  In this paper we present an algorithm which allows single-stage direct
Langevin dynamics simulations of transitions over arbitrary high energy
barriers employing the concept of the energy-dependent temperature (EDT). In
our algorithm, simulation time required for the computation of the
corresponding switching rate does not increase with 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 and tends
towards the 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 the highly
optimized FFS version. In addition, our method does not suffer from stability
problems occurring in multi-stage algorithms (like FFS and 'energy bounce'
methods) due to the multiplication of a large number of transition
probabilities between the interfaces.
