The electrostatic interaction between a chemical and its site of biological action is often important in determining biological activity. In order to include this interaction in methods to assess the potential biological activity of large molecules, rapid and reliable techniques are needed for its calculation and characterization. A finite multicenter multipole expansion technique provides a good approximation of the molecular electrostatic potential in circumstances of interest. This technique introduces multipoles at expansion centers within the molecule in addition to atoms. It is difficult to interpret the significance of these multipole terms that are not centered on atoms. Methods are introduced to eliminate the expansion centers and truncate the now infinite multipole expansion. We have found that eliminating all centers with a charge less than .1 of an electron unit has little effect on the results. Two methods for obtaining multipole expansions only at atomic centers are investigated. The expansion of two center charge distributions about the nearest atom is found to give better results than dividing the two center gaussian charge distributions between the atomic centers for the gaussians. (Copyright (c) 1986 by John Wiley and Sons, Inc.)