▎ 摘　　要

The opening of the energy gap and the total energy of the graphene-like bilayers are investigated using ab initio calculations. The studied model consists of a static single layer of graphene interacting with an extra dynamic one placed at a varying vertical distance d in the (AB) stacking arrangement. The effects of the vertical distance variation on the energy gap and the total energy of the system are discussed first. Starting from a distance around the van der Waals length, the energy gap does not depend on the vertical distance variation and the system exhibits graphene-like properties with minor deformations in the lattice size parameter and the energy dispersion behaviour around K points. However, it has been shown that the diagonal distance variation of the graphene-like bilayer modifies the electronic structure properties. This modification depends on an intermediate stacking arrangement between the (AA) and the (AB) configurations. It has been shown that the diagonal distance variation has an influence on the states of p(z), electrons in the (AB) arrangement and it can be explored to open the energy gap. (C) 2014 Elsevier Ltd. All rights reserved.