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 Parviz Rashidi-Ranjbar a, * , Abdolreza Sadjadi b , Gholam Hossein Shafiee b , Cina Foroutan-Nejad a a Department of Chemistry, Faculty of Science, University of Tehran, Enghelab Avenue, Tehran 14155-6455, Iran b Department of Chemistry, Islamic Azad University of Kazeroon, Kazeroon, Fars 73135-168, Iran Received 18 July 2007; received in revised form 13 January 2008; accepted 16 January 2008 Available online 29 January 2008 Abstract 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 struc- ture 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 mol- ecules 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 E total/ n c in different type of SWCNTs has been solved rigorously. Ó 2008 Elsevier B.V. All rights reserved. Keywords: Single wall carbon cluster; SWCNTs; Ab initio; QTAIM; Homologous series, Nanotubes; Chemical bond; Electron density 1. Introduction Soon after the discovery of C 60 [1], a new form of Car- bon cluster [2–8] known as multi-wall nanotube was detected experimentally by Iijima [9]. The possibility of the existence of single wall carbon nanotubes (SWCNTs) was predicted theoretically [10,11] followed by experimen- tal works [12]. SWCNTs are assumed theoretically to be the rolled sheet of graphene and are classified as (n, n) or armchair, (n, m) or chiral and (n, 0) or zigzag; only the arm- chair has been detected experimentally so far [13]. The SWCNTs serve as the best theoretical models in physics and chemistry for searching the properties of multi-wall nanotubes too [14]. Molecular mechanics [15], semi-empir- ical [16], ab initio and DFT [17] calculations are used to study the structure and bonding of SWCNTs. Band theory and quantum mechanical based models have been used to predict the electrical conductance properties [11,17–19]. The difference between HOMO and LUMO energies is used to investigate the band gaps, this difference usually 0166-1280/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2008.01.021 * Corresponding author. Tel.: +98 21 66495291; fax: +98 21 66405141. E-mail addresses: ranjbar@khayam.ut.ac.ir (P. Rashidi-Ranjbar), Abdi_1374@kau.ac.ir (A. Sadjadi). www.elsevier.com/locate/theochem Journal of Molecular Structure: THEOCHEM 856 (2008) 79–87