Journal of Mathematical Chemistry

, Volume 51, Issue 3, pp 868–880 | Cite as


  • M. J. Bucknum
  • Dasari L. V. K. Prasad
  • E. A. Castro
Original Paper


This communication describes a novel structural-type that could be the basis for a potentially new allotrope of C. The novel structural-type is called “exocyclobutadieneite”, and it is thus named for the 1,3-dimethylenecyclobutane generating fragment that the lattice is based upon. It is a 3-,4-connected network consisting of slightly distorted tetrahedral vertices, and slightly distorted pairs of trigonal planar vertices. The lattice can be derived from a known mineral structure called Cooperite (PtS or PdO) by a topologically isomorphic substitution of trigonal planar atom pairs, for square planar vertexes, in the parent Cooperite unit cell. As such, the new pattern bears a distinct counterpoint relationship with its sibling structural-type called the glitter lattice, which has already been described by the authors in several other papers. And whereas glitter is generated by a topologically isomorphic substitution of trigonal planar atom pairs for the square planar vertices in the Cooperite unit cell, in a fashion that extends the unit cell vertically along the crystallographic c-axis, the exocyclobutadieneite structure is generated, in counterpoint, by such an isomorphic substitution that extends the unit cell horizontally along the a- and b-axes. Both the resulting glitter and exocyclobutadieneite structural-types possess AB\(_{2}\) stoichiometry (where A is a tetrahedral vertex and B is a trigonal planar vertex) and both occur in the tetragonal symmetry space group P4\(_{2}\)/mmc (#131). The networks differ, however, in the special positions adopted by the vertices in the resultant unit cells, and in their respective topology, as is evidenced by consideration of the Wells point symbols and Schläfli symbols for the 2 tetragonal networks. These differences are illustrated further in the course of the discussion to follow.


Graphene Sheet Isomorphic Substitution Point Symbol Crystalline Pattern Barrelene 
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.



One of the authors (MJB) thanks Professor Michael O’Keeffe of Arizona State University for helpful discussions of the topology of C networks. All of the authors thank Professor Roald Hoffmann of Cornell University for his help and advice in preparing this manuscript on the exocyclobutadieneite net.


  1. 1.
    A.F. Wells, Three Dimensional Nets and Polyhedra, 1st edn. (Wiley, New York, 1977)Google Scholar
  2. 2.
    A.F. Wells, Further Studies of Three-dimensional Nets, American Crystallographic Association, Monograph \(\#8\), 1st edn. (ACA Press, Pittsburgh, 1979)Google Scholar
  3. 3.
    M. O’Keeffe, M.A. Peskov, S.J. Ramsden, O.M. Yaghi, Acc. Chem. Res. 41, 1782 (2008)Google Scholar
  4. 4.
    G. Kresse, J. Furthmüler, Phys. Rev. B. 54, 11169 (1996)CrossRefGoogle Scholar
  5. 5.
    M.J. Bucknum, R. Hoffmann, J. Am. Chem. Soc. 116, 11456 (1994)CrossRefGoogle Scholar
  6. 6.
    K.M. Merz, R. Hoffmann, A.T. Balaban, J. Am. Chem. Soc. 109, 6742 (1987)CrossRefGoogle Scholar
  7. 7.
    L.A. Carreira, R.O. Carter, J.R. Durig, J. Chem. Phys. 59, 812 (1973)CrossRefGoogle Scholar
  8. 8.
    H. Oberhammer, S.H. Bauer, J. Am. Chem. Soc. 91, 10 (1969)CrossRefGoogle Scholar
  9. 9.
    M.J. Bucknum, E.A. Castro, J. Math. Chem. 50(5), 1034 (2012)CrossRefGoogle Scholar
  10. 10.
    L. Pauling, The Nature of the Chemical Bond, 3rd edn. (Cornell University Press, Ithaca, 1960)Google Scholar
  11. 11.
    M.J. Bucknum, E.A. Castro, J. Math. Chem. 42(1), 117 (2009)CrossRefGoogle Scholar
  12. 12.
    M.J. Bucknum, E.A. Castro, J. Math. Chem. 40(4), 327 (2006)CrossRefGoogle Scholar
  13. 13.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)CrossRefGoogle Scholar
  14. 14.
    P.E. Blöchl, Phys. Rev. B. 50, 17953 (1994)CrossRefGoogle Scholar
  15. 15.
    G. Kresse, D. Joubert, Phys. Rev. B. 59, 1758 (1999)CrossRefGoogle Scholar
  16. 16.
    J. Donohue, The Structure of the Elements, 1st edn. (Wiley, NY, 1974)Google Scholar
  17. 17.
    M.J. Bucknum, E.A. Castro, J. Math. Chem. 36(4), 381 (2004)CrossRefGoogle Scholar
  18. 18.
    M.J. Bucknum, I. Stamatin, E.A. Castro, Mol. Phys. 103(20), 2707 (2005)CrossRefGoogle Scholar
  19. 19.
    A.Y. Liu, M.L. Cohen, Science 245, 841 (1989)CrossRefGoogle Scholar
  20. 20.
    M.J. Bucknum, B. Wen, E.A. Castro, J. Math. Chem. 48(3), 816 (2010)CrossRefGoogle Scholar
  21. 21.
    M.J. Bucknum, E.A. Castro, J. Math. Chem. 39(3–4), 611 (2006)CrossRefGoogle Scholar
  22. 22.
    M.J. Bucknum, E.A. Castro, J. Chem. Theory Comput. 2(3), 775 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • M. J. Bucknum
    • 1
    • 2
  • Dasari L. V. K. Prasad
    • 3
  • E. A. Castro
    • 2
    • 1
  1. 1.Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)Buenos AiresArgentina
  2. 2.INIFTAUniversidad Nacional de La PlataBuenos AiresArgentina
  3. 3.Department of Chemistry and Chemical BiologyCornell UniversityIthacaUSA

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