Metadynamics: A Unified Framework for Accelerating Rare Events and Sampling Thermodynamics and Kinetics

Metadynamics is an enhanced sampling algorithm in which the normal evolution of the system is biased by a history-dependent potential constructed as a sum of Gaussians centered along the trajectory followed by a suitably chosen set of collective variables. The sum of Gaussians forces the system to escape from local free energy minima and is used to iteratively build an estimator of the free energy. This original idea has been developed and improved over the years in several variants, which nowadays allow addressing in a unified framework some of the most important tasks of molecular simulations: computing the free energy as a function of the collective variables, accelerating rare events, and estimating unbiased kinetic rate constants. This chapter provides a survey of the many formulations of metadynamics with an emphasis on the underlying theoretical concepts and some hints on the appropriate manner of using this approach for solving complicated real-world problems.