  We use density functional theory to quantify finite size and shape effects
for gold nanoclusters. We concentrate on the computation of binding energy as a
function of bond length for icosahedral and cuboctohedral clusters. We find
that the cuboctoheral gold clusters have lower energy for 13 atoms. For 55
atoms we find that the icosahedral gold clusters have lower binding energy. We
also introduce a one parameter family of geometries that interpolate between
the icosahedral and cuboctohedral clusters that is parametrized by an angle
variable. We determine the binding energy dependence on shape as a function of
the angle variable for 13 and 55 atom clusters with a minimum at the
cuboctohedral point and icosahedral point respectively. We also compute the
binding energy for the 147 atom gold nanocluster and show that the binding
energy of the icosahedral cluster is lower than the 147 atom cuboctohedral gold
cluster. We also compute the binding energy of the $Au_{55}O_2$ molecule with
possible applications to catalysis.
