  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)
