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Banerjee, A., Harbola, M.K. Van der Waals coefficients for alkali metal clusters and their size dependence. Pramana - J Phys 66, 423–433 (2006). https://doi.org/10.1007/BF02704395

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