Fundamental modes of vibrations in polyatomic molecules

• Vibrational spectroscopy, especially as applied in Infrared (IR) Spectroscopy, is a vital tool in pharmaceutical analysis.

• Understanding the vibrational modes of polyatomic molecules is essential to interpreting IR spectra.

• For polyatomic molecules, there are various ways the atoms can vibrate, and these vibrational movements are termed as 'modes.'

• The number of these vibrational modes (or fundamental modes) for a non-linear molecule is given by the formula 3N-6, where N is the number of atoms in the molecule.

• For linear molecules, the number of vibrational modes is 3N-5.
  

The fundamental modes of vibrations in polyatomic molecules can be categorized into two major types:

1. Stretching Vibrations:

1. Symmetric Stretching: All atoms in the molecule move towards or away from the center of mass uniformly. This keeps the molecule's shape unchanged.

2. Asymmetric Stretching: Different atoms in the molecule move towards or away from the center of mass at different rates. This changes the molecule's shape.
   

2. Bending Vibrations (or Deformation Vibrations):

1. Scissoring (or Symmetric Bending): Two atoms move towards or away from each other while staying in the plane of the molecule.

2. Rocking: One part of the molecule rocks in the plane of the molecule.

3. Wagging: One part of the molecule wags in and out of the plane of the molecule.

4. Twisting (or Torsional Vibration): One part of the molecule moves in a way that twists it out of the plane of the molecule.