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A very recently developed optimization algorithm for carbon clusters (Cns) (Yen and Lai J Chem Phys 142:084313, 2015) is combined separately with different empirical bond-order potentials which were proposed also for carbon materials, and they are applied to calculate the lowest energy structures of Cns studying their structural changes at different size n. Based on predicted structures, we evaluate the practicality of four analytic bond-order empirical potentials, namely the Tersoff, Tersoff–Erhart–Albe, first-generation Brenner and second-generation Brenner (SGB) potentials. Generally, we found that the cluster Cn (n = 3–60) obtained by the SGB potential undergoes a series of dramatic structural transitions, i.e., from a linear → a single ring → a multi-ring/quasi-two-dimensional bowl-like → three-dimensional fullerene-like shape; such variability of structural forms was not seen in the other three potentials. On closer examination of the Cns calculated using this potential and further comparing them with those obtained by the semiempirical density functional tight-binding theory calculations, we found that these Cn are more realistic than similar works reported in the literature. In this respect, due to its potential applications in the study of chemically complex systems of different atoms especially chemical reactions (Che et al. Theor Chem Acc 102:346, 1999), the SGB potential can, moreover, be used to investigate larger size Cn, and calculated structural results by this potential are naturally input configurations for higher-level density functional theory calculations. Another most remarkable finding in the present work is the Cn results calculated by Tersoff–Erhart–Albe empirical potential. It predicts a two-dimensional development of graphene structure, exhibiting always a zigzag edge in the optimized clusters. This empirical potential can thus be applied to study graphene-related materials such as that shown in a recent paper (Yoon et al. J Chem Phys 139:204702, 2013). [ABSTRACT FROM AUTHOR]

We study magnetic properties of carbon clusters Cn by combining the spin-polarized parametrized density functional tight-binding (SDFTB) theory with an unbiased modified basin hopping (MBH) optimization algorithm. With an intent to develop a physically self-consistent technique, we deliberately treat valence electronic charges, spin charges and ionic charges on equal footing. Within the density functional tight-binding (DFTB) theory, we examine the effect of using the orbital angular-momentum unresolved and resolved schemes in calculating the on-site Coulombic energy which, we judge, will have subtle but significant influence on the Cn’s magnetism, their topologies and the change with size n their conformational structures. As a concrete means to substantiate our conjecture, we apply the SDFTB/MBH method to Cns and determine their stable magnetic structures within the angular-momentum resolved scheme. Our calculations show that the lowest energy Cn changes from a linear-chain shape for n = 3-9, turns over to a singlet monocyclic ring for n = 10-18, becomes a polycyclic ring for n = 19-25 and finally assumes a cage-like geometry at n = 26. Except for n = 4, 6 and 8, all other Cns are found unmagnetized. Accordingly, the newly discovered n that marks the first occurrence of a bi- to tridimensional transition occurs at n = 26, and this size is in contrast to n = 24 which was predicted by similar calculations using the unresolved scheme. Our calculations reveal furthermore two different features. The first one is that the predicted optimized geometries for all of the Cns, except for C24, are structurally the same as the size n = 3-23 of Cn calculated by the DFTB/MBH employing the unresolved orbital angular-momentum scheme. As a result, the present calculations which employ the resolved angular-momentum scheme thus showed that the latter affects only the larger size Cn starting at C24; this finding redefines therefore the turnover transition point of Cn from a bidimensional planar at n = 25 to a tridimensional cage-like at n = 26. The second feature is that the SDFTB/MBH method yields only triplet C4, C6 and C8, whereas in our previous work employing DFTB/MBH, not only C4 and C6, all of C13, C15, C17, C19, C22 and C23 were predicted to carry a magnetic moment of 2 μB. These differences in the magnetism obtained are attributed to the combined use of both the SDFTB/MBH procedure and the orbital angular-momentum resolved scheme. [ABSTRACT FROM AUTHOR]