“…To calculate the intensities of dipole transitions, it is necessary to know the potential energy U(r) and the electric dipole moment d(r) of the molecule as functions of the internuclear distance r. In the case of transitions with a small change in the vibrational quantum number v, as a rule, v ≤ 2, the shape of these functions does not affect the result, but this is not the case for higher overtones. In particular, using the example of calculations of the intensities of transitions v ← 0 for SiO, CS, CO, and LiCl, it was shown that the use of non-analytical functions with discontinuous derivatives, for example, splines, leads to nonphysical saturation of the intensities at v ≥ 5 for SiO [10], v ≥ 7 for CS [1,11], CO and LiCl [10]. Therefore, in modern calculations, only analytic functions are used [12], but the problem still remains, since, as we will see, additional restrictions are needed.…”