Advanced sampling techniques for numerical simulations

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Main topics

General introduction to the “rare events” problem. Introduction to the concepts of free energy, rate constant, mean-first-passage time, separation of time scales, committor distribution, etc.

Computing the free energy in complex systems:

• Thermodynamic integration and umbrella sampling techniques. Ferrenberg and Swendsen method for computing the density of states and weighted-histogram analysis
• Free energies from non-equilibrium processes: the Jarzynski equality for the irreversible work. Relation with the second principle of thermodynamics.
• History-dependent reconstruction of the free energy: metadynamics and Wand-Landau sampling.

Techniques for computing the rate constants:

• Classical transition state theory. Kramers theory and Chandler method for computing the recrossing corrections.
• Methods for finding the saddle point in complex potential energy surfaces: nudged elastic band, eigenvalue following and the dimer method.
• Path integral formulation of the rare event problem: transition path sampling. Methods for computing the committor distribution (finite-temperature string, etc.)