Examples: CH4, CCl4, SF6
For the case of I = IA = IB = IC the rotational energy is given with:
We recieve the respective quantum mechanical equation if we shift to the operators H and J:
The eigenvalues to J² are already known:
J²⋅Ψ = J(J+1) h²⋅Ψ
with J = 0, 1, 2, ...
It became common practice to write this equation in a form with the rotational constant B which has the unit of the wavenumber, cm-1. The product term hcB equals the fraction h2/2I.
With c denoting the speed of light, the transformation between the moment of inertia I and rotational constant B is