Data Analysis for Iodine Vibronic Spectrum
If you have trouble assigning peaks, use the Deslandres Table supplied below.
In these directions, pay close attention to the symbols.
v'' = (the letter vee) vibrational energy level number for the ground electronic state
v' = vibrational energy level number for the excited electronic state
 = (Greek letter nu) Difference in wavenumbers between two peaks
1. Compare your spectrum to that in Figure 2 page 428 and assign the peaks to specific
transitions (v'' → v'). Or use the canned data and skip to step 5.
2. Determine the wavelength of each assigned peak.
3. Convert all wavelengths () to wavenumbers ( in cm-1).
4. Arrange your data in a Deslandres Table. See the example on page 430. The highest
value you will have for v'' will be 2. You might not even have peaks that you can tell
originate from v'' = 2. In that case, the highest value of v'' will be 1.
The peaks in your first column (v''=0) are absorbances that all originate from the
lowest vibrational level in the ground electronic state.
The peaks in the second column (v''=1) are absorbances that all originate from the
second vibrational level in the ground electronic state.
5. For each column on the Deslandres table, calculate the difference in wavenumber
[ = (v'+1) - (v') ] between successive row entries. Keep the values for each
column separate and make new columns on your table to enter your  values. This
calculates the spacing between the vibrational levels in the excited electronic state.
6. Plot the wavenumber difference versus the excited electronic state vibrational level
number (  vs v' ). That’s y versus x. The plot will yield parameters that appear in
equation (2) on page 425.
Slope =  2~e~
xe
x e .
Use these to calculate a value for ~
xe
y-intercept = ~e  2~e~
For comparison, you should separately plot the data from each column of the Deslandres
table for which you’ve calculated  values. In theory, they should give the same slope
and intercept.
7. Now calculate the difference in wavenumber [ ''= (v''+1) - (v'') ] between
column entries for each row. Keep the values for each row separate and make new
columns on your table to enter your  values. This won’t give as many values as step 5
because you at most have three columns of data and thus only two differences, , per
row. This calculates the spacing between the vibrational levels in the ground electronic
state.
8. Plot the wavenumber differences versus the ground electronic state vibrational level
number (  vs v'' ).
Slope =  2~e~
xe
y-intercept = ~e  2~e~
xe
Use these to calculate a value for ~
xe .
For comparison, you should separately plot the data from each row of the Deslandres
table for which you’ve calculated  values. Each plot has only two points. In theory,
they should give the same slope and intercept.
9. Algebraically solve equation (3) page 425 for ~el .
xe , ~e , ~e~
xe , ~e , the
Calculate a value for ~el by putting in your values for ~e~
wavenumber for a particular peak on your spectrum [~ (v', v'')] and the v' and v'' for that
peak. Do this for at least 7 peaks from your spectrum and calculate an average ~el .
10. Calculate the dissociation energy, De using equation (5) page 425. This is the
dissociation energy taken from the very bottom of the potential on the ground electronic
state.
Repeat to calculate the dissociation energy, De , which is the dissociation energy taken
from the bottom of the potential for the excited electronic state.
See figure 1 on page 424.
11. Calculate the dissociation energy, D0 using equation (6) page 426. This is the
dissociation energy taken from the lowest vibrational state of the ground electronic state.
Repeat to calculate the dissociation energy, D0 , which is the dissociation energy taken
from the lowest vibrational state of the excited electronic state.
12. Use your value for De and calculate De using equation (7) on page 426 and
compare to the value of De found in step 10.
13. Calculate a force constant for each state (ground and excited) using equation (8) on
page 426.
14. Calculate a Morse potential parameter, , for each state using equation (10).
15. Use the value for re given on page 431, your values for   and De to plot a Morse
curve using equation (9). This means put in values for r (which is plotted on the x axis)
and calculate values for U (r  re) (which is plotted on the y axis).
Note that U (r  re) means the potential, U, which is a function of r  re . It does NOT
mean multiply U by r  re .
However, on the right side of the equals sign in equation (9)  (r  re ) DOES mean
multiply   by r  re .
Note that when r  re the potential¸U, is zero. See figure 1. Your plot should look
similar to the bottom curve.
You can generate the plot either by putting the equation into a spreadsheet program and
let the computer do the graph, or calculate a few values of U by hand for a few values of
r (some larger than re and some smaller) and then plot.
16. Use your value for the ground state force constant (step 13) and on the same graph
do a harmonic oscillator plot. You need to look up the equation for the harmonic
oscillator yourself since we studied it extensively in lecture.
Compare the plots from step 15 and 16.
Look up literature values for the constants found and compare to your calculated values.
That’s it.
See the table on the next page.
DesLandres table for Iodine (cm-1)
v"
v'
8
9
10
11
12
13
14
15
16
17
18
19
20
0
1
17205
17309
17410
17510
17609
17706
17800
17895
16991
17094
17194
17294
17392
17488
17583
17676
2
16260
16365
17470
16573
16667
16782
16882
16983
17082
17179
17276
17373
17470