Vibration Rotation Spectra

Vibration Rotation Spectra
The vibrational transition is invariably accompanied by a change in the rotational quantum number. Thus one actually observes a transition from a state (0, J) i.e. n=0, and rotational quantum number J to a state (1, J ). If one assumes that the rotational constant in the two vibrational states are same, one can write that the frequency of a vibration-rotation transition is given by:
……(1)
Obviously, if ?J=0 i.e. J =J, there should be a pure vibration transition at a frequency ?0. However, a pure vibrational transition is never observed because the selection rule for rotational transition is ?J=±1. Thus a vibration-rotation spectrum consists of two series of lines one at a frequency higher than ?0 and another at a frequency lower than ?0 . Such a spectrum involving simultaneous vibration and rotational transitions is called a vibration-rotation spectrum.
a. P Branch
The so called P branch of a vibration-rotation spectrum arises in the case ?J=-1 i.e. J =J-1. From following equation


In this case the frequency of transition is given by
…(3)
Note that one can not have a line in P branch for J=0 because that would imply negative J . Hence, in this case J=1,2,3 …

b. R Branch
The R branch corresponds to the case ?J=+1 i.e. J =J+1.
…(4)
In this case J=0, 1, 2 …..
The vibration energy is estimated from the position of the centre of the series of lines arises from R and P bands. In many molecules the rotational lines are very close. This vibration-rotation line is often referred to as a vibration band. The P and R –branches of a vibration-rotation spectrum are shown in Fig. 1.








Fig.1. P and R branches of a vibration-rotation spectrum.