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 62. The PMF constraint force, virial and contributions to the stress tensor are obtained in a manner analogous 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_4reports the PMF constraint virial, \({\cal W}_{PMF}\), for each simulation. Users can convert this to the PMF constraint force from
where is \(d_{PMF}\) the constraint distance between the two groups used to define the reaction coordinate.
The routines pmf_shake and pmf_rattle are called to apply
corrections to the atomic positions and respectively the atomic
velocities of all particles constituting PMF units.
In presence of both bond constraints and PMF constraints. The constraint procedures, i.e. SHAKE or RATTLE, for both types of constraints are applied iteratively in order bonds-PMFs until convergence of \({\cal W}_{PMF}\) reached. The number of iteration cycles is limited by the same limit as for the bond constraints’ procedures (SHAKE/RATTLE).