Ab initio insights on the shapes of platinum nanocatalysts.

Catalytic, chemical, optical, and electronic properties of nanocrystals are strongly influenced by their faceting. A variational approach based on quantum mechanical energies is introduced to evaluate stable and metastable shapes of Pt nanocrystals. The method leads to a nanoscale equation of state, which is solved self-consistently. It is found that the surface energy dependence on the lattice parameter is the key factor controlling the equilibrium stability of the crystal shapes. The variational approach, capable of predicting the changes in the hierarchy of crystals' shapes with respect to size, explains experimental results and establishes a new direction to search for better catalysts.