Journal of Molecular Modeling

, Volume 18, Issue 8, pp 3887–3902

Architectures, electronic structures, and stabilities of Cu-doped Gen clusters: density functional modeling

Original Paper


The present study reports the geometries, electronic structures, growth behavior, and stabilities of neutral and ionized copper-doped germanium clusters containing 1–20 Ge atoms within the framework of linear combination of atomic orbitals density functional theory (DFT) under the spin-polarized generalized gradient approximation. It was found that Cu-capped Gen (or Cu-substituted Gen+1) and Cu-encapsulated Gen clusters mostly occur in the ground state at a particular cluster size (n). In order to explain the relative stabilities of the ground-state clusters, parameters such as the average binding energy per atom (BE), the embedding energy (EE), and the fragmentation energy (FE) of the clusters were calculated, and the resulting values are discussed. To explain the chemical stabilities of the clusters, parameters such as the energy gap between the highest occupied and the lowest unoccupied molecular orbitals (the HOMO–LUMO gap), the ionization energy (IP), the electron affinity (EA), the chemical potential (μ), the chemical hardness (η), and the polarizability were calculated, and the resulting values are also discussed. Natural atomic orbital (NAO) and natural bond orbital (NBO) analyses were also used to determine the electron-counting rule that should be applied to the most stable Ge10Cu cluster. Finally, the relevance of the calculated results to the design of Ge-based superatoms is discussed.


Contributions of the valance orbitals of the Ge and Cu atom(s) to the HOMO of the ground-state icosahedral Ge10Cu cluster obtained from NBO analysis. The numbers below the clusters represent the occupancies of the HOMO orbitals


Clusters and nanoclusters Binding energy Density functional theory Electron affinity Embedding energy Ionization potential 


  1. 1.
    Brown WL, Freeman RR, Raghavachari K, Schluter M (1987) Science 235:860–865CrossRefGoogle Scholar
  2. 2.
    Zhang X, Li G, Gao Z (2001) Rapid Comm Mass Spectrum 15:1573–1576CrossRefGoogle Scholar
  3. 3.
    Khanna SN, Rao BK, Jena P (2002) Phys Rev Lett 89:016803–016806CrossRefGoogle Scholar
  4. 4.
    Archibong EF, St-Amant A (1998) J Chem Phys 109:962–972CrossRefGoogle Scholar
  5. 5.
    Benedict LX, Puzer A, Willimson AJ, Grossman JC, Galli G, Klepeis JE, Raty JY, Pankratov O (2003) Phys Rev B 68:85310–85318CrossRefGoogle Scholar
  6. 6.
    Ho KM, Shvartzburg AA, Pan B, Lu ZY, Wang CZ, Wacker JG, Fye JL, Jarrold MF (1998) Nature 392:580–582CrossRefGoogle Scholar
  7. 7.
    Shvartzburg AA, Jarrold MF (1999) Phys Rev A 60:1235–5CrossRefGoogle Scholar
  8. 8.
    Jarrold MF, Bower JE (1992) J Chem Phys 96:9180–9190CrossRefGoogle Scholar
  9. 9.
    Kumar V, Kawazoe Y (2001) Phys Rev Lett 87:045503–045504CrossRefGoogle Scholar
  10. 10.
    Kumar V, Kawazoe Y (2002) Phys Rev Lett 88:235504–4CrossRefGoogle Scholar
  11. 11.
    Bandyopadhyay D (2009) Nanotechnology 20:275202–275212CrossRefGoogle Scholar
  12. 12.
    Rothlisberger U, Andreoni W, Parrinello M (1994) Phys Rev Lett 72:665–668CrossRefGoogle Scholar
  13. 13.
    Kaxiras E, Jackson K (1993) Phys Rev Lett 71:727–730CrossRefGoogle Scholar
  14. 14.
    Zdetsis AD (2007) Phys Rev B 76:075402–075405CrossRefGoogle Scholar
  15. 15.
    Zhang D, Ma C, Lin C (2007) J Phys Chem C 111:17099–17103CrossRefGoogle Scholar
  16. 16.
    Kumar V, Kawazoe Y (2007) Phys Rev B 75:155425–11CrossRefGoogle Scholar
  17. 17.
    Beck SM (1987) J Chem Phys 87:4233–4234CrossRefGoogle Scholar
  18. 18.
    Beck SM (1989) J Chem Phys 90:6306–6312CrossRefGoogle Scholar
  19. 19.
    Hiura H, Miyazaki T, Kanayama T (2001) Phys Rev Lett 86:1733–1736CrossRefGoogle Scholar
  20. 20.
    Ohara M, Miyajima K, Pramann A, Nakajima A, Kaya K (2002) J Phys Chem A 106:3702–3705CrossRefGoogle Scholar
  21. 21.
    Bandyopadhyay D (2008) J Appl Phys 104:084308–7CrossRefGoogle Scholar
  22. 22.
    Bandyopadhyay D (2009) Mol Simul 35:381–394CrossRefGoogle Scholar
  23. 23.
    Bandyopadhyay D, Kumar M (2008) Chem Phys 353:170–176CrossRefGoogle Scholar
  24. 24.
    Kumar M, Bhattacharrya N, Bandyopadhyay D (2012) J Mol Model 18:405–418CrossRefGoogle Scholar
  25. 25.
    Bandyopadhyay D, Kaur P, Sen P (2010) J Phys Chem A 114:12986–12991CrossRefGoogle Scholar
  26. 26.
    Bandyopadhyay D, Sen P (2010) J Phys Chem A 114:1835–1842CrossRefGoogle Scholar
  27. 27.
    Gingerich KA, Schmude RW Jr, Baba MS, Meloni G (2000) J Chem Phys 112:7443–7448CrossRefGoogle Scholar
  28. 28.
    Negishi Y, Kawamata H, Hayakawa F, Nakajima A, Kaya K (1998) Chem Phys Lett 294:370–376CrossRefGoogle Scholar
  29. 29.
    Yoshida S, Fuke K (1999) J Chem Phys 111:3880–3890CrossRefGoogle Scholar
  30. 30.
    Wang J, Chen X, Liu JH (2008) J Phys Chem A 112:8868–8876CrossRefGoogle Scholar
  31. 31.
    Han JG (2000) Chem Phys Lett 324:143–148CrossRefGoogle Scholar
  32. 32.
    Stroppa A, Kresse G, Continenza A (2011) Phys Rev B 83:085201–085205CrossRefGoogle Scholar
  33. 33.
    Zhao WJ, Wang YX (2009) J Mol Struct (THEOCHEM) 901:18–23CrossRefGoogle Scholar
  34. 34.
    Janssens E, Lievens P (2011) Adv Nat Sci Nanosci Nanotechnol 2:023001–023008CrossRefGoogle Scholar
  35. 35.
    Negishi Y, Kawamata H, Hayase T, Gomei T, Kishi R, Hayakawa F, Nakajima A, Kaya K (1997) Chem Phys Lett 269:199–207CrossRefGoogle Scholar
  36. 36.
    Huheey JE, Keiter EA, Keiter RL (2000) In: Inorganic chemistry: principles of structure and reactivity, 4th edn. HarperCollins, New YorkGoogle Scholar
  37. 37.
    Sen P, Mitas L (2003) Phys Rev B 68:155404–4CrossRefGoogle Scholar
  38. 38.
    Reveles JU, Khanna SN (2005) Phys Rev B 72:165413–165418CrossRefGoogle Scholar
  39. 39.
    Wigner E, Witmer EE (1928) Z Physik 51:859–886CrossRefGoogle Scholar
  40. 40.
    Guo LJ, Zhao G, Gu Y, Liu X, Zeng Z (2008) Phys Rev B 77:195417–195418CrossRefGoogle Scholar
  41. 41.
    Koyasu K, Akutsu M, Mitsui M, Nakajima A (2005) J Am Chem Soc 127:4998–4999CrossRefGoogle Scholar
  42. 42.
    Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1992) Phys Rev B 46:6671–6678CrossRefGoogle Scholar
  43. 43.
    Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1993) Phys Rev B 48:4978–4978CrossRefGoogle Scholar
  44. 44.
    Perdew JP, Burke K, Wang Y (1996) Phys Rev B 54:16533–16537CrossRefGoogle Scholar
  45. 45.
    Burke K, Perdew JP, Wang Y (1997) In: Dobson JF, Vignale G, Das MP (eds) Electronic density functional theory: recent progress and new directions. Plenum, New York, pp 28–111Google Scholar
  46. 46.
    Dunning TH Jr, Hay PJ (1976) In: Schaefer III HF (ed) Modern theoretical chemistry, vol 3. Plenum, New York, pp 1–28Google Scholar
  47. 47.
    Hay PJ, Wadt WR (1985) J Chem Phys 82:299–310Google Scholar
  48. 48.
    Fuentealba P, Preuss H, Stoll H, Szentpály LV (1982) Chem Phys Lett 89:418–422Google Scholar
  49. 49.
    Wang J, Han JG (2005) J Chem Phys 123:064306–064321Google Scholar
  50. 50.
    Han JG, Hagelberg F (2001) J Mol Struct (THEOCHEM) 549:165–180Google Scholar
  51. 51.
    Nagendran S, Sen SS, Roesky HW, Koley D, Grubmüller H, Pal A, Herbst-Irmer R (2008) Organometallics 27:5459–5463Google Scholar
  52. 52.
    Lombardi JR, Davis B (2002) Chem Rev 102:2431–2460Google Scholar
  53. 53.
    Morse MD (1993) Chemical bonding. In: The late transition metals: the nickel and copper group dimers, vol 1. JAI Inc., GreenwichGoogle Scholar
  54. 54.
    Wang YS, Chao SD (2011) J Phys Chem A 115:1472–1485Google Scholar
  55. 55.
    Khon W, Sham LJ (1965) Phys Rev 140:A1133–A1138Google Scholar
  56. 56.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Zakrzewski VG, Montgomery J A Jr, Stratmann RE, Burant JC, Dapprich S, Millam JM, Daniels AD, Kudin KN, Strain MC, Farkas O, Tomasi J, Barone V, Cossi M, Cammi R, Mennucci, B, Pomelli C, Adamo C, Clifford S, Ochterski J, Petersson GA, Ayala PY, Cui Q, Morokuma K, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Cioslowski J, Ortiz JV, Baboul AG, Stefanov BB, Liu B, Liashenko A, Piskorz P, Komaromi I, Gomperts R, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Andres JL, Gonzalez C, Head-Gordon M, Replogle ES, Pople JA (2004) Gaussian 03, revision E01. Gaussian Inc., WallingfordGoogle Scholar
  57. 57.
    de Heer WA (1993) Rev Mod Phys 65:611–676Google Scholar
  58. 58.
    Parr RG, Chattaraj PK (1991) J Am Chem Soc 113:1854–1855Google Scholar
  59. 59.
    Pearson RG (1987) J Chem Edu 64:561–567Google Scholar
  60. 60.
    Ayers PW, Parr RG (2008) J Chem Phys 128:184108–184116Google Scholar
  61. 61.
    Hati S, Datta D (1994) J Phys Chem 98:10451–10454Google Scholar
  62. 62.
    Ghanti TK, Ghosh SK (1994) J Phys Chem 98:9197–9201Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Physics DepartmentBirla Institute of Technology and SciencePilaniIndia

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