Buckets Instead\nof Umbrellas for Enhanced Sampling\nand Free Energy Calculations

Umbrella sampling has been a workhorse\nfor free energy\ncalculations\nin molecular simulations for several decades. In conventional umbrella\nsampling, restraining bias potentials are strategically applied along\none or several collective variables. Major drawbacks associated with\nthis method are the requirement of a large number of bias windows\nand the poor sampling of the transverse coordinates. In this work,\nwe propose an alternate formalism that departs from the traditional\numbrella sampling to mitigate these issues, where we replace umbrella-type\nrestraining bias potentials with bucket-type wall potentials. This\nmodification permits one to formulate an efficient computational strategy\nleveraging wall potentials and metadynamics sampling. This new method,\ncalled “bucket sampling”, can significantly reduce the\ncomputational cost of obtaining converged high-dimensional free energy\nsurfaces. Extensions of the proposed method with temperature acceleration\nand replica exchange solute tempering are also demonstrated.