Syllabus

Module-1 (8 hours)
Classical dynamics: Phase spaces and the Lagrangian and Hamiltonian formulations, the Liouville equation and equilibrium solutions, classical time evolution operator and numerical integrators, force field, molecular dynamics

Module-2 (10 hours)
Thermodynamics of real gases and liquids: Radial distribution function, Mayer f-function

Module-3 (8 hours)
Dynamics on free energy surface: Non-equilibrium free energy methods, Jarzynski's and Crook's theorems, equilibrium free energy methods, free energy perturbation, thermodynamic integration

Module-4 (4 hours)
Monte Carlo simulation: Importance sampling, Markov models, parallel tempering

Module-5 (6 hours)
Stochastic dynamics: Derivation of generalized Langevin dynamics for model systems, fluctuation-dissipation theorem, memoryless Langevin and Brownian dynamics, probability distributions and Fokker-Planck equations

To obtain an overview of simulation techniques and algorithms to study molecular systems using classical mechanics.

To understand how thermodynamic observables can be calculated for N interacting particles.

To learn how many-body dynamics can be interpreted in terms of molecular events on the free energy landscape.

To understand the balance between fluctuation and dissipation in dynamics of a particle in contact with a heat bath.

CO1: On successful completion of this course, the students will be able to appreciate various modeling and simulation based approaches to solve physical problems.
CO2: They should be able to write efficient algorithms to propagate dynamics according to the equation of motion.
CO3: They should be able to compute various physical observables from simulations and compare with experiments.
CO4: They should be able to explain the dynamics of a complex multidimensional system by projecting the free energy surface onto a few essential degrees of freedom.

H.J.C. Berendsen, Simulating the Physical World, Cambridge University Press

M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford University Press

Mark E. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation, Oxford University Press

D. Frenkel, B. Smit, Understanding Molecular Simulations: From Algorithms to Applications, Academic Press