New insight into the stability and property of linear carbon clusters

At DFT/B3LYP/6-31G** theoretical level, we investigated the optimized parameters and bonding character of linear Cn (2 ⩽ n ⩽ 12) clusters. The analyzing results indicated two different structure tendencies. Firstly, the lowest frequencies of linear Cn clusters fell gradually with the increase of “n” values, which implied the instability of long-chain linear clusters. Furthermore, infrared, raman and absorption spectrum showed the tendency of forming annular structure was obvious with the increase of carbon atoms too. Secondly, comparing the energies and the HOMO-LUMO (H-L) gaps, we found that symmetric odd clusters preferentially adopted linear structure with high H-L gap, while even clusters were unable to form symmetric structures and they usually displayed annular structure. Consequently, the most stable structures of Cn clusters were the integrated aforementioned two rules. On the other hand, we also studied their bonding character with the aid of molecular orbital (MO) and natural bond orbital (NBO) calculations. The results revealed that all carbon atoms of even linear clusters were sp hybridization. Interestingly, except sp hybridization, Cn clusters with odd “n” also had special non-hybridized carbon atoms in the middle. It was emphasized that the fringe carbon atoms of all Cn clusters were sp hybridization though they formed a single bond. Besides, with the help of NBO and MO calculations, we believed that C2 molecule may be sp hybridization with quadruple bonding.