When vibrational transitions are observed in an electronic absorption spectrum, these transitions can be used to determine dissociation energies. Specifically, a Birge€“Sponer plot is constructed where the energy difference between successive vibrational transitions n and n + 1 (ΔG_n+1/2) (see figure) is plotted versus the vibrational level number. Note that G does not refer to the Gibbs energy in this context.

The central idea behind the approach is that the dissociation energy is equal to the sum of these energy differences from n = 0 to the dissociation limit:

a. For the ground state of I2 the following values for ΔG versus n were determined (J. Chem. Phys. 32 (1960): 738.

If the potential function can be described by a Morse potential [Equation (19.5)], ΔG will be a linear function of n + 1/2. Construct a Birge€“Sponer plot (ΔG versus n + 1/2) using the given data, and, using the best fit to a straight line, to determine the value of n where ΔG = 0. This is the I₂ ground-state vibrational quantum number at dissociation.

b. The area under the Birge€“Sponer plot is equal to the dissociation energy, D₀. This area can be determined by summing the ΔG values from n = 0 to n at dissociation [determined in part (a)]. Perform this summation to determine D₀ for ground state I₂. You can also integrate the best fit equation to determine D₀.

D. De AG12 AG512 AG312 AG12 D-G/2 + G/2+G5/2 G+1/2 n=0