oscillator strengths in the visible absorption spectrum of i 2 (a sentimental retrospective) joel...
TRANSCRIPT
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.