1. Perturbation Analysis of the (0,0) Band of the A 2Π3/2 – X 2Σ+ transition in Zirconium Nitride, ZrN
Kaitlin Womack, Taylor Dahms, Leah O’Brien
Department of Chemistry
Southern Illinois University Edwardsville
Jessica Spencer and James O’Brien
Department of Chemistry and Biochemistry
University of Missouri – St. Louis

2. Previous Work: Bates & Dunn (1976)
Observed A 2Π-X 2Σ+
Noted Strong Perturbations in A 2Π3/2
4 “gaps” in R21 and Q2
3 “gaps” in R2 and Q21
Suggested Perturbers
2Δ (x 2)
Vibrational, from v=1 of A 2Π1/2
Bates, J.K.; Dunn, T. M. Can. J. Phys. 1976, 54,

3. Bates, J.K.; Dunn, T. M. Can. J. Phys. 1976, 54, 1216-1223.

4. Previous Work: Cheung et al.
Suggested possible perturbing states
At high J 2Δ
At low J
4Σ–3/2
Would split e/f levels differently
Similar to TiN
Perturbations found in all six branches
Seven perturbations listed
In the e-levels
J′= 4.5 and 13.5
In the f-levels
J′= 8.5 and 18.5
Both Λ-doubling components
J′= 39.5, 44.5, and 56.5
Cheung, A. S-C.; Li, H.; Jiang, H.; Chen, H. J. Mol. Spectrosc. 2001, 210,

5. Reduced Energy Plot for 2Π3/2 Excited State
Rotational Energy
E=BJ(J+1)
Plot of E vs. J(J+1)
Linear, with slope equal to B if unperturbed
Cheung, A. S-C.; Li, H.; Jiang, H.; Chen, H. J. Mol. Spectrosc. 2001, 210,

6. Experimental Design
ZrN gas molecules produced in Zr-lined copper hollow cathode
Applied discharge of 0.58A
1.45 torr of argon and helium
trace amount of nitrogen

7. Experimental Design
Spectra recorded using Bruker IFS125M Fourier transform spectrometer
Resolution of 0.02 cm-1
Recorded 9,000-26,000 cm-1 region
Data collection took approximately 2 weeks and over 8,000 scans

8. A 2Π3/2 – X 2Σ+ Spectra

9. Fitting the A 2Π1/2 –X 2Σ+ Transition
Fit the A 2Π1/2 – X 2Σ+ component separately to determine ground state parameters
Average residuals < cm-1
Used PGOPHER, a spectral simulation and fitting program
Ground state parameters held fixed when fitting the A 2Π3/2 – X 2Σ+ component

10. New Calculations by Zou: L-S States of ZrN
Wenli Zou, Unpublished Work (2014)

11. Our Approach to Analysis of Perturbations
Concentrate on the huge perturbations at low J
Perturbers must be Ω = ½ since perturbation occurs at different J for e/f levels
No 4Σ– state below 25,000 cm-1

12. Wenli Zou, Unpublished Work (2014)
Vibrations of the 2Π state
Vibrations of the 2Σ+ state
Vibrations of the 4Π½ state
Wenli Zou, Unpublished Work (2014)

13. Relevant Perturbations
L±S± Spin-Orbit
Same Ω and S, Different Σ and Λ
Example: 2Π3/2 and 2Δ3/2
S-uncoupling
Same Λ and S, Different Σ and Ω
Example: 2Π3/2 and 2Π1/2
L-uncoupling
Same Σ and S, Different Λ and Ω
Example: 2Π3/2 and 2Δ5/2 or 2Π3/2 and 2Σ1/2,
For the v=0 4Π½ perturbing state, use 2Π½ state and S- uncoupling interaction: B0~ cm-1
For the v=2 2Σ+ perturbing state, use L-uncoupling interaction: B2~ cm-1
Lefebvre-Brion, H.; Field, R.W. Perturbations in the Spectra of Diatomic Molecules
Wenli Zou, unpublished work (2014)

14. PGOPHER and Perturbations
Added two perturbers to excited manifold, selected appropriate interaction, gave initial T,B, γ, and p values
Interaction is set to zero in this figure
In the input file, changed rank of excited state at each perturbation
Used Reduced Energy plot (right) to estimate crossings
E-B2Π3/2J(J+1) vs J

15. Reduced Energy Plots
e-levels
f-levels

16. Optimize Interaction with Perturbers
Molecular constants of the perturbing state are the same for e/f levels
Value of interaction is different for e/f levels
Needed to fit A 2Π3/2 - X 2Σ1/2 component separately
Slowly (varied only 1 or 2 parameters at a time) fit data
Ground state constants held fixed
Fitted through J′= 49.5
Fit residuals near the perturbations < 0.1 cm-1
Other fit residuals < 0.02 cm-1

17. Deperturbed Molecular Constants

18. Simulated Spectra and Fortrat Diagrams

19. Experimental and Simulated Spectra

20. Summary
Perturbations have been observed in the (0,0) band of the A 2Π3/2-X 2Σ+ transition of ZrN
Perturbing states at low J’ identified as:
v=2 of the (II) 2Σ+ state
v=0 of the (I) 4Π½ state
Deperturbed fit with molecular constants
Average residual < 0.1 cm-1
No previous analysis of A 2Π3/2
New calculations by Wenli Zou invaluable
B-values of perturbing states consistent with calculations
This work in progress

21. Thank you for your attention!
Acknowledgements
Laboratory Groups
Leah C. O’Brien: Kaitlin Womack and Taylor Dahms (SIU- Edwardsville)
James J. O’Brien: Jessica Spencer (UM-St. Louis)
National Science Foundation
Wenli Zou (post-doc at Southern Methodist U)
Thank you for your attention!

23. 12s-> 6p ½ lower than 3/2
5p-> 12s 3/2 lower than 1/2

24. Comparison of Initial Fit with Previous Data
X 2Σ+ B
D x 107
γ x 103
γD x 107
This Work
(37)
4.73(12)
-1.40(15)
-7.32(99)
aCheung et al.
(4)
4.53(1)
-2.58(1)
bBates & Dunn
0.4830(7)
6(1)
-5(3)
A 2Π1/2 T0 A
(15)
567.02*
(38)
4.66(16) p
pD x 107
H x 1011
(10)
5.50(67)
-3.83(19)
Errors in parenthesis are one std. dev.
* value held constant in fit
a Cheung, A. S-C.; Li, H.; Jiang, H.; Chen, H. J. Mol. Spectrosc. 2001, 210,
b Bates, J.K.; Dunn, T. M. Can. J. Phys. 1976, 54,