# Rotational Transitions

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### Reference Materials[edit]

- Rotational Vibrational Coupling (Wikipedia)
- Rovibrational Spectroscopy (UC Davis)
- Rotational Vibrational Spectroscopy (Wikipedia)

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## Rotational Transitions

### 1 Order of Magnitude Energies

Molecules can rotate, and have rotational energies that depend on their angular momentum. If is the quantum angular momentum number,

For small ,

So the electronic, vibrational, and rotational energy states have contributions that scale with the electron-to-nucleus mass ratio:

Rotational energies can be described using the angular momentum number :

where , is the moment of inertia, and for diatomic molecules, we can use the reduced mass :