Possible lower energy isomer of carbon clusters Cn (n = 11, 12) via particle swarm optimization algorithm: Ab initio investigation

Abstract

The low energy structures of neutral carbon clusters Cn (n = 11, 12) are predicted by means of particle swarm optimization and quantum chemistry calculation. The energy and geometrical structure of these isomers are further optimized by DFT, MP2 and CCSD computation methods. The relative Gibbs free energy below 5000 K was calculated, which indicates that C11 clusters are more sensitive to temperature. We also illustrate the computational simulated IR spectra obtained at B3LYP/cc-pVTZ level, which shown the vibrational modes and vibrational regions of different structural isomers. Combining nuclear independent chemical shift (NICS) and harmonic oscillator measure of aromaticity (HOMA), we have analyzed the aromaticity of the three single-ring structures and found that C11 cluster is not aromatic, while the ground stated structure of C12 is anti-aromaticity. Chemical bond analysis of the ground state is performed by Adaptive Natural Density Partition (AdNDP) injunction with electron localization function (ELF), it is found that the 2c-2e bonds of C11 and C12 planar ring structures presented strong and weak alternations, respectively, and their multi-central bonds were strongly dependent on the symmetry of molecular configuration. Finally, topological and natural bond orbital (NBO) analysis indicate that there is no electrostatic interaction in the Cn (n = 11, 12) clusters, and the high angular momentum orbital has a primary contribution to negative natural valance electron configuration. From the electronic configuration, we can see that the natural hybridized orbit of C11 and C12 clusters is mainly composed of sp hybrids.