Potential of Mean Force (PMF) Constraints and the Evaluation of Free Energy

A generalization of bond constraints can be made to constrain a system to some point along a reaction coordinate. A simple example of such a reaction coordinate would be the distance between two ions in solution. If a number of simulations are conducted with the system constrained to different points along the reaction coordinate then the mean constraint force may be plotted as a function of reaction coordinate and the function integrated to obtain the free energy for the overall process [36]. The PMF constraint force, virial and contributions to the stress tensor are obtained in a manner analagous to that for a bond constraint (see previous section). The only difference is that the constraint is now applied between the centres of two groups which need not be atoms alone. DL_POLY_2 reports the PMF constraint virial, W, for each simulation. Users can convert this to the PMF constraint force from

$$G_{\rm PMF} = - {\cal W}_{\rm PMF} / d_{\rm PMF}$$

where $d_{\rm PMF}$ is the constraint distance between the two groups used to define the reaction coordinate.