Understanding Normal Modes of Objects - Linear vs Non-Linear Particles

[ajayguhan]

What does one mean by normal mode of an object? Why is it 3n-5 for linear particles, 3n-6 for non linear particle where n is the number of particle.

 

[mikeph]

A normal mode is a specific type of vibration that a molecule can exhibit. They are "normal" because each type of vibration is distinct and cannot be replicated by any combination of the other types. Any possible type of vibration that a molecule can exhibit is just a combination of its normal modes.

The numbers can probably be derived from symmetry arguments, I don't know how, but it's easier just to draw out molecules for n = 2 and 3 and try to convince yourself that there is an agreement with the formulas.

 

[ajayguhan]

Is there any book which explained it in more detailed manner! That you could recommend?

 

[mikeph]

There are loads, Bernath (2005) is pretty good for a conceptual overview in the context of spectroscopy, should be in most scientific libraries. But if you're serious about molecular spectroscopy... Penner or Herzberg are solid, detailed (if a little old) texts.

 

[ajayguhan]

Thanks