Structural modifications of graphyne layers consisting of carbon atoms in the sp- and sp²-hybridized states

A model scheme is proposed for obtaining layered compounds consisting of carbon atoms in the sp- and (vnsp)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 modifications 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 calculations 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-graphyne, which should be the most stable structural modification of graphyne