A Hypothetical Dense 3,4-Connected Carbon Net and Related B2C and CN2 Nets Built from 1,4-Cyclohexadienoid Units

Abstract

This paper describes the geometrical and electronic structure of a hypothetical 3 ,4-co~ected tetragonal allotrope of carbon (space group P42/mmc, No. 131) built from 1,4-cyclohexadiene rings. The three-dimensional net, containing trigonal and tetrahedral atoms in a ratio of 2:1, has a calculated density of 3.12 g/cm3, intermediate between graphite and diamond. Band structure calculations for this net have been performed using the extended Huckel method. One-dimensional substructures of a polyquinoid, polyspiroquinoid, and polycyclophane nature are instructive in approaching the electronic structure of the full net. These substructures point to the importance of through-space interactions of the stacked olefin units in the net, separated by only 2.53 A. It is apparent that interaction leads to substantial dispersion of the n and n* bands, the highest occupied and lowest unoccupied bands in the tetragonal structure, respectively. The resulting density of states profile is that of a metal, with a significant n-n* band overlap at the Fermi level. Related nets formed by substituting boron and nitrogen into the trigonal sites of the lattice are studied as well. The electron count on the atom in the trigonal sites in the lattice significantly affects the band structure about the Fermi level; B2C should be metallic, and CN2 an insulator. Diamond, graphite, and Cml are allotropes of carbon in which space is filled with perfectly tetrahedral, perfectly trigonal, and approximately trigonal carbon atoms, respectively. These structures are not the only ones to fill space in this way,2 at least on paper.3 Of special interest are possible allotropes which would be dense, have interesting properties (e.g. conductivity), and share some of the structural features of the known allotropes, their 3and 4-connectedness4 for instance. In this contribution we suggest one hypothetical carbon structure which combines 3and 4-co~ected atoms, built upon the 1,4-cyclohexadiene motif,5 1, and look at its likely electronic * Author to whom all correspondence should be addressed. @ Abstract published in Advance ACS Abstracts, November 1, 1994. (1) (a) Wells, A. F. Three Dimensional Nets and Polyhedra; Wiley: New York, 1977. (b) Wells, A. F. Further Studies of Three-Dimensional Nets; ACA Monograph No. 8; American Crystallographic Association: Pittsburgh, 1979. (c) Donohue, J. The Structure of the Elements, Wiley: New York, 1974. (d) Kratschmer, W.; Huffmann, H. Nature 1990,347, 354. (e) Kroto, H.; Heath, J. R.; O'Brien, S. C.; Curl, R. F.; Smalley, R. F. Nature 1985, 318, 162. (f) Osawa, E. Kagaku 1970, 25, 85. (9) Bundy, F. P.; Kasper, J. S. J. Chem. Phys. 1967, 46, 3437. (h) Aust, R. B.; Drickamer, H. G. Science 1963, 140, 817. (2) (a) Zeger, L.; Kaxiras, E. Phys. Rev. Lett. 1993, 70, 2920-2922. (b) Muller, D. A.; Tzou, Y.; Raj, R.; Silcox, J. Nature 1993, 366, 725. (c) Renschler, C. L.; Pouch, J.; Cox, D. M. Eds. Novel Forms of Carbon; Materials Research Society Symposium Proceedings, Vol. 270; Materials Research Society: Pittsburgh, 1992. (d) Moshary, F.; Chen, N. H.; Silvera, I. F.; Brown, C. A.; Dom, H. C.; de Vries, M. S.; Bethune, D. S. Phys. Rev. Lett. 1992, 69, 466-469. (e) Iijima, S. Nature 1991, 354, 56. (f) Utsumi, W.; Yagi, T. Science 1991,252, 1542-1544. (g) Hirai, H.; Kondo, K. Science 1991, 253,772-774. (h) Spear, K. E.; Phelps, A. W.; White, W. B. J . Mater. Res. 1990,5,2277. (i) Angus, J. C.; Hayman, C. C. Science 1988,241, 1988. (i) Stankevich, V.; Nikerov, M. V.; Bochvar, D. A. Russ. Chem. Rev. 1987, 53, 670. (k) Melnitchenko, V. M.; Nikulin, Y. N.; Sladkov, A.M. Carbon 1985,23, 3-7. (1) Stankevich, I. V.; Nikerov, M. V.; Bochvar, D. A. Russ. Chem. Rev. 1984, 53, 640. (m) Whittaker, A. G.; Watts, E. J.; Lewis, R. S.; Anders, E. Science 1980, 209, 1512-1514. (n) Whittaker, A. G.; Tooper, B. J . Am. Ceram. SOC. 1974, 57,443-446. (0) Bochvar, D. A.; Galpem, E. G. Dokl. Akad. Nauk. SSSR 1973, 209, 612. (p) El Gorsey, A.; Donnay, G. Science 1968, 161, 363-364. (9) Ergun, S. Carbon 1968,6, 141-149. (r) Drickamer, H. Science 1967,156, 1183-1188. (s) Bundy, F. P. J. Chem. Phys. 1963, 38, 631. 0002-7863/94/1516-11456$04.50/0 properties. The space-filling structure in question is shown in