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It is proposed a new approach to construction of the potential function of diatomic molecules as a sum of the known perturbed Morse oscillator function, the Simons-Parr-Finlan molecular potential in the middle of the potential curve, function of the -Cn/Rn type at the large internuclear distances. Within this approach it is presented a precise scheme for computing the molecular spectral parameters, namely, vibrational, rotational, centrifugal constants for the electronic states of diatomics. As application it was carried out calculation of the of molecular constants (cm-1) for the X1Σ+ B1Π states of the KRb dimer and rubidium dimer and performed further comparison with experimental data. Within consistent approach to calculation of the electron-nuclear γ transition spectra (set of vibrationrotational satellites in molecule) of molecule there are obtained the estimates for vibration-rotationnuclear transition probabilities in a case of the emission and absorption spectrum of nucleus 127I(E(0)g = 203 keV) in the molecule of H127I for different approximations of the for potential curves: the hadmonic oscillator, the Dunham model and presented approach.