Recent
experiments have shown that PdGa nanocrystallites act as
highly selective and reactive catalyst for selective hydrogenation
of acetylene to ethylene. Motivated by these experimental results
we have studied the mechanism and energetics of the above reaction
on low indexed (100) and (110) PdGa surfaces using first-principles
density functional theory based calculations. We find that the energetically
favorable (100) surface created by cleaving the crystal in the less
dense region shows reasonably good selectivity and high reactivity.
The reactivity on this surface is comparable to that observed on Pd(111)
surfaces. Since this surface termination is stable over a wide range
of Ga chemical potential and hence is likely to occupy a substantial
fraction of the surface area of PdGa nanocrystallites, we suggest
this termination is responsible for the selectivity and reactivity
exhibited by PdGa. In contrast to other surfaces where hydrogen adsorption
and dissociation is followed by acetylene adsorption and hydrogenation,
on this surface we identify a novel reaction mechanism in which hydrogen
dissociation occurs in the presence of acetylene. A careful analysis
of the factors determining the selectivity shows that selectivity
results due to an interplay between surface roughness and chemical
nature of the reactive ensemble.