Linear Top

All diatomic molecules and all linear molecules: $HCCH$, $NCCN$, $CO_2$.

Due to the small mass of electron, linear molecules show almost zero moment of inertia with respect to the molecular 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:

$$E_{J} = B\cdot J(J+1)$$ (46)

This is the same equation as for spherical top. Nevertheless we should have in mind that for linear top the energy levels are $(2J+1)$-fold degenerated according to the number of projections of $J$ onto the external axis. 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 molecular axis. Together with an $(2J+1)$ degeneracy respective to a fixed external orientation of the angular momentum, we find for an energy level of a spherical top a $(2J+1)^2$-fold degeneracy.

For all known masses of a molecule and fixed distances between them, we are able to calculate its moment of inertia 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.

Auf diesem Webangebot gilt die Datenschutzerklärung der TU Braunschweig mit Ausnahme der Abschnitte VI, VII und VIII.