I am holding the course Advanced sampling techniques for numerical simulations, in which the most recent techniques for simulating rare events, exploring the phase space and computing the free energy are summarized:

  1. 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.

  2. 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.
    • History-dependent reconstruction of the free energy: metadynamics and Wand-Landau sampling.

  3. Techniques for computing the rate constants:
    • Classical transition state theory. Kramers theory and Bennett-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.).

  4. The lecture notes for the course can be downloaded here