The internal potential energy function for a diatomic molecule is approximated by the Morse potential
V(r)=V0(1−e−(r−a)/b)2−V0,
where r is the distance of separation of the two atoms, and V0, a, b are positive constants. Make a sketch of the Morse potential.
Suppose the molecule is restricted to vibrational motion in which the centre of mass G of the molecule is fixed, and the atoms move on a fixed straight line through G. Show that there is a single equilibrium configuration for the molecule and that it is stable. If the atoms each have mass m, find the angular frequency of small vibrational oscillations of the molecule.