We have designed two-dimensional borocarbonitrides (poly-butadiene-cyclooctatetraene framework BC₂N) with hexagonal unit cells, which are stable according to the cohesive energy, phonon dispersion, ab initio molecular dynamics, and elastic modulus results. They are n-type semiconductors with strain-tunable direct band gaps (1.45–2.20 eV), an ultrahigh electron mobility (5.2 × 10⁴ cm² V⁻¹ s⁻¹ for β-BC₂N), and strong absorption (an absorption coefficient of up to 10⁵ cm⁻¹). The intrinsic electric field due to the Janus geometry of α-BC₂N reduces the recombination of photo-generated carriers. The band edge positions of α-BC₂N and β-BC₂N are suitable for photocatalytic hydrogen production, achieving high solar-to-hydrogen efficiencies of 17% and 12%, respectively, in excess of the typical target value of 10% for industrial application. Both γ-BC₂N and δ-BC₂N can be used as electron donors in type-II heterostructures with two-dimensional transition metal dichalcogenides, and the power conversion efficiency of a solar cell based on these heterostructures can be as high as 21%, approaching the performance of perovskite-based solar cells.

Two novel superhard 3D sp³ hybridized carbon allotropes (Cmmm-C₃₂ and P6/mmm-C₅₄) are proposed in this work through first-principles calculations. Both Cmmm-C₃₂ and P6/mmm-C₅₄ have a honeycomb structure. P6/mmm-C₅₄ shows a wide direct bandgap (3.564 eV), while Cmmm-C₃₂ shows an ultrawide indirect bandgap (5.051 eV), as determined using the HSE06 hybrid functional. The hardnesses of Cmmm-C₃₂ and P6/mmm-C₅₄ are 83.72 and 54.01 GPa, respectively, and their calculated ideal strengths further confirm their superhardness characteristics. P6/mmm-C₅₄ is isotropic in the (001) plane. The minimum thermal conductivities of Cmmm-C₃₂ and P6/mmm-C₅₄ are larger than those of diamond-C, illustrating that Cmmm-C₃₂ and P6/mmm-C₅₄ are potential semiconductor device materials.

A metastable sp³-bonded carbon allotrope, Penta-C₂₀, consisting entirely of carbon pentagons linked through bridge-like bonds, was proposed and studied in this work for the first time. Its structure, stability, and electronic and mechanical properties were investigated based on first-principles calculations. Penta-C₂₀ is thermodynamically and mechanically stable, with equilibrium total energy of 0.718 and 0.184 eV/atom lower than those of the synthesized T-carbon and supercubane, respectively. Penta-C₂₀ can also maintain dynamic stability under a high pressure of 100 GPa. Ab initio molecular dynamics (AIMD) simulations indicates that this new carbon allotrope can maintain thermal stability at 800 K. Its Young’s modulus exhibits mechanical anisotropy. The calculated ideal tensile and shear strengths confirmed that Penta-C₂₀ is a superhard material with a promising application prospect. Furthermore, Penta-C₂₀ is a direct band gap carbon based semiconducting material with band gap of 2.89 eV.