Convergence of DFT results on the zigzag edge reconstruction with respect to the parameters of the model of semi-infinite graphene
Convergence of the energetics of reactions at graphene edges in density functional theory calculations with respect to geometrical parameters of the atomistic model of a semi-infinite graphene layer was investigated. As an example of such reaction, we considered the first stage of reconstruction of zigzag graphene edges, formation of the first pentagon-heptagon (57) pair. As a model, we used a zigzag graphene nanoribbon (ZGNR) under periodic boundary conditions. We computed the reaction energy for ZGNRs of different widths in simulation cells of different length, fixing different numbers of zigzag rows at the edge opposite to the one where the reconstruction takes place in such a manner that interatomic distances between these atoms are the same as in bulk graphene and considering carbon and hydrogen termination of the opposite edge. Our calculations showed that to converge the results, the ZGNR should consist minimum of 6 zigzag rows and the distance between the periodic images of 57 pairs along the ZGNR axis should be at least 6a0, where a0 is the lattice constant of graphene. It was demonstrated that fixation of atoms at the edge opposite to the one where the reconstruction takes place and the way this edge is terminated almost do not affect the results. Furthermore, we studied how the edge magnetization changes during the formation of 57 pairs and showed that the ordering of spins at the opposite nanoribbon edges should switch from the antiparallel (antiferromagnetic) to parallel one (ferromagnetic) upon decreasing the distance between the pairs. The calculations were performed using the Perdew-Burke-Ernzerhof functional as implemented in the VASP code.