On the nature of interlayer interactions in a system of two graphene   fragments
  With the help of the quantum chemistry methods we have investigated the nature of interlayer interactions between graphene fragments in different stacking arrangements (AA and AB). We found that the AB stacking pattern as the ground state of the system, is characterized by the effective inter-band orbital interactions which are barely present in the AA. Their vanishing induces electronic decoupling between the graphene layers, so that the bonding interaction $\Delta E_{oi}$ between the flakes is drastically reduced from -0.482 eV to -0.087 eV as the stacking pattern is changed from AB to AA. The effective way to improve the bonding interaction between layers preserving the same AA lattice order is to induce rotation of the layer. As the flake is rotated, the bonding interactions are improved mostly due to suppression of the Pauli repulsion which in turn increases the interlayer orbital interactions, while the inter-band part of those remain negligible on the whole range of the rotation angle. The Pauli repulsion is also found to be the main force moving apart two fragments as the stacking pattern is changed from AA to AB. This enhances the equilibrium interlayer distance, which for the AA staking is larger than the established value for the AB stacking (3.4 A) 
Julia Berashevich and Tapash Chakraborty
cond-mat.mes-hall