In general, the analytical form of the PES is unknown and we must resort to a numerical fitting. It is from a computational point of view highly desirable to obtain the Hamiltonian in a sum-over-product form. This is not directly the case in the n-mode expansion, but a sum-over-product form can be obtained by fitting all the individual bar-potentials of the PES to a direct product of one-mode functions. This will give a PES of the general form