Structure–Property Relationships in Boron–Carbon–Nitride Nanocages: Heteroatom Patterning and Symmetry Effects on Nonlinear Optical Response and Hydrogen Adsorption

Boron–carbon–nitride nanocages represent a novel and unexplored class of nanostructures that integrate the features of boron, nitrogen, and carbon-based frameworks, offering unique electronic and optical properties. This study presents a systematic density functional theory (DFT) investigation of the size- and symmetry-dependent electronic features, nonlinear optical (NLO) properties, and hydrogen storage capabilities of different B_nC_2nN_n configurations derived from C₂₀, C₂₄, C₂₈, and C₃₂ fullerene skeletons. A prominent B–N equatorial band, bridging the upper and lower carbon caps, appears to significantly enhance molecular stability. Symmetry impact was notable, with the highest symmetry nanocage (B₆C₁₂N₆, C_6v) exhibiting the most reduced hyperpolarizability due to constrained electronic distribution, while lower symmetry counterparts, such as B₇C₁₄N₇ (C₁), demonstrated superior NLO performance driven by asymmetric charge polarization. The presence of boron and nitrogen heteroatoms within the cage framework not only improves the electronic stability but also avails several adsorption sites toward H₂ molecules. The most optimal binding sites on each BC₂N nanocage (ranging from − 4.8 to − 5.6 kJ/mol) were correlated with the computed natural bond orbital (NBO) charges and polarizability. These findings shall lead to a rational design of BCN cage-like nanostructured materials that combine heteroatom patterning and motivating future studies with controlled functionalization/metal decoration to maximize storage capacity while preserving strong NLO activity.