An extended cluster expansion for ground states of heterofullerenes

It is challenging to determine the ground states of heterofullerenes due to the numerous isomers. Taking the C(60-n)B(n) heterofullerenes (1 ≤ n ≤ 4) as an example, our first-principles calculations with the isomer enumeration present the most stable structure of C(57)B(3), which is energetically favored by 0.73 eV than the reported counterpart. It was difficult to conduct the enumeration for the isomers with n beyond 4 because of the expensive first-principle calculations. Here, we propose a nomenclature to enhance structural recognition and adopt an extended cluster expansion to describe the structural stabilities, in which the energies of the heterofullerenes with various concentrations are predicted by linear combination of the multi-body interactions. Unlike the conventional cluster expansion, the interaction parameters are derived from the enumeration of C(60-n)B(n) (n = 1~4), where there are only 4 coefficients to be fitted as a function of composition for the consideration of local bonding. The cross-validation scores are 1~2 meV per atom for both C(55)B(5) and C(54)B(6), ensuring the ground states obtained from our model are in line with the first-principles results. With the help of the structural recognition, the extended cluster expansion could be further applied to other binary systems as an effective complement to the first-principle calculations.