Electronic Spectroscopy

Electronic Spectroscopy
The electronic spectroscopy involves transition between different electronic states. Let us consider the potential energy curve of a molecule. The potential energy (PE) curve refers to the plot of potential energy against the inter-nuclear co-ordinate. According to equation" " the potential energy (V) for a simple harmonic oscillator is proportional to the square of the vibrational co-ordinate, q. Thus the plot of V against q should a parabola (figure 1).

Fig. 1. (a) Potential energy diagram of a simple harmonic oscillator (b) Potential energy diagram of a real molecule.

In fig. 1a the horizontal lines corresponds to different vibrational quantum numbers (n). In a particular electronic state the vibration energy of the molecule increases with increase in the vibrational quantum number. It is evident that for a simple harmonic motion, the inter-nuclear distance, q never becomes infinite. In other words, the molecule never dissociates. But in actual case, most molecule dissociates at an energy greater than the bond dissociation energy (D0). The potential energy curve for a real molecule is shown in fig. 1b. In this case, it is evident that when the potential exceeds D0 the inter-nuclear coordinate becomes infinite. The particular form of potential which gives rise to such a curve is called Morse potential, U(r) and is given by:
….(1)

At a distance q=q0, the energy is zero and hence, q0 is the equilibrium internuclear (bond) distance. D is equal to D0 plus the zero point vibration energy (1/2h?0). The particular form of the PE curve shown in fig. 1b in which the molecule remains bound at least for some energy corresponds to bound or bonded state. In some states the inter-nuclear distance is infinite at all energies. Such a curve corresponds to a dissociative state. If a molecule is excited to such a state the molecule dissociates immediately. Such dissociation by excitation is known as photo-dissociation.