Single-stage direct Langevin dynamic simulations of transitions over arbitrarily high energy barriers: Concept of energy-dependent temperature

In this paper we present an algorithm which allows single-stage direct Langevin dynamics simulations of the escape rate over arbitrarily high energy barriers employing the concept of the energy-dependent temperature (EDT). In our algorithm, simulation time required for the computation of the escape rate does not increase with the energy barrier. This is achieved by using in simulations an effective temperature which depends on the system energy: around the energy minima this temperature is high, whereas it tends towards room temperature when the energy approaches the saddle point value. Switching times computed via our EDT algorithm show an excellent agreement with results obtained with the established forward flux sampling (FFS) method. As the simulation time required by our method does not increase with the energy barrier, we achieve a very large speedup when compared even to our highly optimized FFS version with interfaces placed equidistantly in the energy space. In addition, our method does not suffer from stability problems occurring in multistage algorithms (like FFS and "energy bounce" methods) due to the multiplication of a large number of transition probabilities between the interfaces.