1. A First-Principles Model of Fermi Resonance in the Alkyl CH Stretch Region: Application to Hydronaphthalenes, Indanes, and Cyclohexane Funded by NSF and DOE Molecular Spectroscopy Symposium, June, 2014 Nathanael Kidwell, Tim Zwier, Danny Tabor, and Ned Sibert

2. DPE C 2h DPOE C 2h DPE C 2 DPOE C 2 Probing molecular structure with CH chromophores with the Zwier Group at Purdue Our goal is to develop theoretical models that will enable us to use the CH stretch as a probe of environment. Initial work focuses on developing Hamiltonians that allow us to predicting spectra of the molecules based on input from electronic structure theory and couplings that are scaled to the DPE C 2h spectrum.

3. so/ss so so/ss ss/so as ss/so ss as ss/so

4. Background CH 2 Scissor CH Sym Stretch CH Asym Stretch 1450 cm -1 2960 cm -1 2980 cm -1 Images from Molecular Vibration; Wikipedia, the free encyclopedia 1500 3000 Wavenumber (cm -1 ) A / ss as so

5. 2900 3000 ss as 2900 3000 1) Calculate E ss, E as, E so and W with DFT. 2) Scale the results using a, b, and c. 3) For different X-CH2-Y species use the same a, b, and c. The Strategy The Hamiltonian Stretch-Bend Fermi Coupling

6. An Aside One can use either a symmetrized representation Or one can use a localized representation

7. Complication No. 1 The spectra are extremely congested. Solution Find a good experimentalist.

8. Complication No. 2 Normal modes are sensitive to small potential changes. Solution Use local modes. Local modes are insensitive to small potential changes. Local modes potentials are transferrable. The local mode picture is approximate.

9. 1476 cm -1 1479 cm -1 The CH 2 Scissor Vibrations of Tetralin NM picture hides interactions with scissor modes

10. 1466 cm -1 The Scaled & Localized CH 2 Scissor Vibrations of Tetralin

11. Enough with the preliminaries. Onto the main event.

12. THN I2M tetralin A C A B 14DHN A A B A indane A B A indene 12DHN B A B A A

13. Comparison to Normal Mode Results

14. Model Hamiltonian Start with a zero order Hamiltonian and dipole Add some Fermi coupling terms Pick a basis, diagonalize the H matrix, and calculate the spectrum. B3LYP/6-311+G(d,p)

15. 12DHN Spectra With anharmonic terms included.

16. 12DHN Spectra CH 2 Decoupling Approximation

17. Calculate bilinear terms in dipole 14DHN Spectra

18. Comparison of Model Results to Experimental Results

19. CH 2 Decoupling Approximation

20. Concluding Remarks Developed a model for CH 2 stretches. Hamiltonian has parameters that are fit to one member of a group of similar species. Working to extend to CH 3 groups. Working to better parameterize the Hamiltonian. Would like to add waters.

21. On to CH 3 groups!

22. CH 3 -CD 3 R1R1 22 11 R2R2 R3R3 33