Density functional theory is used to calculate the minimum energy structures of zigzag and armchair graphene and boron nitride nanoribbons having a single vacancy and more than 100 atoms. The effect of fluorine substitution on the structure of graphene nanoribbons is also investigated. The frequencies of the structures have been calculated to verify the absence of imaginary frequencies indicating the structures are at a minimum on the potential energy surface. The results show the presence of a vacancy or substitution of a different kind of atom in the nanoribbons causes significant distortion of the ribbons from two dimensions. (c) 2013 Elsevier B.V. All rights reserved.