Britta A. Johnson and Edwin L. Sibert III

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Presentation transcript:

A Zero-Order Picture of the Jahn-Teller Coupled Region of the Infrared Spectrum of CH3O and CD3O Britta A. Johnson and Edwin L. Sibert III University of Wisconsin—Madison International Symposium on Molecular Spectroscopy Urbana-Champaign Thursday, June 23, 2016

Methoxy Radical Methoxy has a doubly degenerate ground state (X2E) Therefore, moderate JT coupling with respect to three vibrational e modes Also experiences small spin-orbit coupling C3v Cs

Create Hamiltonian/Potential Fit Developed fitted quartic potential force field (based upon scans taken using CCSD(T)/cc-pVTZ) Generated Hamiltonian which includes Jahn-Teller coupling Fermi coupling Anharmonicity Barckholtz, T. A.; Miller, T. A. Int. Rev. Phys. Chem. 1998, 17, 435-524.

CH3O Spectra: Comparison to Experiment 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.

Eighteenth Excited State Decomposition of eighteenth excited state into normal mode basis.

Normal Modes: Modes 2, 3, 5, and 6 are important for this region of the spectrum. Mode Symmetry Wavenumber (cm-1) Description 1 a1 2967.94 CH stretch 2 1435.70 Umbrella 3 1076.89 CO stretch 4 e 3042.42 5 1438.02 HCH bend 6 1075.09 CHO rock Modes 5 and 6 are the strongest Jahn-Teller coupled modes.

Full Correlation Diagram

Partitioned Hamiltonian

Partitioned Hamiltonian

Partitioned Hamiltonian

Partitioned Hamiltonian

Partitioned Hamiltonian Everything else is included here: Higher order JT terms Fermi coupling Etc.

Partitioned Hamiltonian

Partitioned Hamiltonian

Construct the Zero-Order Hamiltonian, H0 Two degenerate electronic surfaces: treat as diabats. As first approximation, place 9 harmonic normal modes on each diabat with Morse oscillator to model CH stretches Q6x

The Zero-Order Hamiltonian, H0 Two degenerate electronic surfaces: treat as diabats.

Zero-Order Hamiltonian, H0 Two degenerate electronic surfaces: treat as diabats. This form is extended to the other 6 modes in the system. No coupling between electronic surfaces

Eighteenth Excited State (2009 cm-1) B C D E F G Overlap diagrams are used to measure quality of representation Decomposition of eigenstate into the zero-order basis The I2 is the “percentage” of the eigenstate that is made up of that zero-order state

Eighteenth Excited State (2009 cm-1) B C D E F G Inverse Participation Number: Roughly the number of zero-order states need to represent the eigenstate

Eigthteenth Excited State (2009 cm-1) B C D E F G

Linear JT Coupling in Mode 6 The potential (only with respect to mode 6): Now have off-diagonal coupling between the two electronic states. Diagonalizable (diabatic to adiabatic transformation)

Shape of Potentials Q5/Q6 representation Q6x/Q6y representation Upper Adiabat Lower Adiabat Upper Adiabat Lower Adiabat Q6 Q6y Q5 Q5 Q6x Q6x Each coordinates ranges 0 to 3 Each coordinates ranges -3 to 3

Eigthteenth Excited State (2009 cm-1) B C D E F G

Zero-Order Hamiltonian: H1JT6

Zero-Order Hamiltonian: H1JT6

Linear and Quadratic Coupling in Mode 6 Upper Adiabat Lower Adiabat Q6x/Q6y representation

Zero-Order Hamiltonian: H1JT6 Have three options: 1. Include linear and quadratic coupling in mode 6

Eigthteenth Excited State (2009 cm-1) K L

Zero-Order Hamiltonian: H1JT6 Have three options: 1. Include linear and quadratic coupling in mode 6 2. Include linear coupling in mode 5 and mode 6

Zero-Order Hamiltonian-Linear JT in Mode 5 and 6 For a single mode This has logical extension to include a second linear Jahn-Teller coupled mode (mode 5) Diagonalize

Zero-Order Hamiltonian-Linear JT in Mode 5 and 6 For a single mode This has logical extension to include a second linear Jahn-Teller coupled mode (mode 5) Diagonalize

Eigthteenth Excited State (2009 cm-1) J

Zero-Order Hamiltonian: H1JT6 Have three options: 1. Include linear and quadratic coupling in mode 6 2. Include linear coupling in mode 5 and mode 6 3. Include linear and quadratic JT in mode 5 and 6

Zero-Order Hamiltonian: HJT

Participation Numbers for CH3O l = 1 l = 0

CD3O: Can we use the same method? 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.

CD3O: Can we use the same method? Here we have a new type of Jahn-Teller coupling which we have separated.

CD3O: Can we use the same method?

CD3O: Can we use the same method? B

Conclusions: We developed a potential force field that reproduces the experimental spectra for CH3O and CD3O We partitioned the correlation diagram to study the effects different coupling elements have on eigenstates. By creating a series of zero-order Hamiltonians, we are able to visualize the decomposition of eignestates into the zero-order states.

Acknowledgements Sibert Group Y.P. Lee’s Group NSF Ned Sibert Danny Tabor Dr. Jayashree Nagesh Y.P. Lee’s Group NSF