2. Non Rigid Rotor
We have assumed so far that the bond length remains fixed during
rotation of the molecule - this is the rigid rotor model. However, as the
molecule rotates the atoms are subject to centrifugal forces which
stretch the bonds - this is the non-rigid rotor model.
Centrifugal forces due to rotation, which are significant especially at
high rotational angular velocities, are balanced by restoring forces
which keep the molecule from flying apart. The centrifugal force may
be readily calculated from the centrifugal acceleration, which in turn is
the rate of change of radial velocity of the rotating system.
3. Non Rigid Rotor
Hooke's law states for an elastic bond:
F=-k(r-𝑟𝑒𝑞)=4𝜋2𝜔2𝑐2m
F = restoring force (N)
r = bond length; req = equilibrium bond length (m)
k = force constant (Nm-1)
c = vibrational frequency (cm-1)
m = reduced mass (kg)
4. The Non-Rigid Rotor
Non-rigid rotor model for diatomic molecules:
𝜀𝐽=BJ(J+1)-D𝐽2(𝐽 + 1)2
Centrifugal distortion force
D=
ℎ3
32𝜋4.
𝐼2.
𝑅2 .
𝑘𝐶
The first term is the rigid rotor model, and the second term is a
correction for the centrifugal distortion. It is important to consider this
for high values of J.
For the energy of the non-rigid rotor, we need to take into account now
the rotational kinetic energy, as well as the potential energy
corresponding to the restoring force.
