A model scheme is proposed for obtaining layered compounds consisting of carbon atoms in the sp and sp 2 hybridized states. This model is used to find the possibility of existing the following seven basic structural modifications of graphyne: α , β1 , β2 , β3 , γ1 , γ2 , and γ3 graphyne. Polymorphic modifica tions β3 graphyne and γ3 graphyne are described. The basic structural modifications of graphyne contain diatomic polyyne chains and consist only of carbon atoms in two different crystallographically equivalent states. Other nonbasic structural modifications of graphyne can be formed via the elongation of the carbyne chains that connect three coordinated carbon atoms and via the formation of graphyne layers with a mixed structure consisting of basic layer fragments, such as α-β graphyne, α-γ graphyne, and β-γ graphyne. The semiempirical quantum mechanical MNDO, AM1, and PM3 methods and ab initio STO6 31G basis calcu lations are used to find geometrically optimized structures of the basic graphyne layers, their structural parameters, and energies of their sublimation. The energy of sublimation is found to be maximal for γ2 gra phyne, which should be the most stable structural modification of graphyne.

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In the present paper, a theoretical study of the structure and electronic properties of new polymorphic conformations of graphyne layers modeled on layers of graphene L 3-12 was performed. Graphyne layers have been constructed by replacing carbon-carbon bonds between three-coordinated (sp 2-hybridized) atoms in the graphene layer of L 3-12 with diatomic carbyne chains. Geometric optimization and examination of electronic properties of novel graphyne architectures were performed within the framework of density functional theory using the gradient approximation. Calculations have shown the possibility of stable existence of three main polymorphic conformations of graphyne layers. The graphyne layers were designed by incorporating a carbyne chain into the initial L 3-12-graphene layer by following rules: for the γ-L 3-12-graphyne layer, one bond of each three-coordinated atom was substituted by a carbyne chain, for the β-L 3-12-graphyne layer, two bonds of those atoms were replaced, and for α-L 3-12-graphyne layers three bonds were replaced. The sublimation energy of the graphyne layers is in the range from 6.52 to 6.61 eV / atom that is less than the sublimation energy of the original L 3-12 graphene layer (6.66 eV / atom) as well as the sublimation energy of hexagonal graphene (7.76 eV / atom). However, the value of the sublimation energy of the graphyne layers is in the range of experimentally synthesized carbon materials that are stable under normal conditions. All the graphyne layers studied in this work are semiconductors with the energy gaps widths from 0.18 to 0.91 eV.

The structure of seven new polymorphic varieties of graphyne layers has been calculated using the density functional theory at the generalized gradient approximation. The model of graphyne layers is based on 4-6-12 graphene layer. For graphyne layers the sublimation energy varies in the range from 6.62 to 7.08 eV atom−1, the band gap ranges from 0 to 0.643 eV. The structures of polymorphs of the graphyne are characterized by deformation parameter the value of which correlates well with the sublimation energy.