Tuesday, December 6, 2022

Electromagnatic radiation :- Vibrational Spectroscopy

 Vibrational Spectroscopy:

Vibrational spectroscopy can be thought of by starting with a simple harmonic 

oscillator (SHO) model. In this model, we consider two atoms joined by a bond to be 

equivalent to two masses joined by a spring. The spring can be compressed, forcing 

the spheres close to each other - stretched, moving them apart - or allowed to freely 

come to rest in the spheres' equilibrium positions. This can be shown in a potential 

energy curve:




However, not all energies are possible. The possible vibrational states are given by the 

vibration quantum number, v, and vibrational selection rule Δv = ±1. 

The energy of each level, E

, is given by

h

E 

 

2

1

 

(the second ν is the Greek character nu, the fundamental frequency). The 

fundamental frequency is given by the equation ν = (1/2π)×(k/μ)1/2, where μ is the 

reduced mass of the molecule, and k is thebond force constant. Notice that this k is 

similar to the spring force constant from Hooke's Law F = -kx. This leads to a potential 

energy surface that looks like this:





As you can see, the energy levels are equally spaced, and the equilibrium bond length 

is constant for all energy levels. However, this model is imperfect - it does not account 

for the posibility of bond dissociation (under this model, the bond would never break, 

no matter the magnitude of the vibrational energy). It also does not account for extra 

repulsive effects at very small bond lengths caused by the electroweak force. This is 

the force which prevents atoms for being forced together as the distance between them 

gets very small (the reason nuclear fusion only occurs at very high temperatures, for 

example). A model which takes into account these factors, and which more accurately 

models a vibration diatomic molecule, is the Anharmonic Oscillator (AHO), and the 

corresponding potential energy surface called the Morse potential. The potential 

energy curve now looks like this:





Notice how the expectation (or average) bond length, rexp is no longer the same for all 

energy levels. One effect of the anharmonicity is this deformation as the energy of the 

vibrations increases. Another is that now, the vibrational energy levels are no longer 

equally spaced, but instead get closer together as the vibrational quantum number 

increases. This model also illustrates that there aren't an infinite number of vibrational 

energy levels - above some energy, the bond breaks and the molecule dissociates.

Vibrational energies occur roughly in the 100 - 4000 cm-1 (about 1 - 50 kJ mol-1), 

or infra-red (IR) region of the electromagnetic spectrum. The fundamental principle 

for obtaining a vibrational spectra is that the electric dipole moment of the molecule 

must change during the vibration. If there is no change in dipole moment, then this 

particular vibration will not give rise to any absorption in the IR region. An example 

of this can be seen below for the symmetric stretch (Σg+) mode of carbon dioxide. 

Because both C=O bond lengths change exactly in phase, there is never a net dipole 

moment on the molecule. A homonuclear diatomic molecule such as dioxygen O2

has 

zero dipole moment, so it has no IR spectrum.

The number of modes (types) of vibration can be predicted for a molecule, containing 

N atoms, using the following general expressions.










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Electromagnatic radiation :- Vibrational Spectroscopy

  Vibrational Spectroscopy : Vibrational spectroscopy can be thought of by starting with a simple harmonic  oscillator (SHO) model. In this ...