Building Physical Carbon Nanoparticles from Small-World Networks: Density Functional Theory Calculations

We have performed B3LYP/6-31G* Density Functional Theory calculations on carbon cluster nanoparticles built with (pseudo) small-world network topologies to determine whether they are stable and can exist in nature. Such particles may have novel material properties due to their (pseudo) small-world nature [1]. We have embedded a ring of carbons with one or more small-world connections made with and without additional carbon atoms. No carbon is allowed to make more than four bonds. The energy per atom of these (pseudo) small-world carbon systems is compared with benchmark carbon clusters including monocyclic rings, linear rods, graphene fragments, and various fullerenes from C$_{20}$ to C$_{60}$. The energy per atom and vibrational frequency calculation results for these materials indicate that there are pure-carbon small-world nanomaterials that are reasonable for real world synthesis. We present both NMR and IR spectra for these nanoparticles. [1] M.A. Novotny, \textit{et al}, J. Appl. Phys, \textbf{97}, 10B309 (2005).