μ-tempered metadynamics: Artifact independent convergence times for wide hills

Recent analysis of well-tempered metadynamics (WTmetaD) showed that it converges without mollification artifacts in the bias potential. Here we explore how metadynamics heals mollification artifacts, how healing impacts convergence time, and whether alternative temperings may be used to improve efficiency. We introduce "$\mu$-tempered" metadynamics as a simple tempering scheme, inspired by a related mollified adaptive biasing potential (mABP), that results in artifact independent convergence of the free energy estimate. We use a toy model to examine the role of artifacts in WTmetaD and solvated alanine dipeptide to compare the well-tempered and $\mu$-tempered frameworks demonstrating fast convergence for hill widths as large as $60^{\circ}$ for $\mu$TmetaD.