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Ligand Addition Energy and the Stoichiometry of Colloidal Nanocrystals

Kim De Nolf (UGent) , Michael Sluydts (UGent) , Veronique Van Speybroeck (UGent) , Stefaan Cottenier (UGent) and Zeger Hens (UGent)
(2016)
Author
Organization
Abstract
Over the past 5 years, chemical formulas have been put forward for a 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. Despite its apparent simplicity, current literature provides little theoretical support for this rule, where in particular the question as to how general it is, has remained unanswered. As a result, nanocrystal simulations typically take experimentally determined stoichiometries as a starting point, without addressing the question whether this is the most stable composition of a nanocrystal in the first place. Here, we introduce an approach for the computational analysis of the nanocrystal stoichiometry 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 from the reference reservoir when the LAE becomes endothermic, the last negative LAE determines the thermodynamically prefered nanocrystal composition. 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 an infinitely periodic slab separated from identical copies by a vacuum. For ZnSe and CdSe, we mostly find that ligands adsorb up to a composition in line with the sum rule, with addition energies turning endothermic for further ligand adsorption. Exceptions occur for small and strongly oxidizing ligands such as fluorine (CdSe and ZnSe) or oxygen. With InP on the other hand, 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. Finally, we show that the concept of the LAE can be used to analyze the interaction of nanocrystals with ligand reservoirs in general, including examples such as exposure of nanocrystals to ambient conditions or specific reagents during advanced heterostructure synthesis or ligand exchange reactions.

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Chicago
De Nolf, Kim, Michael Sluydts, Veronique Van Speybroeck, Stefaan Cottenier, and Zeger Hens. 2016. “Ligand Addition Energy and the Stoichiometry of Colloidal Nanocrystals.” In .
APA
De Nolf, K., Sluydts, M., Van Speybroeck, V., Cottenier, S., & Hens, Z. (2016). Ligand Addition Energy and the Stoichiometry of Colloidal Nanocrystals. Presented at the MRS.
Vancouver
1.
De Nolf K, Sluydts M, Van Speybroeck V, Cottenier S, Hens Z. Ligand Addition Energy and the Stoichiometry of Colloidal Nanocrystals. 2016.
MLA
De Nolf, Kim, Michael Sluydts, Veronique Van Speybroeck, et al. “Ligand Addition Energy and the Stoichiometry of Colloidal Nanocrystals.” 2016. Print.
@inproceedings{7213357,
  abstract     = {Over the past 5 years, chemical formulas have been put forward for a 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. Despite its apparent simplicity, current literature provides little theoretical support for this rule, where in particular the question as to how general it is, has remained unanswered. As a result, nanocrystal simulations typically take experimentally determined stoichiometries as a starting point, without addressing the question whether this is the most stable composition of a nanocrystal in the first place.
Here, we introduce an approach for the computational analysis of the nanocrystal stoichiometry 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 from the reference reservoir when the LAE becomes endothermic, the last negative LAE determines the thermodynamically prefered nanocrystal composition. 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 an infinitely periodic slab separated from identical copies by a vacuum. For ZnSe and CdSe, we mostly find that ligands adsorb up to a composition in line with the sum rule, with addition energies turning endothermic for further ligand adsorption. Exceptions occur for small and strongly oxidizing ligands such as fluorine (CdSe and ZnSe) or oxygen. With InP on the other hand, 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. Finally, we show that the concept of the LAE can be used to analyze the interaction of nanocrystals with ligand reservoirs in general, including examples such as exposure of nanocrystals to ambient conditions or specific reagents during advanced heterostructure synthesis or ligand exchange reactions.},
  author       = {De Nolf, Kim and Sluydts, Michael and Van Speybroeck, Veronique and Cottenier, Stefaan and Hens, Zeger},
  language     = {eng},
  location     = {Phoenix, AZ, USA},
  title        = {Ligand Addition Energy and the Stoichiometry of Colloidal Nanocrystals},
  year         = {2016},
}