This cluster is considered as a separate “molecule” and for it‘s calculation the usual quantum chemistry methods are applied. The advantage of the clusters approach is it‘s applicability for modelling real situations of impurity atoms and - if necessary - taking into consideration a possible distortion of the crystal lattice.

However, the usual cluster approach has a deficiency. Is the “infinity” crystal substituted by a group of atoms, a problem with atoms lying on the edge of the cluster arises. The presence of such atoms with torn bonds distorts the energy spectrum of the crystal. This distortion can be diminished by increasing the size of the cluster, but the approximation to the exact value is very slow.

This deficiency can instead be removed by connecting the torn bonds with each other and hereby closing them. A similar procedure, the so-called “periodical boundary conditions”, is applied in studying the energy spectrum of the infinite ideal crystals. The special feature of our approach is the application the closing procedure of these bonds to small clusters to study crystals with distorted regularity properties (such as impurity, edges and other). In this paper, the CC approach is applied to graphene, a relatively new material 