A force field that accounts for the quantum chemical reality of interacting atoms must include Coulomb interactions between bonded atoms. The short-range nature of such 1,2 interactions necessitates atomic multipole moments in addition to point charges. However, the close proximity of bonded atoms would normally lead to a divergent multipolar expansion. A special algorithm presented here, within the scope of the previously presented multipole shifting method [M. Rafat and P. L. A. Popelier, J. Chem. Phys. 124, 144102 (2006)], shows that convergence can nevertheless be achieved by a suitable selection of multipole displacements. The algorithm is applied to improve the convergence of the multipolar expansion within the quantum theory of atoms in molecules approach.