What does the moment of inertia for a molecule mean? How is it useful? Most importantly, how would I go about solving it for a triatomic molecule?
The moment of inertia is defined for a molecule as it would be for any other solid: you consider the nuclei as points with mass, ignore the mass of the electrons, and you can then calculate either the scalar moment of inertia or the tensor of the same name.
The moment of inertia of a molecule is involved in the quantification of its rotational movements. Of the top of my head, the two areas of chemistry where this plays a big role are:
- rotational spectroscopy: the rotation of a molecule is quantized, and the value that the angular momentum can take are related to the moment of inertia of the molecule.
- the rotational entropy of a molecule is linked through statistical mechanics to its inertia tensor.