Introduction to High Resolution Spectroscopy 
Introduction Rotational Vibrational Miscellaneous

Rotation of Molecules
  
 
The difficulty in moving an object is related to its mass - the heavier the object the larger the force required to move it. The resistance of an object to being moved is known as its 'inertia'. The resistance of an object to being rotated is similarly known as rotational inertia. The rotational inertia is related to the objects moment of inertia - the analogue of mass. For a point mass, the moment of inertia is related to its mass (m) and its distance from the rotation axis (r). The heavier the mass, the greater the resistance to rotation. The further from the axis, the greater the resistance to rotation.

An interactive model is available to illustrate this.

Overall, the moment of inertia I is given by,

I = mr2

The rotation of three-dimensional objects like molecules can be quite complicated but as they can be considered to be made up from collections of point masses (or atoms), the above relationship can be used to work out the overall moment of inertia for any molecule. The dependence of I on r leads to one of the major reasons for studying molecular rotations - working out highly accurate bond lengths.

It is convenient to break the rotations down into those about three mutually perpendicular directions, called the principal axes of rotation. Each molecule therefore has three moments of inertia corresponding to the resistance to rotation about these axes. The three moments are usually labelled IA, IB and IC. Because of molecular shapes and symmetries, some of these moments may be zero or may be the same. It is therefore convenient to group molecules according to the relationship between the moments.

Linear molecules

Linear molecules such as HCl, HCCH and CO2 can rotate in three ways:

   

  • The two types of end-over-end rotation are equally difficult (rotate the molecule to show this) so IB = IC.
  • Rotation about the bond axis takes no energy so IA = 0.

Follow the links below for more information on the energy levels and rotational spectroscopy of linear molecules:

  1. energy levels:
  2. microwave spectrum:
  3. intensity of microwave lines:
Once you have covered all of the available resources for rotational spectroscopy, you should test your knowledge and understanding with the self test.


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