# P Q R Branches in IR Spectra

## P Q R Branches in IR Spectra

We know that each vibrational energy level of a molecule has a series of closely spaced rotational energy levels. Vibrational - rotational transitions are caused by the absorption of infra red light for which the selection rule is ΔJ = -1, 0 +1, where J and v are the rotational and vibrational quantum numbers respectively.

If ΔJ = -1, we get P Branch (Lines with frequency lower than the fundamental frequency)

If ΔJ = 0, we get Q Branch (Vibration transition occurs without being accompanied by rotational transition)

If ΔJ = +1, we get R Branch (Lines with frequency higher than the fundamental frequency)

For a diatomic molecule like HCl, we have only one fundamental vibrational mode and hence, we expect only one infrared absorptional band according to 3n − 5 rule-

3 x 2 − 5 = 1

Diatomic molecules are always linear. However, even under low resolution, it gives two bands designated as R and P bands.

The Q band is not at all expected because it is possible only when the moment of inertia I = 0 as we know that-

E_{J} = [h^{2}/8π^{2}I] J(J + 1)

ΔE_{J}, J = 0 only when I = 0.

Hence, it shows only ΔJ = +1 (R Branch) and ΔJ = -1 (P Branch) transition under 𝜈_{o} → 𝜈_{1}. These R and P bands split under high resolution due to the so many associated rotational transitions.