  We use energy landscape methods to investigate the response of a supercooled
liquid to random pinning. We classify the structural similarity of different
energy minima using a measure of overlap. This analysis reveals a
correspondence between distinct particle packings (which are characterised via
the overlap) and funnels on the energy landscape (which are characterised via
disconnectivity graphs). As the number of pinned particles is increased, we
find a crossover from glassy behavior at low pinning to a structure-seeking
landscape at high pinning, in which all thermally accessible minima are
structurally similar. We discuss the consequences of these results for theories
of randomly pinned liquids. We also investigate how the energy landscape
depends on the fraction of pinned particles, including the degree of
frustration and the evolution of distinct packings as the number of pinned
particles is reduced.
