2.1.3 Polyatomic Oscillators

Sections 2.1.1 and 2.1.2 introduced the ideas of molecular oscillations in the context of a diatomic molecule. Generalization to polyatomic molecules means many oscillators are in one molecule, and the system can not be considered as simply a collection of diatomic oscillators. Rather, the groups of atoms vibrate in modes.

• We assume that all modes are independent. This means energy cannot flow from one mode to another. This is a reasonable assumption for most of the experiments we conduct in the forensic laboratory, and making this assumption allows us to view the molecule as a collection of separate modes. Each mode has its own frequency.
• Modes for molecules involve complex motions of the individual atoms. An easy visualization of the atomic motions for molecular modes may not be possible, but the frequency of such modes can be measured.
• Non-linear molecules have $3N-6$ vibrational modes, but not all (or indeed any) need have allowed IR transitions. $N$ is the number of atoms in the molecule.
• Linear molecules have $3N-5$ vibrational modes, but any or all may not be allowed IR transitions.