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

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

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

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

Significance: Quantum Computatio n

Significance: 2D Infrared Spectroscopy

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

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

2D IR (AcPhCN, Rubtsov and coworkers)

Cross peak signal h

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 states)  This work: Generalizes collision integral approach (Bagratashvili, Kuzmin, Letokhov, Stuchebrukhov, 1985). Determines environment effect self-consistently (Generalized Marcus-Levich-Jortner method)

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).

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

Definition of rate constant: reorganization energy

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

Self-consistent definition of relaxation times: collision integral method

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

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

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.

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.

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

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