Advertisement

Photoabsorption in sodium clusters: first principles configuration interaction calculations

  • Pradip Kumar Priya
  • Deepak Kumar Rai
  • Alok ShuklaEmail author
Regular Article

Abstract

We present systematic and comprehensive correlated-electron calculations of the linear photoabsorption spectra of small neutral closed- and open-shell sodium clusters (Na n , n = 2 − 6), as well as closed-shell cation clusters (Na n +, n = 3, 5). We have employed the configuration interaction (CI) methodology at the full CI (FCI) and quadruple CI (QCI) levels to compute the ground, and the low-lying excited states of the clusters. For most clusters, besides the minimum energy structures, we also consider their energetically close isomers. The photoabsorption spectra were computed under the electric-dipole approximation, employing the dipole-matrix elements connecting the ground state with the excited states of each isomer. Our calculations were tested rigorously for convergence with respect to the basis set, as well as with respect to the size of the active orbital space employed in the CI calculations. These calculations reveal that as far as electron-correlation effects are concerned, core excitations play an important role in determining the optimized ground state geometries of various clusters, thereby requiring all-electron correlated calculations. But, when it comes to low-lying optical excitations, only valence electron correlation effects play an important role, and excellent agreement with the experimental results is obtained within the frozen-core approximation. For the case of Na6, the largest cluster studied in this work, we also discuss the possibility of occurrence of plasmonic resonance in the optical absorption spectrum.

Graphical abstract

Keywords

Clusters and Nanostructures 

Supplementary material

References

  1. 1.
    Y. Kawazoe, T. Kondow, K. Ohno, Clusters and Nanomaterials Theory and Experiment(Springer, Berlin, 2002) Google Scholar
  2. 2.
    J.A. Alonso, Structure and properties of atomic nanoclusters (Imperial Coll., London, 2005)Google Scholar
  3. 3.
    J. Jellinek, Theory of Atomic and Molecular Clusters with a Glimpse at Experiments(Springer, Berlin, 1999) Google Scholar
  4. 4.
    W.A. de Heer, Rev. Mod. Phys. 65, 611 (1993)ADSCrossRefGoogle Scholar
  5. 5.
    W. Ekardt, Metal Clusters (Wiley, New York, 1999)Google Scholar
  6. 6.
    J. Bowlan, A. Liang, W.A. de Heer, Phys. Rev. Lett. 106, 043401 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    M. Brack, Rev. Mod. Phys. 65, 677 (1993)ADSCrossRefGoogle Scholar
  8. 8.
    C. Wang, S. Pollack, M.M. Kappes, Chem. Phys. Lett. 166, 26 (1990)ADSCrossRefGoogle Scholar
  9. 9.
    K. Clemenger, Phys. Rev. B 32, 1359 (1985)ADSCrossRefGoogle Scholar
  10. 10.
    D.E. Beck, Phys. Rev. B 30, 6935 (1984)ADSCrossRefGoogle Scholar
  11. 11.
    W. Ekardt, Phys. Rev. Lett. 52, 1925 (1984)ADSCrossRefGoogle Scholar
  12. 12.
    C. Yannouleas, R.A. Broglia, M. Brack, P.F. Bortignon, Phys. Rev. Lett. 63, 255 (1989)ADSCrossRefGoogle Scholar
  13. 13.
    V. Bonačić-Kouteckỳ, J. Gaus, M. Guest, L. Češipva, J. Koutecký, Chem. Phys. Lett. 206, 528 (1993)ADSCrossRefGoogle Scholar
  14. 14.
    B.K. Rao, P. Jena, Phys. Rev. B 32, 2058 (1985)ADSCrossRefGoogle Scholar
  15. 15.
    J.L. Martins, J. Buttet, R. Car, Phys. Rev. B 31, 1804 (1985)ADSCrossRefGoogle Scholar
  16. 16.
    I. Boustani, W. Pewestorf, P. Fantucci, V. Bonačić-Kouteckỳ, J. Koutecký, Phys. Rev. B 35, 9437 (1987)ADSCrossRefGoogle Scholar
  17. 17.
    V. Bonačić-Kouteckỳ, P. Fantucci, J. Koutecký, Phys. Rev. B 37, 4369 (1988)ADSCrossRefGoogle Scholar
  18. 18.
    B.K. Rao, P. Jena, Phys. Rev. B 37, 2867 (1988)ADSCrossRefGoogle Scholar
  19. 19.
    V. Bonačić-Kouteckỳ, P. Fantucci, J. Kouteckỳ, J. Chem. Phys. 91, 3794 (1989)ADSCrossRefGoogle Scholar
  20. 20.
    V. Bonačić-Kouteckỳ, P. Fantucci, J. Koutecký, Chem. Rev. 91, 1035 (1991)CrossRefGoogle Scholar
  21. 21.
    V. Bonačić-Kouteckỳ, J. Pittner, C. Fuchs, P. Fantucci, M. Guest, J. Kouteckỳ, J. Chem. Phys. 104, 1427 (1996)ADSCrossRefGoogle Scholar
  22. 22.
    V. Bonačić-Kouteckỳ, P. Fantucci, J. Kouteckỳ, Chem. Phys. Lett. 166, 32 (1990)ADSCrossRefGoogle Scholar
  23. 23.
    U. Röthlisberger, W. Andreoni, J. Chem. Phys. 94, 8129 (1991)ADSCrossRefGoogle Scholar
  24. 24.
    S.A. Blundell, C. Guet, R.R. Zope, Phys. Rev. Lett. 84, 4826 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    M.B. Torres, L.C. Balbás, J. Phys.: Condensed Matter 14, 5795 (2002)ADSGoogle Scholar
  26. 26.
    I.A. Solov’yov, A.V. Solov’yov, W. Greiner, Phys. Rev. A 65, 053203 (2002)ADSCrossRefGoogle Scholar
  27. 27.
    S. Kümmel, M. Brack, P.G. Reinhard, Phys. Rev. B 62, 7602 (2000)ADSCrossRefGoogle Scholar
  28. 28.
    J.M. Pacheco, J.L. Martins, J. Chem. Phys. 106, 6039 (1997)ADSCrossRefGoogle Scholar
  29. 29.
    M. Moseler, H. Häkkinen, U. Landman, Phys. Rev. Lett. 87, 053401 (2001)ADSCrossRefGoogle Scholar
  30. 30.
    A. Rubio, J.A. Alonso, X. Blase, L.C. Balbás, S.G. Louie, Phys. Rev. Lett. 77, 247 (1996)ADSCrossRefGoogle Scholar
  31. 31.
    M.A.L. Marques, A. Castro, A. Rubio, J. Chem. Phys. 115, 3006 (2001)ADSCrossRefGoogle Scholar
  32. 32.
    J.O. Joswig, L.O. Tunturivuori, R.M. Nieminen, J. Chem. Phys. 128, 014707 (2008)ADSCrossRefGoogle Scholar
  33. 33.
    B.J. Wang, Y. Xu, S.H. Ke, J. Chem. Phys. 137, 054101 (2012)ADSCrossRefGoogle Scholar
  34. 34.
    G. Pal, G. Lefkidis, H.C. Schneider, W. Hübner, J. Chem. Phys. 133, 154309 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    G. Pal, Y. Pavlyukh, W. Hãbner, H.C. Schneider, Eur. Phys. J. B 79, 327 (2011)ADSCrossRefGoogle Scholar
  36. 36.
    W.R. Fredrickson, W.W. Watson, Phys. Rev. 30, 429 (1927)ADSCrossRefGoogle Scholar
  37. 37.
    A. Herrmann, M. Hofmann, S. Leutwyler, E. Schumacher, L. Wöste, Chem. Phys. Lett. 62, 216 (1979)ADSCrossRefGoogle Scholar
  38. 38.
    C.R. Chris Wang, S. Pollack, D. Cameron, M.M. Kappes, J. Chem. Phys. 93, 3787 (1990)ADSCrossRefGoogle Scholar
  39. 39.
    M. Broyer, G. Delacrétaz, P. Labastie, R. Whetten, J. Wolf, L. Wöste, Zeitschrift für Physik D Atoms, Molecules and Clusters 3, 131 (1986)ADSCrossRefGoogle Scholar
  40. 40.
    C.R.C. Wang, S. Pollack, T.A. Dahlseid, G.M. Koretsky, M.M. Kappes, J. Chem. Phys. 96, 7931 (1992)ADSCrossRefGoogle Scholar
  41. 41.
    M. Schmidt, H. Haberland, Eur. Phys. J. D 6, 109 (1999)ADSGoogle Scholar
  42. 42.
    W.D. Knight, K. Clemenger, W.A. de Heer, W.A. Saunders, Phys. Rev. B 31, 2539 (1985)ADSCrossRefGoogle Scholar
  43. 43.
    W.A. de Heer, K. Selby, V. Kresin, J. Masui, M. Vollmer, A. Chatelain, W.D. Knight, Phys. Rev. Lett. 59, 1805 (1987)ADSCrossRefGoogle Scholar
  44. 44.
    K. Selby, M. Vollmer, J. Masui, V. Kresin, W.A. de Heer, W.D. Knight, Phys. Rev. B 40, 5417 (1989)ADSCrossRefGoogle Scholar
  45. 45.
    K. Selby, V. Kresin, J. Masui, M. Vollmer, W.A. de Heer, A. Scheidemann, W.D. Knight, Phys. Rev. B 43, 4565 (1991)ADSCrossRefGoogle Scholar
  46. 46.
    M.E. Casida, J. Mol. Struc.: Theochem 914, 3 (2009)CrossRefGoogle Scholar
  47. 47.
    A. Shukla, Phys. Rev. B 65, 125204 (2002)ADSCrossRefGoogle Scholar
  48. 48.
    A. Shukla, Chem. Phys. 300, 177 (2004)ADSCrossRefGoogle Scholar
  49. 49.
    A. Shukla, Phys. Rev. B 69, 165218 (2004)ADSCrossRefGoogle Scholar
  50. 50.
    P. Sony, A. Shukla, Phys. Rev. B 75, 155208 (2007)ADSCrossRefGoogle Scholar
  51. 51.
    P. Sony, A. Shukla, Phys. Rev. B 71, 165204 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    H. Chakraborty, A. Shukla, J. Phys. Chem. A 117, 14220 (2013)CrossRefGoogle Scholar
  53. 53.
    H. Chakraborty, A. Shukla, J. Phys. Chem. 141, 164301 (2014)CrossRefGoogle Scholar
  54. 54.
    S. Sahu, A. Shukla, Nanoscale Res. Lett. 5, 714 (2010)ADSCrossRefGoogle Scholar
  55. 55.
    R. Shinde, A. Shukla, Nano Life 2, 1240004 (2012)CrossRefGoogle Scholar
  56. 56.
    R. Shinde, A. Shukla, Phys. Chem. Chem. Phys. 16, 20714 (2014)CrossRefGoogle Scholar
  57. 57.
    R. Shinde, A. Shukla, Eur. Phys. J. D 67, 98 (2013)ADSCrossRefGoogle Scholar
  58. 58.
    L.E. McMurchie, S.T. Elbert, S.R. Langhoff, E.R. Davidson, MELD package from the Quantum Chemistry Program Exchange (QCPE), Indiana University, Bloomington, Indiana, USAGoogle Scholar
  59. 59.
    J.M. Turney, A.C. Simmonett, R.M. Parrish, E.G. Hohenstein, F. Evangelista, J.T. Fermann, B.J. Mintz, L.A. Burns, J.J. Wilke, M.L. Abrams et al., WIREs Comput. Mol. Sci. 2, 556 (2012)CrossRefGoogle Scholar
  60. 60.
    K.L. Schuchardt, B.T. Didier, T. Elsethagen, L. Sun, V. Gurumoorthi, J. Chase, J. Li, T.L. Windus, J. Chem. Information and Modeling 47, 1045 (2007), pMID: 17428029CrossRefGoogle Scholar
  61. 61.
    D. Feller, J. Comput. Chem. 17, 1571 (1996)CrossRefGoogle Scholar
  62. 62.
    T. Ozaki, H. Kino, Phys. Rev. B 69, 195113 (2004)ADSCrossRefGoogle Scholar
  63. 63.
    P. Calaminici, K. Jug, A.M. Köster, J. Chem. Phys. 111, 4613 (1999)ADSCrossRefGoogle Scholar
  64. 64.
    V. Bonačić-Kouteckỳ, P. Fantucci, J. Kouteckỳ, J. Phys. Chem. 93, 3802 (1990)CrossRefGoogle Scholar
  65. 65.
    M. Schmidt, C. Ellert, W. Kronmüller, H. Haberland, Phys. Rev. B 59, 10970 (1999)ADSCrossRefGoogle Scholar
  66. 66.
    C. Ellert, M. Schmidt, T. Reiners, H. Haberland, Zeitschrift für Physik D Atoms, Molecules and Clusters 39, 317 (1997)ADSCrossRefGoogle Scholar
  67. 67.
    V.Bonačić-Kouteckỳ, P. Fantucci, J. Kouteckỳ, Phys. Rev. B 37, 4369 (1988)ADSCrossRefGoogle Scholar
  68. 68.
    V. Bonačić-Kouteckỳ, J. Pittner, C. Scheuch, M.F. Guest, J. Koutecký, J. Phys. Chem. 96, 7938 (1992)CrossRefGoogle Scholar
  69. 69.
    J. Blanc, V.B. Koutecký, M. Broyer, J. Chevaleyre, P. Dugourd, J. Koutecký, C. Scheuch, J.P. Wolf, L. Wöste, J. Chem. Phys. 96, 1793 (1992)ADSCrossRefGoogle Scholar
  70. 70.
    M.D. Deshpande, D.G. Kanhere, P.V. Panat, I. Vasiliev, R.M. Martin, Phys. Rev. A 65, 053204 (2002)ADSCrossRefGoogle Scholar
  71. 71.
    M.D. Deshpande, D.G. Kanhere, I. Vasiliev, R.M. Martin, Phys. Rev. B 68, 035428 (2003)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Pradip Kumar Priya
    • 1
  • Deepak Kumar Rai
    • 1
  • Alok Shukla
    • 1
    Email author
  1. 1.Department of PhysicsIndian Institute of Technology BombayMumbaiIndia

Personalised recommendations