Pivotal role of the B₁₂-core in the structural evolution of B₅₂-B₆₄ clusters

An icosahedral B₁₂ cage is a basic building block of various boron allotropes, and it also plays a vital role in augmenting the stability of fullerene-like boron nanoclusters. However, the evolution of compact core-shell structures is still a puzzle. Using a genetic algorithm combined with density functional theory calculations, we have performed a global search for the lowest-energy structures of B clusters with n = 52-64, which reveals that bilayer and core-shell motifs frequently alternate as the ground state. Their structural stability is assessed, and the competition mechanism between various patterns is also elucidated. More interestingly, an unprecedented icosahedral B₁₂-core half-covered structure is identified at B₅₈, which bridges the gap between the smallest core-shell B₄@B₄₂ and the complete core-shell B₁₂@B₈₄ cluster. Our findings provide valuable insights into the bonding pattern and growth behavior of medium-sized boron clusters, which facilitate the experimental synthesis of boron nanostructures.