Activation energies by molecular dynamics with constraints

Recently Tobias and Broods introduced a method to compute by molecular dynamics with constraints the probability density P(≈r) = < δ(r − ≈r) &>; associated with rate values≈r of a spatial coordinate r. In this Letter we extend their approach to the case of a general reaction coordinate ξ(r), an arbitrary function of the configuration-space coordinates. The generalized version is shown to be the integral form of the free energy calculation in the constrained-reaction-coordinate ensemble where the mean force is computed as an average in a ξ-constrained ensemble. The two approaches are shown to be of equal computational efficiency for a very simple Lennard-Jones test case.