In a first principle computational study, using density functional theory, we have identified four types of 2D carbon sheets, similar to graphene, made entirely of non-regular hexagons. In one case, we get a structure where the non-regular hexagons have four sides of length d₁ = 1.416 Å and two sides of length d₂ = 1.68 Å. Next case, in the non-regular hexagons the side d₁ (two times) and d₂ (four times) are exchanged. In two other cases, the non-regular hexagons have three pairs (opposite sides) of different lengths (d₁ = 1.529 Å, d₂ = 1.567 Å, and d₃ = 1.612 Å; d₁ = 1.387 Å, d₂ = 1.348 Å, and d₃ = 1.387 Å). By propper choice of the non-regular hexagon sides, one could arrive at a 2D carbon system like graphene, but with a tunable band gap. The structure is more stable when the system has more number of regular C–C bonds than the longer C–C bonds. Due to its non-regular hexagons, special atomic configuration, this system may have, like graphene, unusual properties. It is semiconducting, and there is no need to functionalize it for opening the band gap as is the case with graphene.

中文翻译：

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非规则六角形二维碳，石墨烯的同素异形体：第一性原理计算研究。

在使用密度泛函理论的第一个原理计算研究中，我们确定了四种类型的2D碳板，类似于石墨烯，完全由不规则六边形制成。在一种情况下，我们得到一种结构，其中非规则六边形具有四个长度为d ₁  = 1.416Å的边和两个长度为d ₂  = 1.68Å的边。在下一种情况下，在非正六边形中，边d ₁（两次）和d ₂（四次）被交换。在另外两种情况下，非正六边形具有三对不同长度的（相对的边）（d ₁  = 1.529Å，d ₂  = 1.567Å和d ₃  = 1.612Å；d ₁  = 1.387Å，d ₂  = 1.348Å  ，d ₃ = 1.387Å）。通过propper选择非正六边形边，人们可以到达像石墨烯的二维碳系统，但有一个可调带隙。当系统具有比规则C-C键更长的规则C-C键数量时，结构会更稳定。由于其不规则的六边形，特殊的原子构型，因此该系统可能像石墨烯一样具有异常的特性。它是半导体，不需要像石墨烯那样将其功能化以打开带隙。