1. Conical Intersections between Vibrationally Adiabatic Surfaces in Methanol Mahesh B. Dawadi and David S. Perry Department of Chemistry, The University of Akron, Akron OH 44325 Acknowledgements

2.  Born-Oppenheimer approximation: - Adiabatic separation of electronic and nuclear motion  Jahn-Teller effect and E ⊗ e conical intersection  Zwanziger and Grant E ⊗ e formalism: C 3V symmetry  JT scaling linearly plus Renner-Teller scaling quadratically vs distortion ρ  A set of 4 conical intersections  Vibrational adiabatic approximation: Methanol  Xu et al: CH stretches as a function of γ  Both Jahn-Teller and Renner-Teller couplings  No ρ-dependence  Vibrational conical intersections  Ultrafast vibrational relaxation Introduction R.G. McKinlay, J.M. Zurek, M.J. Paterson, Adv. Inorg. Chem. 62, 351 (2010). J. W. Zwanziger and E. R. Grant, J. Chem. Phys. 87, 2954 (1987). L.-H. Xu, J.T. Hougen, R.M. Lees, J. Mol. Spectrosc. 293-294, 38 (2013). P. Hamm and G. Stock, Phys. Rev. Lett. 109, 173201 (2012). 2

3. Conical Intersections between Vibrationally Adiabatic Surfaces in Methanol 3

4.  Ab initio Levels: MP2/6-311+G(3df,2p) Staggered Eclipsed Methanol Asymmetric CH-Stretch Frequencies Global Minimum Torsional Saddle Conical intersections (CIs) ρ =93.6° ρ = 61.9° Eclipsed-CI ρ = 0° C 3v geometry γ = 60˚, 180˚, 300˚ γ = 0˚, 120˚, 240˚ 4

5. Methanol Asymmetric CH-Stretches: Frequencies and Force constants  Ab initio Levels: MP2/6-311+G(3df,2p) B3LYP/6-31+G(2d,p) 5

6. Computed Points and Conical Intersections CIs Staggered Eclipsed Global Minimum Torsional Saddle γ = 60˚, 180˚, 300˚ γ = 0˚, 120˚, 240˚ ρ =93.6° ρ = 61.9° Eclipsed-CI ρ = 0° C 3v geometry 6

7. Computed Frequencies Along the Torsional MEP Table 5 of L.-H. Xu, J.T. Hougen, J.M. Fisher, R.M. Lees, J. Mol. Spectrosc. 260, 88 (2010). Fig.9. of L.-H. Xu, J.T. Hougen, R.M. Lees, J. Mol. Spectrosc. 293-294, 38 (2013). ν2ν2 ν9ν9 Torsional saddle Global minimum 7

8. Model Calculation 8

9. and eigenvalues in wavenumber: L.-H. Xu, J.T. Hougen, R.M. Lees, J. Mol. Spectrosc. 293-294, 38 (2013). J. W. Zwanziger and E. R. Grant, J. Chem. Phys. 87, 2954 (1987).  Extension of Zwanziger and Grant model to large distortion angle, ρ 9

10. ρ-Dependent Model Parameters  Polynomial expansions in ρ  Fit of data points (C s -symmetry) Staggered Eclipsed  Fit rms of 0.9 cm -1 for All 318 ab intio points for Cs and non-Cs geometries 10

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12. A Seam of Conical Intersections 12

13. A Seam in 3-D: r CO, ρ, γ  CIs at ρ = 61.9˚ and 93.6˚ belong to same seam of CIs r CO Eclipsed methanol, γ =0˚ 13

14. Conclusions  7 conical intersections found in methanol  accessible at low energies  become seams in 3-D and higher  Implications for spectroscopy  a test of the adiabatic concept  level patterns in torsionally excited states  states with mixed geometric phase  Implications for dynamics  localized ultrafast energy transfer P. Hamm and G. Stock, Phys. Rev. Lett. 109, 173201 (2012). 14

15. Thank you Questions or Comments? 15

16. Computed Frequencies Along The MEP Table 5 of L.-H. Xu, J.T. Hougen, J.M. Fisher, R.M. Lees, J. Mol. Spectrosc. 260, 88 (2010) Fig.9. of L.-H. Xu, J.T. Hougen, R.M. Lees, J. Mol. Spectrosc. 293-294, 38-59 (2013) New model XHL model ν2ν2 ν9ν9 16

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