# Calculating a PMF using the free-energy code¶

The free-energy coupling-parameter approach (see sec. Free energy calculations) provides several ways to calculate potentials of mean force. A potential of mean force between two atoms can be calculated by connecting them with a harmonic potential or a constraint. For this purpose there are special potentials that avoid the generation of extra exclusions, see sec. Exclusions. When the position of the minimum or the constraint length is 1 nm more in state B than in state A, the restraint or constraint force is given by $$\partial H/\partial \lambda$$. The distance between the atoms can be changed as a function of $$\lambda$$ and time by setting delta-lambda in the mdp file. The results should be identical (although not numerically due to the different implementations) to the results of the pull code with umbrella sampling and constraint pulling. Unlike the pull code, the free energy code can also handle atoms that are connected by constraints.

Potentials of mean force can also be calculated using position restraints. With position restraints, atoms can be linked to a position in space with a harmonic potential (see Position restraints). These positions can be made a function of the coupling parameter $$\lambda$$. The positions for the A and the B states are supplied to grompp with the -r and -rb options, respectively. One could use this approach to do targeted MD; note that we do not encourage the use of targeted MD for proteins. A protein can be forced from one conformation to another by using these conformations as position restraint coordinates for state A and B. One can then slowly change $$\lambda$$ from 0 to 1. The main drawback of this approach is that the conformational freedom of the protein is severely limited by the position restraints, independent of the change from state A to B. Also, the protein is forced from state A to B in an almost straight line, whereas the real pathway might be very different. An example of a more fruitful application is a solid system or a liquid confined between walls where one wants to measure the force required to change the separation between the boundaries or walls. Because the boundaries (or walls) already need to be fixed, the position restraints do not limit the system in its sampling.