Embedding Tensor for Two-Dimensional Carbon Allotropes
Description
Data set for paper "Graph Embedding Tensor: Unifying Topological Description, Symmetry Detection, and Structure Generation for Two-dimensional Carbon Allotropes". The embedding tensor approach allows for a coordinate-free search algorithm of 2D carbon allotropes. It also allows for the determination of symmetry and approximate coordinates. Data provided here are examples of embedding tensors for all structures obtained with up to 14 atoms per unit cell in 2D carbon crystals with threefold atomic coordination. Also included are all the CIF files for the 97 structures including pentagonal and higher rings. The 97 structures are shown in balls-and-sticks representation (with symmetry) in the PDF file included.
Files
Steps to reproduce
To reproduce the tensor data, take a threefold-coordinated structure in 2D. Identify and enumerate the faces, the edges, and the atoms, then create a tensor where \Phi_{ijk} = 1 if vertex k is part of edge j, which is itself part of face i; all other elements of the tensor are zero. The tensors are shown as text files. The <.fev> format starts with a line containing three integers indicating the number of faces (n_f), edges (n_e) and vertices (n_v), in this order. In the following lines it has the (n_f) x (n_e) x (n_v) elements (either 0 or 1) of the embedding tensor, one per line. The writing order of the elements in the file is in the form of a triple-loop, with the inner loop corresponding to the vertices and the outer loop being associated to the faces. The CIF files correspond to the relaxed structures obtained using the AIREBO potential, which was used to refine the coordinates obtained using the fast algorithm described in the paper. The primitive cells are shown in the PDF files included.
Institutions
- Pennsylvania State University
- Universidade Federal do Piaui