Research Article The Electronic Structure of Short Carbon Nanotubes: The Effects of Correlation Vijay Gopal Chilkuri, 1 Stefano Evangelisti, 1 Thierry Leininger, 1 and Antonio Monari 2,3 1 Laboratoire de Chimie et Physique Quantiques, IRSAMC, Universit´ e de Toulouse et CNRS, 118 Route de Narbonne, 31062 Toulouse Cedex, France 2 Universit´ e de Lorraine, Nancy, T´ eorie-Mod´ elisation-Simulation, SRSMC, Boulevard des Aiguillettes, 31062 Vandœuvre-l` es-Nancy, France 3 CNRS, T´ eorie-Mod´ elisation-Simulation, SRSMC, Boulevard des Aiguillettes, 31062 Vandœuvre-l` es-Nancy, France Correspondence should be addressed to Stefano Evangelisti; stefano.evangelisti@irsamc.ups-tlse.fr Received 20 April 2015; Revised 16 July 2015; Accepted 5 August 2015 Academic Editor: Ashok Chatterjee Copyright © 2015 Vijay Gopal Chilkuri et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis paper presents a tight binding and ab initio study of fnite zig-zag nanotubes of various diameters and lengths. Te vertical energy spectra of such nanotubes are presented, as well as their spin multiplicities. Te calculations performed using the tight binding approach show the existence of quasi-degenerate orbitals located around the Fermi level, thus suggesting the importance of high-quality ab initio methods, capable of a correct description of the nondynamical correlation. Such approaches (Complete Active Space SCF and Multireference Perturbation Teory calculations) were used in order to get accurate ground and nearest excited-state energies, along with the corresponding spin multiplicities. 1. Introduction Besides the two lightest elements, hydrogen and helium, carbon is one of the most widespread elements in the universe and one of the best known ones. Indeed, its three-dimension allotropic forms, diamond and graphite, are well known since the antiquity. For this reason, the recent discovery of new low-dimensional allotropic forms, such as fullerenes, carbon nanotubes, and graphene, came out rather unexpected [1, 2]. In a few years, a completely new branch of science was born, whose scientifc and technological impact can hardly be overestimated. Indeed, these fndings had, and still have, an enormous importance in the discovery of novel and advanced materials and have been one of the key factors in the development of nanoscience. Te peculiar properties of graphene (that concern both the “infnite” ideal sheet and fnite nonoislands) raise new challenging theoretical problems, whose understanding and modeling will bring signifcant insight in our comprehension of the structure of matter. Nanotubes, which can be obtained from a graphene stripe by enrolling it along longitudinal axes, present an even larger spectrum of interesting behaviors. It is clear that a better understanding of these systems would make our knowledge of the general properties of solid-state physics and chemistry much deeper. Te new allotropic forms of carbon share the particu- larity of being all of low dimensionality. Indeed, the almost spherical fullerene [3] can be considered as a quasi-zero- dimensional (0D) structure, while the graphene one-atom- thick surface is a strictly two-dimensional (2D) structure. Between these two extreme cases are located the carbon nan- otubes that can be considered as essentially one-dimensional (1D) materials. Te presence of carbon -conjugated lattice, usually resembling a honeycomb hexagonal lattice, is the common feature to all these forms and is at the origin of their striking properties. Indeed, the strength of the carbon- carbon sigma bond and the rigidity of the resulting structure confer graphene and nanotubes a great stability and rigidity and make them appealing to be used as building-block fbers for materials having to resist considerable stress [4]. Another remarkable aspect that should be stressed is the hydrophobicity and the resistance of these materials, a fact Hindawi Publishing Corporation Advances in Condensed Matter Physics Volume 2015, Article ID 475890, 14 pages http://dx.doi.org/10.1155/2015/475890