Enhanced sampling in the well-tempered ensemble

We introduce the well-tempered ensemble (WTE) which is the biased ensemble sampled by well-tempered metadynamics when the energy is used as collective variable. WTE can be designed so as to have approximately the same average energy as the canonical ensemble but much larger fluctuations. These two properties lead to an extremely fast exploration of phase space. An even greater efficiency is obtained when WTE is combined with parallel tempering. Unbiased Boltzmann averages are computed on the fly by a recently developed reweighting method [M. Bonomi, J. Comput. Chem. 30, 1615 (2009)]. We apply WTE and its parallel tempering variant to the 2d Ising model and to a Gō model of HIV protease, demonstrating in these two representative cases that convergence is accelerated by orders of magnitude.