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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

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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

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Conical Intersections between Vibrationally Adiabatic Surfaces in Methanol 3

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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

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

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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

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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

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Model Calculation 8

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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

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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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A Seam of Conical Intersections 12

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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

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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

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Thank you Questions or Comments? 15

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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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