1. Deducing Anharmonic Coupling Matrix Elements from Picosecond Time- Resolved Photoelectron Spectra Katharine Reid (Julia Davies, Alistair Green) School of Chemistry, University of Nottingham

2. Intramolecular vibrational energy redistribution (IVR) Timescale: tens of picoseconds

3. 1.What is the timescale? 2. What is the mechanism (which dark states are involved)? 3. Can we influence the process? (Bond-selective chemistry, coherent control, mode-specificity) 4. What can we learn about chemical reactivity? Questions

5. Time-resolved photoelectron spectroscopy t = 0 t1t1 t2t2

6. Photoelectron imaging

7. Laser system Pulse width 1 ps Bandwidth ~15 cm -1 Independently tunable (and scannable!) pump and probe

8. IVR in toluene 6a 1 /10b 1 16b 1 Picosecond absorption spectrum

9. The 6a 1 /10b 1 16b 1 Fermi resonance in S 1 toluene

10. Characterized by dispersed fluorescence – Hickman, Gascooke and Lawrance JCP (1996) Excitation of the eigenstate at 462 cm -1 (predominantly 10b 1 16b 1 ) Excitation of the eigenstate at 457 cm -1 (predominantly 6a 1 ) This should provide a good test of our technique … The 6a 1 /10b 1 16b 1 Fermi resonance in S 1 toluene

11. Probing a two-level prepared wavepacket In photoelectron spectroscopy (PES) we can, depending on our resolution, see “signatures” of harmonic oscillator levels a and b. If we use a laser pulse of appropriate duration we expect that the photoelectron peak intensities will oscillate at  12. Different photoelectron peaks may have different sensitivities to the wavepacket dynamics.

12. Picosecond photoelectron spectrum at  t = 0 “one-colour” Hammond and Reid, 2006 “SEVI” Davies et al., 2010

13. Photoelectron images 0 ps3 ps6 ps

14. Time-resolved photoelectron spectra One-colour: Hammond and Reid, 2006 Two-colour: Davies et al., 2010

15. Time dependence of the ion origin peak 5.14 cm -1 5.49 cm -1

16. So … there must be a third state involved The S 1 frequency of mode 16a is given as 228 cm -1, so 16a 2 is expected at ~456 cm -1 and is a likely candidate … Courtesy of Warren Lawrance “The two spectra show different intensity for transitions terminating in 16 2 (16a 2 ), consistent with it being involved in the Fermi Resonance” At this level of excitation there are not many options

17. Possible explanation

18. 0 ps 3 ps (a) (b) (c) (d) But what do the other ion states tell us? Ion vibrational states: (a) = 0 0, (b) = 6a 1, (c) = 10b 1 16b 1, (d) = 16a 2

19. Time dependence of peaks (a), (c) and (d) Time delay / picoseconds 0 10b 1 16b 1 16a 2

20. 5.14 cm -1 5.49 cm -1 Fourier transforms for peaks (a) and (c)

21. What about the 16a 2 peak? On resonance Red-shifted

22. Fourier transforms 5.14 cm -1 5.49 cm -1 4.92 cm -1 5.69 cm -1 On resonance Red shifted But there is no plausible coupling of zero-order vibrational states, or torsion-vibration coupling that could cause this …

23. Torsional populations at 10 K

24. Energy level scheme  12 = 5.14 cm -1  12 = 5.49 cm -1  23 = 5.69 cm -1  23 = 4.92 cm -1 (… or the other way round)

25. Formalism (thanks to Felker and Zewail) and similarly for eigenstates |n> in the other torsional ladder. The eigenstates can be expressed as: Normalization requires

26. Formalism For a given observed ion state  where and p n depends on the light intensity at the energy of eigenstate |n> This enables us to simulate the observed beating patterns for chosen coupling matrix elements,  i , and compare with those observed experimentally. The most stringent test is the 16a 2 beating pattern.

27. Simulation of the 16a 2 beating patterns Cosine fit Simulation (a) on resonance

28. Simulation of the 16a 2 beating patterns Cosine fit Simulation (b) off resonance

29. Coupling matrix elements

30. Or to put it another way …

31. Summary Simulations based on the proposed energy level scheme reproduce all observed beating patterns; thus we have determined the anharmonic coupling constants connecting three zero-order states in S 1 toluene. Time-resolved photoelectron spectra can be treated quantitatively in favourable circumstances. The Fermi resonance originally believed to be a two-level system has been shown to be a three-level system, which is “doubled” as a consequence of small changes in vibrational frequencies in two torsional ladders. This provides an explanation for the apparently complex IVR behaviour that has been observed for molecular systems containing methyl rotors, even at quite low densities of states.

32. Acknowledgements Julia Davies Alistair Green Paul Hockett Warren Lawrance EPSRC