The asymptotic pairwise interaction between nonbonded atoms in planar dimers is analyzed. It is pointed out that the second derivative of the energy with respect to the perpendicular coordinates of the two nonbonded atoms enables to extract the parameters of the pairwise electrostatic interaction from the total energy. In the limit of large intermolecular separations the coupling second derivatives of the energy are shown to be determined by the atomic polar and quadrupolar tensors of the isolated monomers. It is further shown that the dipole moment of planar molecules can be expressed in terms of the out of plane Cartesian derivatives of its perpendicular component 〈z〉, and that the molecular quadrupole moments can be expressed in terms of these derivatives and the out of plane Cartesian derivatives of the second moments 〈xz〉 and 〈yz〈. These derivatives form a unique and well defined decomposition of the molecular multipoles into atomic quantities that can be formally interpreted as atomic point charges and point dipoles. These atomic point charges and point dipoles completely determine the asymptotic total and pairwise interactions in planar and rigid dimers.