  The energy landscapes of electrostatically charged particles embedded on
constant mean curvature surfaces are analysed for a wide range of system size,
curvature, and interaction potentials. The surfaces are taken to be rigid, and
the basin-hopping method is used to locate the putative global minimum
structures. The defect motifs favoured by potential energy agree with
experimental observations for colloidal systems: extended defects (scars and
pleats) for weakly positive and negative Gaussian curvatures, and isolated
defects for strongly negative Gaussian curvatures. Near the phase boundary
between these regimes the two motifs are in strong competition, as evidenced
from the appearance of distinct funnels in the potential energy landscape. We
also report a novel defect motif consisting of pentagon pairs.
