The calculation of free-energy differences by constrained molecular-dynamics simulations

In this paper we set out to derive a relation between the constraint force and the derivative of the free energy for a system in which only the reaction coordinate is constrained. Our result differs from the expression by Mülders et al. [J. Chem. Phys. 104, 4869 (1996)] because we take into account the effect of the constraint on the sampled phase-space distribution. The method is illustrated with two prototypical numerical examples.