Density-functional theory (DFT) predictions of materials properties are becoming ever more widespread. With increased use comes the demand for estimates of the accuracy of DFT results. In view of the importance of reliable surface properties, this work calculates surface energies and work functions for a large and diverse test set of crystalline solids. They are compared to experimental values by performing a linear regression, which results in a measure of the predictable and material-specific error of the theoretical result. Two of the most prevalent functionals, the local density approximation (LDA) and the Perdew-Burke-Ernzerhof parametrization of the generalized gradient approximation (PBE-GGA), are evaluated and compared. Both LDA and GGA-PBE are found to yield accurate work functions with error bars below 0.3 eV, rivaling the experimental precision. LDA also provides satisfactory estimates for the surface energy with error bars smaller than 10%, but GGA-PBE significantly underestimates the surface energy for materials with a large correlation energy.
We investigate the relation between the chain length of ligands used and the size of the nanocrystals formed in the hot injection synthesis. With two different CdSe nanocrystal syntheses, we consistently find that longer chain carboxylic acids result in smaller nanocrystals with improved size dispersions. By combining a more in-depth experimental investigation with kinetic reaction simulations, we come to the conclusion that this size tuning is due to a change in the diffusion coefficient and the solubility of the solute. The relation between size tuning by the ligand chain length and the coordination of the solute by the ligands is further explored by expanding the study to amines and phosphine oxides. In line with the weak coordination of CdSe nanocrystals by amines, no influence of the chain length on the nanocrystals is found, whereas the size tuning brought about by phosphine oxides can be attributed to a solubility change. We conclude that the ligand chain length provides a practical handle to optimize the outcome of a hot injection synthesis in terms of size and size dispersion and can be used to probe the interaction between ligands and the actual solute.
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.
We analyze the mechanism of seeded growth reactions used to synthesize colloidal core/shell nanocrystals. Looking at the formation of CdSe/CdS and CdSe/ZnSe using both zinc blende and wurtzite CdSe seeds with a different surface termination, we show that the formation rate of the shell material does not depend on the presence of the seed nanocrystals. This suggests that shells grow by inclusion of CdS or ZnSe initially formed in the reaction mixture, possibly under the form of reactive monomers, and not by successive adsorption and reaction of metal and chalcogen precursors. This insight makes balancing homogeneous nucleation and heterogeneous growth of the shell material key to suppressing spurious secondary nucleation. Through a combination of experimental work and reaction simulations, we argue that this can be effectively achieved by raising the monomer solubility through the concentration of carboxylic acid used in the seeded growth reaction.
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