Predicting nanocrystal shape through consideration of surface-ligand interactions.

Density functional calculations for the binding energy of oleic acid-based ligands on Pb-rich {100} and {111} facets of PbSe nanocrystals determine the surface energies as a function of ligand coverage. Oleic acid is expected to bind to the nanocrystal surface in the form of lead oleate. The Wulff construction predicts the thermodynamic equilibrium shape of the PbSe nanocrystals. The equilibrium shape is a function of the ligand surface coverage, which can be controlled by changing the concentration of oleic acid during synthesis. The different binding energy of the ligand on the {100} and {111} facets results in different equilibrium ligand coverages on the facets, and a transition in the equilibrium shape from octahedral to cubic is predicted when increasing the ligand concentration during synthesis.