Screening for Planar Carbon Allotropes Using Structure Space Sampling

A space-sampling method is used to evaluate which theoretically proposed planar carbon allotropes may be experimentally realized. The key idea is that the frequency of occurrence of an allotrope measures its realizability in experiments. The frequency of occurrence is determined in three steps: first, 6840 random planar structures are generated using a topology-based generator, then these structures are relaxed using density functional theory calculations, and finally, 1662 distinct structures are found by merging the same structures and structures with high frequencies of occurrence are identified. By plotting the frequency of occurrence against the total energy, two allotropes that have not been synthesized yet are proposed. In the two allotropes, OP graphene-Z is more likely to be experimentally realized when accounting for other synthesizability criteria. The relationship between the frequency of occurrence and the geometry structure is also analyzed. Our results shed some light on the direction of the synthesis effort for graphene-like planar allotropes.