When potential energy is plotted against the displacement of a molecule undergoing Harmonic vibrations due to stretching. It represents a parabolic curve with equilibrium point at zero point energy. It is also seen that the vibrational energy levels are equally spaced.
But, however, the molecules are not taken as perfect harmonic oscillators. Because, The atoms approach each other when the molecule is pressed, and the vibrational forces will be greater because of the increase in the electronic cloud. When the pressed molecule is released, the atoms move away from each other and the electronic cloud decreases. This makes the bond weaker.
In harmonic oscillators, the vibrational energy levels are equally spaced. In anharmonic oscillators, the difference between two consecutive vibrational energy levels goes on decreasing. At higher energy levels this difference becomes very less and the transition of energy from one level to another becomes possible. Therefore, for anharmonic oscillator, the transition is not only ?Evib = ±1. but also for higher transitions.
When the bond is stretched considerably, it ruptures and the molecule dissociates. This energy required to dissociate the molecule is known as bond dissociation energy.