The basin hopping optimization algorithm previously developed for finding the lowest energy structures of clusters, both nonmetallic and metallic, is revisited. This state-of-the-art technique is extended by our group (Ref. 33) to carbon clusters studying their varied forms of structural transitions, changing from one cluster geometry to another. This modified optimization algorithm very recently proposed by Yen and Lai(Ref. 33) closely parallels that of the basin hopping method [D. J. Wales and J.P. Doye, J. Phys. Chem. A 101,5111 (1997)], but is discreetly designed to take into account the unique bond-order interactions of the carbon cluster through defining a spatial volume within which its lowest energy structure is searched and through introducing a cut-and-splice genetic operator into the basin hopping technique. The present modified basin hopping method is characteristically distinguishable from the nonmetallic and metallic clusters, technically more thorough in dealing the couplings of valence electrons with ions, and hence is more appropriate for carbon clusters. We discuss in this work the basis of success of the present modified basin hopping technique, and tested it by calculating the lowest energy structures of carbon clusters using four different empirical potentials. It is found here that the cluster Cn, n=3-60, undergoes a series of interesting structural transitions, i.e. its structural geometry changes, in sequence of increasing cluster size n, as linear → single ring → multi rings or quasi-two dimensional bowl-like → cage-like or three dimensional fullerene-like structure, depending on the empirical potential employed in optimization. The modified basin hopping algorithm (Ref. 33) is efficient when it is checked against the popular cut-and-splice technique of Deaven and Ho [Phys. Rev. Lett. 75, 288 (1995)] for two well-known stable carbon clusters of larger size, i.e.C60 and C72. An interesting prediction of one of the empirical potentials, due to Erhart and Albe [Phys. Rev. B71, 035211 (2005)], is its capturing of the development of two-dimensional graphene structure, i.e. the evolution of Cn for n=6, 10, 13, 16, 19, 22, 24, 27 since no such structural sequence is seen in the other three empirical potentials. Our optimization algorithm that combines with the first generation of Brenner potential yields Cn compares very well with those reported by Cai et al. [J. Mol. Struct. (Theochem) 678, 113 (2004)]. For the second generation of Brenner potential, our calculated Cns show regularity in its structural evolution. These Cn
results are more quantitatively behaved than the only similar works by Kosimov et al. [Phys. Rev. B 78, 235433 (2008); Phys. Rev. B 81, 195414 (2010)]. Finally, we draw physical implications from our comparison of Cn obtained from using the first and second generations of Brenner potentials. Keywords: carbon cluster; optimization algorithm; topological transition; fullerene.
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