  Recently, Locatelli and Schoen proposed a transformation of the potential
energy that aids the global optimization of Lennard-Jones clusters with
non-icosahedral global minima. These cases are particularly difficult to
optimize because the potential energy surface has a double funnel topography
with the global minimum at the bottom of the narrower funnel. Here we analyse
the effect of this type of transformation on the topography of the potential
energy surface. The transformation, which physically corresponds to a
compression of the cluster, firstly reduces the number of stationary points on
the potential energy surface. Secondly, we show that for a 38-atom cluster with
a face-centred-cubic global minimum the transformation causes the potential
energy surface to become increasingly dominated by the funnel associated with
the global minimum. The transformation has been incorporated in the
basin-hopping algorithm using a two-phase approach.
