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
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
Mark Ratner & Alex Burin
Igor Rubtsov
Sarah Tesar
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 Computation
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 10000 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,   
Tg=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. 0628092
•PITP and, personally,
Prof. Stamp for support
of ab’s subbatical visit
and ST’s visit