1. Funding: Eiszner family National Science Foundation Martin Gruebele University of Illinois at Urbana-Champaign Daniel Weidinger Plus: Bob Bigwood, Marja Engel, Sandra Lee, Brent Strickler Collaborators: D Leitner E Sibert P Wolynes Praveen Duggirala VIBRATIONAL STATES AT THE DISSOCIATION LIMIT PROTECTED FROM VIBRATIONAL ENERGY FLOW ISMS 2014

2. N†N†  Ε  Reactive volume Total volume This assumes (among other things): All states N † above threshold are delocalized so they in fact can react. What if there are many regular states at dissociation that do not mix, and are ‘protected’ from IVR? Rate ~ Localized states and reaction rates:

3. Put 30,000 cm -1 into a small molecule like water, and you get vibrational states like |7,12,9>. Can we compute what fraction of states near dissociation remains localized? We proved that only a fraction of modes "i" in state |n 1,..n i,…> needs to lie near the edge, and states will be localized. Reason: dissociation energy is size-independent, but energy per mode is not. But put the same into a large molecule, and you get states like |0,1,0,0,1,0,2,0,0,1 … > A state on the “edge” of quantum number space

4. Dilution factor ~ 1/ (# of eigenstates a bright spectral feature dilutes into. into) Non-statistical states (0.7 in 10 3 ) Can this show up in more explicit molecular models? Quantum dynamics of SCCl 2 using a Watson 5th order Hamiltonian -11,000 point ab initio potential/dipole surfaces for 5 lowest-lying electronic states -1:10 4 agreement with energies, 20% agreement with intensities -dilution factors for 3.5 million anharmonic feature states computed to the dissociation limit. S C Cl

5. But what do experiments have to say about the existence of protected states above the dissociation limit?

6. Even at ‘low’ vibrational energy, all kinds of resonances begin to appear: But do they make a complete mess at dissociation? (Wigner/Brody/Porter-Thomas statistics)

7. IVR-unprotected (A) and IVR-protected (B) states

8. Green state: ‘fully protected’ participation ratio ≈ 1 Red state: ‘partly protected’ participation ratio < 1 The experimental result:

9. Can we use this knowledge to control molecular vibrations in large polyatomic molecules? Stanislas Ulam had an interesting ideas in the 1950s… This is now routinely used to steer unmanned planetary space missions… Target moon Fire attitude jet

10. NSF Martin Gruebele Rice University, Houston Brent Strickler How to give the rocket (molecule) little nudges (with photons) at the right times to make it go where you want with as little effort as possible… We proved that indeed, highly excited vibrational states have a fractal structure (when embedded in quantum number space) due to localization near the dissociation limit, permitting laser control. Does it work for molecules (quantum mechanics)?

11. Sunmary: *When exciting molecules to dissociation energy, even in the presence of thermal excitation, the fraction of regular states ‘protected’ from IVR grows with molecular size. *We illustrate this with accurate vibrational calculations and by experimentally detecting such states above the dissociation limit of SCCl 2. *The increased number of localized quantum states with size needs to be taken into account when calculating the available reactive channels in RRKM and transition state theories. *A quantized form of Ulam's theorem predicts the fluence and duration required for connecting two vibrational states by laser control.