  Density functional molecular dynamics simulations have been carried out to
understand the finite temperature behavior of Au$_{19}$ and Au$_{20}$ clusters.
Au$_{20}$ has been reported to be a unique molecule having tetrahedral
geometry, a large HOMO-LUMO energy gap and an atomic packing similar to that of
the bulk gold (J. Li et al., Science, {\bf 299} 864, 2003). Our results show
that the geometry of Au$_{19}$ is exactly identical to that of Au$_{20}$ with
one missing corner atom (called as vacancy). Surprisingly, our calculated heat
capacities for this nearly identical pair of gold cluster exhibit dramatic
differences. Au$_{20}$ undergoes a clear and distinct solid like to liquid like
transition with a sharp peak in the heat capacity curve around 770 K. On the
other hand, Au$_{19}$ has a broad and flat heat capacity curve with continuous
melting transition. This continuous melting transition turns out to be a
consequence of a process involving series of atomic rearrangements along the
surface to fill in the missing corner atom. This results in a restricted
diffusive motion of atoms along the surface of Au$_{19}$ between 650 K to 900 K
during which the shape of the ground state geometry is retained. In contrast,
the tetrahedral structure of Au$_{20}$ is destroyed around 800 K, and the
cluster is clearly in a liquid like state above 1000 K. Thus, this work clearly
demonstrates that (i) the gold clusters exhibit size sensitive variations in
the heat capacity curves and (ii) the broad and continuous melting transition
in a cluster, a feature which has so far been attributed to the disorder or
absence of symmetry in the system, can also be a consequence of a defect
(absence of a cap atom) in the structure.
