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 $D_0,$ greatly exceeds D for the highest T, but merges with simulation at reduced $T\sim 0.50,$ close to the estimated mode-coupling temperature $T_c.$ Since uncorrelated IST’s are associated with a hopping mechanism, the condition $D\sim D_0$ 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.

• Received 27 November 2000

DOI:https://doi.org/10.1103/PhysRevE.64.032201