The potential energy curves for the ground state of diatomic H2 and N2+ molecules are constructed techniques using the five-parameter H-H function. The estimated dissociation energies are 4.61 ± 0.1 eV and 8.70 ± 0.20 eV for H2 and N2+ respectively. The estimated D0 values are in good agreement with literature values. The r-Centroids and Franck-Condon factors for the bands of C1∏u → X1Σ+g of H2 and A2∏u1 → 4Σu+ X of N2+ molecules have been determined. The Franck-Condon factors are evaluated by the approximate analytical method of Jarmain and Fraser. The absence of the bands in these systems is explained.