Question

How many normal modes of vibration exist in the following molecules ? identify each mode and state which are IR active?

a)SO_{2 b)H2O2 c)C6H6}

Answer 1

The degrees of vibrational modes for linear molecules can be calculated using the formula: 3n−5

The degrees of freedom for nonlinear molecules can be calculated using the formula: 3n−6

Where, n = the number of atoms within the molecule of interest.

(a) SO₂ : Non linear molecule: 3 x 3 - 6 = 3 normal modes of vibration

Sulfur dioxide, SO₂: (C_2v) : 2A1 and 1B2.

(b) H₂O₂ : Non linear molecule: 3 x 4 - 6 = 6 normal modes of vibration

Hydrogen peroxide, H₂O₂, (C₂): 3A1 and 2B2  are IR active.

(c) C₆H₆ : 3 x 12 - 6 = 30 normal modes of vibration

Benzene, C₆H₆ (D_6h) : 6e_1u, a_1g and a_2u are IR active