Transforming Two-Dimensional Carbon Allotropes into Three-Dimensional Ones through Topological Mapping: The Case of Biphenylene Carbon (Graphenylene).

In this work, we propose a new methodology for obtaining three-dimensional (3D) carbon allotrope structures from 2D ones through topological mapping. The idea is to select a 3D target structure and "slice" it along different structural directions, creating a series of 2D structures. As a proof of concept, we chose the tubulane structure 12-hexa(3,3) as a target. Tubulanes are 3D carbon allotropes based on cross-linked carbon nanotubes. One of the obtained 2D "sliced" structures was mapped into the biphenylene carbon (BPC). We showed that compressing BPC in-plane, biaxially, followed by compression along the z direction using different strain rates could generate not only the target tubulane 12-hexa(3,3) structure but also at least two others: bcc-C6 and an unreported member of the tubulane family, which we called tubulane X. The methodology proposed here is entirely general; it can be used coupled with any quantum method. Considering that the 2D biphenylene carbon network, which is closely related to BPC, has been recently synthesized, the approach proposed here opens new perspectives to obtain new 3D carbon allotropes from 2D structures.