Approaching a parameter-free metadynamics

TL;DR

This paper derives a parameter-free formulation of metadynamics, providing a deeper understanding of free energy errors and a method to compute exact free energies from existing data without relying on extended Lagrangian frameworks.

Contribution

It introduces a novel derivation of metadynamics from an on-the-fly reweighting scheme, leading to a formula for exact free energy calculation applicable to existing data.

Findings

Provides a more robust understanding of free energy errors

Introduces a formula for exact free energy post-processing

Enables parameter-free metadynamics analysis

Abstract

We present a unique derivation of metadynamics. The starting point for the derivation is an on-the-fly reweighting scheme but through an approximation we recover the standard metadynamics and the well-tempered metadynamics in a general form while never appealing to the extended Lagrangian framework. 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 the metadynamics parameters.