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

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Abstract

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 Ge n (or Cu-substituted Ge n+1) and Cu-encapsulated Ge n 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

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References

  1. Brown WL, Freeman RR, Raghavachari K, Schluter M (1987) Science 235:860–865

    Article  CAS  Google Scholar 

  2. Zhang X, Li G, Gao Z (2001) Rapid Comm Mass Spectrum 15:1573–1576

    Article  CAS  Google Scholar 

  3. Khanna SN, Rao BK, Jena P (2002) Phys Rev Lett 89:016803–016806

    Article  CAS  Google Scholar 

  4. Archibong EF, St-Amant A (1998) J Chem Phys 109:962–972

    Article  CAS  Google Scholar 

  5. Benedict LX, Puzer A, Willimson AJ, Grossman JC, Galli G, Klepeis JE, Raty JY, Pankratov O (2003) Phys Rev B 68:85310–85318

    Article  Google Scholar 

  6. Ho KM, Shvartzburg AA, Pan B, Lu ZY, Wang CZ, Wacker JG, Fye JL, Jarrold MF (1998) Nature 392:580–582

    Article  Google Scholar 

  7. Shvartzburg AA, Jarrold MF (1999) Phys Rev A 60:1235–5

    Article  Google Scholar 

  8. Jarrold MF, Bower JE (1992) J Chem Phys 96:9180–9190

    Article  CAS  Google Scholar 

  9. Kumar V, Kawazoe Y (2001) Phys Rev Lett 87:045503–045504

    Article  CAS  Google Scholar 

  10. Kumar V, Kawazoe Y (2002) Phys Rev Lett 88:235504–4

    Article  Google Scholar 

  11. Bandyopadhyay D (2009) Nanotechnology 20:275202–275212

    Article  Google Scholar 

  12. Rothlisberger U, Andreoni W, Parrinello M (1994) Phys Rev Lett 72:665–668

    Article  Google Scholar 

  13. Kaxiras E, Jackson K (1993) Phys Rev Lett 71:727–730

    Article  CAS  Google Scholar 

  14. Zdetsis AD (2007) Phys Rev B 76:075402–075405

    Article  Google Scholar 

  15. Zhang D, Ma C, Lin C (2007) J Phys Chem C 111:17099–17103

    Article  CAS  Google Scholar 

  16. Kumar V, Kawazoe Y (2007) Phys Rev B 75:155425–11

    Article  Google Scholar 

  17. Beck SM (1987) J Chem Phys 87:4233–4234

    Article  CAS  Google Scholar 

  18. Beck SM (1989) J Chem Phys 90:6306–6312

    Article  CAS  Google Scholar 

  19. Hiura H, Miyazaki T, Kanayama T (2001) Phys Rev Lett 86:1733–1736

    Article  CAS  Google Scholar 

  20. Ohara M, Miyajima K, Pramann A, Nakajima A, Kaya K (2002) J Phys Chem A 106:3702–3705

    Article  CAS  Google Scholar 

  21. Bandyopadhyay D (2008) J Appl Phys 104:084308–7

    Article  Google Scholar 

  22. Bandyopadhyay D (2009) Mol Simul 35:381–394

    Article  CAS  Google Scholar 

  23. Bandyopadhyay D, Kumar M (2008) Chem Phys 353:170–176

    Article  CAS  Google Scholar 

  24. Kumar M, Bhattacharrya N, Bandyopadhyay D (2012) J Mol Model 18:405–418

    Article  CAS  Google Scholar 

  25. Bandyopadhyay D, Kaur P, Sen P (2010) J Phys Chem A 114:12986–12991

    Article  CAS  Google Scholar 

  26. Bandyopadhyay D, Sen P (2010) J Phys Chem A 114:1835–1842

    Article  CAS  Google Scholar 

  27. Gingerich KA, Schmude RW Jr, Baba MS, Meloni G (2000) J Chem Phys 112:7443–7448

    Article  CAS  Google Scholar 

  28. Negishi Y, Kawamata H, Hayakawa F, Nakajima A, Kaya K (1998) Chem Phys Lett 294:370–376

    Article  CAS  Google Scholar 

  29. Yoshida S, Fuke K (1999) J Chem Phys 111:3880–3890

    Article  CAS  Google Scholar 

  30. Wang J, Chen X, Liu JH (2008) J Phys Chem A 112:8868–8876

    Article  CAS  Google Scholar 

  31. Han JG (2000) Chem Phys Lett 324:143–148

    Article  CAS  Google Scholar 

  32. Stroppa A, Kresse G, Continenza A (2011) Phys Rev B 83:085201–085205

    Article  Google Scholar 

  33. Zhao WJ, Wang YX (2009) J Mol Struct (THEOCHEM) 901:18–23

    Article  CAS  Google Scholar 

  34. Janssens E, Lievens P (2011) Adv Nat Sci Nanosci Nanotechnol 2:023001–023008

    Article  Google Scholar 

  35. Negishi Y, Kawamata H, Hayase T, Gomei T, Kishi R, Hayakawa F, Nakajima A, Kaya K (1997) Chem Phys Lett 269:199–207

    Article  CAS  Google Scholar 

  36. Huheey JE, Keiter EA, Keiter RL (2000) In: Inorganic chemistry: principles of structure and reactivity, 4th edn. HarperCollins, New York

  37. Sen P, Mitas L (2003) Phys Rev B 68:155404–4

    Article  Google Scholar 

  38. Reveles JU, Khanna SN (2005) Phys Rev B 72:165413–165418

    Article  Google Scholar 

  39. Wigner E, Witmer EE (1928) Z Physik 51:859–886

    Article  CAS  Google Scholar 

  40. Guo LJ, Zhao G, Gu Y, Liu X, Zeng Z (2008) Phys Rev B 77:195417–195418

    Article  Google Scholar 

  41. Koyasu K, Akutsu M, Mitsui M, Nakajima A (2005) J Am Chem Soc 127:4998–4999

    Article  CAS  Google Scholar 

  42. Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1992) Phys Rev B 46:6671–6678

    Article  CAS  Google Scholar 

  43. Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1993) Phys Rev B 48:4978–4978

    Article  CAS  Google Scholar 

  44. Perdew JP, Burke K, Wang Y (1996) Phys Rev B 54:16533–16537

    Article  CAS  Google Scholar 

  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 28–111

  46. Dunning TH Jr, Hay PJ (1976) In: Schaefer III HF (ed) Modern theoretical chemistry, vol 3. Plenum, New York, pp 1–28

  47. Hay PJ, Wadt WR (1985) J Chem Phys 82:299–310

    Google Scholar 

  48. Fuentealba P, Preuss H, Stoll H, Szentpály LV (1982) Chem Phys Lett 89:418–422

    Google Scholar 

  49. Wang J, Han JG (2005) J Chem Phys 123:064306–064321

    Google Scholar 

  50. Han JG, Hagelberg F (2001) J Mol Struct (THEOCHEM) 549:165–180

    Google Scholar 

  51. Nagendran S, Sen SS, Roesky HW, Koley D, Grubmüller H, Pal A, Herbst-Irmer R (2008) Organometallics 27:5459–5463

    Google Scholar 

  52. Lombardi JR, Davis B (2002) Chem Rev 102:2431–2460

    Google Scholar 

  53. Morse MD (1993) Chemical bonding. In: The late transition metals: the nickel and copper group dimers, vol 1. JAI Inc., Greenwich

  54. Wang YS, Chao SD (2011) J Phys Chem A 115:1472–1485

    Google Scholar 

  55. Khon W, Sham LJ (1965) Phys Rev 140:A1133–A1138

  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., Wallingford

  57. de Heer WA (1993) Rev Mod Phys 65:611–676

    Google Scholar 

  58. Parr RG, Chattaraj PK (1991) J Am Chem Soc 113:1854–1855

    Google Scholar 

  59. Pearson RG (1987) J Chem Edu 64:561–567

    Google Scholar 

  60. Ayers PW, Parr RG (2008) J Chem Phys 128:184108–184116

    Google Scholar 

  61. Hati S, Datta D (1994) J Phys Chem 98:10451–10454

    Google Scholar 

  62. Ghanti TK, Ghosh SK (1994) J Phys Chem 98:9197–9201

    Google Scholar 

Download references

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).

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  1. Physics Department, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031, India

    Debashis Bandyopadhyay

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  1. Debashis Bandyopadhyay
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Correspondence to Debashis Bandyopadhyay.

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Bandyopadhyay, D. Architectures, electronic structures, and stabilities of Cu-doped Ge n clusters: density functional modeling. J Mol Model 18, 3887–3902 (2012). https://doi.org/10.1007/s00894-012-1374-7

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