Examples: CH4, CCl4, SF6
The rotational energy is given for I = IA = IB = IC :
We obtain the corresponding quantum-mechanical equation whether we change to operators H and J:
Hy = J²/2I y = E y
The eigenvalues of J² are as follows:
J² y = J(J
+ 1)h²y
where J = 0, 1, 2, ...
The first factor can be shortened into the rotational constant B [in wavenumbers]:
B [cm-1] = h/4πc
I
B [J] = B [cm-1] · hc
c is the speed of light