Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 2B / Section B / 34 / b / Solution

Write $s=v+1/2$ and complete the square in the Morse oscillator energy:The finite bound-level sequence approaches the dissociation limit at the vertex of this extrapolated parabola. Thus the bond potential-well depth isThe continuous vertex is a convenient way to identify the limit; it is not an additional normalizable bound level at the threshold.