On the connections between microcanonical and canonical ensemble dynamics in liquids

The connection between dynamics in the canonical and microcanonical ensembles is explored in the context of computing activation energies and non-Arrhenius effects. Considering the diffusion coefficient, D, as an example, we show that simple relationships exist between the energy-dependent diffusion coefficient, D(E), the corresponding constant temperature diffusion coefficient, D(T), its activation energy, and the temperature derivative of the activation energy, a key measure of non-Arrhenius behavior. These relationships are used to propose a new approach to calculating activation parameters within the framework of fluctuation theory for dynamics. This method enables more rapid convergence of activation energies and their temperature derivatives, as illustrated for water self-diffusion in both neat water and aqueous TMAO solutions. We also demonstrate that the convergence can be further accelerated by using a rejection algorithm to uniformly sample energies to characterize D(E).