All diatomic and all linear molecules, e.g. HCCH, NCCN, CO2
| Due to the low mass of electrons, 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 of an external axis are (2J+1)-fold degenerate. In contrast, for a spherical top, there is no difference between rotational constants A and B and the quantum number K except 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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Auf diesem Webangebot gilt die Datenschutzerklärung der TU Braunschweig mit Ausnahme der Abschnitte VI, VII und VIII.
