1. The Rotation-Vibration Structure of the SO 2 C̃ 1 B 2 State Derived from a New Internal Coordinate Force Field Jun Jiang, Barratt Park, and Robert Field ISMS 6/22/2015

2. What was known (or thought to be known) about the C̃-State SO 2 ? A double-well structure in the q 3 direction on the PES (unequal equilibrium SO bond lengths) A strong Fermi interaction between ν 1 and ν 3 The separability of the bending mode, ν 2, from ν 1 and ν 3

3. Low-Lying Vibrational Levels of C̃-State SO 2 (0,0,v b ) (0,1,v b ) (0,2,v b ) (0,3,v b ) (1,0,v b ) v b = 0 2 4 6 0 2 4 0 0 0 2 2 2 (v r,v 2,v b ) = T vib — a 1 levels — b 2 levels (predicted)

4. Low-Lying Vibrational Levels of C̃-State SO 2 (0,0,v b ) (0,1,v b ) (0,2,v b ) (0,3,v b ) (1,0,v b ) v 3 = 0 1 2 3 4 5 6 0 1 2 3 4 0 0 0 1 1 2 2 2 1 (v r,v 2,v b ) = T vib — a 1 levels — b 2 levels (predicted)

5. Internal Coordinate Force Field Fit The vibrational band origins of 32 S 16 O 2 and 32 S 18 O 2, and the isotope-shift between the two isotopologues. The A and B rotational constants of the zero- point level and the three fundamental levels of both isotopologues. The five centrifugal distortion coefficients of the zero-point level of the two isotopologues.

6. Vibrational Hamiltonian The nonlinear transformation between internal coordinate force constants and the normal mode force constants have been worked out by Hoy, Mills, and Strey. A. Hoy, I. Mills, and G. Strey, Mol. Phys. 24, 1265 (1972). A. Hoy, J. C. D. Brand, Mol. Phys. 36, 1409 (1978).

7. The Rotational Information Gross anharmonicities in q 3 direction and Fermi- resonances Weighted linear combination of rotational constants Treatment of the centrifugal distortion coefficient follows that of H&B

8. Reduced-Dimension Internal Force Field A small barrier (~100 cm -1 ) ν 3 =212 cm -1 Strong Fermi-133 resonance ν 1 =960 cm -1, 2ν 3 =560 cm -1

9. 2D Internal Force Field P = v r + 1/2 v b

10. Three-Dimensional Internal Force Field Fit P. Nachtigall, J. Hrusak, O. Bludsky, and S. Iwata, Chem. Phys. Lett. 303, 441 (1999).

11. Three-Dimensional Internal Force Field Fit The rms error of 0.9 cm -1 for vibrational band origins below 3000 cm -1 The calculated values of the fitted rotational constants are within (or very close to) 2σ experimental fit uncertainties.

12. Calculated Franck-Condon Factors K. Yamanouchi, M. Okunishi, Y. Endo, and S. Tsuchiya, J. Mol. Struct. 352, 541 (1995). T. Sako, A. Hishikawa, and K. Yamanouchi, Chem. Phys. Lett. 294, 571 (1998). D. Freeman, K. Yoshino, J. Esmond, and W. Parkinson, Planet. Space Sci. 32, 1125 (1984).

14. Vibrational Assignments of the 3D Wavefunctions (1,0,4) r (1,2,2) r Projections of the wavefunction of the 2394 cm -1 state onto the q 1 -q 3 plane at different values of q 2.

15. The Kellman Mode Basis States

16. Vibrational Assignment of the 3D wavefunctions Transform the vibrational Hamiltonian in the normal mode basis into the Kellman mode basis The transformation matrix, V t, is obtained from diagonalization of H t, constructed by setting all the terms that involves interactions between ν 2 and the other two modes to zero.

17. Vibrational Assignment of the 3D wavefunctions in the Kellman basis

18. The bending mode is not separable from the other two modes above 2000 cm -1 Franck-Condon Interference effects are present for levels above 2000 cm -1

19. The Franck-Condon Interference Effects in the 2762 cm -1 state Vibrational term values and Franck-Condon factors (fc) relative to the zero-point level for three states near 2750 cm -1, obtained from the reduced dimension fit. There is only one strong transition observed near 2750 cm -1. The 2762 cm -1 state was originally assigned as a normal mode (1,3,2) state, later corrected as a Kellman type (1,1,4) r level by Sako et al. K. Yamanouchi, M. Okunishi, Y. Endo, S. Tsuchiya, J. Mol. Struct. 352/353, 541 (1995). T. Sako, A. Hishikawa, K. Yamanouchi, Chem. Phys. Lett. 294, 571 (1998).

20. Franck-Condon Interference Effects

21. Franck-Condon Interference effects are prevalent for levels above 2000 cm -1 The bending mode is not separable from the other two modes above 2000 cm -1 Vibrational assignment based on apparent vibrational progressions fails!

22. Level Staggerings in the (0, ν 2, ν b ) progressions Effective ν b frequency E(ν r, ν 2, ν b +1) r -E(ν r, ν 2, ν b ) r

23. The Zigzag Pattern in the Rotational Constants Coriolis Mixing angle: Coriolis selection rule:

24. The effective ν b frequencies go in- and-out of resonance with the ν 2 frequency. This leads to the oscillatory behaviors in the mixing angle across each row and down each column (given t 1 is essentially a constant). ν 2 frequency at 377 cm -1 Coriolis Mixing angle:

25. The Zigzag Pattern in the Rotational Constants The zigzag pattern in the C constants are directly related to the alternating patterns in the Coriolis mixing angles. The value of the C constant is lower (higher) than that of C 000, if the interacting level is below (above) the level of interest. C 000

26. The effective ν b frequency catches up with the ν 2 frequency at v b =5. As a result, (0,0,6) is no longer the lowest energy level in the P 5 polyad. Instead, (0,1,5) r is the lowest energy level in P 5.

27. None of the pure bending levels are Coriolis- perturbed, while their counterparts, with excitations in ν b, are Coriolis-perturbed.

28. Two Rotational Signatures of a Double- well PES Requires only the availability of relatively well-determined rotational constants C 000

29. Conclusions Due to strong Fermi-133 interaction, the Kellman mode basis is a more physical representation of the SO 2 C̃ 1 B 2 state. The bending mode is not separable from the other two modes for levels above 2000 cm -1. The presence of double-well causes anomalies in the rotational structure of the SO 2 C̃ 1 B 2 state.

30. Thank You FIELD GROUP Bob Field Dr. Barratt Park Dr. Carrie Womack Catherine Saladrigas David Grimes Tim Barnum Prof. John Muenter Dr. Steve Coy ALSO STARRING Dr. Andrew Whitehill Dr. Shuhei Ono Prof. Anthony Merer Dr. Yan Zhou Ethan Klein FUNDING!! DOE