All diatomic and all linear molecules, e.g. HCCH, NCCN, CO2
Due to the electrons' low mass, linear molecules display an almost neglectable moment of inertia with respect to the molecule's axis. Therefore, the considerations here are confined to a rotation around the two axes perpendicular to this axis (K = 0). For the rotational energy we obtain the important relation: | ![]() |
EJ = BJ(J + 1) |
This is the same equation as for a spherical top. Nevertheless we need to be aware that for a linear top, the energies respective an external axis are (2J+1)-fold degenerated. In contrast, for a spherical top, there is no difference between rotational constants A and B and the quantum number K accepts one of the (2J+1) arbitrary values that correspond to an orientation of the angular momentum to the molecule's axis. Together with an (2J+1) degeneracy respective to a fixed external orientation of the angular momentum, we find for a level of quantum number J a (2J+1)2-fold degeneracy.
For known masses and constant distances, we are able to calculate the moment of inertia for given molecules and even extend this theoretical approach to energy levels. Some useful formulas that deal with the types of molecules discussed so far can be found here and in Peter Atkins' text book.
Rotational constants of some molecules | |||
Molecule | I / 10-47 kgm2 | B / cm-1 | A / cm-1 |
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