The lowest energy configurations of Cn(n =< 55) clusters are obtained using the energy mini- mization technique with the conjugate gradient (CG) method where a modified Brenner potential is invoked to describe the carbon and hydrocarbon interaction. We found that the ground state configuration consists of a single ring for small number of C atoms and multi-ring structures are found with increasing n, which can be in planar, bowl-like or cap-like form. Contrary to previous predictions, the binding energy Eb does not show even-odd oscillations and only small jumps are found in the Eb(n) curve as a consequence of specific types of edges or equivalently the number of secondary atoms. We found that hydrogenation of the edge atoms may change the ground state configuration of the nanocluster. In both cases we determined the magic clusters. Special attention is paid to trigonal and hexagonal shaped carbon clusters and to clusters having a graphene-like configuration. Trigonal clusters are never the ground state, while hexagonal shaped clusters are only the ground state when they have zigzag edges.Comment: Accepted for publication in Phys. Rev.

Both even-and odd-numbered neutral carbon clusters C n (n = 2-10) are systematically studied using the energy minimization method and the modified Brenner potential for the carboncarbon interactions. Many stable configurations were found and several new isomers are predicted. For the lowest energy stable configurations we obtained their binding energies and bond lengths. We found that for n ≤ 5 the linear isomer is the most stable one while for n > 5 the monocyclic isomer becomes the most stable. The latter was found to be regular for all studied clusters. The dependence of the binding energy for linear and cyclic clusters versus the cluster size n (n = 2-10) is found to be in good agreement with several previous calculations, in particular with ab initio calculations as well as with experimental data for n = 2-5. PACS number(s): 36.40.Mr, 61.46.Bc, 81.05.Uw Corresponding author: A.A. Dzhurakhalov, Abdiravuf.Dzhurakhalov@ua.ac.be Fax: +32-3-2653542