AbstractA procedure is presented which allows a more economical representation of the potential produced by orbital charge distributions in which the orbitals are expanded in terms of a finite set of polynomial Gaussian functions. The basic idea is that the products of pairs of Gaussian basis functions, on which the charge distributions are expanded, are expressed in terms of a new basis set of optimally chosen single Gaussian functions. Such a procedure has been tested in a particular case and a few possible applications have been suggested.