A method is proposed for using isoenergetic configurations formed from many-center Coulomb Sturmians as a basis for calculations on N--electron molecules. Such configurations are solutions to an approximate N-electron Schrödinger equation with a weighted potential, and they are thus closely analogous to the Goscinskian configurations which we have used previously to study atomic spectra. We show that when the method is applied to diatomic molecules, all of the relevant integrals are pure functions of the parameter s=kR, and therefore they can be evaluated once and for alland stored.