The Morse potential has many unique analytic properties, which makes it especially suitable for modelling.
There are lots of systems which can be analysed in exactly the same way (the simplest one is the harmonic oscillator), but within this pattern the feature which makes the Morse potential really unique is overlooked.
Nevertheless, as a matter of fact, the scattering properties of the Morse potential have not found much attention so far, and there still is some work to do.
ij] are parameters associated with a Morse potential for the isolated i-j diatom, which are adjusted by experimental data.
For the case of a LEPS potential, the asymptotic vibrational quantum states of the diatom are the ones of a Morse potential  whose eigenenergies are given by
On the other hand, Berrondo et al  employ the relationship between Morse potential and the two-dimensional harmonic oscillator to deduce the corresponding relation:
Matrix Elements for the Morse potential using ladder operators, Int.
Keywords Hypervirial theorem, coulomb and Morse potentials, langer transformation, matrix elements.
16] to incorporate the modified Morse potential function , to estimate elastic constants and stress-strain relationships of nanotubes under tensile and torsion loadings.
The modified Morse potential function  is simple and is used in the present study.
We also have in mind that the inter-site Morse potential favours the excitation of soliton-like modes.
Coupling the inter-site Morse potential to the on-site Morse potential offers a variety of possibilities as the latter favours the onset of DB (for the case of on-site harmonic oscillations coupled to inter-site harmonic oscillations see  and references therein).