Excitation of the higher overtones involves progressively less and less additional energy and eventually leads to dissociation of the molecule, because the potential energy of the molecule is more like a Morse potential.
12.
In the quantum mechanical picture, the vibrational levels and vibrational wavefunctions are those of quantum harmonic oscillators, or of more complex approximations to the potential energy of molecules, such as the Morse potential.
13.
It clearly shows that the Morse potential is the combination of a short-range repulsion term ( the former ) and a long-range attractive term ( the latter ), analogous to the Lennard-Jones potential.
14.
If a Morse potential is assumed, plotting \ Delta G _ { v + \ frac { 1 } { 2 } } against v + 1 / 2 should give a straight line, from which it is easy to extract v _ { max } from the intercept with the x-axis.
