1. Strange combination band of the cross-shaped complex CO2 – CS2
Nasser Moazzen-Ahmadi
Department of Physics and Astronomy University of Calgary
A.R.W. McKellar
National Research Council of Canada

2. CO2-CS2 observed by Beaudet group
TDLS 2009, Zermatt, Switzerland
CO2-CS2 observed by Beaudet group 2

3. only Ka = even levels in ground state
TDLS 2009, Zermatt, Switzerland
C2v point group
only Ka = even levels in ground state 3

4. TDLS 2009, Zermatt, Switzerland
cross-shaped minimum, but slipped-parallel is only 2.64 cm-1 higher (or 8.25 cm-1 higher zpe) 4

5. TDLS 2009, Zermatt, Switzerland
We observe the same fundamental band, with c-type selection rules, in good agreement with Beaudet
Beaudet (1998)
Present experiment
Theory (Brown et al.) A” B” C”
ΔK”
1.06 e-7
-4.32 e-7
-1.12 e-7
ΔJK”
-1.01 e-7
3.59 e-7
1.03 e-7
ΔJ”
-1.37 e-7
4.65 e-7
1.09 e-7 ν0 5

6. We also observe two CO2-CS2 combination bands:
TDLS 2009, Zermatt, Switzerland
We also observe two CO2-CS2 combination bands:
b-type, origin at cm-1 ( from fundamental)
a-type, origin at cm-1 ( from fundamental)
Clearly the cm-1 combination band is the torsion, and cm-1 is the CO2 bend!!
The b- and a-type selection rules are consistent with this. 6

7. Central portion of the CO2-CS2 torsional combination band
TDLS 2009, Zermatt, Switzerland
Central portion of the CO2-CS2 torsional combination band 7

8. Torsion Theory (Brown et al.)
TDLS 2009, Zermatt, Switzerland
The torsional band seems to be fairly well-behaved (however note ΔK and ΔJK)
Torsion
Ground state
Torsion Theory (Brown et al.) A B C ΔK
-69.5 e-7
-4.32 e-7
-13. e-7
ΔJK
-6.61 e-7
3.59 e-7
20. e-7 ΔJ
6.25 e-7
4.65 e-7
2.8 e-7 ν0
Recall that we observe this band at cm-1 from the fundamental, and calculated torsion was cm-1 !!! 8

9. But the CO2 bend band is bizarre!
TDLS 2009, Zermatt, Switzerland
But the CO2 bend band is bizarre!
We can fit it (quite well), but only by having A’ ~ 0.7 cm-1 and ΔK’ ~ 0.03 cm-1, which is crazy!
Recall this is an a-type band, and only even values of Ka are possible 9

10. CO2 bend, theory (Brown et al.)
TDLS 2009, Zermatt, Switzerland
Crazy parameters are required to fit this band. But the fit is pretty good; intensities and positions of some ΔK = 2 transitions are even predicted well
CO2 bend
Ground state
CO2 bend, theory (Brown et al.) A
0.7084
2.484 B
0.0453 C
0.0331 ΔK
0.0287
-4.32 e-7
ΔJK
3.59 e-7 ΔJ
-80. e-7
4.65 e-7 ν0
[41.880]
41.918 10

11. TDLS 2009, Zermatt, Switzerland
Showing good agreement of observed and simulated spectrum, including intensities.
Note ΔK = 2 transitions. 11

12. TDLS 2009, Zermatt, Switzerland12

13. TDLS 2009, Zermatt, Switzerland
Interestingly, crazy parameters were also predicted for this vibration by Brown et al. In their paper, they only reported J = Ka = 1 levels (which are forbidden).
But now we have their higher calculated levels, and agreement is amazing!
JKa
Observed
Calculated 00
41.880
41.918 11
44.441 22
44.329
44.277 33
48.573 44
46.039
45.942
(Recall that Calc is for pure intermolecular vibrations, while Obs is for intermolecular + CO2 2 vibration.) 13

14. TDLS 2009, Zermatt, Switzerland
JKaKc
Observed
Calculated
Obs -Calc
000
41.880
41.918
-0.038
101
41.960
41.996
-0.036
202
42.117
42.154
-0.037
221
44.329
44.281
+0.048
220
44.274
+0.055
303
42.353
42.391
322
44.564
44.516
321
44.563
44.515
404
42.669
42.709
-0.040
423
44.878
44.821
+0.057
422
44.875
44.827
441
46.039
45.942
+0.097
440 14

15. TDLS 2009, Zermatt, Switzerland
Conclusions
We have excellent agreement between experiment and theory, so this combination band is not so strange, after all!
But what does it mean? Theory is just a black box, in a sense. Is this what Phil Bunker calls “big computer, small brain”?
At least with theory we can look at wavefunctions and fractional parentage.
Can we blame the strange energy level pattern on multiple tunneling paths?
Is there a simple hindered rotation model which might fit the observations? 15