Graph Neural Network Determine the Ground State Structures of Boron or Nitride Substitute C₆₀ Fullerenes

Substitutional doping of fullerenes represents a significant category of heterofullerenes. Due to the vast number of isomers, confirming the ground state structure poses considerable challenges. In this study, we generated isomers of C_60-nB_n and C_60-nN_n with n ranging from 2 to 12. To avoid overlooking the ground state structures, we applied specific filtering rules: no adjacent nitrogen (N) or boron (B) atoms are allowed, and substitutions in meta-positions within pentagons are prohibited when the substitution number n exceeds nine. Approximately 15,000 isomers across various values of n within the range of 2 to 12 for B and N substituted fullerenes were selected and optimized using density functional theory (DFT) calculations, forming our dataset. We developed a Graph Neural Network (GNN) that aggregates both topological connections and its dual graph with ring types as input information to predict their binding energies. The GNN achieved high accuracy, reaching a root mean square error (RMSE) of 1.713 meV. Furthermore, it operates efficiently; indeed, it can predict over six thousand isomers per second on an eight-core PC. Several predicted stable structures were further optimized by DFT to confirm their ground state configurations. The energy cutoffs of each composition were determined through statistical simulations to ensure that the selected ground state structures possess high confidence levels. Notably, new lower-energy structures have been discovered for boron-substituted fullerenes with substitution number ranging from seven to twelve and nitride-substituted fullerenes with substitution number ranging from seven to eleven.