Atomistic simulations play a central role in many fields of science. However, their usefulness is often limited by the fact that many systems are characterized by several metastable states separated by high barriers, leading to kinetic bottlenecks. Transitions between metastable states are thus rare events that occur on significantly longer timescales than one can simulate in practice. Numerous enhanced sampling methods have been introduced to alleviate this timescale problem, including methods based on identifying a few crucial order parameters or collective variables and enhancing the sampling of these variables. Metadynamics is one such method that has proven successful in a great variety of fields. Here we review the conceptual and theoretical foundations of metadynamics. As demonstrated, metadynamics is not just a practical tool but can also be considered an important development in the theory of statistical mechanics.


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