1. Rovibrational Phase- Space Surfaces for Analysis of the υ 3 /2 υ 4 Polyad Band of CF 4 Justin Mitchell, William Harter, University of Arkansas Vincent Boudon, CNRS - Université de Bourgogne

2. CF 4 Dramatic rotation-vibration coupling Similar in structure to other spherical top molecules SF 6, Mo(CO) 6, CH 4, CD 4, CF 4, GeF 4 High resolution is needed for astronomy and atmospheric science A field in need of qualitative analysis

3. How to get more information from phase-space 1. Write Hamiltonian in Tensor Expansion 2. Phase-Space Plots of Tensors 3. Contour with experimental/computational spectra making Rotational Energy Eigenvalue Surface (REES) 4. Topography of Level Clustering (fine structure)

4. 1. Write Hamiltonian in Tensor Expansion 2. Phase-Space Plots of Tensors 3. Contour with experimental/computational spectra making Rotational Energy Eigenvalue Surface (REES) 4. Topography of Level Clustering (fine structure) How to get more information from phase-space

5. Tensor expansion RotationVibration Fitting Term Use vibrational basis Treat rotation operators as classical Champion, Loëte, Pierre, in “Spectroscopy of the Earth’s Atmosphere and Interstellar Medium,” (Rao, Weber, Eds), Academic Press, San Diego, 1992, p 339-422

6. How to get more information 1. Write Hamiltonian in Tensor Expansion 2. Phase-Space Plots of Tensors 3. Contour with experimental/computational spectra making Rotational Energy Eigenvalue Surface (REES) 4. Topography of Level Clustering (fine structure)

7. Rotational Energy Eigenvalue Surface (REES) Constant Total Angular Momentum, J. x,y,z are J x, J y, and J z Contours are Eigenvalues REES will have the same symmetry as the molecule Simple angular momentum relationships give approximate energy values J=30

8. How to get more information 1. Write Hamiltonian in Tensor Expansion 2. Phase-Space Plots of Tensors 3. Contour with experimental/computational spectra making Rotational Energy Eigenvalue Surface (REES) 4. Topography of Level Clustering (fine structure)

9. Local symmetry structures Local symmetry determines clustering patterns C4C4 C3C3 C2C2 C1C1 Harter, Paterson, Galbraith, J. Chem. Phys. 69, 4896, (1978)

10. REES for υ 3 Parameters used are from CF 4, but with B ζ set to zero Cut exists to show lower surfaces Three surfaces because of triplet vibrational state Conical intersections exist between levels Energies calculated using XTDS software Wenger et. al, J. Mol. Spect. 251, 102 (2008)

11. Energy diagram with classical outline for υ 3 Treatment similar to Dhont, Sadovskii, Zhilinskii, Boudon, J. Mol. Spectrosc.201, 95 (2000) Scalar 2nd, 4th... terms removed to keep plot centered

12. υ 3 with C1 structure C 4, C 3, and C 2 axes are high Levels exist in C 1 region Now only 1 level is below the surface J=55

13. REES υ 3 /2 υ 4 CF 4 Interaction of 9 rovibronic phase surfaces Outer surface contours are dappled from scaling Cluster patterns match local symmetry conditions Cone locations predict engies J=60

14. Energy diagram for υ 3 /2 υ 4 More on this from Boudon at RI 09

15. Cone locations predict energies J=60 Surface 6 Surface 3 Surface 4 Surface 5

16. Cone locations predict energies J=50 Surface 6 Surface 3 Surface 4 Surface 5

17. Conclusions REES can predict level clustering REES can predict some parts of spectra though not always to high precision REES adds to the qualitative toolbox for rovibronic spectroscopy Combinations of level diagrams and classical outlines show when behavior is semi-classical or fully quantum