1. Department of Chemistry, University of Wisconsin, Madison
Millimeter-wave spectroscopy and global analysis of the lowest eight vibrational states of deuterated hydrazoic acid (DN3)
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. Considerations for DN3 vs. HN3
DN3 compared to HN3:
More b-type lines in our range
Slower intensity drop off in R line intensity with K
Generally smaller perturbation effects
Published IR data for 2ν6 as well as ground, ν5, ν6, ν4, and ν3
Re-ordering of vibrational energy levels
HN3 A ~611 GHz
DN3 A ~345 GHz
Goal to obtain a simultaneous MMW/ FTIR fit for the 8 lowest vibrational states of DN3
To be successful we need correct assignments and decent starting values for as many spectroscopic constants as possible

3. Excited Vibrational States
HN3
DN3
cm-1 ν3
~1213 cm-1
2ν6
cm-1 ν3
cm-1 ν4
cm-1
2ν6
~ cm-1
ν5+ ν6
~1074 cm-1
~1082 cm-1
ν5+ ν6
2ν5
~991 cm-1
2ν5 ν4
cm-1
cm-1 ν6
cm-1 ν6
cm-1 ν5
cm-1 ν5
0 cm-1
Ground
0 cm-1
Ground

4. Predicted Spectra for HN3 and DN3
Our Range
DN3

5. DN3 Ground State R-Branch
K=1
K=0
K=1
J= 14  13
Spectrum predicted from a fit including K=0 through K=7
K=2
K=3
K=4
K=5
K=8
K=11
K=10
K=9
K=6
K=7
K=1
K=0
K=1
J= 14  13
K=2
Assignments
K=3
K=4
K=5
K=8
K=11
K=10
K=9
K=6
K=7

6. The Spectrum and the Excited states
ground ν6 ν5 ν4 ν3
2ν5
2ν6
ν5+ ν6

7. Extremely Useful Prior IR Works
The pure rotational absorption spectrum DN3 in the far-infrared region
Bendtsen, J. and F. M. Nicolaisen, Journal of Molecular Spectroscopy 1987, 125,
FTIR Spectra and simultaneous analysis of ν5 ν6 and ground
Bendtsen, J.; Hegelund, F.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1988, 128,
FTIR spectra of ν4 and 2ν6
Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1991, 145,
FTIR spectra of ν2 and ν3
Hansen, C. S.; Bendtsen, J.; Nicolaisen, F. M., Journal of Molecular Spectroscopy 1996, 175,

8. Loomis-Wood Plots
Developed a list of ~100 series likely to be a-type R-branches.
Attributed K- states and vibrational states to the series using all available means.
Ran low on unassigned series and states at the same time!
Rigorous checking of assignments.

9. Picking Series out of Loomis-Wood Plots
This series of K=8 cannot cleanly be included in a single state for the ground state because of perturbation with ν5 K=7
This single state fit for the ground state is still very useful in finding lines for K=8 however.

10. Linear Plots and Assignment Confirmation
Make these plots for all series believed to belong to R-Branches.
Slope and intercept of these linear plots proved useful in assigning each series to a state and a K value.
Slopes and intercepts were also useful in obtaining initial values for spectroscopic constants.
(Nominal Frequency Range)
(Using Spurious Harmonic in AMC)

11. Intercepts of K-series plots
B+C of our fit =
B+C of our fit =
Slope = -2ΔJK

12. Fermi Resonances between 2ν6 & ν3 and between 2ν5 & ν4
k663 =
k554 = 13.38
Cubic Force Constants
CCSD(T)/ANO2

13. Using (Frequency / Jupper) vs Jupper2 plots for all K states
Intercept = MHz
Intercept = MHz
-4ΔJ= from SPFIT
-4ΔJ= from SPFIT
Intercept = MHz
-4ΔJ= from SPFIT

14. A 3-State Fit MMW and FTIR data: Ground, ν5, and ν6
A (MHz)
(38)
B (MHz)
(24)
C (MHz)
(24)
ΔJ (kHz)
3.890(30)
ΔJK (kHz)
-10.0(46)
ΔK (kHz)
(254)
δJ (kHz)
0.1767(15)
δK (kHz)
85.(38)
ΦJ (Hz)
-0.171(17)
ΦJK (Hz)
-11.2(21)
ΦKJ (Hz)
-3706.(198)
ΦK (Hz)
(14269)
LKKJ
(3357) LK
(159482)
E (MHz)
(47)
N lines MM
210
N lines IR
349
σ (MHz)
2.5
σ IR (cm-1)
.037 ν6
A (MHz)
(38)
B (MHz)
(24)
C (MHz)
(24)
ΔJ (kHz)
4.189(50)
ΔJK (kHz)
876.3(35)
ΔK (kHz)
(738)
δJ (kHz)
0.279(13)
δK (kHz)
-78.(47)
ΦJ (Hz)
0.167(25)
ΦJK (Hz)
-7.1(24)
ΦKJ (Hz)
473.(181)
ΦK (Hz)
(24901)
LKKJ
(3273) LK
(218238)
E (MHz)
(56)
N lines MM
141
N lines IR
507
σ (MHz)
2.3
σ IR (cm-1)
.024
Perturbation Constants
Ga (MHz)
(87)
Fa (MHz)
6.93(37)
Gb (MHz)
-946.(48)
W05
616.(10)
Ground State
A (MHz)
(30)
B (MHz)
(97)
C (MHz)
(10)
ΔJ (kHz)
4.305(11)
ΔJK (kHz)
397.0(18)
ΔK (kHz)
92837.(63)
δJ (kHz)
(32)
δK (kHz)
301.8(13)
ΦJ (Hz)
0.0034(34)
ΦJK (Hz)
1.45(24)
ΦKJ (Hz)
-104.(13)
ΦK (Hz)
(1566)
LKKJ
-2860.(179) LK
(9792)
E (MHz)
N lines MM
304
N lines IR
620
σ (MHz)
0.47MHz
σ IR (cm-1)
0.0036
14 parameters per state X 3
4 Perturbation terms
vibrational energies allowed to vary
655 MMW transitions
1476 IR transitions
σMMW = 1.83 MHz
σIR = cm-1

15. DN3 Energy Levels and Perturbations
Fermi Resonance
cm-1 ν3
cm-1
2ν6
Gc (Coriolis)
Ga, Fa, Gb (Coriolis)
~1082 cm-1
ν5+ ν6
Ga, Fa, Gb (Coriolis)
~991 cm-1
2ν5 ν4
Fermi Resonance
cm-1
Centrifugal Distortion (W05)
Ga, Fa, Gb (Coriolis)
cm-1 ν6
Ga, Fa, Gb (Coriolis)
cm-1 ν5
W05 (centrifugal distortion)
0 cm-1
Ground

16. Perturbation Terms for Three-State Fit
HN3
CCSD(T)/ANO2
Present Work
Hegelund & Bendtsen 1987
Ga56 (cm-1)
36.77
38.033(12)
[38.06]
Gb56 (cm-1)
(43)
(13)
W05 (cm-1)
0.0345(14)
(7)
DN3
CCSD(T)/ANO2
Present Work
Bendtsen et al 1988
Ga56 (cm-1)
20.74
(29)
[18.86]
Gb56 (cm-1)
(16)
0.071(6)
W05 (cm-1)
0.0206(3)
0.0312(6)

17. Analysis of Splittings in K=1 K=2 and K=3

18. What do K=1, K=2, and K=3 Splittings tell us?
From the Wang Formula:
𝐸 1 + − 𝐸 1 − 𝐽 𝑈𝑝 = 𝐵−𝐶 +ℎ𝑖𝑔ℎ𝑒𝑟 𝑡𝑒𝑟𝑚𝑠
K=1 Splittings
𝐸 2 + − 𝐸 2 − ( 𝐽 𝑈𝑝 −1) 𝐽 𝑈𝑝 ( 𝐽 𝑈𝑝 +1) = (𝐵−𝐶) 2 𝐴− 𝐵+𝐶 2 +ℎ𝑖𝑔ℎ𝑒𝑟 𝑡𝑒𝑟𝑚𝑠
K=2 Splittings
Slopes of Splitting Curves
K=1
K=2
K=3 ν5
Without Ga
414.62
0.0698
2.16*10-6
With Ga
385.30
0.0913
3.68*10-6 ν6
363.22
0.0462
1.09 *10-6
336.29
0.0312
5.65 *10-7

19. Complete K state energy plot
Ground state
Slope =
A-(B+C)/2=
Quadratic term = MHz
-ΔK = MHz
Cubic term = MHz
ΦK =

20. Analyzing the Difference between ν5 & ν6 K Energies
therefore
1 2 𝑠𝑙𝑜𝑝𝑒 ≅ Ga
Ga from slope = cm-1
Ga from our 3-state fit = cm-1
𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 = 𝐸 0 𝑣6 - 𝐸 0 𝑣5
𝐸 0 𝑣6 - 𝐸 0 𝑣5
From intercept = cm-1
𝐸 0 𝑣6 - 𝐸 0 𝑣5
From literature = cm-1

21. Checking Assignments DN3 2ν6
We also found b-type lines for all but 2ν5 and ν5+ν6
2ν6
MHz
(extrapolated from
4 K=0 transitions)
= MHz

22. Summary Accomplished so far:
Assigned a-type R branches for 8 lowest energy vibrational states
Assigned b-type lines for 6 of these states
Achieved a reasonable 3-state fit of combined MMW/ FTIR data
Found ways to extract some key spectroscopic constants from the data
Elusive long-term goal: 8-state fit!

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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also from our group:
FE06 Nick Walters
Millimeter- wave spectroscopy of formyl azide.
Special thanks:
John Stanton
Mark Wendt