20-Nanogold Au20(Td) and Low-Energy Hollow Cages: Void Reactivity

  • E. S. Kryachko
  • F. Remacle
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 22)


Five 20-nanogold low-energy hollow cages are identified at the density functional level by performing a computational search on the corresponding potential energy surfaces in the different charge states. Their structures and stabilities are investigated and compared with the tetrahedral ground-state and space-filled cluster Au20(T d ). Special attention is devoted to the bifunctional reactivity of the studied Au20 hollow cages: the outer, exo-reactivity and the inner, void reactivity. The void reactivity results in endohedrality, i.e. in the existence of @-fullerenes of gold. We analyze the general features of the voids of the reported 20-nanogold fullerenes. The values of ionization potentials and electronaffinities, the molecular electrostatic potential and HOMO and LUMO patterns are invoked for this purpose and compared with those of C60 that has a similar void size. This is on the one hand. On the other, as already known in the literature, the space-filled Au20(T d ) reveals a perfect confinement for some guest atoms. The mechanism of the formation of void of Au20(T d ) that enables to trap a guest is illustrated by using a guest gold atom which is repelled by the so called ‘interior’ atoms of Au20(T d ). The computed repulsion energy provides a rough estimate of the energy needed to form a void inside this cluster.


Charge State Outer Space Gold Cluster Gold Atom Molecular Electrostatic Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was partially supported by the AIP ‘Clusters and Nanowires’ Project of the Belgian Federal Government and the EC FET proactive NanoICT Project ‘MOLOC’. One of the authors, E. S. K., gratefully thanks FNRS (Belgium) and the FRFC project 2.4.594.10.F for supporting his stay at the University of Liège and the Organizing Committee of the QSCP-XV, in particular the Chair Philip E. Hoggan, for the kind invitation, the generous hospitality, and the excellent organization. E. S. K. also thanks Benjamin Soulé de Bas, Mike J. Ford, Alessandro Fortunelli, Uzi Landman, Pekka Pyykkö, Gernot Frenking, and the reviewer for the valuable suggestions and comments.


  1. 1.
    (a) Kroto HW, Heath JR, OBrien SC, Curl RF, Smalley RE (1985) Nature (London) 318:162; (b) Heath JR, Zhang Q, O’Brien SC, Curl RF, Kroto HW, Smalley RE (1987) J Am Chem Soc 109:359; (c) Kroto HW, Heath JR, OBrien SC, Curl RF, Smalley RE (1987) Astrophys J 314:352Google Scholar
  2. 2.
    Heath JR, O’Brien SC, Zhang Q, Lui Y, Curl RF, Kroto HW, Tittel FK, Smalley RE (1985) J Am Chem Soc 107:7779CrossRefGoogle Scholar
  3. 3.
    See e. g.: (a) Elkind FD, O’Brien SC, Carl RF, Smalley RE (1988) J Am Chem Soc 110:4464; (b) Cox DX, Trevor DJ, Reckmann KC, Kaldor A (1986) J Am Chem Soc 108:2457; (c) Ross MM, Callaham JH (1991) J Phys Chem 95:5720; (d) Alvare MM, Gillan EG, Holczer K, Kaner RB, Min KS, Whetten RL (1991) J Phys Chem 95:10561; (e) Weisker T, Bohme DK, Hrusak J, Kratschmer W, Schwarz H (1991) Angew Chem Int Ed Engl 30:884; (f) Saunders M, Jimenez-Vazquez HA, Cross RJ, Poreda RJ (1993) Science 259:1428; (g) Shinohara H (2000) Rep Prog Phys 63:843; (h) Nishibori E, Takata M, Sakata M, Tanaka H, Hasegawa M, Shinohara H (2000) Chem Phys Lett 330:497; (i) Peres T, Cao BP, Cui WD, Khing A, Cross RJ, Saunders M, Lifshitz C (2001) Int J Mass Spectrom 210:241; (j) Murata Y, Murata M, Komatsu K (2003) J Am Chem Soc 125:7152; (k) Shiotani H, Ito T, Iwasa Y, Taninaka A, Shinohara H, Nishibori E, Takata M, Sakata M (2004) J Am Chem Soc 126:364; (l) Hu YH, Ruckenstein E (2005) J Am Chem Soc 127:11277; (m) Klingeler R, Kann G, Wirth I (2001) J Chem Phys 115:7215Google Scholar
  4. 4.
    (a) Cioslowski JJ (1995) Am Chem Soc 117:2553; (b) Hu YH, Ruckenstein E (2005) Am Chem Soc 127:11277; (c) Belash IT, Bronnikov AD, Zharikov OV, Palnichenko AV (1990) Synth Met 36:283; (d) Dunlap BI, Ballester JL, Schmidt PP (1992) J Phys Chem 96:9781; (e) Guha S, Nakamoto K (2005) Coord Chem Rev 249:1111; (f) Turker L, Gumus S (2006) Poly Aromat Comp 26:145; (g) Jantoljak H, Krawez N, Loa I, Tellgmann R, Campbell EEB, Litvinchuk AP, Thomsen CZ (1997) Phys Chem (Munchen) 200:157; (h) Koltover VK (2006) J Mol Liq (2006) 127:139; (i) Gromov A, Krawez N, Lassesson A, Ostrovskii DI, Campbell EEB (2002) Curr Appl Phys 2:51; (j) Popok VN, Azarko II, Gromov AV, Jönsson M, Lassesson A, Campbell EEB (2005) Solid State Commun 133:499; (k) Johnson RD, de Vries MS, Salem J, Bethune DS, Yannoni CS (1992) Nature 355:239; (l) Zhao YL, Pan XM, Zhou DF, Su ZM, Wang RS (2003) Synth Met 135:227; (m) Cioslowski J, Fleischmann ED (1991) J Chem Phys 94:3730Google Scholar
  5. 5.
    Odom TW, Nehl CL (2008) The so called 3M’s principle: make, measure, model. ACS Nano 2:612CrossRefGoogle Scholar
  6. 6.
    (a) Wang L-S, Conceicao J, Jin CM, Smalley RE (1991) Chem Phys Lett 182:5; (b) Boltalina OV, Siderov LN, Sukhanova EV, Sorokin ID (1993) Rapid Commun Mass Spectrom 7:1009; (c) Brink C, Andersen LH, Hvelplund P, Mather D, Volstad JD (1995) Chem Phys Lett 233:52; (d) Chen G, Cooks RG, Corpuz E, Scott LT (1996) J Am Soc Mass Spectrom 7:619; (e) Wang XB, Ding LF, Wang LS (1999) J Chem Phys 110:8217; (f) For current reference see also Betowski LD, Enlow M, Riddick L, Aue DH (2006) J Phys Chem 110:12927Google Scholar
  7. 7.
    Generally speaking, the existence of endohedral fullerenes alone does not mean the independent existence of the corresponding hollow cages. See e. g.: Kareev IE, Kuvychko IV, Shustova NB, Lebedkin SF, Bubnov VP, Anderson OP, Popov AA, Boltalina OV, Strauss SH (2008) Angew Chem Int Ed 47:6204Google Scholar
  8. 8.
    Heiz U, Landman U (2006) Nanocatalysis. Springer, New YorkGoogle Scholar
  9. 9.
    (a) Hammer B, Nørskov JK (1995) Nature (London) 376:238; (b) Valden M, Lai X, Goodman DW (1998) Science 281:1647; (c) Sanchez A, Abbet S, Heiz U, Schneider W-D, Häkkinen H, Barnett RN, Landman U (1999) J Phys Chem A 103:9573; (d) Schmid G, Corain B (2003) Eur J Inorg Chem 3081Google Scholar
  10. 10.
    (a) Haruta M, Kobayashi T, Sano H, Yamada N (1987) Chem Lett 405;(b) Haruta M, Yamada N, Kobayashi T, Iijima S (1989) J Catal 115:301; (c) Haruta M, Tsubota S, Kobayashi T, KageyamaH, Genet MJ, Delmon B (1993) J Catal 144:175; (d) Haruta M (1997) Catal J Today 36:153; (e) Iizuka Y, Tode T, Takao T, Yatsu KI, Takeuchi T, Tsubota S, Haruta M (1999) Catal J Today 187:50; (f) Shiga A, Haruta M (2005) Appl Catal A Gen 291:6; (g) Date M, Okumura M, Tsubota S, Haruta M (2004) Angew Chem Int Ed 43:2129Google Scholar
  11. 11.
    Gardea-Torresday JL, Parson JG, Gomez E, Peralta-Videa J, Troiani HE, Santiago P, Yacaman MJ (2002) Nano Lett 2:397CrossRefGoogle Scholar
  12. 12.
    (a) Pyykkö P (2004) Angew Chem Int Ed 43:4412; (b) Pyykkö P (2005) Inorg Chim Acta 358:4113; (c) Pyykkö P (2008) Chem Soc Rev 37:1967Google Scholar
  13. 13.
    (a) Häkkinen H, Landman U (2000) Phys Rev B 62:R2287; (b) Häkkinen H, Moseler M, Landman U (2002) Phys Rev Lett 89:033401; (c) Häkkinen H, Yoon B, Landman U, Li X, Zhai HJ, Wang LC (2003) J Phys Chem A 107:6168; (d) Bonac̆ić-Koutecký V, Burda J, Mitric R, Ge MF, Zampella G, Fantucci P (2002) J Chem Phys 117:3120; (e) Furche F, Ahlrichs R, Weis P, Jacob C, Gilb S, Bierweiler T, Kappes MM (2002) J Chem Phys 117L:6982; (f) Gilb S, Weis P, Furche F, Ahlrichs R, Kappes MM (2002) J Chem Phys 116:4094; (g) Lee HM, Ge M, Sahu BR, Tarakeshwar P, Kim KS (2003) J Phys Chem B 107:9994; (h) Wang JL, Wang GH, Zhao JJ (2002) Phys Rev B 66:035418; (i) Xiao L, Wang L (2004) Chem Phys Lett 392:452; (j) Olson RM, Varganov S, Gordon MS, Metiu H, Chretien S, Piecuch P, Kowalski K, Kucharski S, Musial M (2005) J Am Chem Soc 127:1049; (k) Koskinen P, Häkkinen H, Huber B, von Issendorff B, Moseler M (2007) Phys Rev Lett 98:015701; (l) Han VK (2006) J Chem Phys 124:024316; (m) Fernández EM, Soler JM, Garzón IL, Balbás LC (2004) Phys Rev B 70:165403; (n) Fernández EM, Soler JM, Balbás LC (2004) Phys Rev B 73:235433; (o) Remacle F, Kryachko ES (2004) Adv Quantum Chem 47:423; (p) Remacle F, Kryachko ES (2005) J Chem Phys 122:044304; (q) Johansson MP, Lechtken A, Schooss D, Kappes MM, Furche F (2008) Phys Rev A 77:053202; (r) Häkkinen H (2008) Chem Soc Rev 37:1847; (s) Huang W, Wang L-S (2009) Phys Rev Lett 102:153401Google Scholar
  14. 14.
    This term was borrowed from: (a) McAdon MH, Goddard WA III (1988) J Phys Chem 92:1352; (b) Glukhovtsev MN, Schleyer PVR (1993) Isr J Chem 33:455; (c) Danovich D, Wu W, Shaik S (1999) J Am Chem Soc 121:3165; (d) de Visser SP, Kumar D, Danovich M, Nevo N, Danovich D, Sharma PK, Wu W, Shaik S (2006) J Phys Chem A 110:8510; (e) See also Ritter SK (2007) C&EN January 29:37Google Scholar
  15. 15.
    Historically, the concept of a hollow cage is rooted to the fifth century B.C. when Democritus postulated the existence of immutable atoms characterized by size, shape, and motion. A motion of atoms requires the existence of a free, unoccupied, or empty space, or a void (nothingness) as a real entity [16]. The concept of the free space (free volume) was exploited 135 years ago by J. D. van der Waals in his PhD thesis [17] (see also Ref. [18] as current reference), as the volume which complements the volume excluded by a moleculeGoogle Scholar
  16. 16.
    (a) See e. g. the online Edition of the Encyclopaedia Britannica; (b) Also: Prigogine I, Stengers I (1984) Order out of Chaos. Mans new dialogue with nature. Bantam Books, Toronto, p 3Google Scholar
  17. 17.
    van der Waals JD (1873) Continu”ıteit van den Gas en Vloeistoftoestand (The English translation: “On the Continuity of the Gas and Liquid State”), PhD thesis. University of Leiden, LeidenGoogle Scholar
  18. 18.
    Kryachko ES (2008) Int J Quantum Chem 108:198CrossRefGoogle Scholar
  19. 19.
    (a) A Fullerene Work Party (1997) Pure Appl Chem 69:1411; (b) Chemical Abstracts, Index Guide 19921996, Appendix IV 162163; (c) Miyazaki T, Hiura H, Kanayama T (2002) Theoretical study of metal-encapsulating Si cage clusters: revealing the nature of their peculiar geometries. ArXiv: cond-mat/0208217v1. Accessed 12 Aug 2002; (d) See also: Ward J (1984) The artifacts of R. Buckminster Fuller: a comprehensive collection of his designs and drawings, vol 3. Garland, New YorkGoogle Scholar
  20. 20.
    Hoyer W, Kleinhempel R, Lörinczi A, Pohlers A, Popescu M, Sava F (2005) J Phys Condens Matter 17:S31. “The void size is defined as the diameter of the sphere of maximum size that can be introduced in an interstice without intersecting any surrounding atom defined by its radius. The position of the centre of a void is obtained by moving the starting position inside an interstice in small aleatory steps and retaining only those movements that increase the radius of the sphere that can be introduced in the interstice”Google Scholar
  21. 21.
    Bulusu S, Zeng XC (2006) J Chem Phys 125:154303CrossRefGoogle Scholar
  22. 22.
    Bulusu S, Li X, Wang L-S, Zeng XC (2006) Proc Natl Acad Sci USA 103:8326CrossRefGoogle Scholar
  23. 23.
    (a) Wang JL, Wang GH, Zhao JJ (2002) Phys Rev B 66:035418; (b) Fa W, Luo C, Dong JM (2005) Phys Rev B 72:205428Google Scholar
  24. 24.
    Pyykkö P, Runeberg N (2002) Angew Chem Int Ed 41:2174CrossRefGoogle Scholar
  25. 25.
    Gao Y, Bulusu S, Zeng XC (2005) J Am Chem Soc 127:156801Google Scholar
  26. 26.
    (a) Xing X, Yoon B, Landman U, Parks JH (2006) Phys Rev B 74:165423; (b) It is interesting to note that the hollow cage Au16 was obtained in [23b] by removing the four vertex atoms of the ground-state gold cluster Au20(T d and by a further relaxation of the resultant one. Absolutely the reverse procedure to that proposed in the present work to obtain the hollow cage VIGoogle Scholar
  27. 27.
    Li J, Li X, Zhai H-J, Wang L-S (2003) Science 299:864CrossRefGoogle Scholar
  28. 28.
    (a) Apra E, Ferrando R, Fortunelli A (2006) Phys Rev B 73:205414; (b) Ref. [13m]; (c) de Bas BS, Ford MJ, Cortie MB (2004) J Mol Struct (Theochem) 686:193; (d) Fernndez EM, Soler JM, Balbs LC (2006) Phys Rev B 73:235433; (e) Wang J, Bai J, Jellinek J, Zeng XC (2007) J Am Chem Soc 129:4110; (f) Krishnamurty S, Shafai GS, Kanhere DG, de Bas BS, Ford MJ (2007) J Phys Chem A 111:10769Google Scholar
  29. 29.
    Xing X, Yoon B, Landman U, Parks JH (2006) Phys Rev B 74:165423CrossRefGoogle Scholar
  30. 30.
    Johansson MP, Sundholm D, Vaara J (2004) Angew Chem Int Ed 43:2678CrossRefGoogle Scholar
  31. 31.
    Schmid G (2008) Chem Soc Rev 37:1909, and references thereinGoogle Scholar
  32. 32.
    Schweikhard L, Herlert A, Vogel M (1999) Philos Mag B 79:1343CrossRefGoogle Scholar
  33. 33.
    (a) The NIST,, reports only two of them dealing with the first electron affinity; (b) Taylor KJ, Pettiette-Hall CL, Cheshnovsky O, Smalley RE (1992) J Chem Phys 96:3319; (c) See also: von Issendorff B, Cheshnovsky O (2005) Annu Rev Phys Chem 56:549; (d) Bulusu S, Zeng XC (2006) J Chem Phys 125:154303Google Scholar
  34. 34.
    See e.g. Last I, Levy Y, Jortner J (2002) Proc Natl Acad Sci USA 99:9107 and references thereinGoogle Scholar
  35. 35.
    Karttunen AJ, Linnolahti M, Pakkanen TA, Pyykkö P (2008) Chem Commun 465Google Scholar
  36. 36.
    (a) King RB, Chen Z, Schleyer PVR (2004) Inorg Chem 43:4564; (b) Kryachko ES, Remacle F (2007) Int J Quantum Chem 107:2922; (c) See also: (a) Kryachko ES, Remacle F (2007) J Chem Phys 127:194305; (d) Kryachko ES, Remacle F (2008) Mol Phys 106:521; (e) Gruene P, Rayner DM, Redlich B, van der Meer AFG, Lyon JT, Meijer G, Fielicke A (2008) Science 321:674Google Scholar
  37. 37.
    Molina LM, Hammer B (2005) J Catal 233:399CrossRefGoogle Scholar
  38. 38.
    Kryachko ES, Remacle F (2010) J Phys Conf Ser 248:012026CrossRefGoogle Scholar
  39. 39.
    (a) Hay PJ, Wadt WR (1985) J Chem Phys 182:270, 299; (b) Wadt WR, Hay PJ (1985) J Chem Phys 82:284Google Scholar
  40. 40.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2004) GAUSSIAN 03 (Revision C.02). Gaussian Inc., WallingtonGoogle Scholar
  41. 41.
    (a) Curl RF, Smalley RE (1988) Science 242:1017; (b) Cai Y, Guo T, Jin C, Haufler RE, Chibante LPF, Fure J, Wang L, Alford JM, Smalley RE (1991) J Phys Chem 95:7564; (c) Wang L-M, Bulusu S, Zhai HJ, Zeng XC, Wang LS (2007) Angew Chem Int Ed 46:2915Google Scholar
  42. 42.
    (a) Gu X, Ji M, Wei SH, Gong XG (2004) Phys Rev B 70:205401; (b) Fa W, Zhou J, Luo C, Dong J (2006) Phys Rev B 73:085405; (c) Jalbout AF, Contreras-Torres FF, Prez LA, Garzn IL (2008) J Phys Chem A 112:353Google Scholar
  43. 43.
    (a) Schlyer PVR, Maerker C, Dransfeld A, Jiao H, Hommes NJRvE (1996) J Am Chem Soc 118:6317; (b) Chen Z, Wannere CS, Corminboeuf C, Puchta R, Schleyer PVR (2005) Chem Rev 105:3842Google Scholar
  44. 44.
    (a) Sanderson RT (1951) Science 114:670; (b) Idem (1955) Science 121:207; (c) Idem (1952) J Am Chem Soc 74:272Google Scholar
  45. 45.
    (a) Scrocco E, Tomasi J (1973) Topics Curr Chem 42:95; (b) Politzer P, Truhlar DG (eds) (1981) Chemical applications of atomic and molecular electrostatic potentials. Plenum, New York; (c) Pullman A, Pullman B (1981) Chemical applications of atomic and molecular electrostatic potentials. Plenum, New York, p 381; (d) Murray JS, Sen K (eds) (1996) Molecular electrostatic potentials, concepts and applications, theoretical and computational chemistry, vol 3. Elsevier, AmsterdamGoogle Scholar
  46. 46.
    (a) Tielens F, Andrés J (2007) J Phys Chem C 111:10342; (b) Wang D-L, Sun X-P, Shen H-T, Hou D-Y, Zhai Y-C (2008) Chem Phys Lett 457:366Google Scholar
  47. 47.
    (a) Claxton TA, Shirsat RN, Gadre SR (1994) J Chem Soc Chem Commun 6:731; (b) Mauser H, Hirsch A, van Eikema Hommes NJR, Clark T (1997) J Mol Model 3:415Google Scholar
  48. 48.
    (a) In fact, our statement is in concord with the following statement: “It has been generally accepted that extractable EMFs [EMF=endohedral metallofullerenes] take on endohedral structures. However, definitive proof of the structure must be performed for each EMF”. Ref. [48b]; (b) Yamada M, Akasaka T, Nagase S (2010) Acc Chem Res 43:92Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • E. S. Kryachko
    • 1
    • 2
  • F. Remacle
    • 2
  1. 1.Bogolyubov Institute for Theoretical PhysicsKiev-143Ukraine
  2. 2.Department of Chemistry, Bat. B6cUniversity of LiègeLiègeBelgium

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