Archetypal energy landscapes

Energy landscapes hold the key to understanding a wide range of molecular phenomena. The problem of how a denatured protein re-folds to its active state (Levinthal's paradox) has been addressed in terms of the underlying energy landscape, as has the widely used 'strong' and 'fragile' classification of liquids. Here we show how three archetypal energy landscapes for clusters of atoms or molecules can be characterized in terms of the disconnectivity graphs of their energy minima - that is, in terms of the pathways that connect minima at different threshold energies. First we consider a cluster of 38 Lennard-Jones particles, whose energy landscape is a 'double funnel' on which relaxation to the global minimum is diverted into a set of competing structures. Then we characterize the energy landscape associated with the annealing of C 60 cages of buckministerfullerene, and show that it provides experimentally accessible clues to the relaxation pathway. Finally we show a very different landscape morphology, that of a model water cluster (H 2 O) 20 , and show how it exhibits features expected for a 'strong' liquid. These three examples do not exhaust the possibilities, and might constitute substructures of still more complex landscapes.