1. Oscillator Strengths in the Visible Absorption Spectrum of I 2 (A Sentimental Retrospective) Joel Tellinghuisen Department of Chemistry Vanderbilt University Nashville, TN 37235

2. In the beginning …

3. and about the same time … Led to an estimation of the transition strength over extended R from -dependence of radiative decay.

4. revisited and updated … A  X and C  X continua found to be ~10% weaker than before, but not much overall change in µ e 2 for B  X, and question of “smoothness” unresolved.

5. With time, agreement worsens! New analysis emphasized  dependence of total radiative decay A T and utilized a little-known but very useful sum rule, where  (R) = U (R)  U  (R). Results supported peaked structure for  e 2 (R):

7. So, who cares?

8. Only pre-2000 Columbus presentation by me on this topic.. Goals: (1) Confirm or deny “smoothness” in  e 2 (R) in absorption region; subject of rest of today’s talk. (2) Reliable simulation of absorption at any resolution. Recall that in line absorption,  e 2   k d, where k is the absorption coefficient over the line.

9. Preliminary to today — here in 2006 [Gerstenkorn & Luc atlas (1978)]  Ordinate scale quantitative; source?  A key-chain red laser pointer (< 5$ bulk)

10. Mode structure in red laser pointers (RLPs) is simple. The two spectra in each plot below were taken for the same RLP at different times, with strong and weak batteries in one case.

11. But the key-chain model showed surprisingly little side-mode emission — estimated at only ~2% in the illustrated case.

12. Results: B  X transition strength from integrated lines and A  X continuum from background. Illustrated for strong doublet near 15 308.4 cm –1 [P94 in 6-5 band and R85 in 4-4].

13. Experiment: Beam from RLP is directed to source input slit (set wide, 5 nm) on a UV-vis spectrophotometer (Shimadzu). After laser has run for several minutes, it is turned off for 10-20 s and then back on. Absorbance is measured as a function of time, while the cell body temperature (T 1 ) and cold-finger temperature (T 2 ) are also logged (data from thermistor probes).

14. Spectral lines are identified and used for calibration. A double exponential fn of the time is usually adequate (triple exponential used in simulations below).

15. Voila!

16. Analysis: Select line, measure back- ground and integration limits. Compute area under line. Repeat for spectra recorded at other I 2 pressures. Fit areas and baselines to straight lines. Slopes yield  A-X and  e 2 B-X.

17. Results: Degree of scatter disappointing, and much larger than it should be from individual error estimates. Next: Try direct fitting of each spectrum.  A-X = 39.4(4)  e 2 = 1.256(14)

18. In direct fitting, a reliable line shape function is essential. Use sum of Gaussians to compensate for hyperfine-dominated line profiles — different for even and odd J”.

20. Fit Model: 6 calibration parameters (1 frozen) 5 background 13 line shape 3 widths (Doppler frozen) 5  2 component strengths (even and odd) e2e2 0-5 ad hoc corrections to line positions corrections to intensities for selected J” (test for constancy of  e 2 )

21. Results for one spectrum, recorded at 9 I 2 concentrations No line-to line variability evident here — average fs ~1.02. With correction for side modes in laser,  e 2 > 1.3 D 2. Scatter still larger than it should be; this is unfortunately not a rare observation for such fitting of very abundant, precise data to complex nonlinear models. Nonetheless, performance of direct fit lends confidence to simulated spectra for applications like environmental monitoring.