The electrostatic interaction energy between a quantum chemical charge distribution and an arbitrary external potential is approximated using the expectation value of distributed multipole operators fitted to the electrostatic potential. This operator, by construction, yields the best possible representation of the interaction energy in the framework of a limited multi-centered multipole expansion of the interacting charge distributions. The use of this operator may be particularly advantageous in quantum/classical mixed calculations, because it ensures a smooth transition between quantum chemical and molecular mechanical modeling of the electrostatic interaction between subsystems. (C) 2002 Published by Elsevier Science B.V.