An algorithm to find minimum free-energy paths using umbrella integration

Abstract

The calculation of free-energy barriers by umbrella sampling and many other methods is hampered by the necessity for an a priori choice of the reaction coordinate along which to sample. We avoid this problem by providing a method to search for saddle points on the free-energy surface in many coordinates. The necessary gradients and Hessians of the free energy are obtained by multidimensional umbrella integration. We construct the minimum free-energy path by following the gradient down to minima on the free-energy surface. The change of free energy along the path is obtained by integrating out all coordinates orthogonal to the path. While we expect the method to be applicable to large systems, we test it on the alanine dipeptide in vacuum. The minima, transition states, and free-energy barriers agree well with those obtained previously with other methods.