Free energy reconstruction from metadynamics or adiabatic free energy dynamics simulations

In molecular dynamics simulations, most enhanced sampling methods are traditionally associated with one particular estimator to calculate the free energy surface (FES), such as the histogram, the mean force, or the bias potential. Here, we start from the realization that four enhanced sampling methods, metadynamics and well-tempered metadynamics (in their extended Lagrangian form), as well as driven adiabatic free energy dynamics (dAFED) and unified free energy dynamics (UFED), can be used in combination with any of the three above-mentioned FES estimators. We compare the convergence properties of these estimators on the alanine dipeptide and a sodium ion solvation shell. We find that the mean force estimator is superior in all cases. We also show that it can be marginally beneficial to combine information from the histogram and the force, provided that both are of comparable accuracy.