CY 6120 : Molecular and Statistical Reaction Dynamics and Scattering Statistical dynamics

Transition state Theory – Thermodynamics formulation; micro-canonical and variational transition state theory; flexible transition states. Unimolecular reaction dynamics, RRK and RRKM models, thermal activation, density of state. State preparation and intra molecular vibration energy distribution; stochastic master equation approach dynamical approaches to unimolecular reaction rates.

Electron transfer reactions, Marcus model. Statistical density operator for molecular states and the equations of motion for chemical system; Chemical reactions in solutions, diffusion equation, Kramer‘s and Grote –Hynes models. Quantum theory of reaction rates – flux-flux correlation function approach. Kubo formalism Quantum transition state theory.

Molecular dynamics:

Potential energy surface, bimolecular reaction, elementary quantum dynamics. Microscopic reversibility and detailed balance. Different forms for intermolecular potentials. Statistical sampling for simulations. The Metropolis Monte Carlo method; finite difference methods such as verlet algorithm and predictor-corrector methods. Introduction to quantum Monte Carlo. Procedure. Introduction to time-correlation and autocorrelation functions.

Molecular Scattering (elementary aspects only):

Bimolecular collisions, collision number two-body classical scattering. Cross sections, intermolecular potentials, import parameter principle of microscopic reversibility. Quantum theory of scattering: particles in central potentials partial waves, Born approximation optical theorem. Formal time independent scattering theory. The S matrix. The Lippmann – Schwinger equation – for structureless particles. Rate of change of observables, collision rates in ensembles and the relaxation equation. The wave (Moller) operator and time dependent collision theory, time reversal and reciprocity

Text Books:

1. Steinfeld, J. I., Francisco, J.S. and W.L., Chemical Kinetics and Dynamics, Prentice Hall, New Jersey, 1998.
2. Baer, T and Hase, W.L., Unimolecular Reaction Dynamics: Theory Experiments, Oxford University Press, Oxford, 1996.
3. Allen, D.J. and Tildesley, M.P., Computer Simulation in Liquids, Oxford University Press , U.S.A., 1996.
4. Haile, J.M., Molecular Dynamics Simulations, Wiley, U.S.A.,
5. Taylor, J.R., Scattering Theory: The Quantum Theory of Non-relativistic Collisions, Dover, New York, 2006.
6. Levine, R.D., Molecular Reaction dynamics, Cambridge University Press, 2006.
7. Levine, R.D., Quantum Mechanics of Molecular Rate Processes, Dover, New York, 1999.
8. H. Miller, in Dynamics of Chemical Reactions, ed.R.E. Wyatt, Marcel-Dekker, U.S. A., 1998.