what is mutual exclusion principle? explain with example
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In molecular spectroscopy, the rule of mutual exclusion states that no normal modes can be both Infrared and Raman active in a molecule that possesses a centre of symmetry. This is a powerful application of group theory to vibrational spectroscopy, and allows one to easily detect the presence of this symmetry element by comparison of the IR and Raman spectra generated by the same molecule.[1]
The rule arises because in a centrosymmetric point group, IR active modes, which must transform according to the same irreducible representationgenerated by one of the components of the dipole moment vector (x, y or z), must be of ungerade (u) symmetry, i.e. their character under inversion is -1, while Raman active modes, which transform according to the symmetry of the polarizability tensor (product of two coordinates), must be of gerade (g) symmetry since their character under inversion is +1. Thus, in the character table there is no irreducible representation that spans both IR and Raman active modes, and so there is no overlap between the two spectra.[2]
This does not mean that a vibrational mode which is not Raman active must be IR active: in fact, it is still possible that a mode of a particular symmetry is neither Raman nor IR active. Such spectroscopically "silent" or "inactive" modes exist in molecules such as ethylene (C2H4), benzene (C6H6) and the tetrachloroplatinate ion (PtCl42−).[3]
The rule arises because in a centrosymmetric point group, IR active modes, which must transform according to the same irreducible representationgenerated by one of the components of the dipole moment vector (x, y or z), must be of ungerade (u) symmetry, i.e. their character under inversion is -1, while Raman active modes, which transform according to the symmetry of the polarizability tensor (product of two coordinates), must be of gerade (g) symmetry since their character under inversion is +1. Thus, in the character table there is no irreducible representation that spans both IR and Raman active modes, and so there is no overlap between the two spectra.[2]
This does not mean that a vibrational mode which is not Raman active must be IR active: in fact, it is still possible that a mode of a particular symmetry is neither Raman nor IR active. Such spectroscopically "silent" or "inactive" modes exist in molecules such as ethylene (C2H4), benzene (C6H6) and the tetrachloroplatinate ion (PtCl42−).[3]
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The mutual exclusion principle was given by Dr. K.G. Srinivasamurthy. In a molecule with a center of symmetry that the vibrations that are Raman active are mostly Infrared inactive.
It is also vice-verse. It means that no normal modes can have both the forms( raman and infrared) at the same time.
It allows us to known the symmetry element by comparison between the infrared form and active form.
Example: Argon's has 1 electron in the 1s orbital and they satisfy the exclusion principle as they have opposite spins.
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