In order to obtain wave functions, energies, and energy derivatives for molecular systems, we present a general approximation procedure based on distribution theory. We found in the testing functions space of distribution theory, an appropriate mathematical basis to overcome theoretical difficulties related with the standard perturbational method in which the Born–Huang proposal is supported and that have been worked unsuccessfully until now. Specifically, we refer to two problems: the separation between nuclear and electronic coordinates and the existence of expansions convergent toward ground-state wave functions. Using generalized functions and their properties, we begin by proving that the expectation value of electronic energy for molecules are analytic functions of the nuclear coordinates. We show that this result could be expressed in a particular set of 3N−6 internal coordinates. We also obtain new expressions for energy derivatives. These developments are made for the nonrelativistic Schrödinger Hamiltonian. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 121–132, 1999