12. Energetics of Multi-shell Clusters

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.