In this chapter, we take up the study of infra red (IR) spectrometry-another common spectroscopic technique used by organic and inorganic chemists for structure elucidation and compound identification.
You know that the bond between two atoms in a molecule is not rigid. It has elasticity and as a consequence the atoms in the molecule do not remain fixed in their positions.  They are in a constant state of motion around their mean position. The molecule is said to be undergoing vibrational motion. The quantum mechanical treatment of the molecular vibrational motion shows that it is quantised. As the transitions between these quantised energy levels can be brought out by using EM radiation in the infrared range it gives rise to an IR spectrum. As the excitation among the quantized vibrational energy levels of the molecules is involved, the IR spectroscopy is also known as vibrational spectroscopy. Let us learn about the vibration motion of the molecules and origin of IR spectrum. We begin with diatomic molecules.

Vibrations of Diatomic Molecules

A vibrating diatomic molecule, AB can be visualised as a simple harmonic oscillator in Fig. 3.1. The two atoms A and B (shown as balls) are assumed to be joined by a bond (shown as a spring) of length req and molecule is oscillating around its mean position, req.   
The quantised energy levels obtained by the quantum mechanical treatment of the harmonic oscillator are given in Fig 3.2 (a). A higher energy corresponds to a larger amplitude of oscillation. The harmonic oscillator model of a diatomic molecule however, is oversimplified and has some limitations. For example, such a molecule would never dissociate no matter how much of the energy we provide. More and more energy would just increase the amplitude of vibration. This, as you know, is in contradiction with the actual situation as the real molecules do dissociate. The real molecules are not like harmonic oscillators; these have some element of anharmonicity. When we consider the anharmonic nature of the vibrating diatomic molecule, the energy levels get modified.

Necessary Condition for Observing IR Spectrum

The presence of quantised energy levels does not ensure transitions amongst them
when the radiation of appropriate wavelength is made to fall on it. For the oscillating electrical field of the EM radiation to interact with the vibrating molecule, it is essential that the molecule has a fluctuating or oscillating dipole moment. In the absence of such a dipole moment the radiation cannot interact with the molecule and we say that the vibration in the molecule is IR inactive. For example, a homonuclear diatomic molecule like H2 would not give an IR spectrum because it does not have a dipole moment and also it does not generate a fluctuating dipole moment. On the other hand, HBr gas has a dipole moment and it does absorb in the IR region. Now, if a molecule has a fluctuating dipole moment, which transitions would we observe? For this we need to know about the selection rule.