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Triatomic linear CO_{2} molecule has three atoms. (n = 3). Therefore, the molecule has 3n degrees of freedom. For linear molecules there will be (3n - 5) fundamental vibrations. Therefore, 3n - 5 = 3(3) - 5 = 9 - 5 = 4
CO_{2} molecule will have 4 fundamental vibrations. These modes of vibrations are:
Symmetrical Stretching
Asymmetrical Stretching
Symmetrical Bending (Scissoring)
In symmetrical stretching there is a partial charge separation due to two oxygen atoms. The magnetic moments get cancelled and the molecule is non-polar. This is also true according to symmetric stretching of both oxygen atoms at two ends. Hence, the molecule is IR inactive.
In unsymmetrical stretching, one end is stretched and at the other end there is compression. This produces fluctuating dipole moment. Thus this vibration is IR active.
In symmetrical bending there are two bending vibrations and they differ only in the direction and have the same frequency. Hence, these vibrations will be IR active.
The modes of vibrations in a molecule where they differ only in the direction but with the same frequency are said to be degenerated. Because of this, the linear molecule like CO_{2} will have one extra mode of vibration as compared to non-linear molecule like H_{2}O.
If we see the IR spectra of CO_{2} molecule the frequency 2349 cm^{-1} to unsymmetric vibrations whereas 667 cm^{-1}, two symmetric bending modes. ii)asymmetric stretching (2349 cm^{-1})(iii) two types of bending vibrations (667 cm^{-1})
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