  We investigate how parameters of the model of semi-infinite graphene based on
a graphene nanoribbon under periodic boundary conditions affect the accuracy of
ab initio calculations of reactions at graphene edges by the example of the
first stage of reconstruction of zigzag graphene edges, formation of a
pentagon-heptagon pair. It is shown that to converge properly the results, the
nanoribbon should consist of at least 6 zigzag rows and periodic images of the
pair along the nanoribbon axis should be separated by at least 6 hexagons. The
converged reaction energy and activation barrier for formation of an isolated
pentagon-heptagon pair are found to be -0.15 eV and 1.61 eV, respectively. It
is also revealed that such defects reduce the graphene edge magnetization only
locally but ordering of spins at opposite nanoribbon edges switches from the
antiparallel (antiferromagnetic) to parallel one (ferromagnetic) upon
increasing the defect density.
