Exotic Allotropes of Carbon

Abstract

Carbon allotropes, including triple-, double-, and single periodic, and finite non-periodic, nanostructures have been designed by using map operations and their topological and energetic properties studied. Two allotropes of the diamond D5 are discussed in this chapter: the dense hyper-diamond, with an “anti”-diamantane structure, and a quasi-diamond, which is a five-fold symmetry quasicrystal with “syn”-diamantane structure. Some substructures of these allotropes are proposed as possible intermediates in the synthesis of some hyper-graphenes and their energetics evaluated at Hartree-Fock, DFT (B3LYP) and DFTB levels of theory. A topological description of D5_anti network and derived hyper-graphenes, in terms of the net parameter and Omega polynomial, is also given.