Energy landscapes for diffusion: Analysis of cage-breaking processes

A wide spectrum of potential energy barriers exists for binary Lennard-Jones systems. Here we examine the barriers and cage-breaking rearrangements that are pertinent to long-term diffusion. Single-step cage-breaking processes, which follow high-barrier routes, are identified, and different methods and criteria for defining a cage-breaking process are considered. We examine the extent to which a description of cage-breaking within the energy landscape is a description of long-term diffusion. This description includes the identification of cage-breaks that are reversed, and those that are productive towards long-term diffusion. At low temperatures, diffusion is adequately described by productive cage-breaks, or by considering all cage-breaks and accounting for the effect of reversals. To estimate the diffusion constant we require only the mean square displacement of a cage-break, the average waiting time for a cage-break, and a measure of the number of reversed cage-breaks. Cage-breaks can be visualized within the potential energy landscape using disconnectivity graphs, and we compare the use of productive cage-breaks with previous definitions of "megabasins" or "metabasins."