Advertisement

Theoretical Chemistry Accounts

, Volume 129, Issue 3–5, pp 413–422 | Cite as

Structural and electronic trends among group 15 polyhedral fullerenes

  • Antti J. KarttunenEmail author
  • Mikko Linnolahti
  • Tapani A. Pakkanen
Regular Article

Abstract

We have investigated the structural and electronic characteristics of tetrahedral, octahedral, and icosahedral fullerenes composed of group 15 elements phosphorus, arsenic, antimony, and bismuth. Systematic quantum chemical studies at the DFT and MP2 levels of theory were performed to obtain periodic trends for the structural principles, stabilities, and electronic properties of the elemental nanostructures. Calibration calculations for polyhedral clusters with up to 20 atoms showed the applied theoretical approaches to be in good agreement with high-level CCSD(T)/cc-pVTZ results. By studying fullerenes up to P888, As540, Sb620, and Bi620, we found their structures and stabilities to converge smoothly toward their experimental bulk counterparts. The diameters of the largest studied cages were 4.8, 3.7, 4.8, and 5.1 nm for the P, As, Sb, and Bi fullerenes, respectively. Comparisons with the experimentally known allotropes of the studied elements suggest the predicted polyhedral cages to be thermodynamically stable. All studied group 15 polyhedral fullerenes were found to be semiconducting, and density of states analysis illustrated clear periodic trends in their electronic structure. Relativistic effects become increasingly important when moving from P to Bi and taking the spin–orbit effects into account by using a two-component procedure had a significant positive effect on the relative stability of bismuth clusters.

Keywords

Ab initio calculations Antimony Arsenic Bismuth Phosphorus Fullerenes 

Notes

Acknowledgments

Financial support from the Finnish Funding Agency for Technology and Innovation, European Union/European Regional Development Fund (grant 70026/08), and from the Academy of Finland is gratefully acknowledged.

Supplementary material

214_2010_874_MOESM1_ESM.txt (2.2 mb)
Cartesian coordinates of polyhedral fullerenes composed of phosphorus. (TXT 2284 kb)

References

  1. 1.
    Tenne R, Seifert G (2009) Recent progress in the study of inorganic nanotubes and fullerene-like structures. Ann Rev Mater Res 39:387–413CrossRefGoogle Scholar
  2. 2.
    Greenwood NN, Earnshaw A (1997) Chemistry of the elements. Butterworth-Heineman, OxfordGoogle Scholar
  3. 3.
    Karttunen AJ, Linnolahti M, Pakkanen TA (2008) Structural principles of polyhedral allotropes of phosphorus. ChemPhysChem 9:2550–2558CrossRefGoogle Scholar
  4. 4.
    Pyykko P, Desclaux JP (1979) Relativity and the periodic system of elements. Acc Chem Res 12:276–281CrossRefGoogle Scholar
  5. 5.
    Pyykko P (1988) Relativistic effects in structural chemistry. Chem Rev 88:563–594CrossRefGoogle Scholar
  6. 6.
    Seo DK, Hoffmann R (1999) What determines the structures of the group 15 elements? J Solid State Chem 147:26–37CrossRefGoogle Scholar
  7. 7.
    Keyes RW (1953) The electrical properties of black phosphorus. Phys Rev 92:580CrossRefGoogle Scholar
  8. 8.
    Goodman NB, Ley L, Bullett DW (1983) Valence-band structures of phosphorus allotropes. Phys Rev B 27:7440CrossRefGoogle Scholar
  9. 9.
    Gonze X, Michenaud J, Vigneron J (1990) First-principles study of As, Sb, and Bi electronic properties. Phys Rev B 41:11827CrossRefGoogle Scholar
  10. 10.
    Pyykko P (1979) Interpretation of secondary periodicity in the periodic system. J Chem Res S380–S381Google Scholar
  11. 11.
    Bernhardt TM, Stegemann B, Kaiser B, Rademann K (2003) Crystalline structures of Sb4 molecules in antimony thin films. Angew Chem Int Ed 42:199–202CrossRefGoogle Scholar
  12. 12.
    Haeser M, Schneider U, Ahlrichs R (1992) Clusters of phosphorus: a theoretical investigation. J Am Chem Soc 114:9551–9559CrossRefGoogle Scholar
  13. 13.
    Han J, Morales JA (2004) A theoretical investigation on fullerene-like phosphorus clusters. Chem Phys Lett 396:27–33CrossRefGoogle Scholar
  14. 14.
    Seifert G, Heine T, Fowler PW (2001) Inorganic nanotubes and fullerenes. Eur Phys J D At Mol Opt Plasma Phys 16:341–343Google Scholar
  15. 15.
    Moses MJ, Fettinger JC, Eichhorn BW (2003) Interpenetrating As-20 fullerene and Ni-12 icosahedra in the onion-skin [As@Ni-12@As-20](3−) ion. Science 300:778–780CrossRefGoogle Scholar
  16. 16.
    Shen M, Schaefer HF III (1994) Dodecahedral and smaller arsenic clusters: As[sub n], n = 2, 4, 12, 20. J Chem Phys 101:2261–2266CrossRefGoogle Scholar
  17. 17.
    Baruah T, Pederson MR, Zope RR, Beltrán MR (2004) Stability of Asn [n = 4, 8, 20, 28, 32, 36, 60] cage structures. Chem Phys Lett 387:476–480CrossRefGoogle Scholar
  18. 18.
    Karttunen AJ, Linnolahti M, Pakkanen TA (2007) Icosahedral and ring-shaped allotropes of arsenic. ChemPhysChem 8:2373–2378CrossRefGoogle Scholar
  19. 19.
    Nava P, Ahlrichs R (2008) Theoretical investigation of clusters of phosphorus and arsenic: fascination and temptation of high symmetries. Chem Eur J 14:4039–4045CrossRefGoogle Scholar
  20. 20.
    Sattler K, Muehlbach J, Recknagel E (1980) Generation of metal clusters containing from 2 to 500 atoms. Phys Rev Lett 45:821CrossRefGoogle Scholar
  21. 21.
    Karttunen AJ, Linnolahti M, Pakkanen TA (2007) Icosahedral and ring-shaped allotropes of phosphorus. Chem Eur J 13:5232–5237CrossRefGoogle Scholar
  22. 22.
    Li SF, Gao L, Gong XG, Guo ZX (2008) No cage, no tube: relative stabilities of nanostructures. J Phys Chem C 112:13200–13203CrossRefGoogle Scholar
  23. 23.
    Wahl B, Kloo L, Ruck M (2008) The molecular cluster [Bi10Au2](SbBi3Br9)2. Angew Chem Int Ed 47:3932–3935CrossRefGoogle Scholar
  24. 24.
    Karttunen AJ, Tanskanen JT, Linnolahti M, Pakkanen TA (2009) Structural and electronic trends among group 15 elemental nanotubes. J Phys Chem C 113:12220–12224CrossRefGoogle Scholar
  25. 25.
    Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic-behavior. Phys Rev A 38:3098–3100CrossRefGoogle Scholar
  26. 26.
    Vosko SH, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin-density calculations—a critical analysis. Can J Phys 58:1200–1211CrossRefGoogle Scholar
  27. 27.
    Perdew JP (1986) Density-functional approximation for the correlation-energy of the inhomogeneous electron-gas. Phys Rev B 33:8822–8824CrossRefGoogle Scholar
  28. 28.
    Schaefer A, Horn H, Ahlrichs R (1992) Fully optimized contracted Gaussian-basis sets for atoms Li to Kr. J Chem Phys 97:2571–2577CrossRefGoogle Scholar
  29. 29.
    Weigend F, Ahlrichs R (2005) Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: design and assessment of accuracy. Phys Chem Chem Phys 7:3297–3305CrossRefGoogle Scholar
  30. 30.
    Schafer A, Huber C, Ahlrichs R (1994) Fully optimized contracted Gaussian-basis sets of triple zeta valence quality for atoms Li to Kr. J Chem Phys 100:5829–5835CrossRefGoogle Scholar
  31. 31.
    Metz B, Stoll H, Dolg M (2000) Small-core multiconfiguration-Dirac-Hartree-Fock-adjusted pseudopotentials for post-d main group elements: application to PbH and PbO. J Chem Phys 113:2563–2569CrossRefGoogle Scholar
  32. 32.
    Eichkorn K, Treutler O, Oehm H, Haeser M, Ahlrichs R (1995) Auxiliary basis-sets to approximate coulomb potentials. Chem Phys Lett 240:283–289CrossRefGoogle Scholar
  33. 33.
    Sierka M, Hogekamp A, Ahlrichs R (2003) Fast evaluation of the Coulomb potential for electron densities using multipole accelerated resolution of identity approximation. J Chem Phys 118:9136–9148CrossRefGoogle Scholar
  34. 34.
    Eichkorn K, Weigend F, Treutler O, Ahlrichs R (1997) Auxiliary basis sets for main row atoms and transition metals and their use to approximate Coulomb potentials. Theor Chem Acc 97:119–124Google Scholar
  35. 35.
    Weigend F (2006) Accurate Coulomb-fitting basis sets for H to Rn. Phys Chem Chem Phys 8:1057–1065CrossRefGoogle Scholar
  36. 36.
    Weigend F, Haeser M (1997) RI-MP2: first derivatives and global consistency. Theor Chem Acc 97:331–340Google Scholar
  37. 37.
    Weigend F, Haeser M, Patzelt H, Ahlrichs R (1998) RI-MP2: optimized auxiliary basis sets and demonstration of efficiency. Chem Phys Lett 294:143–152CrossRefGoogle Scholar
  38. 38.
    Hattig C, Weigend F (2000) CC2 excitation energy calculations on large molecules using the resolution of the identity approximation. J Chem Phys 113:5154–5161CrossRefGoogle Scholar
  39. 39.
    Haettig C, Hellweg A, Koehn A (2006) Distributed memory parallel implementation of energies and gradients for second-order Moller-Plesset perturbation theory with the resolution-of-the-identity approximation. Phys Chem Chem Phys 8:1159–1169CrossRefGoogle Scholar
  40. 40.
    Hellweg A, Haettig C, Hoefener S, Klopper W (2007) Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn. Theor Chem Acc 117:587–597CrossRefGoogle Scholar
  41. 41.
    Woon DE, Dunning TH (1993) Gaussian-basis sets for use in correlated molecular calculations. 3. The atoms aluminum through argon. J Chem Phys 98:1358–1371CrossRefGoogle Scholar
  42. 42.
    Wilson AK, Woon DE, Peterson KA, Dunning TH (1999) Gaussian basis sets for use in correlated molecular calculations. IX. The atoms gallium through krypton. J Chem Phys 110:7667–7676CrossRefGoogle Scholar
  43. 43.
    Deglmann P, Furche F, Ahlrichs R (2002) An efficient implementation of second analytical derivatives for density functional methods. Chem Phys Lett 362:511–518CrossRefGoogle Scholar
  44. 44.
    Ahlrichs R, Baer M, Haeser M, Horn H, Koelmel C (1989) Electronic-structure calculations on workstation computers—the program system turbomole. Chem Phys Lett 162:165–169CrossRefGoogle Scholar
  45. 45.
    Armbruster MK, Weigend F, van Wuellen C, Klopper W (2008) Self-consistent treatment of spin-orbit interactions with efficient Hartree-Fock and density functional methods. Phys Chem Chem Phys 10:1748–1756CrossRefGoogle Scholar
  46. 46.
    CFOUR, Coupled-Cluster techniques for Computational Chemistry, a quantum-chemical program package by J. F. Stanton, J. Gauss, M. E. Harding, P. G. Szalay with contributions from A. A. Auer, R. J. Bartlett, U. Benedikt, C. Berger, D. E. Bernholdt, Y. J. Bomble, L. Cheng, O. Christiansen, M. Heckert, O. Heun, C. Huber, T.-C. Jagau, D. Jonsson, J. Jusélius, K. Klein, W. J. Lauderdale, D. A. Matthews, T. Metzroth, D. P. O’Neill, D. R. Price, E. Prochnow, K. Ruud, F. Schiffmann, W. Schwalbach, S. Stopkowicz, A. Tajti, J. Vázquez, F. Wang, J. D. Watts and the integral packages MOLECULE (J. Almlöf and P. R. Taylor), PROPS (P. R. Taylor), ABACUS (T. Helgaker, H. J. Aa. Jensen, P. Jørgensen, and J. Olsen), and ECP routines by A. V. Mitin and C. van Wüllen. For the current version, see http://www.cfour.de
  47. 47.
    Harding ME, Metzroth T, Gauss J, Auer AA (2008) Parallel calculation of CCSD and CCSD(T) analytic first and second derivatives. J Chem Theory Comput 4:64–74CrossRefGoogle Scholar
  48. 48.
    Chin Tang A, Qiang Huang F (1995) Stability rules of icosahedral (Ih or I) fullerenes. Chem Phys Lett 247:494–501CrossRefGoogle Scholar
  49. 49.
    Tang AuChin, Huang FuQiang (1996) Electronic structures of octahedral fullerenes. Chem Phys Lett 263:733–741CrossRefGoogle Scholar
  50. 50.
    Odom TW, Huang J, Kim P, Lieber CM (2000) Structure and electronic properties of carbon nanotubes. J Phys Chem B 104:2794–2809CrossRefGoogle Scholar
  51. 51.
    Saunders M (1991) Buckminsterfullerane—the inside story. Science 253:330–331CrossRefGoogle Scholar
  52. 52.
    Dodziuk H, Nowinski K (1996) ‘Horror vacui’ or topological in-out isomerism in perhydrogenated fullerenes: C60H60 and monoalkylated perhydrogenated fullerenes. Chem Phys Lett 249:406–412CrossRefGoogle Scholar
  53. 53.
    Linnolahti M, Karttunen AJ, Pakkanen TA (2006) Remarkably stable icosahedral fulleranes: C80H80 and C180H180. ChemPhysChem 7:1661–1663CrossRefGoogle Scholar
  54. 54.
    Linnolahti M, Kinnunen NM, Pakkanen TA (2006) Structural preferences of single-walled silica nanostructures: nanospheres and chemically stable nanotubes. Chem Eur J 12:218–224CrossRefGoogle Scholar
  55. 55.
    Kraetschmer W, Lamb LD, Fostiropoulos K, Huffman DR (1990) Solid C60: a new form of carbon. Nature 347:354–358CrossRefGoogle Scholar
  56. 56.
    Bulgakov AV, Bobrenok OF, Kosyakov VI (2000) Laser ablation synthesis of phosphorus clusters. Chem Phys Lett 320:19–25CrossRefGoogle Scholar
  57. 57.
    Bulgakov AV, Bobrenok OF, Kosyakov VI, Ozerov I, Marine W, Heden M, Rohmund F, Campbell EEB (2002) Phosphorus clusters: synthesis in the gas-phase and possible cagelike and chain structures. Phys Solid State 44:617–622CrossRefGoogle Scholar
  58. 58.
    Bulgakov AV, Bobrenok OF, Ozerov I, Marine W, Giorgio S, Lassesson A, Campbell EEB (2004) Phosphorus cluster production by laser ablation phosphorus cluster production by laser ablation. Appl Phys A Mater Sci Process 79:1369–1372Google Scholar
  59. 59.
    Sedo O, Vorac Z, Alberti M, Havel H (2004) Laser ablation synthesis of new phosphorus and phosphorus-sulfur clusters and their TOF mass spectrometric identification. Polyhedron 23:1199–1206CrossRefGoogle Scholar
  60. 60.
    Špalt Z, Alberti M, Peña-Méndez E, Havel J (2005) Laser ablation generation of arsenic and arsenic sulfide clusters. Polyhedron 24:1417–1424CrossRefGoogle Scholar
  61. 61.
    Derrouiche S, Loebick CZ, Pfefferle L (2010) Optimization of routes for the synthesis of bismuth nanotubes: implications for nanostructure form and selectivity. J Phys Chem C 114:3431–3440CrossRefGoogle Scholar
  62. 62.
    Li L, Yang YW, Huang XH, Li GH, Ang R, Zhang LD (2006) Fabrication and electronic transport properties of Bi nanotube arrays. Appl Phys Lett 88:103119CrossRefGoogle Scholar
  63. 63.
    Park C, Sohn H (2007) Black phosphorus and its composite for lithium rechargeable batteries. Adv Mater 19:2465–2468CrossRefGoogle Scholar
  64. 64.
    Pfitzner A (2006) Phosphorus remains exciting!. Angew Chem Int Ed 45:699–700CrossRefGoogle Scholar
  65. 65.
    Jayasekera B, Somaskandan K, Brock SL (2004) Liberation of pnicogen chains from Cu2P1.8As1.2I2: synthesis and characterization of a new allotrope of P–As. Inorg Chem 43:6902–6904CrossRefGoogle Scholar
  66. 66.
    Zhang H, Balasubramanian K (1992) Electronic structure of the group V tetramers (P4–Bi4). J Chem Phys 97:3437CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Antti J. Karttunen
    • 1
    Email author
  • Mikko Linnolahti
    • 1
  • Tapani A. Pakkanen
    • 1
  1. 1.Department of ChemistryUniversity of Eastern FinlandJoensuuFinland

Personalised recommendations