  We report on the structure and adsorption properties of Pd$_n$ ($n=1-4$)
clusters supported on the rutile TiO$_2$ (110) surfaces with the possible
presence of a surface oxygen vacancy or a subsurface Ti-interstitial atom. As
predicted by the density functional theory, small Pd clusters prefer to bind to
the stoichiometric titania surface or at sites near subsurface Ti-interstitial
atoms. The adsorption of Pd clusters changes the electronic structure of the
underlying surface. For the surface with an oxygen vacancy, the charge
localization and ferromagnetic spin states are found to be largely attenuated
owing to the adsorption of Pd clusters. The potential energy surfaces of the Pd
monomer on different types of surfaces are also reported. The process of
sintering is then simulated via the Metropolis Monte Carlo method. The presence
of oxygen vacancy likely leads to the dissociation of Pd clusters. On the
stoichiometric surface or surface with Ti-interstitial atom, the Pd monomers
tend to sinter into larger clusters, whereas the Pd dimer, trimer and tetramer
appear to be relatively stable below 600 K. This result agrees with the
standard sintering model of transition metal clusters and experimental
observations.
