Linear Top

Linear Molecules such as, for instance HCCH, NCCN, CO2; all diatomic molecules
Linear molecules possess, due to its small electron masses, very small inertia moment of corresponding axis, i.e. we need to consider only rotation around both axes perpendicular to molecular axis (K = 0). Therefore we obtain the following important formula for rotational energy of fixed rotator:

EJ = BJ(J + 1)

This equation coincides with that of the spherical top but we must take into consideration the (2J + 1)-fold degeneracy relative to the external axis for the linear top. However, the rotational constant A shouldn't be distinguished from B and K for spherical top and it can take (2J + 1)-values of kinetic moment orientation relatively one of the molecular axes. At the same time, owing to the (2J + 1)-fold degeneracy of the external space-fixed kinetic moment orientation we obtain (2J + 1)2-fold degeneracy for the quantum number J.

Having binding distance and atomic masses we can calculate the inertia moment (and also the energy levels, that's for sure). One can find few useful expressions here for the so far treated cases (read Atkins, S. 451).

Table of few rotational constants
Molecule | I / 10-47 kgm2 | B / cm-1 | A / cm-1
H2 | 0,46 | 60,85 |
D2 | 0,92 | 30,44 |
HCl | 2,69 | 10,59 |
OH | 1,51 | 18,91 |
O2 | 1,98 | 1,44 |
N2 | 1,43 | 1,998 |
I2 | 771 | 0,037 |
NH3 | 2,81 4,41 | 9,98 | 6,34 oblate
CH3Cl | 63,6 0,18 | 0,444 | 5,02 prolate
CCl4 | 485 | 5,24 |