We have, within the framework of the molecular mechanics method SIBFA, improved the formulation of the Coulomb (electrostatic) energy contribution to the intermolecular interaction energy. This was done by integrating "overlap-like" terms into two components of the multipolar development used to calculate this contribution in SIBFA. The calibration of the new component is done on five water dimers by fitting this augmented electrostatic contribution to the corresponding E-c term. Several tests are done on (i) representative neutral and ionic hydrogen-bonded complexes; (ii) the complexes of metal cations (Cu(I) and Cu(II)) with a neutral or an anionic ligand; and (iii) a representative stacked complex. The improvement brought by the new formulation reduces the difference between the ab initio (E-c) and molecular mechanics (E-MTP*) values by almost an order of magnitude when compared to the values of E-MTP calculated using the standard method.