3,4-Connected carbon nets: through-space and through-bond interactions in the solid state

Abstract

A theoretical study of a series of “honeycombed” or ”layered” 3,4-connected nets is presented. The most significant feature of this series of nets is that they have infinite stacks of carbon-carbon double bonds in close contact with each other. Two of these nets have structures that not only contain stacks of 3-connected centers but also have infinite 1-dimensional polymeric units related to cis-polyacetylene. We employ tight-binding band structure calculations on selected examples of these nets to determine their electronic properties. The consequences of a stacked structure are analyzed by calculating the band structure of infinite layers (stacks) of ethylenes. Some of these carbon nets may be metallic. We also show that through-space and through-bond (hyperconjugative) interactions are important in the solid state, but the overall effect of these interactions varies according to the area of k-space that is being sampled. Pursuing our continuing interest in alternative structures of diamond and graphite,’ we decided to study a series of 3,4-connected nets. There are a number of reasons for examining these nets: first, they have an intermediate valency between graphite (3-connected) and diamond (4-connected); second, the density of the nets we will be studying here is intermediate (-3.0 g/cm3) between that of diamond (3.51 g/cm3) and graphite (2.27 g / ~ m ~ ) ; ~ and third, these nets are interesting because they have close intrastack distances (2.3 to 2.8 A) thereby allowing for greater (especially T ) band dispersions (this may make these nets metallic). Before proceeding to a discussion of the electronic properties of these nets we would like to review briefly the current status of the allotropy of carbon. The structurally well-characterized allotropes of carbon are restricted to only two main types: diamond (cubic and hexagonal) and graphite (hexagonal and rh~mbohedra l ) .~ In cubic (1) and hexagonal diamond (2) each carbon atom is tetrahedrally surrounded by four other carbon atoms at a distance of 1.545 A. The structural differences between these two diamond forms can be envisioned in this way: 1 can be imagined to consist of an infinite network of adamantyl moieties, all chair cyclohexane rings, whereas in 2 there are some chair and some boat six-membered T Cornell University. *The Polytechnic. 0002-7863/87/ 1509-6742$01.50/0 rings. Both hexagonal (3) and rhombohedral (4) graphite contain hexagonal carbon layers linked by van der Waals forces. The difference, though, between these two forms lies in the stacking of these sheets. In 3 every third layer repeats (ABAB ...) with the first and second layers displaced away from each other in such a way that one-half of the atoms in each layer are above and below the center of the hexagon in the neighboring layer. 4, on the other hand, has every fourth layer repeating to give an ABCABC ... stacking pattern. There is some evidence for other carbon allotrope^.^ The best studied of these is karbin, sometimes called ~ h a o i t e . ~ . ~ Its structure is thought to contain carbon in alkyne or cumulene needles, 5. Though there has been much work on karbin, our opinion is that (1) Hoffmann, R.; Hughbanks, T.; Kertesz, M.; Bird, P. H. J . Am. Chem. SOC. 1983, 105, 4831. Hoffmann, R.; Eisenstein, 0.; Balaban, A. T. Proc. Nutl. Acad. Sci. U.S.A. 1980, 7 7 , 5588. Balaban, A. T.; Rentia, C. C.; Ciupitu, E. Rev. Roum. Chim. 1968, 13, 231; erratum: Ibid. 1968, 13, 1233. (2) These are theoretical densities calculated from idealized geometries and should be considered as an upper limit to the experimental densities. (3) Donohue, J. The Structure ofthe Elements; Wiley: New York, 1974. (4) S,e the following recent review of experimental and theoretical work: Stankevich, I . V.; Nikerov, M. V.; Bochvar, D. A. Usp. Khim. 1984,53, 1101; Russ. Chem. Reu. 1984, 53, 640. (5) For a review on karbin see: Mel’nichenko, V . M.; Sladkov, A. M.; Nikulin, Yu. N . Usp. Khim. 1982, 51 , 736; Russ. Chem. Reu. 1982, 51, 421. (6) Whittaker, A. G. Science 1978, 200, 763.