Approaching a parameter-free metadynamics

We present a unique derivation of metadynamics. This work leads to a more robust understanding of the error in the computed free energy than what has been obtained previously. Moreover, a formula for the exact free energy is introduced. The formula can be used to post-process any existing well-tempered metadynamics data, allowing one, in principle, to obtain an exact free energy regardless of the metadynamics parameters.

Figure 1

Error as a function of $\alpha$ with and without deconvolution.