Number of equidistant neighbors on honeycomb lattice

Abstract A convenient scheme is presented for calculating potential energy of van der Waals interacting bilayer graphene and other similar 2D compounds. It is based on the notion of the existence of two types of local symmetry of carbon atoms ordering, a 3- and 6-fold one. Potential energy of an atom is expressed as a sum of contributions from rings of equidistant atoms on neighboring layer. Methods are described to compute the radius of rings of equidistant atoms and number of atoms they contain. Exact positions of atoms are found as well, allowing to apply the introduced method in modelling of anisotropic potentials and to be used when twisting between layers is present.