α -, β -, and γ -TODD-G: Novel 2D planar carbon allotropes

We report a comprehensive first-principles investigation of three novel two-dimensional carbon allotropes: α -, β -, and γ -TODD-Graphene (TODD-G), composed of 3–8–12–16, 3–8–12–16, as 3–4–8–12 interconnected carbon rings with sp/sp 2 hybridization, respectively. Structural optimization, phonon spectra, and ab initio molecular dynamics confirm their thermal and dynamic stability. All phases exhibit metallic electronic character, with distinct Dirac-like features and tilted Dirac cones suggesting anisotropic charge transport. Mechanical analysis reveals tunable anisotropy: α -TODD-G is strongly anisotropic, β -TODD-G displays moderate anisotropy, and γ -TODD-G shows near-isotropic mechanical response. Optical spectra further distinguish the phases, with γ -TODD-G showing pronounced absorption in the infrared, while α - and β -TODD-G absorb mainly in the visible and UV regions.