Application of quantum theory of atoms in molecules on small single wall (6, 0) zigzag carbon clusters. Part I: Topological analysis of electron density, structure and bonding

The Rho(r) functions of (6, 0)2, (6, 0)3 and (6, 0)4 zigzag single wall carbon clusters, SWCCs, were analyzed by quantum theory of atoms in molecules (QTAIM). Topological analysis of Rho(r) revealed the chemical bonds' nature and structure of cited species. It is found that molecular graph and classical frame derived from interatomic distances of clusters are in agreement and all topological rings are strain free. The direct information about the magnitude of electron density inside these clusters has been presented for the first time via the study of Laplacian of electron density. The Laplacian of Rho(r) revealed the zones of charge concentration and charge depletion. This analysis showed that inside the clusters are essentially empty space, they might be used for building a special type of quantum devices. The existence of possible (6, 0) SWCC family was investigated and established that they belong to the quantum mechanical homologous series. The latter relationship has been described on the basis of fundamental partitioning theorems of QTAIM. The structure of (6, 0)1 was computed as the smallest possible (6, 0) zigzag SWCC, which turned out not to be a local minimum, demonstrating that the smallest possible (6, 0) SWCC is (6, 0)2. The zigzag single wall carbon clusters (SWCCs) could be recognized as the smaller size molecules of the zigzag single wall carbon nanotubes. Topological similarities were found in SWCCs which help to construct the large size molecules i.e. SWCNTs and predict their chemical properties without doing time consuming ab initio calculations. The mystery of the convergence of Etotal/nc in different type of SWCNTs has been solved rigorously.