How to interpret rotational, electronic, vibrational energy levels

[fog37]

Hello Forum,

I am confused about the concept of rotational energy levels, electronic energy levels, and vibrational levels. A graph of "Energy versus Distance" is usually presented and the various horizontal bars represent the energy levels, which are simply energy amounts.

The energy of a molecule/atom or system of atoms/molecules can be decomposed in 3 parts: rotational, vibrational and electronic energy (translational energy should also be included).

1. Rotational energy is associated to the rotation of the entire structure of the molecule (nuclei+electrons).
2. Vibrational energy is associated to the vibration of the entire molecule.
3. Electronic energy refers to the excitation of the electrons inside the molecule only.

I read that the electronic ground state has, "contains", several vibrational energy levels. What does that exactly mean that an energy level contains other energy levels? Are there multiple vibrational energy levels inside the electronic ground state?

Some books explain that the vibrational levels are indexed for each electronic state while rotational levels are indexed only for one vibrational state...What does that really mean?

This is how I envision it: when a molecule absorbs energy from an external source its outer electron may remain in the ground state while the molecule is vibrating/rotating at the same time (i.e. the molecule is in an excited rotational/vibrational state) or the electrons may be in an excited state while the whole molecule is also rotating and/or vibrating...

• The rotational energy levels represents the discrete (quantized) energies associated to the molecule or atom when the it is rotating, correct?
  
• How about electronic energy levels? Do those electronic energies correspond to the energies associated with electrons when they are excited inside atoms or molecules?
  
• The vibrational energy levels correspond to the energy that a molecule/atom has due to its vibrational motion (state), correct?

Am I on the right track?


Thanks,
Fog37

 

[Simon Bridge]

The energy that varies with distance is the potential energy function.
The energy "levels" are the energy eigenvalues.

The eigenvalues usually refer to the whole "thing" spoken of - unless the context (or other statements) indicate otherwise. So molecular levels are the energy eigenstates for the entire molecule.

It is difficult to say what a particular description means without the context. i.e. it would be unusual to think of electrons carrying any vibrational energy from the molecule. Perhaps someone is alluding to the Frank-Condon principle - where vibration and electron states can be closely linked?

Often books are a bit off-hand with their terminology, which can be confusing. This also makes comparing statements from different books tricky - you cannot always assume that the same words mean the same things. The trick is to look closely at the definitions and at the maths used.

I think your last three bullet points would be a common meaning when talking about molecules - the electronic, rotational, and vibrational, states would be contributions to the internal energy of the molecule. Energy may go to vibrating or spinning the molecule, or to exciting it's electrons. It may also go to translating the molecule - which would be external kinetic energy.