Theoretical Prediction of Three-Dimensional $sp^2$-free Graphyne-Based Nanomaterials via Density Functional Theory

The search for carbon-based materials with tailored dimensionality and properties remains an important topic in materials science, particularly for applications in electronics, photonics, and nanomechanics. Among the emerging platforms in this context, graphyne (GY) represents a class of two-dimensional (2D) carbon allotropes composed of benzene rings connected by acetylenic linkages, yielding networks containing both $sp$- and $sp^2$-hybridized carbon atoms. By analogy with the transformation of $sp^2$ carbon networks such as graphene into $sp^3$-bonded diamond through interlayer covalent bonding, we construct three-dimensional (3D) GY-derived frameworks (3DGY) by covalently connecting stacked $α$-, $β$-, and $γ$-GY sheets via out-of-plane acetylene bridges. This approach converts the original $sp^2$ nodes into $sp^3$ centers while preserving the $sp$ character of the acetylenic segments, producing fully $sp$-$sp^3$ carbon networks. Structural relaxation shows that the $α$-derived framework does not converge to a stable configuration within this scheme, whereas the $β$- and $γ$-3DGY phases form stable architectures. Density functional theory (DFT) calculations, combined with ab initio molecular dynamics (AIMD) simulations, confirm the energetic, thermal, and dynamical stability of these two systems and are further used to investigate their structural, mechanical, electronic, and optical properties. Mechanical analysis reveals anisotropic elastic behavior, whereas electronic structure calculations show indirect band gaps of approximately 0.15 eV for $β$-3DGY and 1.65 eV for γ-3DGY. Optical calculations further reveal anisotropic responses, with absorption extending from the infrared to the visible. These results identify β-3DGY and γ-3DGY as new three-dimensional carbon allotropes with distinct mechanical, electronic, and optical properties.