Oscillator Strengths in the Visible Oscillator Strengths in the Visible

Absorption Spectrum of IAbsorption Spectrum of I22

(A Sentimental Retrospective)(A Sentimental Retrospective)

Joel Tellinghuisen

Department of ChemistryVanderbilt UniversityNashville, TN 37235

In the beginning …

and about the same time …

Led to an estimation of the transition strength over extended R from -dependence of radiative decay.

revisited and updated …

AX and C X continua found to be ~10% weaker than before,

but not much overall change in µe

2 for BX,

and question of “smoothness” unresolved. 0.4

0.6

0.8

1.0

1.2

1.4

450 500 550 600 650

19821973line absorption "

|e|2 (D

2)

nm

"

With time, agreement worsens!

New analysis emphasized dependence of total radiative decay AT and utilized a little-known but very useful sum rule,

AT ( ) 3

e(R) 2 3(R)e

2(R)

where (R) = U (R) U(R). Results supported peaked structure for e

2(R):

0.0

0.5

1.0

1.5

2.0

2.5

2.5 3.0 3.5 4.0 4.5

B-X transition strengths, ~1994

Brewer and T. ('72)

Koffend, et al. ('79)

Bhale et al. ('85)

Kirillov ('83)

Lamrini et al. ('94)e 2

(D2)

R ()

JT ('82)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

6 8 10 30 50 70

Brewer & T ('72)Vigue et al. ('81)Lamrini et al ('94)Fit AFit BFit C

AT

(106/s)

v'

0.0

0.5

1.0

1.5

2.0

2.5

2.5 3.0 3.5 4.0 4.5

B & T ('72)

Koffend ('79)

Kirillov ('83)

e 2

(D2)

R(Å)

Fit C

So, who cares?

Only pre-2000 Columbus presentation by me on this topic ..

Goals:

(1) Confirm or deny “smoothness” in e2(R) in absorption region;

subject of rest of today’s talk.

(2) Reliable simulation of absorption at any resolution.

Recall that in line absorption, e2 k d, where k is the

absorption coefficient over the line.

Preliminary to today — here in 2006

[Gerstenkorn & Luc atlas (1978)]

Ordinate scale quantitative; source?

A key-chain red laser pointer (< 5$ bulk)

0.00

0.01

0.02

0.03

196.0 196.4 196.8 197.2 197.6 198.0 198.4

Ab

so

rba

nc

e

- 15000 cm-1

651 652 653 654nm

x 100

673 674 675 676nm

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.

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

-20 -10 0 10 20 30

- 15290 cm-1

x 60

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].

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1

Abs

orba

nce

- 15 300 cm-1

0.000

0.005

0.010

0.015

0.000

0.001

0.002

0 1 2 3 4 5

Abs

orb

anc

e Are

a (cm-1)

[I2] (10-5 mol/l)

= 36.84(21)

|e|2 = 1.220(13) D 2

0.4

0.6

0.8

1.0

1.2

1.4

450 500 550 600 650

|e|2

(D2)

nm

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 (T1) and cold-finger temperature (T2) are also logged (data from thermistor probes).

0.00

0.02

0.04

0.0640

41

42

0 20 40 60 80 100 120

A

T1 17

T2

A

T(C)

t(s)

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

5.0

5.5

6.0

6.5

0 20 40 60 80 100

-

15

33

0 (

cm1

)

t (s)

y = a + b*exp(-c*x) + d*exp(...

ErrorValue

0.0156444.7965a

0.0402791.5127b

0.00119270.024604c

0.0537470.45755d

0.00690820.095916f

NA1.1826e-05Chisq

NA1R

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

5.0 5.5 6.0 6.5

A

- 15330 (cm 1)

6-5 band4-4 band

P77R83

R63

P76

R62 P55P56

Voila!

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

5.4 5.5 5.5 5.6 5.6

A

15330 (cm 1)

R83, 6-5

Analysis: • Select line, measure back-

ground and integration limits.

• Compute area under line.

• Repeat for spectra recorded at other I2 pressures.

• Fit areas and baselines to straight lines.

• Slopes yield A-X and e2

B-X.

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0 1 2 3 4 5 6 7

area

line

are

a

[I2] (10

5 mol/L)

y = a + b*x

ErrorValue3.359748e-051.436507e-05a7.782624e-060.0003128978b

NA1.25937e-08ChisqNA0.9978417R

y = c*x

ErrorValue3.10333e-060.0003159164c

NA1.29226e-08ChisqNA0.9977853R

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0 1 2 3 4 5 6 7

back

A

[I2] (10

5 mol/L)

y = a + b*x

ErrorValue

0.0005364531-0.01042238a

0.00012426570.004020457b

NA3.210729e-06Chisq

NA0.996673R

Results:

1.10

1.20

1.30

1.40

1.50

1.60

1.70

-10

0

10

20

30

40

50

60

20 40 60 80 100

e

2

(D2)

(A-X)

J"

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)

e2 = 1.256(14)

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”.

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

4.94 4.96 4.98 5.00 5.02 5.04 5.06

P77 (6-5)spec2

A

15330 (cm 1)

y = gaus1(x) + gaus2(x) + ga...

ErrorValue

0.000934870.035053a

8.8896e-050.0068252b

0.00105430.013392c

0.000952810.041137d

0.000177175.0032f

0.00108670.031052g

0.000774970.014634h

8.9371e-050.01375p

0.000925850.030058q

NA0.00014778Chisq

NA0.9994R

cc=0.00533; [calculated Doppler]Gaus1(x) = (a*exp(-.5*(x-(f+b))^2/cc^2));Gaus2(x) = (d*exp(-.5*(x-f)^2/cc^2));Gaus3(x) = (g*exp(-.5*(x-(f-b))^2/cc^2));Gaus4(x) = (h*exp(-.5*(x-(f-2*b))^2/cc^2));Gaus5(x) = (q*exp(-.5*(x-(f+2*b))^2/cc^2))

Gaus6(x) = (c*exp(-.5*(x-(f-3*b))^2/cc^2));gaus1(x) + gaus2(x) + gaus3(x) + gaus4(x) + gaus5(x) + gaus6(x) + p -.0012*(x-5);

0.01

0.03

0.05

0.07

0.09

4.96 4.98 5.00 5.02 5.04

P77 6-5 band

A

- 15330 (cm 1)

0.02

0.04

0.06

-0.005

0.000

0.005

5.0 5.5 6.0 6.5

residuals

A

15330 (cm 1

)

6.25 6.30 6.35 6.40 6.45

4 4 R62

6 5 P76

5.45 5.50 5.55 5.60 5.65 5.70 5.75 5.80

4.96 4.98 5.00 5.02 5.04 5.06

Fit Model:

6 calibration parameters (1 frozen)

5 background

13 line shape

3 widths (Doppler frozen)

52 component strengths (even and odd)

e2

0-5 ad hoc

corrections to line positionscorrections to intensities for selected J”

(test for constancy of e2)

1.20

1.25

1.30

1.35 0.9

1.0

1.1

0 1 2 3 4 5 6 7

w/ Int. adjustmentsmub

f77

f83

e2

f

[I2] (10 5 M)

Results for one spectrum, recorded at 9 I2 concentrations

• No line-to line variability evident here — average fs ~1.02.

• With correction for side modes in laser, e

2 > 1.3 D2.

• 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.