Making the best of a bad situation: a multiscale approach to free energy calculation

Authors: Michele Invernizzi1*, Michele Parrinello2*

  1. Department of Physics, ETH Zurich c/o USI Campus, 6900 Lugano, Switzerland
  2. Department of Chemistry and Applied Biosciences, ETH Zurich c/o USI Campus, 6900 Lugano, Switzerland
  • Corresponding authors emails:,

DOI10.24435/materialscloud:2019.0004/v4 (version v4, submitted on 17 September 2019)

How to cite this entry

Michele Invernizzi, Michele Parrinello, Making the best of a bad situation: a multiscale approach to free energy calculation, Materials Cloud Archive (2019), doi: 10.24435/materialscloud:2019.0004/v4.


Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently and reconstruct the free energy landscape. In methods like metadynamics, the quality of these collective variables plays a key role in convergence efficiency. Unfortunately in many systems of interest it is not possible to identify an optimal collective variable, and one must deal with the non-ideal situation of a system in which some slow modes are not accelerated.
We propose a two-step approach in which, by taking into account the residual multiscale nature of the problem, one is able to significantly speed up convergence. To do so, we combine an exploratory metadynamics run with an optimization of the free energy difference between metastable states, based on the recently proposed variationally enhanced sampling method. This new method is well parallelizable and is especially suited for complex systems, because of its simplicity and clear underlying physical picture.

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File name Size Description
MD5MD5: 61e04ef11828c4401377cee63b7b056c
59.1 MiB data and scripts for reproducing the paper's figures
MD5MD5: 2c25d25baabfce8a35387111f432829e
63.3 KiB input files for the simulations


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.


enhanced sampling free energy metadynamics

Version history

17 September 2019 [This version]

21 May 2019

16 April 2019

22 January 2019