Inherent-structure dynamics and diffusion in liquids

The self-diffusion constant D is expressed in terms of transitions among the local minima (inherent structures, IS) of the N-body potential-energy surface or landscape, and their correlations. The formulas are evaluated and tested against simulation in the supercooled, unit-density Lennard-Jones liquid. The approximation of uncorrelated IS-transition (IST) vectors D₀, greatly exceeds D for the highest T, but merges with simulation at reduced T∼0.50, close to the estimated mode-coupling temperature T_c. Since uncorrelated IST’s are associated with a hopping mechanism, the condition D∼D₀ provides a new way to identify the crossover to hopping. The results suggest that theories of diffusion in deeply supercooled liquids may be based on weakly correlated IST’s.