The Electronic Spectrum of Iodine

The vibrational-electronic spectrum of I2 in the region from 500-650 nm displays a large number of well-defined bands which, for the most part, correspond to v'<-- 0 transitions connecting the v" = 0 vibrational level of the ground electronic state (denoted as X1S+) to many different vibrational levels v' of the excited B3P electronic state. Under the conditions of this experiment (i.e., low resolution), the rotational lines within each band are not resolved. However, the peaks may be identified as R-branch band heads (1). For a molecule as heavy as I2, the position of each band head is within a few tenths of one cm-1 of the band origin (2), and for the purposes of this experiment, the distinction between the two may be ignored.

The general features of the absorption spectrum are shown below:

Each small bump, or peak, such as the (26,0) band labelled on the spectrum, corresponds to a transition between two vibrational levels and is called a band. Each band is comprised of several hundred lines, each of which involves different upper and lower rotational quantum numbers; as mentioned, these lines are not resolved in the present experiment. The region of maximum absorption in each band is caused by many of these lines falling together; it is called the band head. The set of all of these bands is referred to as the visible band system of I2.

If the sample is hot, then excited vibrational levels of the ground state may be populated, and these also will absorb light. The hot bands arising from absorption from v"=1 and v"=2 are shown very approximately on the absorption spectrum above.

At a point called the convergence limit, the spacing between bands decreases to zero. Beyond this convergence limit, the spectrum is continuous because the excited state of the I2 molecule is not bound. One of the purposes of this experiment is to identify this convergence limit accurately.

The variation of potential energy of I2 with internuclear distance is conveniently represented on a potential energy diagram. Figure 1 shows the variation in potential energy for the I2 molecule in its ground (X) state and its second (B) excited electronic state. This figure illustrates the parameters to be calculated, and uses the standard spectroscopic notation (2). In the present exercise, we will be concerned with extracting the parameters se, w'e, w'ec'e, w"e, and w"ec"e, E* (the convergence limit), D0", De", and De' from the experimentally determined spectrum.

Procedure

Collect the absorption spectrum of I2 from 500 - 650 nm using the Cary double-beam spectrophotometer. Place a few crystals of iodine in one of the 10 cm cells, and cap the cell. Place this cell in the light path at the front of the instrument, and place the other 10 cm cell in the rear path as a reference. Instructions for using the Cary are located next to the instrument. From the Start/All Programs button, select Cary WinUV, and select the Scan program. Set up the instrument as follows: spectral bandwidth (SBW) 0.2 nm; signal averaging time 0.033 sec; data interval 0.020 sec. The y-axis scale will vary depending on the amount of iodine placed in the cell; you will probably have to make a few runs to determine a reasonable value. A value of 1.00 is a good starting point. No parameters other than those listed here will require adjustment. When you have collected an acceptable spectrum, write the data file out to a diskette as a tab-delimited ASCII file (instructions are located next to the instrument). Using Mathcad, Excel, or Origin, import and plot the absorption spectrum.

Data Reduction and Analysis

Fig. 2 shows a sample absorption spectrum for I2. Shown on Fig. 2 are vibrational level assignments which should assist you in assigning your spectrum. In this experiment, we observe transitions from the v"=0 level of the X state to v'=55, 54,...,15 level of the excited B electronic state. Note that we also see transitions originating from v"=1 level of the X state , as well as transitions originating from v"=2. As can be seen from the spectrum, the intensity of these 'hot bands' swamps the intensity of the transitions originating from the v"=0 state. These intensities may be calculated from statistical mechanical principles.

Once you have plotted the I2 spectrum, assign the transitions as shown on Fig. 2. As an internal calibration, note that the v'= 26 <-- v" = 0 band has a peak at 543.47 nm. Use the difference (if any) between this value and your (26,0) band center to correct your wavelengths. Measure the band centers as accurately and consistently as possible (you will need to 'zoom in' on regions of the spectrum using Mathcad or Origin to do this accurately).

Make a table showing the assigned band origin and its energy in cm-1, corrected for vacuum (consult the CRC Handbook for the refractive index of air.) The following data, due to Steinfeld, et. al.,(3) may be of some help also in assigning the bands. For the v"=0 progression, proceed as far as you can go towards the dissociation limit in assigning the bands (you should be able to assign all the way to v"=55 or 56.)

Table 1. Numbering of Band Heads for Iodine

v' v" wavelength/nm v' v" wavelength/nm v' v" wavelength/nm
27 0 541.2 18 1 571.6 13 2 595.7
28 0 539.0 19 1 568.6 14 2 592.0
29 0 536.9 20 1 565.6 15 2 588.5

To ensure that your peak assignments are consistent, you will prepare a Deslandres table with your data. This is probably best done with Excel. Your instructor will show you how to make up a Deslandres table.

If T' and T" represent the electronic term energies of the B and X states of I2, respectively, and G(v') and G(v") represent their vibrational energies, then, ignoring rotational energy changes, the energy of a transition will be given by

s = T 'e - T "e + G(v') - G(v") (1)

For the case studied here, T "e is zero, since it refers to the ground electronic state while T 'e equals se , the frequency of the hypothetical transition between the minima of the two curves (Fig. 1).

The vibrational term values may be written as

G(v) = we(v + 1/2) - wece(v + 1/2)2 + wege(v + 1/2)3 + ... (2)

where we is the frequency for infinitesimal amplitudes of vibration and wece, wege etc., are anharmonicity constants. If only the first two terms in this expression are taken, then the transition frequency becomes

s = se + w'e(v' + 1/2) - w'ec'e(v' + 1/2)2 - w"e(v" + 1/2) + w"ec"e(v" + 1/2)2 (3)

Eq.(3) is suitable for multiple linear regression using a model function of the form

y = b0 + b1x1 + b2x12 + b3x2 + b4x22 (4)

Perform the linear regression analysis as directed, and report, in table form, the required spectroscopic parameters and their standard deviations.

For the calculation of E* (the convergence limit), D0", De", and De', use equations 7-11 of Ref. 4 below. Report your calculated values and their standard deviations.

Compare your calculated results to published experimental values. Turn in a plot of the spectrum and a copy of the Deslandres table with your report.

References

  1. Barrow, G. "Introduction to Molecular Spectroscopy", McGraw-Hill, New York, 2nd Ed. 1962, Ch. 10 pp 238-244.
  2. Herzberg, G., "Spectra of Diatomic Molecules", 2nd Ed., D. Van Nostrand Co., 1950, p 171.
  3. Steinfeld, J., Zare, R., Jones, L., Lesk, M., and Klemperer, W., J. Chem. Phys. 42, 25(1965).
  4. McNaught, I., J. Chem. Ed. 57, 101(1980) and references therein.
  5. Shoemaker, D, Garland, C., and Nibler, J., "Experiments in Physical Chemistry", McGraw-Hill, New York, 6th Ed. (1996) and references therein.
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