On the use of bond-counting rules in predicting the stability of C12B6N6 fullerene

The stability and the BN-substitution pattern of C12B6N6 fullerene have been investigated by bond-counting rules (BCR) with density functional theory (DFT) calculations (B3LYP/6-31G*). It is found that while the simple BCR by including only the nearest-neighbor terms can serve as an effective guide to look for the low-energy alloy configurations, contributions beyond simple BCR by including more than two-body terms are essential for a quantitative description. The substitutions of BN units in the cage seem to follow a continuity pattern in the low-energy configurations. Though all the alloy configurations have positive mixing energy, the low-energy isomers are quite stable (less than 150 meV/atom). We expect that these fullerene structures can be synthesized under the high temperature and nonequilibrium experimental conditions offered by the modem growth techniques such as laser ablation, direct-current arc, and chemical vapor deposition.