A technique for constructing the Pade representation is developed on the basis of the perturbation theory to describe vibrational–rotational spectra of diatomic molecules. The procedure provides fast summation of the series over the rotational quantum numbers. The physical meaning of Pade approximants becomes clear by examining the problem of the molecular potential function. The theoretical investigations are applied to calculations which show good prospects of the proposed approach in examples of solving the inverse problems on the force constants of the H2 molecule. The values of the potential function obtained for the repulsive part of the potential up to the dissociation limit agree well with its "experimental" RKR–values.