Novel B-C binary fullerenes following the isolated B₄C₃ hexagonal pyramid rule

B-C binary monolayers and fullerenes (borafullerenes) have received considerable attention in recent years. Inspired by the newly reported B₄C₃ semiconducting boron carbide monolayer isovalent to graphene (Tian et al., Nanoscale, 2019, 11, 11099), we predict herein at density functional theory level a new class of borafullerenes (1-8) following the isolated B₄C₃ hexagonal pyramid rule. The spherically aromatic borafullerenes C_5h B₂₀C₃₅ (1), C₅ B₂₀C₄₅ (2), C_5h B₂₀C₅₅ (3), and C₅ B₂₀C₆₅ (4) isovalent to C₅₀, C₆₀, C₇₀, and C₈₀, respectively, possess five isolated B₄C₃ hexagonal pyramids evenly distributed on the waist around the C₅ molecular axis, while S₁₀ B₄₀C₅₀ (5), C₅ B₄₀C₆₀ (6), S₁₀ B₄₀C₇₀ (7), and C₅ B₄₀C₈₀ (8) encompass ten isolated B₄C₃ pyramids symmetrically distributed on the cage surface. Detailed orbital and bonding analyses indicate that these borafullerenes follow similar σ and π-bonding patterns with their fullerene analogues, with three delocalized 7c-2e π bonds forming a local π-aromatic system over each isolated B₄C₃ hexagonal pyramid. The calculated formation energies of the (B₄C₃)_nC_60-6n (n = 1-5) series isovalent to C₆₀ appear to increase almost linearly with the number of isolated B₄C₃ pyramids in the system. The IR, Raman, and UV-vis spectra of the prototypical B₂₀C₄₅ (2) are theoretically simulated to facilitate its future spectral characterization.