A ZeroOrder Picture of the Infrared Spectra of

A Zero-Order Picture of the Infrared Spectra of CH 3 O and CD 3 O: Assigning Low-Lying States in CH 3 O and CD 3 O Britta A. Johnson and Edwin L. Sibert III University of Wisconsin—Madison International Symposium on Molecular Spectroscopy Monday, June 19, 2017

Degenerate Ground State • C 3 v Cs 2 px 2 py 2 pz

Degenerate Ground State: Gaussian Wavepacket • Can also see complexity of behavior by allowing a Gaussian wavepacket to travel through the conical intersection C 3 v Cs

Generate Potential Force Field • Developed fitted quartic potential force field (based upon scans taken using CCSD(T)/cc-p. VTZ) • 1280 points along the Cs geometry • This force field includes • • Jahn-Teller coupling Fermi coupling Spin-orbit coupling Anharmonic effects

At the C 3 v geometry: Mode Symmetry Wavenumber (cm-1)* Description 1 a 1 2967. 94 CH stretch 2 a 1 1435. 70 Umbrella 3 a 1 1076. 89 CO stretch 4 e 3042. 42 CH stretch 5 e 1438. 02 HCH bend 6 e 1075. 09 CHO rock *found using a fitted potential force from CCSD(T)/cc-p. VTZ scans

Vibronic Spectrum: CH 3 O isolated in a p-H 2 matrix Lee Y. -F. ; Chou W. -T. ; Johnson, B. A. ; Tabor, D. P. ; Sibert, E. L. ; Lee Y. -P J. Mol. Spectrosc. 2015, 310, 57 -67.

Vibronic Spectrum: CH 3 O isolated in a p-H 2 matrix cm-1 Harmonic with Spin -Orbit Coupling cm-1

Harmonic Approximation Mode Symmetry Wavenumber (cm-1) 1 a 1 2967. 94 2 a 1 1435. 70 3 a 1 1076. 89 4 e 3042. 42 5 e 1438. 02 6 e 1075. 09

3: Complex Problems with Complex Hamiltonians Mode 1 Lower Frequency e Modes Symmetry Wavenumber (cm ) Will Experience the a 2967. 94 Strongest Jahn-Teller Coupling -1 1 2 a 1 1435. 70 3 a 1 1076. 89 4 e 3042. 42 5 e 1438. 02 6 e 1075. 09

Partitioned Hamiltonian Everything else is included here: • Higher order JT terms • Fermi coupling • Etc. Johnson and Sibert. JCP 146, 174112 (2017)

Harmonic Approximation

H 0 Approximation Two degenerate electronic surfaces: treat as diabats. Q 6 x As first approximation, place 9 harmonic normal modes on each diabat with Morse oscillator to model CH stretches

H 0 Approximation: Mode 6 Mode: Frequency (cm-1) 3042. 42 1438. 02 -279. 9 1075. 09 674. 49

H 0 Approximation

Linear Jahn-Teller Coupling in One Mode Lower Adiabat Upper Adiabat Q 6 Q 5

Linear Jahn-Teller Coupling in One Mode Lower Adiabat Upper Adiabat Q 6 Q 5

Linear Jahn-Teller Coupling in One Mode Diagonalize (diabatic to adiabatic transformation) Now have off-diagonal coupling between the two electronic states.

Linear Jahn-Teller Coupling in One Mode Upper Adiabat Lower Adiabat Q 6 Q 5

Linear Jahn-Teller Coupling in One Mode A C B F

Linear Jahn-Teller Coupling in One Mode A C B F

Linear Jahn-Teller Coupling in Two Modes Diagonalize

Linear Jahn-Teller Coupling in Two Modes A’ B’ D’ G’

Quadratic Jahn-Teller Coupling in a Single Mode

Quadratic Jahn-Teller Coupling in a Single Mode

Ground State H 0 Approximation Overlap between the eigenfunctions and the model wavefunctions (a) (b) * *

Ground State with Linear Jahn-Teller in Mode (a) (b) * *

Modulated Jahn-Teller Coupling Through Near-Degenerate Modes

Modulated Jahn-Teller Coupling Through Near-Degenerate Modes

Modulated Jahn-Teller Coupling Through Near-Degenerate Modes Mode Symmetry Wavenumber (cm-1) 2 a 1 1134. 55 3 a 1 998. 94 5 e 1041. 2 6 e 832. 68

Conclusion • CH 3 O has a doubly degenerate ground electronic state-this leads to Jahn-Teller coupling in the IR spectra • Used fitted force field to theoretically produce IR spectra • By partitioning Hamiltonian into pieces, we obtain correlation diagrams that allow potentials/wavefunctions with different coupling to be plotted. Johnson and Sibert. JCP 146, 174112 (2017) C 3 v Cs

Acknowledgements • The Sibert Group • Current: Ned Sibert • Past: • Danny Tabor • Amber Jain • Jaysheree Nagesh • Lee Group • Prof. Y. -P. Lee • Karolina Houpa • Funding: NSF