1. Department of Chemistry, University of Wisconsin, Madison
Towards a Global Fit of the Combined Millimeter-wave and High Resolution FTIR Data for the Lowest Eight Vibrational States of Hydrazoic Acid (HN3)
International Symposium of Molecular Spectroscopy, Urbana-Champaign, Illinois
June 26, 2015
Brent K. Amberger, R. Claude Woods, Brian J. Esselman, Robert J. McMahon,
Department of Chemistry, University of Wisconsin, Madison

2. Our Equilibrium Structure Determination of HN3
Observations between GHz
at room temperature
-14 Isotopologues Studied
-High level corrections for vibration-rotation interactions, xrefit in CFOUR used for structure determination
(John Stanton)

3. Available HN3 Transitions in our Range 260-360 GHz
a-type R branches
b-type R and P branches

4. HN3 Ground R-Branch K=1 J= 13  12 K=1
Spectrum predicted from single state fit of K=0 through K=5
K=0
K=2
K=3
K=10
K=4
K=9
K=8
K=7
K=5
K=6
K=1
K=1
K=0
Actual Assignments
K=2
Perturbed lines are often very perturbed
K=3
The highly perturbed lines are also the lowest intensity lines
K=10
K=4
K=8
K=7
K=5
K=9
K=6

5. Ground and Excited Vibrational State Transitions

6. Vibrational States and Perturbations
cm-1 ν3
Fermi Resonance
Gc (Coriolis)
~1213 cm-1
2ν6
cm-1 ν4
Ga, Fa, Gb (Coriolis)
~ cm-1
ν5+ ν6
Ga, Fa, Gb (Coriolis)
~1074 cm-1
2ν5
Fermi
Resonance
Centrifugal Distortion (W05)
Ga, Fa, Gb (Coriolis)
606.4 cm-1 ν6
Ga, Fa Gb (Coriolis)
537.3 cm-1 ν5
Centrifugal Distortion (W05)
0 cm-1
Ground

7. Extremely Useful Prior Infrared Studies
Pure rotational ground state far IR
Bendtsen, J.; Nicolaisen F. M. , Journal of Molecular Spectroscopy 1986, 119,
FTIR spectra and analysis of ν5, ν6 and ground state
(i) Bendtsen, J.; Hegelund, F.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1986, 118,
(ii)Hegelund, F.; Bendtsen, J., Journal of Molecular Spectroscopy 1987, 124,
IR spectrum of ν4
Bendtsen, J.; Nicolaisen, F. M. Journal of Molecular Spectroscopy 1989, 133,
FTIR spectra and analysis of ν3 and ν4
Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1992, 152,
Tunable diode laser spectrum of ν3
Yamada, K. and Takami, M., Journal of Molecular Spectroscopy ,
BUT….

8. K Energies for the Vibrational Statesν3 ν4
ground ν6 ν5

9. K Energies for the Vibrational States
Estimated values for 2ν5, 2ν6 and ν5+ ν6 ν3 ν4
2ν6
ν5+ ν6
ground ν6
2ν5 ν5

10. Using IR data to Find Pure Rotational Transitionsν5
Finding HN3 v –
12 3 9
12 3 9
P- branch IR transitions
R- branch IR transitions
12 3 9
11 3 8
Ground state
MHz
MHz

11. Linear Plots of Freq/Jup vs. Jup2
Steep negative slope
Steep negative slope
modest negative slope
(most common)
positive slope!

12. Examples of Perturbed K-States
Steep negative slope (highly perturbed)
These two mutually perturbing states are easily recognized as perturbed due to abnormal slopes for their K values.
Positive slope (highly perturbed)

13. Intercepts of Linear Plots vs. K2

14. Previous slide average shifted by one in K
The average is much smoother than either separately.

15. A 3-State Fit of Millimeter-wave Data: Ground, ν5, and ν6
Ground State
A (MHz)
(86)
B (MHz)
(35)
C (MHz)
(35)
ΔJ (kHz)
4.8886(25)
ΔJK (kHz)
(73)
ΔK (kHz)
(66)
δJ (kHz)
(78)
δK (kHz)
201.(17)
ΦJ (Hz)
(19)
ΦJK (Hz)
-1.17(10)
ΦKJ (Hz)
579.0(27)
E (MHz)
[0]
N lines
132
σ (MHz)
0.36
ν5 (537.3 cm-1)
A (MHz)
(25)
B (MHz)
(85)
C (MHz)
(85)
ΔJ (kHz)
4.7422(33)
ΔJK (kHz)
(43)
ΔK (kHz)
(690)
δJ (kHz)
(86)
δK (kHz)
416.(18)
ΦJ (Hz)
(29)
ΦJK (Hz)
35.04(27)
ΦKJ (Hz)
(11)
E (MHz)
[ ]
N lines
136
σ (MHz)
0.77
ν6 (606.4 cm-1)
A (MHz)
(25)
B (MHz)
(90)
C (MHz)
(90)
ΔJ (kHz)
5.2144(52)
ΔJK (kHz)
(43)
ΔK (kHz)
(1170)
δJ (kHz)
(27)
δK (kHz)
371.(20)
ΦJ (Hz)
(59)
ΦJK (Hz)
-22.03(36)
ΦKJ (Hz)
25958.(13)
E (MHz)
[ ]
N lines 82
σ (MHz)
1.05
Perturbation Terms
Ga /MHz
(400)
Fa /MHz
7.28(71)
Gb /MHz
1912.1(13)
W05
1034.4(43)
Energies of states were fixed
11 parameters per state X 3
4 Perturbation terms
350 total transitions including a and b type….
σ = 0.73 MHz

16. The Higher Excited Vibrational States
HN3
cm-1 ν3
Fermi Resonance
Gc (Coriolis)
~1213 cm-1
2ν6
cm-1 ν4
Ga, Fa, Gb (Coriolis)
~ cm-1
ν5+ ν6
Ga, Fa, Gb (Coriolis)
~1074 cm-1
2ν5
Fermi
Resonance
Centrifugal Distortion (W05)
Ga, Fa, Gb (Coriolis)
Ga, Fa, Gb (Coriolis)
606.4 cm-1 ν6
537.3 cm-1 ν5
Centrifugal Distortion (W05)
0 cm-1
Ground

17. Infrared and Microwave Patterns are the Same for ν3 and ν4
Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1992, 152,
ΔB4 = (B+C)K of ν4 – (B+C)K of ground state
ΔB3 = (B+C)K of ν3 – (B+C)K of ground state

18. Infrared – Microwave (B+C)K for ν3 and ν4

19. Adding ν3 and ν4 (with K shifted by 1)
Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1992, 152,
Consistent with the ΔK = 1 selection rules for c-type Coriolis resonance (Gc)

20. b-type transitions for ν3 and ν4
Perturbations bring a Q-branch series for ν3 into our range.
b-type lines with J values ranging from 1 to 12.

21. Confident Assignment of the 2ν5 R-series
Trendline on linear (less perturbed) region gives access to:
Intercept = B+C
Slope = -ΔJK

22. Next Steps
Obtain solid assignments of a-type R-branches for ν5+ν6 and 2ν6.
Find and assign b-type transitions for 2ν5, ν5+ν6, and 2ν6.
Use linear least-squares plots to obtain as many initial values for as many parameters as possible.
Obtain 5-state non-linear least-squares fit (SPFIT) for higher energy excited vibrational states. Determine the critical perturbation parameters for these higher states
Ultimately obtain an 8-state global fit (“The Holy Grail”).

23. Thanks for Listening! The Research Group Professor Bob McMahon
Professor Claude Woods
Dr. Brian Esselman
Brent Amberger
Ben Haenni
Zachary Heim
Steph Knezz
Matisha Kirkconnell
Vanessa Orr
Cara Schwarz
Nick Walters
Maria Zdanovskaia
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Stay tuned for DN3 talk
FE02 Brent Amberger
also from our group:
FE06 Nick Walters
Millimeter- wave spectroscopy of formyl azide.
Special thanks:
John Stanton
Mark Wendt