The moments of inertia of symmetric rotors play a fundamental role in understanding their rotational dynamics and spectroscopic behaviour.
In such molecules, two of the three moments of inertia are equal, while the third is different. The unique moment of inertia, denoted by , describes rotation around an axis known as the principal axis. The other two, which are equal, are denoted by
. If
, the molecule is known as a prolate symmetric rotor (shaped like a cigar) and rotates more easily around the principal axis. Examples include NH3 and CHCl3. If
, the molecule is called an oblate symmetric rotor (flattened like a disc), and it rotates more easily around an axis perpendicular to the disc. Examples include C6H6 and BF3.
Question
Is a trans-MA2B4 complex a prolate or an oblate symmetric rotor?
Answer
It is a prolate rotor if the axial atoms (A) are farther from the central metal M than the equatorial atoms (B), and an oblate rotor if the axial atoms are closer to M than the equatorial atoms.
In the next few articles, we will derive the moments of inertia of a few common prolate and oblate symmetric rotors.