https://doi.org/10.1351/goldbook.08196
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:
- 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.
- Selection of two geometric variables as reaction coordinates allows a free-energy surface to be computed as a two-dimensional PMF.
- Molecular simulations often yield Helmholtz energies, not Gibbs energies, but for condensed phases the difference is usually neglected.