I need help calculating the energy levels of the excited states of an O2 molecule.

I've already calculated the zero-point energy, but I am unsure of how to proceed. I know the potential energy function and the frequency of vibrations.

Question

I need help calculating the energy levels of the  excited states of an O2 molecule.

I've already calculated the zero-point energy, but I am unsure of how to proceed.  I know the potential energy function and the frequency of vibrations.

anonymous · Answer

To what degree of accuracy?  It sounds like you mean excited vibrational states, and in the crudest approximation you just imagine it's a SHO and use the standard quantum mechanical result for the location of the energy levels above the bottom of the potential well.  Those energy levels will generall be expressed as$$\hbar \omega ( n + \frac{1}{2})$$

anonymous · Answer

Keep in mind each vibrational level will be subdivided into rotational levels as well, and these can be calculated using the quantum solution to the rigid rotor problem.  Not sure if you need that.

anonymous · Answer

Thank you so much.  The wording in the problem was very confusing, it literally just says "calculate the zero-point energy and the energy between successive states".

I think the SHO will be accurate enough.  Thank you!