Multithermal-multibaric molecular simulations from a variational principle

Authors: Pablo M. Piaggi1*, Michele Parrinello1*

  1. Department of Chemistry and Applied Biosciences, ETH Zurich, c/o USI Campus, Via Giuseppe Buffi 13, CH-6900, Lugano, Switzerland; Facoltà di Informatica, Istituto di Scienze Computazionali, and National Center for Computational Design and Discovery of Novel Materials (MARVEL), Università della Svizzera italiana (USI), Via Giuseppe Buffi 13, CH-6900, Lugano, Switzerland
  • Corresponding authors emails:,

DOI10.24435/materialscloud:2019.0016/v1 (version v1, submitted on 03 May 2019)

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How to cite this entry

Pablo M. Piaggi, Michele Parrinello, Multithermal-multibaric molecular simulations from a variational principle, Materials Cloud Archive (2019), doi: 10.24435/materialscloud:2019.0016/v1.


We present a method for performing multithermal-multibaric molecular dynamics simulations that sample entire regions of the temperature-pressure (TP) phase diagram. The method uses a variational principle [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] in order to construct a bias that leads to a uniform sampling in energy and volume. The intervals of temperature and pressure are taken as inputs and the relevant energy and volume regions are determined on the fly. In this way the method guarantees adequate statistics for the chosen TP region. We show that our multithermal-multibaric simulations can be used to calculate all static physical quantities for all temperatures and pressures in the targeted region of the TP plane. We illustrate our approach by studying the density anomaly of TIP4P/Ice water.

This record includes input and output files, and Jupyter Notebooks describing the analysis of the simulations and the creation of the figures for the paper.

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File name Size Description
MD5MD5: f11abc58ed343ae022e9b7151aa88138
1.4 KiB README file with description of the other files
MD5MD5: 2ebcb695bb97c3f15ffc056465a9d8a2
3.1 GiB A simulation of liquid TIP4P/Ice water in the multithermal-multibaric ensemble. References computed in the isothermal-isobaric ensemble. A Jupyter Notebook with the code used to generate the results shown in the paper.
MD5MD5: 3069e54e8dcd72436d06bd22500862c7
15.6 KiB Source files that should be added to Plumed v2.4 in order to perform and analyze the simulations.
MD5MD5: 55f40385246a187324533a0c43e20938
9.8 MiB A simulation of liquid Na in the multicanonical ensemble. References computed in the canonical ensemble at different temperatures. A Jupyter Notebook with the code used to generate the results shown in the paper.


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


enhanced sampling multithermal-multibaric water density anomaly Wang Landau multicanonical

Version history

12 June 2019

07 May 2019

03 May 2019 [This version]