Cyclo-graphyne (CGY): Porous 2D Carbon Allotrope

• Cyclo-graphyne (CGY) is a two-dimensional carbon allotrope with a porous network of sp/sp²-hybridized atoms that exhibits ultranarrow-gap semimetallicity and Dirac cones.
• Its well-defined 8.5 Å pores, varied C–C bond lengths, and distinctive vibrational signatures make it a strong candidate for gas separation and optoelectronic devices.
• Density functional theory results show that CGY is thermally stable up to 1000 K, mechanically compliant, and ideally suited for flexible nanoelectronics.

Searching arXiv for the provided paper and closely related graphyne literature for support. arxiv_search.run({"^^^^^^^^2query2 OR title:\2^^^^^^^^"Cyclo-Graphyne: A Highly Porous and Semimetallic 2D Carbon Allotrope with Dirac Cones\"","max_results":5,"sort_by":"submittedDate"}) arxiv_search.run({"^^^^^^^^2query2 semimetallic 2D carbon allotrope Dirac cones","max_results":^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2query2^^^^,"sort_by":"relevance"}) Cyclo-graphyne (CGY) is an emerging two-dimensional carbon allotrope characterized by a porous network of sp/spPRESERVED_PLACEHOLDER_^^^^2query2^^^^-hybridized carbon atoms and a semimetallic electronic structure with Dirac cones. Density functional theory has been used to characterize its structural, energetic, dynamical, thermal, electronic, mechanical, optical, and vibrational properties, identifying a combination of large pores, ultranarrow-gap semimetallicity, mechanical compliance, and distinctive spectroscopic signatures. Within this characterization, CGY is described as energetically viable, dynamically stable, thermally stable up to at least ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2query2query2query2^^^^ K in ab initio molecular dynamics, and optically and mechanically isotropic in-plane, which positions it as a candidate for gas capture and separation, flexible nanoelectronics, and optoelectronics (&&&^^^^2query2^^^^&&&).

^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^. Crystal structure and bonding topology

CGY crystallizes in the hexagonal space group P6/mmm (No. ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2sort_by2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^), with lattice vectors PRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^ Å and angles $\alpha=\beta=90^\circ$, $\gamma=120^\circ$. Its framework contains five distinct C–C bond lengths: ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^.225 Å, ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^.24^^^^2query2^^^^ Å, ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^.347 Å, ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^.36^^^^2query2^^^^ Å, and ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^.4^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^9 Å. The shortest bonds, around ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^.225 Å, correspond to acetylenic C$\equiv$C linkages formed by sp-hybridized carbon atoms, whereas the longer bonds in the ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^.36^^^^2query2^^^^– OR title:\2^^^^.4^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^9 Å range are associated with sp$^2$-hybridized carbon atoms located at the vertices of triangular and tetragonal ring motifs (&&&^^^^2query2^^^^&&&).

The pore architecture is a defining structural feature. The unit-cell description identifies ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\22^^^^-membered pores with alternating triangular and tetragonal character, and the overall summary specifies pores of approximately 8.5 Å. This porous arrangement is inseparable from the mixed hybridization pattern: the acetylenic linkages provide short, stiff connectors, while the sp$^2$ vertices define the larger polygonal framework. In structural terms, CGY belongs to the broader family of graphyne-like carbon networks but is distinguished by the coexistence of a highly open lattice and hexagonal crystallographic symmetry.

2. Energetic viability, phonons, and thermal robustness

The energetic characterization reports a cohesive energy of $E_{\rm coh}=-8.32$ eV/atom and a formation energy relative to graphene of $E_{\rm form}=+0.91$ eV/atom. These values are described as comparable to those of other synthesized graphynes, and CGY is further stated to be only $\sim 0.27$ eV/atom less favorable than PRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2query2^^^^-GY, which is already synthesized. In that context, the reported energetics are taken as evidence of strong interatomic bonding and of CGY being a promising synthetic target (&&&^^^^2query2^^^^&&&).

Dynamical stability is supported by phonon dispersion calculations showing no modes with imaginary frequencies along PRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^–M–K–PRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\22^^^^. The vibrational spectrum contains high-frequency optical branches associated with CPRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^3C stretching in the 6^^^^2query2^^^^–7^^^^2query2^^^^ THz range, equivalent to 2^^^^2query2query2query2^^^^–233^^^^2query2^^^^ cmPRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^4, including values near 65 THz (2^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2sort_by2query2^^^^ cmPRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^5) at PRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^6, 67 THz (224^^^^2query2^^^^ cmPRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^7) at M, and 62 THz (2^^^^2query2Cyclo-Graphyne semimetallic 2D carbon allotrope Dirac cones2query2^^^^ cmPRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^8) at K. Mid-range optical modes occur around 45 THz, or approximately ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2submittedDate2query2query2^^^^ cmPRESERVED_PLACEHOLDER_^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^9, and the acoustic branches originate at ^^^^2query2^^^^ cm$\alpha=\beta=90^\circ$^^^^2query2^^^^ with LA/TA/ZA linear or quadratic dispersions. The isolated high-frequency bands are identified as fingerprints of the acetylenic linkages.

Thermal stability was examined by ab initio molecular dynamics in the NVT ensemble using Nosé–Hoover dynamics at 3^^^^2query2query2^^^^ K and ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2query2query2query2^^^^ K, with a ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^ fs time step over a total time of 5 ps. Under these conditions, the total energy and temperature remained bounded within $\alpha=\beta=90^\circ$^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^ of the target temperature, and no C–C bond rupture or structural collapse was observed during 5 ps at ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2query2query2query2^^^^ K. The reported interpretation is that CGY is suitable for high-temperature applications such as gas separation membranes.

3. Electronic structure and Dirac semimetallicity

CGY is reported to be semimetallic with an ultranarrow band gap. The calculated gap is approximately ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\22^^^^ meV at the PBE level and approximately ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^5 meV with HSE^^^^2query2^^^^6. At the same time, the band structure exhibits two Dirac cones, with Dirac points located along the $\alpha=\beta=90^\circ$2 and $\alpha=\beta=90^\circ$3 paths rather than exactly at high-symmetry points. Their reciprocal-space positions are given in fractional coordinates as $\alpha=\beta=90^\circ$4 and $\alpha=\beta=90^\circ$5 (&&&^^^^2query2^^^^&&&).

Near each Dirac point, the dispersion is linear and is expressed as

$\alpha=\beta=90^\circ$6

The estimated Fermi velocity is $\alpha=\beta=90^\circ$7 m/s, which is stated to be of the same order as graphene. The density of states vanishes linearly at $\alpha=\beta=90^\circ$8, consistent with Dirac behavior, and the projected density of states indicates comparable sp/sp$\alpha=\beta=90^\circ$9 contributions within $\gamma=120^\circ$^^^^2query2^^^^ eV of the Fermi level.

A recurrent point of clarification is that the material is not described as strictly gapless. The coexistence of two Dirac cones with a finite but ultranarrow PBE/HSE^^^^2query2^^^^6 gap is presented explicitly as semimetallicity rather than idealized zero-gap behavior. Within the reported interpretation, this electronic structure implies massless fermions and high mobility and therefore supports relevance to flexible nanoelectronics.

4. Elastic response and mechanical compliance

The reported in-plane elastic stiffness constants, in 2D units of N/m, are $\gamma=120^\circ$^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^, $\gamma=120^\circ$2, and $\gamma=120^\circ$3. These values satisfy the Born–Huang stability conditions $\gamma=120^\circ$4 and $\gamma=120^\circ$5, which is presented as confirmation of mechanical stability (&&&^^^^2query2^^^^&&&).

From these elastic constants, the derived mechanical properties are a Young’s modulus of 3^^^^2query2^^^^.9 N/m, equivalently $\gamma=120^\circ$6 GPa·nm, a shear modulus of 8.74 N/m, and a Poisson’s ratio of ^^^^2query2^^^^.77. The in-plane response is reported to be nearly identical along the $\gamma=120^\circ$7 and $\gamma=120^\circ$8 directions, reflecting hexagonal isotropy. Relative to graphene, CGY has a Young’s modulus of approximately one-eleventh of graphene’s value ($\gamma=120^\circ$9 N/m) and a Poisson’s ratio about four times larger than graphene’s ($\equiv$^^^^2query2^^^^).

This combination of low in-plane stiffness and large Poisson’s ratio is the basis for describing CGY as highly compliant. In the source characterization, the significance assigned to this response is suitability for bendable and foldable electronics. A plausible implication is that the porous lattice and mixed sp/sp$\equiv$^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^ bonding topology are directly linked to this unusual softness relative to dense hexagonal carbon sheets, although the mechanical section itself reports the result rather than a separate deformation mechanism.

5. Optical response

The in-plane dielectric response is reported to be isotropic, with $\equiv$2. For the imaginary part of the dielectric function, $\equiv$3, the absorption onset occurs at approximately ^^^^2query2^^^^.7 eV, followed by a first sharp peak near ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^.^^^^2query2^^^^ eV in the near-infrared and strong ultraviolet peaks between 4 eV and 7 eV. For the real part, $\equiv$4, the static value is $\equiv$5, the dispersion is weak in the visible range, and slight minima appear near 3 eV (&&&^^^^2query2^^^^&&&).

The absorption coefficient $\equiv$6 is negligible below ^^^^2query2^^^^.7 eV and reaches a maximum of approximately $\equiv$7 cm$\equiv$8 in the ultraviolet. The reflectivity $\equiv$9 is about 3^^^^2query2^^^^% in the infrared below ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^ eV, decreases to below ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2query2^^^^% in the visible, and then rises again to roughly ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^5–2^^^^2query2^^^^% in the ultraviolet.

These results define a spectral profile that combines strong UV absorption with IR reflectivity. The reported significance is relevance to optoelectronic and photodetector applications. Because the in-plane optical response is isotropic, any device concepts based on these calculated spectra would not rely on crystallographic orientation within the basal plane.

6. Raman and infrared fingerprints, and research significance

CGY exhibits distinct Raman-active modes at ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2id:(Lima et al., 22 Sep 2025) OR title:\2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^9 cm$^2$^^^^2query2^^^^ and ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^337 cm$^2$^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^, both assigned to in-plane sp$^2$2 symmetric vibrations, and at 2^^^^2query2^^^^44 cm$^2$3 and 2^^^^2query2^^^^95 cm$^2$4, assigned to symmetric C$^2$5C stretching. The infrared-active spectrum includes modes at 2^^^^2query2^^^^3 cm$^2$6 for out-of-plane bending, 489 cm$^2$7 for strong acetylenic bending, 7^^^^2query2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^ cm$^2$8 for asymmetric acetylenic bending, a broad set from 9^^^^2query2^^^^7 to ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^494 cm$^2$9 associated with mixed sp/sp$^2$^^^^2query2^^^^ bending and stretching, and high-frequency C$^2$^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^C stretching features at ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^986, 2^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2sort_by2query2^^^^, and 2^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2^^^^85 cm$^2$2 (&&&^^^^2query2^^^^&&&).

The source characterization emphasizes that the Raman and infrared signatures are sufficiently distinctive to provide an unambiguous experimental fingerprint, especially the Raman peak near 2^^^^2query2^^^^44 cm$^2$3 and the infrared feature near 489 cm$^2$4. This is important because the identification of porous carbon allotropes often depends on correlating structural motifs with high-frequency acetylenic vibrations and lower-frequency bending modes.

Taken together, the reported properties place CGY at the intersection of porous 2D carbon chemistry and Dirac semimetal physics. The combination of approximately 8.5 Å pores, semimetallicity with two Dirac cones, thermal robustness up to at least ^^^^2id:(Lima et al., 22 Sep 2025) OR title:\2query2query2query2^^^^ K in the reported AIMD protocol, highly compliant and isotropic mechanics, and distinctive optical and vibrational responses is the stated basis for its consideration in gas capture and separation, flexible nanoelectronics, and UV/IR optoelectronic devices. Within the specific comparison given, its formation energy being only $^2$5 eV/atom less favorable than already synthesized $^2$6-GY further supports its status as a plausible synthetic target.