Energetics of Multi-shell Clusters

  • Mircea Vasile Diudea
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 10)


Multi-shell clusters may be viewed as realizations of abstract structures, representing ways of the space filling, either in compact or spongy manner, by cells representing shapes of the geometrical bodies; such structures refer rather to crystal/quasi-crystal state than to molecules. This chapter brings some computational arguments in the favor of (carbon) nanostructures described within the book. Aggregation of C20 shapes within the D5 diamond, with adamantane-like “Ada”, diamantane-like “Dia”, and fivefold stars substructures were designed and computed at DFTB level of theory. Hyper-graphenes derived from the D5 substructures were also considered. Analogously, C60-based hyper-graphenes were designed and substructures computed at DFTB, HF and DFT levels of theory. Aggregation of C60 in clusters of tetrahedral or icosahedral symmetry were designed and computed at DFT or MP6 levels of theory. Networks with C60[2+2] cycloadducts, in several topologies were also computed. An atlas section illustrates the discussed multi-shell polyhedral clusters and crystal networks.

Supplementary material


  1. Adams GB, O’Keeffe M, Demkov AA, Sankey OF, Huang Y-M (1994) Wide-band-gap Si in open fourfold-coordinated clathrate structures. Phys Rev B 49(12):8048–8053CrossRefGoogle Scholar
  2. Aradi B, Hourahine B, Frauenheim T (2007) DFTB+, a sparse matrix-based implementation of the DFTB method. J Phys Chem A 111:5678–5684CrossRefGoogle Scholar
  3. Austin SJ, Fowler PW, Hansen P, Manolopoulos DE, Zheng M (1994) Fullerene isomers of C60 Kekulé counts versus stability. Chem Phys Lett 228:478–484CrossRefGoogle Scholar
  4. Benedek G, Colombo L (1996) Hollow diamonds from fullerenes. Mater Sci Forum 232:247–274CrossRefGoogle Scholar
  5. Bhattacharya D, Klein DJ, Oliva JM, Griffin LL, Alcoba DR, Massaccesi GE (2014) Icosahedral symmetry super-carborane and beyond. Chem Phys Lett 616–617:16–19CrossRefGoogle Scholar
  6. Bhattacharya D, Klein DJ, Ortiz Y (2016) The astounding buckyball buckyball. Chem Phys Lett 647:185–188CrossRefGoogle Scholar
  7. Blatov VA, Carlucci L, Ciani G, Proserpio DM (2004) Interpenetrating metal-organic and inorganic 3D networks: a computer-aided systematic investigation. Part I. Analysis of the Cambridge structural database. CrystEngComm 6:377–395CrossRefGoogle Scholar
  8. Blatov VA, Delgado-Friedrichs O, O’Keeffe M, Proserpio DM (2007) Three-periodic nets and tilings: natural tilings for nets. Acta Crystallogr Sect A Found Crystallogr 63(5):418–425CrossRefGoogle Scholar
  9. Blatov VA, O'Keeffe M, Proserpio DM (2009) Vertex-, face-, point-, Schläfli-, and Delaney-symbols in nets, polyhedra and tilings: recommended terminology. CrystEngComm 12(1):44–48CrossRefGoogle Scholar
  10. Böhme B, Guloy A, Tang Z, Schnelle W, Burkhardt U, Baitinger M, Yu G (2007) Oxidation of M4Si4 (M = Na, K) to clathrates by HCl or H2O. J Am Chem Soc 129:5348–5349CrossRefGoogle Scholar
  11. Cigher S, Diudea MV (2006) Kekulé structure counter. “Babes-Bolyai” University, ClujGoogle Scholar
  12. David WIF, Ibberson RM, Matthewman JC, Prassides K, Dennis TJS, Hare JP, Kroto HW, Taylor R, Walton DRM (1991) Crystal structure and bonding of ordered C60. Nature 353:147–149CrossRefGoogle Scholar
  13. Delgado-Friedrichs O, O’Keeffe M (2005) Crystal nets as graphs: terminology and definitions. J Solid State Chem 178(8):2480–2485CrossRefGoogle Scholar
  14. Diudea MV (2010) Diamond D5, a novel allotrope of carbon. Stud Univ Babes-Bolyai Chem 55(4):11–17Google Scholar
  15. Diudea MV (2013) Hyper-graphenes. Int J Chem Model 5:211–220Google Scholar
  16. Diudea MV, Nagy CL (2007) Periodic nanostructures. Springer, DordrechtCrossRefGoogle Scholar
  17. Diudea MV, Nagy CL (2012) All pentagonal ring structures related to the C20 fullerene: diamond D5. Diam Relat Mater 23:105–108CrossRefGoogle Scholar
  18. Diudea MV, Vukičević D (2007) Kekulé structure count in corazulenic fullerenes. J Nanosci Nanotechnol 7:1321–1328CrossRefGoogle Scholar
  19. Diudea MV, Ilić A, Varmuza K, Dehmer M (2010) Network analysis using a novel highly discriminating topological index. Complexity 16(6):32–39CrossRefGoogle Scholar
  20. Elstner M, Porezag D, Jungnickel G, Elsner J, Haugk M, Frauenheim T, Suhai S, Seifert G (1998) Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties. Phys Rev B 58:7260–7268CrossRefGoogle Scholar
  21. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam NJ, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09 Rev. A.1. Gaussian Inc., WallingfordGoogle Scholar
  22. Guloy A, Ramlau R, Tang Z, Schnelle W, Baitinger M, Yu G (2006) A quest-free germanium chlatrate. Nature 443:320–323CrossRefGoogle Scholar
  23. Haddon RC (1987) Rehybridization and π-orbital overlap in nonplanar conjugated organic molecules: π-Orbital axis vector (POAV) analysis and three-dimensional hückel molecular orbital (3D-HMO) theory. J Am Chem Soc 109:1676–1685CrossRefGoogle Scholar
  24. Haddon RC (1990) Measure of nonplanarity in conjugated organic molecules: which structurally characterized molecule displays the highest degree of pyramidalization? J Am Chem Soc 112:3385–3389CrossRefGoogle Scholar
  25. Ilić A, Diudea MV (2010) Super-index Cluj-Niš software program. “Babes-Bolyai” University, ClujGoogle Scholar
  26. Kyani A, Diudea MV (2012) Molecular dynamics simulation study on the diamond D5 substructures. Central Eur J Chem 10(4):1028–1033Google Scholar
  27. Meier WM, Olson DH (1992) Atlas of zeolite structure types, 3rd edn. Butterworth-Heineman, LondonGoogle Scholar
  28. Nagy CL, Diudea MV (2009) Nano studio. Babes–Bolyai University, ClujGoogle Scholar
  29. Nagy CL, Diudea MV (2013) Diamond D5. In: Nagy CL, Diudea MV (eds) Diamond and related nanostructures. Springer, Dordrecht, pp 91–105CrossRefGoogle Scholar
  30. Onoe J, Ito T, Kimura SI, Shima H, Toda Y, Yoshioka H (2012) One-dimensional uneven peanut-shaped C60 polymer: a quantum electronic system in Riemannian space. Fullerenes Nanotubes Carbon Nanostruct 20:1–16CrossRefGoogle Scholar
  31. Paquette LA, Vazeux M (1981) Threefold transannular epoxide cyclization. Synthesis of a heterocyclic C17-hexaquinane. Tetrahedron Lett 22:291–294CrossRefGoogle Scholar
  32. Prinzbach H, Wahl F, Weiler A, Landenberger P, Wörth J, Scott LT, Gelmont M, Olevano D, Sommer F, von Issendoef B (2006) C20 carbon clusters: Fullerene-boat-sheet generation, mass selection, photoelectron characterization. Chem Eur J 12:6268–6280CrossRefGoogle Scholar
  33. Schwarz U, Wosylus A, Böhme B, Baitinger M, Hanfland M, Grin Y (2008) A 3D network of four-bonded germanium: a link between open and dense. Angew Chem Int Ed 47:6790–6793CrossRefGoogle Scholar
  34. Schwerdtfeger P, Wirz LN, Avery J (2015) The topology of fullerenes. WIREs Comput Mol Sci 5:96–145CrossRefGoogle Scholar
  35. Szefler B, Diudea MV (2012) On molecular dynamics of the diamond D5 seed. Struct Chem 23(3):717–722CrossRefGoogle Scholar
  36. Vukičević D, Klein DJ (2005) Characterization of distribution of pi-electrons amongst benzenoid rings for Randić’s “algebraic” Kekulé structures. J Math Chem 37:163–170CrossRefGoogle Scholar
  37. Zhang H, Ye D, Liu Y (2010) A combination of Clar number and Kekulé count as an indicator of relative stability of fullerene isomers of C60. J Math Chem 48:733–740CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Mircea Vasile Diudea
    • 1
  1. 1.Department of Chemistry, Faculty of Chemistry and Chemical EngineeringBabes-Bolyai UniversityCluj-NapocaRomania

Personalised recommendations