Efficiency analysis of reaction rate calculation methods using analytical models I: The 2D sharp barrier

We analyze the efficiency of different methods for the calculation of reaction rates in the case of two simple analytical benchmark systems. Two classes of methods are considered: the first are based on the free energy calculation along a reaction coordinate and the calculation of the transmission coefficient, the second on the sampling of dynamical pathways. We give scaling rules for how this efficiency depends on barrier height and width, and we hand out simple optimization rules for the method-specific parameters. We show that the path sampling methods, using the transition interface sampling technique, become exceedingly more efficient than the others when the reaction coordinate is not the optimal one.