Ligand Addition Energies and the Stoichiometry of Colloidal Nanocrystals
Authors : Michael Sluydts, Kim De Nolf, Veronique Van Speybroeck, Stefaan Cottenier, and Zeger Hens
Affiliations : Center for Molecular Modeling, Ghent University, 9000 Gent, Belgium; Physics and Chemistry of Nanostructures, Ghent University, 9000 Gent, Belgium, Center for Nano and Biophotonics, Ghent University, 9000 Gent, Belgium; Center for Molecular Modeling, Ghent University, 9000 Gent, Belgium; Center for Molecular Modeling, Ghent University, 9000 Gent, Belgium, Department of Materials Science and Engineering, Ghent University, 9000 Gent, Belgium; Physics and Chemistry of Nanostructures, Ghent University, 9000 Gent, Belgium, Center for Nano and Biophotonics, Ghent University, 9000 Gent, Belgium;
Resume : The nonstoichiometry of colloidal nanocrystals such as CdSe and PbS is typically explained by attributing a formal charge, equal to its most common oxidation state, to each constituent atom and capping ligand. A neutral nanocrystal is obtained by the zero sum of these formal charges. Despite its simplicity this “oxidation-number sum rule” has little theoretical support within current literature. We introduce the ligand addition energy, defined as the energy gained or expended upon the transfer of one ligand from a reservoir to a metal-rich surface. By calculating successive addition energies, using ab initio methods, the thermodynamically stable surface composition is determined as the last exothermic addition step. This has been calculated for the combination of CdSe, ZnSe and InP surfaces with chalcogen, halogen and hydrochalcogen ligands. In many cases, the oxidation-number sum rule is valid, but exceptions occur for each studied material, most notably when the surface is exposed to small oxidative ligands. For InP these violations are more severe and extend to the entire chalcogen family. We also find that electronegativity rather than chemical hardness is a reasonable predictor for ligand addition energies; the most exothermic addition energies being obtained for the most electronegative ligands. We propose the ligand addition energy to be a valuable quantity for future computational studies on the structure, stability and reactivity of nanocrystal surfaces.