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(1)) has been addressed in terms of the underlying energy landscape(2-7), as has the widely used 'strong' and 'fragile' classification of liquids(8-9) Here we show how three archetypal energy landscapes for clusters of atoms or molecules can be characterized in terms of the disconnectivity graphs(10) 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 to 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 (H2O)(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.