Energy landscapes hold the key to understanding a wide range of molecu
lar phenomena. The problem of how a denatured protein re-folds to its
active state (Levinthal's paradox(1)) has been addressed in terms of t
he underlying energy landscape(2-7), as has the widely used 'strong' a
nd 'fragile' classification of liquids(8-9) Here we show how three arc
hetypal energy landscapes for clusters of atoms or molecules can be ch
aracterized in terms of the disconnectivity graphs(10) of their energy
minima-that is, in terms of the pathways that connect minima at diffe
rent threshold energies. First we consider a cluster of 38 Lennard-Jon
es particles, whose energy landscape is a 'double funnel' on which rel
axation to the global minimum is diverted into a set of competing stru
ctures. Then we characterize the energy landscape associated with the
annealing of C-60 cages to buckministerfullerene, and show that it pro
vides experimentally accessible clues to the relaxation pathway. Final
ly we show a very different landscape morphology, that of a model wate
r 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.