1. Semiclassical model for localization and vibrational dynamics in polyatomic molecules Alexander L. Burin Quantum Coherent Properties of Spins – III Many thanks to Enrique del Barco, Stephen Hill and Philip Stamp for inviting me

2. Mark Ratner & Alex Burin Sarah Tesar Igor Rubtsov Semiclassical Model for Vibrational Dynamics in Polyatomic Molecules: Investigation of Internal Vibrational Relaxation Alexander L. Burin, Sarah L. Tesar, Valeriy M. Kasyanenko, Igor V. Rubtsov, and Grigory I. Rubtsov J. Phys. Chem. C, v. 114, pp 20510–20517 (2010) MARK RATNER FESTSCHRIFT

3. Motivation  n-atomic molecule possesses 3n-6 independent vibrational modes (harmonic approximation)  These modes are coupled by a weak anharmonic interaction

4. Problems  Evolution of excited state. Would the molecule remember its initial excitation?  What is lifetime of excited state?  What are energy relaxation pathways?

5. Significance: Quantum Computatio n

6. Significance: 2D Infrared Spectroscopy

7. Outline  Localization (Stewart, McDonald)  2DIR spectroscopy problems (Rubtsov)  Summary of previous theoretical work  Problems  Self-consistent collision integral model  Preliminary results  Comparison to experiments  Conclusion; future plans  Acknowledgement

9. Localization vs. thermalization N<10 – localization N>>10 - delocalization

10. 2D IR (AcPhCN, Rubtsov and coworkers)

11. Cross peak signal h

12. Theoretical approaches  Local random matrix model (e. g. Bigwood, Gruebele, Leitner, Wolynes). Replaces anharmonic interaction with random matrix elements. Gives reasonable prediction for localization transition using free parameter for interaction strength  Exact solution of Schrödinger equations on the restricted basis set of global harmonic states (e. g. Dreyer, Moran, Mukamel, 2003). Uses first principles anharmonic force constants, accurate enough in Density Fuctional Theory (Barone, 2005). Restricted to small molecules and low temperature (no more than 10000 states)  This work: Generalizes collision integral approach (Bagratashvili, Kuzmin, Letokhov, Stuchebrukhov, 1985). Determines environment effect self-consistently (Generalized Marcus-Levich-Jortner method)

13. Hamiltonian and Perturbation  Frequencies and interactions can be determined using first principle DFT method (Gaussian 09). The method works well for infrared absorption spectra (Barone, 05).

14. Model of anharmonic transitions Driving force Transition rates (Marcus 1955)

15. Definition of rate constant: reorganization energy

16. Definition of rate constant: preexponential factor Non-adiabatic or environment controlled adiabatic regimes (Rips, Jortner, 1987)

17. Self-consistent definition of relaxation times: collision integral method

18. Application of theory to 1,4-acetylbenzonitrile (AcPhCN)

19. Localization transition,    T g =129K, N(129)=30, consistent with Stewart and McDonald, 1982

20. Relaxation times at room temperature The calculated relaxation times of the CN and CO stretches are 1.6 ps and 7.0 ps. Consistent with experimentally measured lifetimes in AcPhCN of 1.8 and 3.9 ps.

21. Energy transport at room temperature, CN stretch is excited at t=0, CO excitation energy is probed Solvent has been treated in rate equation approximation,  =50ps. Maximum shift is reached at t=16ps. Consistent with experimental estimate of 12 ps.

22. Summary and Future Plans  New self-consistent collision integral approach to investigate internal vibrational relaxation in polyatomic molecules is proposed  Application of method to the representative AcPhCN molecule shows that this method predicts localization transition temperature, mode decay rates and internal kinetics consistently with the experiment  The modification of the method within the framework of small polaron transport theory and applications to other molecules are in progress

23. Acknowledgements Funding and Support NSF Grant No. 0628092 PITP and, personally, Prof. Stamp for support of ab’s subbatical visit and ST’s visit