Energy barriers and activated dynamics in a supercooled Lennard-Jones liquid

Abstract

We study the relation of the potential energy landscape (PEL) topography to relaxation dynamics of a small model glass former of Lennard-Jones type. The mechanism under investigation is the hopping between superstructures of PEL minima, called metabasins (MBs). Guided by the idea that the mean durations of visits to MBs should reflect the local PEL structure, we first derive the effective depths of MBs from dynamics, by the relation E(app)=d ln /dbeta, where beta=1/k(B)T. Second, we establish a connection of E(app) to the barriers that surround MBs. As the consequence of a rugged PEL, it turns out that escapes from MBs do not happen by single hops between PEL minima, but correspond to complicated multiminima sequences. We introduce the concept of return probabilities to the bottom of the MBs in order to judge when the attraction range of a MB has been left. The energy barriers overcome can then be identified. These turn out to be in good agreement with the effective depths E(app), calculated from dynamics. We are thus able to relate MB lifetimes to their local structure. Moreover, we can trace back the overall diffusive dynamics to the population of MBs and to their local topology, i.e., to purely thermodynamic and structural quantities. Single energy barriers are identified with the help of a new method, which accurately performs a descent along the ridge between two minima. We analyze the population of transition regions between minima, called basin borders. No indication for the mechanism of diffusion to change around the mode-coupling temperature can be found. We discuss the question whether the one-dimensional reaction paths connecting two minima are relevant for the calculation of reaction rates at the temperatures under study.