Investigation of Sixfold Symmetry of Transition Metal Doped TM₃Si₁₂ Clusters

This paper employs a genetic algorithm (GA) in conjunction with density functional theory (DFT) to explore a range of tri-transition metal (tri-TM) doped Si₁₂ anti-hexagonal prism clusters, specifically TM₃Si₁₂ clusters featuring either single or dual types of TM atoms. The investigation encompasses neutral, cationic, and anionic states. Our findings reveal that most clusters exhibit remarkable stability and diverse magnetic properties. The HOMO-LUMO gap results for the cluster series are elucidated by an electron-counting rule, providing a more detailed explanation than previous theories.