Over the past 5 years, chemical formulas have been put forward for a select number of colloidal nanocrystals, including CdSe and PbS. These follow a simple chemical principle, where the number of excess cations and anionic ligands take such values that an overall neutral nanocrystal is obtained when each constituent is given a formal charge equal to its most common oxidation state, a procedure we refer to as the oxidation-number sum rule. This zero-charge composition will be the most stable composition in apolar solvents – where the high Coulomb charging energy favors uncharged nanocrystals – and is the reference point to understand charge stabilization of nanocrystals in polar environments by adsorption of small, inorganic moieties. Despite its apparent simplicity, current literature provides little theoretical support for the oxidation-number sum rule, where in particular the question as to how general the rule is, has remained unanswered.

Here, we introduce an approach for the computational analysis of the composition of zero charge by means of the ligand addition energy (LAE), which we define as the energy gained or expended upon the binding of one additional ligand from a reference state to a nanocrystal. As ligands will stop adsorbing when the LAE becomes positive, the last negative LAE determines the nanocrystal’s composition of zero charge. We have calculated LAEs for CdSe, ZnSe and InP nanocrystals in combination with chalcogenide, halogenide and hydrochalcogenide ligands, using density-functional theory where each facet of the nanocrystal surface is represented by a(n infinitely) periodic slab (flat surface) separated from identical copies by a vacuum. For ZnSe and CdSe, we find that the zero-charge composition is in line with the sum rule, except for small and strongly oxidizing ligands such as fluorine (CdSe and ZnSe) or oxygen. With InP, more important deviations from the sum rule are observed, where most notably all chalcogenides feature persistently negative LAEs. Although this result could be linked to the lower electronegativity of phosphorus – rendering oxidation by chalcogenides more likely – the calculations show that care must be taken to relate trends in LAE to a single chemical concept such as electronegativity differences or chemical hardness. Nevertheless, the results point out that the occurrence of well-defined chemical formulas for the zero-charge composition of nanocrystals may be limited to specific combinations of materials and ligands.