1. Analysis of the Rotationally Resolved Spectra to the Degenerate (𝑒′) Upper-State Vibronic Levels in the Electronic Transition of NO3
Henry Tran, Terrance Codd, Mourad Roudjane, Dmitry Melnik, Terry A. Miller
Department of Chemistry and Biochemistry
The Ohio State University
TH10
70th International Symposium on Molecular Spectroscopy

2. The Jahn-Teller Problem
No JT
JT1+JT2
Strong JT2
Energy e a1
v=1 e a1 a2
Near triple degeneracy
v=0 e a2 e
D3h
C2v

3. Introduction NO3 has 4 vibrational modes.
We have assigned the 3 , 4 and 3 + 4 fundamental bands assuming moderate to strong Jahn-Teller (JT) coupling in the A state. An analysis of the rotational structure in this state will provide more information about the geometry of NO3.
As JT coupling increases, NO3 distorts from D3h to C2v.
The parallel bands ( 𝑎 1 ′′ vibronic symmetry) have been satisfactorily analyzed using an oblate symmetric top, corresponding to the high symmetry D3h configuration.
The perpendicular bands (𝑒′ vibronic symmetry) were not able to be analyzed using the same model. We have implemented a modified rovibronic Hamiltonian for vibronically coupled systems with better success.

4. The Hamiltonian
Vibronic eigenfunctions can belong to one of six irreducible representations in the D3h geometry.
We use a Wang-type symmetrized rovibronic basis which is a linear combination of products of vibronic eigenfunctions and Hund’s Case (b) rotational basis functions.
N: Rotational Angular Momentum
S: Spin Angular Momentum
K: Projection of N onto the principal axis
J: Total Angular Momentum ( J = N + S )
ρ: Parity

5. The Hamiltonian
The parallel bands were analyzed using an oblate symmetric top model with centrifugal distortion and spin rotation in the form given by Hirota et al. and NSSW.
[1]
[1] E. Hirota, T. Ishiwata, K. Kawaguchi, M. Fujitake, N. Ohashi, and I. Tanaka, J. Chem. Phys, 107, 2829 (1997).

6. The Hamiltonian
Since the perpendicular bands terminate on vibronically degenerate levels, we will consider a Hamiltonian which takes into account vibronic coupling effects between all six irreducible representations as well as spin-orbit coupling.
Terms Quantifying JT Distortions

7. The Hamiltonian
For this analysis, we include the coupling between the degenerate E levels, but since the Aj and E levels are well separated, we expect negligible Aj - E coupling and we will focus on the E block.

8. The Hamiltonian
The E block in a wang-type symmetrized basis has the form
[1] Brown, J. M. Rotational Energy Levels of Symmetric Top Molecules In 2E States Mol. Phys., 20, 817, (1971).
[2] Watson, J, K. G., Jahn-Teller and L-uncoupling Effecs on the Rotational Energy Levels of Symmetric and Spherical Top Molecules. J. Mol. Spec. 103, (1984).

9. Simulation Results
The rotationally resolved, cavity ring-down spectra of the perpendicular bands have been collected and analyzed using the mentioned model.
Transitions were assigned iteratively and a least squares regression of free parameters was used to fit the simulation
For the X state, we use the oblate symmetric top Hamiltonian with spin-rotation and set the parameters to values recorded by Kawaguchi et al.
Centrifugal distortion constants and spin-rotation along the principal axis were fixed to values determined in the analysis.
Parameters presented are in cm-1 unless otherwise specified.
[1]
[1] Kentarou Kawaguchi, Ryuji. Fujimori, Jian Tang, Takashi Ishiwata. FTIR Spectroscopy of NO3: Perturbation Analysis of the ν3+ν4 State, J. Phys. Chem. A, 117 (50), (2013).

10. Simulation

11. Simulation

12. Simulation

13. Simulation

14. Simulation

15. Simulation

16. Simulation

17. Simulation

18. Simulation

19. Split Line Analysis
In some parts, the simulation predicts one line where two lines appear in the experiment, seeming to split the intensity of the predicted line.

20. Split Line Analysis
We assume the split occurs from an accidental degeneracy between a bright state and a dark state.
where I is intensity and B and R refer to the blue and red end of the doublet respectively.
where is the frequency in cm-1 and B and R are as defined above.
[1]
[1] Codd, Terrance. Spectroscopic Studies of the State of NO3. Dissertation, The Ohio State University (2014).

21. Split Line Analysis
Representative Split Line Assignment for
We can calculate the unperturbed frequencies of a two state perturbation and compare with the simulated frequency.
One of each pair should match the simulation.

22. Split Line Analysis
Representative Split Line Assignment for
We can calculate the unperturbed frequencies of a two state perturbation and compare with the simulated frequency.
One of each pair should match the simulation.
Two state model has shown to be effective in initial analysis.
Where does the dark level come from?
P Branch

23. Comparison of Simulations Using Oblate Symmetric Top
[1]
[1] Kentarou Kawaguchi, Ryuji. Fujimori, Jian Tang, Takashi Ishiwata. FTIR Spectroscopy of NO3: Perturbation Analysis of the ν3+ν4 State, J. Phys. Chem. A, 117 (50), (2013).

24. Discussion
[1]
[1]
[1] Discussion with Stanton Group.

25. Discussion

26. Discussion
[1] Watson, J, K. G., Jahn-Teller and L-uncoupling Effecs on the Rotational Energy Levels of Symmetric and Spherical Top Molecules. J. Mol. Spec. 103, (1984).

27. Discussion [1] *For linear Jahn-Teller effect
[1] Watson, J, K. G., Jahn-Teller and L-uncoupling Effecs on the Rotational Energy Levels of Symmetric and Spherical Top Molecules. J. Mol. Spec. 103, (1984).

28. Discussion
[1] T. Codd, M.-W. Chen, M. Roudjane, J. F. Stanton, T. A. Miller. Jet Cooled Cavity Ringdown Spectroscopy of the A-X transition of the NO3 Radical, J. Phys. Chem, 142 (50), (2015).

29. Discussion

30. Discussion
The theoretical value for h1 corresponds to a greater distortion and localization in the PES well.
Possible that the pseudorotation is relatively fast on the rotational timescale, and the average structure is symmetric.
Greater Localization
Greater Delocalization

31. Summary
Split lines were observed in the rotational structure, suggesting perturbations likely from high energy rovibrational levels from the ground state.
Previously, the parallel bands in the transition have been fit using an oblate symmetric top Hamiltonian with spin-rotation.
The perpendicular bands in this transition are generally well-simulated using an oblate top Hamiltonian with spin-rotation, spin-orbit, coriolis, and Jahn- Teller terms. Our initial analysis again shows small effects from Jahn-Teller distortions and a significant contribution from vibrational angular momentum to coriolis coupling.
One possible explanation is a relatively greater delocalization on the rotational timescale.

32. Acknowledgements The Miller Group Dr. Terry A. Miller Meng Huang
Dr. Dmitry Melnik
Dr. Terrance Codd
Dr. Mourad Roudjane