Question

Discuss the strengths and weaknesses of the Harmonic Oscillator model system to describe the vibrational motion of a diatomic molecule . Where is the model a good approximation for vibrational motion? Where does the model break down and why ? How can the model be improved?

Please include diagrames and models and provide a full explanation this is the second time posting please answer the full question

Answer 1

The Harmonic oscillator is a good model for studying the vibrations of a diatomic molecule when the frequency of oscillations is low or in other words when the energy given to the oscillator is low. But the problem with a perfect harmonic oscillator problem is that it cannot predict bond dissociation. For this reason, another model potential is used called the Morse potential given by

where r is the distance between the atoms and

where K is the equivalent spring constant at the lowest point. See figure below.

where the blue curve shows the Morse potential and the green shows the harmonic which is a good approximation for Morse potential for low energy levels. Also, note that the harmonic potential admits equally spaced levels whereas the Morse potential levels occur with decreasing spacing.