Ligand Addition Energies and the Stoichiometry of Colloidal Nanocrystals

Experimental nonstoichiometries of colloidal nanocrystals such as CdSe and PbS are accounted for by attributing to each constituent atom and capping ligand a formal charge equal to its most common oxidation state to obtain an overall neutral nanocrystal. In spite of its apparent simplicity, little theoretical support of this approach-called here the oxidation-number sum rule-is present in the current literature. Here, we introduce the ligand addition energy, which we define as the energy gained or expended upon the transfer of one ligand from a reference state to a metal-rich solid surface. For the combination of CdSe, ZnSe and InP with either chalcogen, halogen or hydrochalcogen ligands, we compute successive ligand addition energies using ab initio methods and determine the thermodynamically stable surface composition as that composition where ligand addition turns endothermic. We find that the oxidation-number sum rule is valid in many situations, although exceptions occur for each material studied, most notably when exposed to small oxidative ligands. In the case of InP, however, violations are more severe, extending toward the entire chalcogen ligand family. In addition, we find that electronegativity rather than chemical hardness is a reasonable predictor for ligand addition energies, with the most electronegative ligands yielding the most exothermic addition energies. Finally, we argue that the ligand addition energy will be a most useful quantity for future computational studies on the structure, stability and reactivity of nanocrystal surfaces.