Rule of Mutual Exclusion in Raman Spectra

Rule of Mutual Exclusion

Rule of Mutual Exclusion in Raman Spectra

Point groups of molecules with center of symmetry have two sets of irreducible representations. Representations which are symmetric with respect to inversion are called 'g' representation and representations which are antisymmetric with respect to inversion are called 'u' inversion.
The coordinate x-becomes -x on inversion of a cartesian coordinate x through the centre of inversion. All representations generated by x, y or z must belong to a 'u' representation. However, the product of two coordinates x and y does not change sign on inversion (-x, -y = xy). The product xy generates a 'g' representation. All the other quadratic or binary coordinates also generate the 'g' representation. Hence, it is clear that in centrosymmetric molecules, the vibrational modes belonging to 'g' symmetry are Raman active and the modes belonging to 'u' symmetry are infrared active. This rule is called mutual exclusion rule. In other words, we can say that if a molecule has a center of symmetry, then Raman active vibrations are infrared inactive and infrared active vibrations are Raman inactive.
If there is no center of symmetry, then some (but not necessarily all) vibrations may be both Raman and infrared active. Thus, the Raman and infrared spectra having no common bands show that the molecule has a centre of symmetry but here caution is necessary because a vibration may be Raman active but too weak to be observed. If some of the bands are present in both the Raman and infrared spectra, it is certain that the molecule has no center of symmetry. Examples are- C₆H₆, C₂H₂, C₂H₄, CS₂ etc.

Molecules	Point Group	Symmetry Species	IR Active Species	Raman Species
CO2	D∞h	A1g, A1u, E1u	A1u, E1u	A1u
trans-N2F2	C2h	3Ag, Au, 2Bu	Au, Bu	Ag
H2O	C2v	2A1, B2	A1, B2	A1, B2
NH3	C3v	2A1, 2E	A1, E	A1, E
BF3	D3h	A'1, 2E', A"2	A"2, E'	A'1, E', A"2

Molecules with center of symmetry namely CO₂, N₂Fe possecess modes which are infrared active and Raman inactive and vice-versa. Molecules like H₂, NH₃ and BF₃ don't have center of symmetry active in both infrared and Raman spectra.