rXXXX American Chemical Society A dx.doi.org/10.1021/jp110704x | J. Phys. Chem. C XXXX, XXX, 000–000 ARTICLE pubs.acs.org/JPCC Properties of Carbon Nanotubes: An ab Initio Study Using Large Gaussian Basis Sets and Various DFT Functionals Raffaella Demichelis,* ,† Yves No € el, ‡ Philippe D’Arco, ‡ Michel R  erat, § Claudio M. Zicovich-Wilson, ^ and Roberto Dovesi z † Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA 6845, Australia ‡ Institut des Sciences de la Terre de Paris (UMR 7193 UPMC-CNRS), UPMC, Paris Universitas, France § Equipe de Chimie Physique, IPREM UMR5254, Universit  e de Pau et des Pays de l'Adour, F-64000 Pau, France ^ Facultad de Ciencias, Universidad Aut onoma del Estado de Morelos, Av. Universidad 1001, Col. Chamilpa, 62209 Cuernavaca, Morelos, Mexico z Dipartimento di Chimica IFM, Universit  a di Torino and NIS -Nanostructured Interfaces and Surfaces - Centre of Excellence, Via P. Giuria 7, 10125 Torino, Italy b S Supporting Information 1. INTRODUCTION The performance of 12 functionals, corresponding to three different levels of approximation of the exchange-correlation term (E XC ) 1,2 within the density functional theory (DFT), 3À5 i.e., local density approximation (LDA), generalized gradient approximation (GGA, including newly developed E XC func- tionals parametrized for solids 6À8 ) and hybrid methods, and the effect of basis sets of increasing size, ranging from 3-21G (nine atomic orbitals per C atom, AOs) to 6-1111(2d,f) (34 AOs), in the description of the electronic, structural, dielectric, and elastic properties of a subset of zigzag and armchair single- walled (SW) carbon nanotubes (CNTs) are explored. The relative stability of SWCNTs with respect to two other carbon allotropes, i.e., diamond and graphene, is investigated, too. The calculation of the considered properties is then extended to the series of the (n, 0)-zigzag and (n, n)-armchair SWCNTs with n ranging from 8 to 35 and from 5 to 24, respectively, corresponding to tubes with radii up to 16 Å (up to 140 atoms in the unit cell), using the 6-1111G(d) basis set and the B3PW (B3LYP for polarizabilities) functional. The n 1 and n 2 indices multiply the a B 1 and a B 2 lattice vectors of the monolayer (graphene in the present case) and are sufficient to define the rolling direction of the nanotube, its radius, and its chirality (see Figure 1 in refs 9À14 and the interactive animations Received: November 9, 2010 Revised: March 24, 2011 ABSTRACT: The structural, electronic, dielectric, and elastic properties of zigzag and armchair single-walled carbon nano- tubes are investigated at different DFT levels (LDA, GGA, hybrids) with Gaussian type basis sets of increasing size (from 3-21G to 6-1111G(2d,f)). The longitudinal and transverse polarizabilities are evaluated by using the Coupled Perturbed HartreeÀFock and KohnÀSham computational schemes, which take into account the orbital relaxation through a self- consistent scheme. It is shown that the difference between the frequently adopted SOS (sum over states, uncoupled) and the fully coupled results is far from being negligible and varies as a function of the tensor component and the adopted functional. Helical symmetry is fully exploited. This allows simulation of tubes larger (up to 140 atoms in the unit cell) than in previous studies by using extended basis sets and severe computational conditions. All the 12 functionals considered here provide similar results for the structural and the elastic properties and for the relative stability among nanotubes and with respect to graphene. On the contrary, the stability with respect to diamond, which has a quite different density than that of nanotubes, sensitively depends on the adopted functional. The band gap and the longitudinal polarizability are strongly dependent on the level of approximation: hybrid functionals provide the least deviation from experimental data. In general, data obtained for (n, n), (3n, 0), (3n þ 1, 0), and (3n þ 2, 0) rolling directions approach the slab limit for large radii following four distinct trends.