Vibrational Spectroscopy
Introduction to Spectroscopy; Part 3
Vibrational motion of a diatomic molecule can be
considered as a simple oscillator. Therefore the hook’s law can be applied.
(Equation 01)
The frequency of a vibration is an important
property of the vibrational transition. (Equation 02)
Understanding the molecular vibration:
Light (Energy) is absorbed when radiation
frequency is equal to the frequency of vibration in a molecule. Covalent bonds
vibration at only certain allowed frequencies and basically these vibrations
include stretching and bonding. For a vibrational spectrum; The dipole moment of the molecule must change during the vibration.
Symmetric stretching
Anti Symmetric stretching
Bending
Degree of Freedom
For a molecule with "N" atoms, total degree of freedom is given by 3N which include translation (3 df) rotaion ( linear 2 df / non linear 3df ) and vibration ( the rest; linear 3N- df/ nonlinear 3N-6)
For the simple harmonic oscillator the vibration energy is given by equation 03 and equation 04 is the conversion of same equation to spectroscopic units.It is important to know that these equation are only applicable to simple harmonic oscillator. We should observe that the lowest vibrational energy obtained by replacing the v=0 into the equation 03. This implies that the vibrational energy can not be zero for any diatomic molecule.
Selection Rules:
1. Change of dipole moment during the excitation.
2. Δv = +1 or Δv= -1
Even though asymmetric stretching and bending give change in dipole moment, symmetric stretching gives no change in dipole moment.
The energy gap
1. Change of dipole moment during the excitation.
2. Δv = +1 or Δv= -1
Even though asymmetric stretching and bending give change in dipole moment, symmetric stretching gives no change in dipole moment.
The energy gap
the Energy gap between the energy levels are equal.
The Hook Law can be applied at the low temperature
At the high temperature, simple harmonic oscillator can not observed.
The harmonic oscillator is applicable only for small approximation from the equilibrium internucler distance
Anharmonicity
For larger deviations the inter-molecular potential energy is better described by Morse potential.
image; https://en.wikipedia.org/wiki/Morse_potential
Comments
Post a Comment