Journal of Molecular Modeling

, Volume 18, Issue 1, pp 405–418 | Cite as

Architecture, electronic structure and stability of TM@Ge(n) (TM = Ti, Zr and Hf; n = 1-20) clusters: a density functional modeling

  • Manish Kumar
  • Nilanjana Bhattacharyya
  • Debashis Bandyopadhyay
Original Paper

Abstract

The present study reports the geometry, electronic structure and properties of neutral and anionic transition metal (TM = Ti, Zr and Hf)) doped germanium clusters containing 1 to 20 germanium atoms within the framework of linear combination of atomic orbitals density functional theory under spin polarized generalized gradient approximation. Different parameters, like, binding energy (BE), embedding energy (EE), energy gap between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO), ionization energy (IP), electron affinity (EA), chemical potential etc. of the energetically stable clusters (ground state cluster) in each size are calculated. From the variation of these parameters with the size of the clusters the most stable cluster within the range of calculation is identified. It is found that the clusters having 20 valence electrons turn out to be relatively more stable in both the neutral and the anionic series. The sharp drop in IP as the valence electron count increases from 20 to 21 in neutral cluster is in agreement with predictions of shell models. To study the vibrational nature of the clusters, IR and Raman spectrum of some selected TM@Gen (n = 15,16,17) clusters are also calculated and compared. In the end, relevance of calculated results to the design of Ge-based super-atoms is discussed.

Keywords

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

Notes

Acknowledgments

Complete computations using Gaussian 03 were performed at the cluster computing facility, Harish-Chandra Research Institute, Allahabad, UP, India (http://cluster.hri.res.in).

References

  1. 1.
    Ho KM, Shvartsberg AA, Pan B, Lu ZY, Wang CZ, Wacker JG, Fye JL, Jarrod MF (1998) Nature 392:582–585CrossRefGoogle Scholar
  2. 2.
    Wang J, Chen X, Liu JH (2008) J Phys Chem A 112:8868–8876CrossRefGoogle Scholar
  3. 3.
    Zhao WJ, Wang YX (2008) Chem Phys 352:291–296CrossRefGoogle Scholar
  4. 4.
    Jarrold MF, Constant VA (1991) Phys Rev Lett 67:2994–2997CrossRefGoogle Scholar
  5. 5.
    Benedict LX, Puzer A, Willimson AJ, Grossman JC, Galli G, Klepeis JE, Raty JY, Pankratov O (2003) Phys Rev B 68:85310–85317CrossRefGoogle Scholar
  6. 6.
    Brown WL, Freeman RR, Raghavachari K, Schluter M (1987) Science 235:860–865CrossRefGoogle Scholar
  7. 7.
    Hiura H, Miyazaki T, Kanayama T (2001) Phys Rev Lett 86:1733–1736CrossRefGoogle Scholar
  8. 8.
    Hayashi S, Kanzaya Y, Kataoka M, Nagarede T, Yamamoto K (1993) Z Phys D Atom Mol Cl 26:144–146CrossRefGoogle Scholar
  9. 9.
    Bandyopadhyay D, Kaur P, Sen P (2010) J Phys Chem A 114:12986–12991CrossRefGoogle Scholar
  10. 10.
    Polman A (2002) Nat Matters 1:10–12CrossRefGoogle Scholar
  11. 11.
    Bandyopadhyay D, Sen P (2010) J Phys Chem A 114:1835–1842CrossRefGoogle Scholar
  12. 12.
    Jarrold MF, Bower JE (1992) J Chem Phys 96:9180–9190CrossRefGoogle Scholar
  13. 13.
    Kumar V, Kawazoe Y (2001) Phys Rev Lett 87:045503–045506CrossRefGoogle Scholar
  14. 14.
    Kumar V, Kawazoe Y (2002) Phys Rev Lett 88:235504–235507CrossRefGoogle Scholar
  15. 15.
    Bandyopadhyay D (2008) J Appl Phys 104:084308–084314CrossRefGoogle Scholar
  16. 16.
    Bandyopadhyay D (2009) Mol Simul 35:381–394CrossRefGoogle Scholar
  17. 17.
    Kumar M, Bandyopadhyay D (2008) Chem Phys 353:170–176CrossRefGoogle Scholar
  18. 18.
    Beck SM (1987) J Chem Phys 87:4233–4234CrossRefGoogle Scholar
  19. 19.
    Beck SM (1989) J Chem Phys 90:6306–6312CrossRefGoogle Scholar
  20. 20.
    Ohara M, Miyajima K, Pramann A, Nakajima A, Kaya K (2002) J Phys Chem A 106:3702–3705CrossRefGoogle Scholar
  21. 21.
    Han JG (2000) Chem Phys Lett 324:143–148CrossRefGoogle Scholar
  22. 22.
    Wang JL, Wang GH, Zhao JJ (2001) Phys Rev B 64:205411–305415CrossRefGoogle Scholar
  23. 23.
    Hou XJ, Gopakumar G, Lievens P, Nguyen MT (2997) J Phys Chem A 111:13544–13553CrossRefGoogle Scholar
  24. 24.
    Negishi Y, Kawamata H, Hayase T, Gomei T, Kishi R, Hayakawa F, Nakajima A, Kaya K (1997) Chem Phys Lett 269:199–207CrossRefGoogle Scholar
  25. 25.
    Bandyopadhyay D (2009) Nanotechnology 20:275202–275213CrossRefGoogle Scholar
  26. 26.
    Huheey JE, Keiter EA, Keiter RL (2000) Inorganic Chemistry: principles of structure and reactivity, 4th edn. Harper-Collins College Publisher, New YorkGoogle Scholar
  27. 27.
    Sen P, Mitas L (2003) Phys Rev B 68:155404–155407CrossRefGoogle Scholar
  28. 28.
    Reveles JU, Khanna SN (2005) Phys Rev B 72:165413–165418CrossRefGoogle Scholar
  29. 29.
    Guo LJ, Zhao G, Gu Y, Liu X, Zeng Z (2008) Phys Rev B 77:195417–195424CrossRefGoogle Scholar
  30. 30.
    Wigner E, Witmer EE (1928) Z Phys 51:859–886CrossRefGoogle Scholar
  31. 31.
    Koyasu K, Akutsu M, Mitsui M, Nakajima A (2005) J Am Chem Soc 127:4998–4999CrossRefGoogle Scholar
  32. 32.
    Kumar V (2003) Eur Phys J D 24:227–232CrossRefGoogle Scholar
  33. 33.
    Burke K, Perdew JP et al. (1998) In: Dobson JF, Vignale G, Das MP (eds) Electronic Density Functional Theory: Recent Progress and New Directions. PlenumGoogle Scholar
  34. 34.
    Perdew JP (1991) In: Ziesche P, Eschrig H (eds) Electronic Structure of solids ’91. Akademie, BerlinGoogle Scholar
  35. 35.
    Becke AD (1988) Phys Rev A 38:3098–3100CrossRefGoogle Scholar
  36. 36.
    Lee C, Yang W, Parr RG (1988) Phys Rev B 37:785–789CrossRefGoogle Scholar
  37. 37.
    Wang J, Han GJ (2005) J Chem Phys 123:064306–064321CrossRefGoogle Scholar
  38. 38.
    Han JG, Hagelberg F (2001) J Mol Struct THEOCHEM 549:165–180CrossRefGoogle Scholar
  39. 39.
    Guo P, Ren ZY, Wang F, Bian J, Han JG, Wang GH (2004) J Chem Phys 121:12265–12275CrossRefGoogle Scholar
  40. 40.
    Guo LJ, Liu X, Zhaoa GF, Luo YH (2007) J Chem Phys 126:234704–234710CrossRefGoogle Scholar
  41. 41.
    Nagendran S, Sen SS, Roesky HW, Koley D, Grubmüller H, Pal A, Herbst-Irmer R (2008) Organometallics 27:5459–5463CrossRefGoogle Scholar
  42. 42.
    Khon W, Sham LJ (1965) Phys Rev 140:A1133–A1138CrossRefGoogle Scholar
  43. 43.
    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 E.01. Gaussian, Inc, Wallingford, CTGoogle Scholar
  44. 44.
    Lu J, Nagase S (2003) Chem Phys Lett 372:394–398CrossRefGoogle Scholar
  45. 45.
    Kumar V, Kawazoe Y (2002) Appl Phys Lett 80:859–861CrossRefGoogle Scholar
  46. 46.
    Kumar V, Kawazoe Y (2007) Phys Rev B 75:155425–155435CrossRefGoogle Scholar
  47. 47.
    de Heer WA (1993) Rev Mod Phys 65:611–676CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Manish Kumar
    • 1
  • Nilanjana Bhattacharyya
    • 1
  • Debashis Bandyopadhyay
    • 1
  1. 1.Physics DepartmentBirla Institute of Technology and SciencePilaniIndia

Personalised recommendations