Term: potential of mean force https://doi.org/10.1351/goldbook.08196 Definition: Free energy as a function of a set of coordinates, the negative gradient of which gives the average force acting on that configuration averaged over all other coordinates and momenta within a statistical distribution. If the averaging is performed within a canonical ensemble (constant volume, temperature, and number of particles), the PMF is equivalent to the Helmholtz energy, but if it is performed within an isobaric-isothermal ensemble (constant pressure, temperature, and number of particles), the PMF is equivalent to the Gibbs energy. Notes: 1) Commonly, the PMF acting upon a selected geometric variable and averaged over the coordinates and momenta of all other geometric variables is evaluated for a succession of constrained values of the selected variable, thereby generating (generically) a free-energy profile with respect to the selected reaction coordinate (e.g., a bond distance or angle or a combination of internal coordinates); specifically, this is either a Helmholtz-energy or a Gibbs-energy profile, depending upon the choice of ensemble for the statistical averaging within a computational simulation. 2) Selection of two geometric variables as reaction coordinates allows a free-energy surface to be computed as a two-dimensional PMF. 3) Molecular simulations often yield Helmholtz energies, not Gibbs energies, but for condensed phases the difference is usually neglected. Source: PAC, 2022, 94, 353. 'Glossary of terms used in physical organic chemistry (IUPAC Recommendations 2021)' on page 484 (https://doi.org/10.1515/pac-2018-1010) Citation: 'potential of mean force' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.08196 License: The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. Disclaimer: The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.