Geometries were optimized until all forces on atoms were less than 0.01 eV / Å. The graphite (0001) surface was represented by a slab consisting of three graphene layers. A vacuum region of about 23 Å was inserted between the surface slabs. A rectangular surface unit cell with the dimensions (8.581 Å x 14.863 Å) containing one IL pair, was employed as simplified model for the overlayer structure. This structure had been deduced from the experimental STM images previously. The integration over the first Brillouin zone was done employing a 2x1x1 gamma-centered k-point mesh.