Electronic Spectroscopy

Transitions between different electronic states have vibrational and rotational energies associated with them.  While individual transitions from rotational states cannot be resolved, it is often possible to resolve vibrational transitions in the electronic spectra of gas-phase molecules.

For a given electronic state, the vibrational energy for an anharmonic oscillator is
 

For iodine, electronic transitions occur from the low lying vibrational states (v'' = 0 primarily) of the X electronic state to a series of excited vibrational states (v') in the B electronic state.  Neglecting rotational contributions, the energies (n) of each transition correspond to differences in electronic and vibrational energies:

where is T_el is the energy difference between the potential energy minima of the two electronic states, v' is the quantum number for the vibrational level in the excited electronic state and v'' corresponds to the vibrational quantum number of the ground electronic state.  Transitions occur from a v'' level of the ground electronic state to a v' level of the excited electronic state.  Combining (1) and (2) leads to an energy expression for each vibrational peak in the spectrum:
 

The X state dissociates into two iodine atoms that are each in the ²P_3/2 state.  The B state dissociates into one iodine atom in the ²P_3/2  state and one iodine atom in an excited ²P_1/2 state.  The ²P_1/2 state of  iodine atoms lies 7603.15 cm^-1 above the ²P_3/2  state (Moore, C L. "Atomic Energy Levels, Circular of the National Bureau of Standards, US GPO, Washington, D.C. 1958).

It is possible to calculate the ground state dissociation energy without knowing the specific upper v' states being populated.  The vibrational peak spacings on the absorption band provide information on the difference between adjacent vibrational energy levels of the excited electronic state.  As v' increases, these differences decrease, in theory reaching 0 at the dissociation limit.

A quantum number n is used to represent the vibrational level of the excited state.  The lowest energy transition in the measured spectrum corresponds to an n=0 value.  By plotting the differences in energies between adjacent vibrational peaks vs the quantum number n, a Birge-Sponer extrapolation can be made and plotted to estimate the n corresponding to an energy difference of 0.  The area under the curve can be represented by the 1/2 * x-intercept*y-intercept. By adding this area to the energy of the n=0 transition, the difference in energy between the v''=0 (of the X state) and the dissociated B excited electronic state can be calculated.  Since you already know the ²P_1/2  state lies 7603.15 cm^-1 above the ²P_3/2  state, you now have sufficient information to calculate the dissociation energy for the X state (drawing an energy diagram will help clarify this).

The dissociation energy of the excited electronic state can also be calculated from a separate Birge-Sponer plot of (v'+1/2) vs. DE for adjacent vibrational transitions.  In this case the dissociation energy represents the area from v'=0 to the dissociation limit.

Between 555 nm and 565 nm, a series of doublet peaks can be seen (see lab text).  The peaks on the long wavelength side originate from the v"=1 vibrational state, those on the short wavelength side from the v''=0 state.  At wavelengths below 550 nm, only v''=0 type transitions are observed; above 570 nm, only v''=1 transitions are seen.  For the doublet peaks in this region, the v' levels corresponding to the v''=1 peaks are 2 higher than for the corresponding v' levels from the v''=0 peaks on the doublet (e.g. for v'=20, v''=0; the adjacent peak corresponds to v'=22, v''=1).

Using two transitions originating from  v''=0 and v''=1 levels with the same upper state (v'), one can calculate the energy difference between the v''=0 and v''=1 levels in the X state.  This provides information on the vibrational spacing in the X state and an estimate of  n_e''-2n_ec_e'' (the spacing between v''=1 and v''=0).

Experimental:

You will measure the visible spectrum of I₂ (g) using a double beam spectrophotometer (the diode array does not have sufficient resolution for this experiment).  Place iodine crystals in a quartz cuvette--make sure the cap is on the cuvette.

Set up the instrument to measure from 500-650 nm.  Use a slit width of 1 and a scan speed of 20 nm/min.

To generate sufficient vapor, you need to heat the sample compartment so that it stays fairly warm during the experiment.  Use the heat gun in the NMR room to do this--heat the sample cuvette holder and the metal around it.  Also heat the cuvette prior to placing it in the holder--you should see the violet color of the iodine vapor.  BE VERY CAREFUL during this step.

You may wish to measure a small portion of the spectrum initially--e.g. from 500-550 nm.  Then go back and collect from 540-650 nm.

Obtain a printout of each spectrum and of the peak locations--make sure the threshold is sufficiently low to detect each peak you observe.

Requirements:  Using the normal lab report format, make sure to include the following.

1.  Tabulate collected data and identify the quantum numbers v'' and v' associated with each observed transition.

2.  Determine the excited state parameters n_e', n_ec_e', and n_ey_e'

3.  Determine the Dissociation energy (D_o) of the ground electronic state of iodine.

4.  Determine the Dissociation energies (D_e and D_o ) of the B electronic state.

5.  Draw an energy diagram illustrating the relative energies of the two electronic states and all other calculated energies.
 
6.  Determine the energy difference between the v''=0 and v''=1 levels of the X state.  Determine the relative populations expected for these two levels at a temperature of 323 K.

7.  Explain why the vibrational peaks have different intensities.

8.  Comment on the assumption that molecules are harmonic oscillators.  Base your statement on your observations or calculations.

9.  Compare the dimensions and vibrational frequencies of excited (B) and ground state (X) iodine molecules.
 
10.  Explain why the spacing between vibrational peaks gets closer as the dissociation limit is approached.