# Time-independent free energies from metadynamics via Mean Force Integration

## TL;DR

This paper introduces Mean Force Integration (MFI), a novel method to compute time-independent free energy profiles from biased simulations, enhancing accuracy and efficiency in free energy calculations.

## Contribution

MFI provides a new approach that avoids ensemble bias averaging and can integrate data from multiple simulations, improving free energy estimation in metadynamics.

## Key findings

- Validated against analytical potentials showing accurate free energy profiles.
- Successfully applied to conformational free energy landscape of ibuprofen.
- Demonstrated ability to combine independent simulations for convergence.

## Abstract

Inspired by thermodynamic integration, we propose a method for the calculation of time-independent free energy profiles from history-dependent biased simulations via Mean Force Integration (MFI). MFI circumvents the need for computing the ensemble average of the bias acting on the system c(t) and can be applied to different variants of metadynamics. Moreover, MFI naturally extends to aggregate information obtained from independent metadynamics simulations, allowing to converge free energy surfaces without the need to sample recrossing events in a single continuous trajectory. We validate MFI against one- and two-dimensional analytical potentials and by computing the conformational free energy landscape of ibuprofen in the bulk of its most common crystal phase.