Moving Rotator

We have assumed the binding distance to be unchanged during rotation (stationary rotator), so far. When rotating there are centrifugal forces that can cause the binding distance increase. We limit ourselves to the case of linear rotator here: the binding distance r increase means the increasing of inertia moment (I = µr2). Higher I corresponds to lower B (B ~ 1/I), i.e. we would have the rotational energy which increases a bit slower than Erot = Bstarr J(J + 1). The exact solution of Schroedinger equation is no longer possible, nevertheless one can derive the eigenvalues of energy by using the following series:

Erot = B · J(J + 1) - D · J2(J + 1)2 + ...

where D is a small correction, D << B.

It's immediately clear here that deviation from the stationary rotator appears when the binding is more weak. The weak binding corresponds however to lower vibrational energy (Evib = h w(v + ½); w = (k/µ)½; k: force constant). The quantity D can be obtained from spectra.
We will consider the selection rules for rotational spectra further.