In this article, single-crystalline tetrahedral Ag3PO4 microcrystals with exposed {111} facets was successfully synthesized via a facile wet chemical method. The tetrahedral Ag3PO4 with exposed {111} facets showed the highest photocatalytic activity in visible light irradiation among the {111}, {110} and {100} facets. By DFT calculations, it is demonstrated that the surface energy of the {111} facets is higher than that of the {110} and {100} facets. It was found that the largest band gap of the Ag3PO4 {111} surface is likely to suppress the recombination of electron–hole pairs by exploring the electronic structures of the different surfaces of Ag3PO4. Meanwhile, the dispersion between the valence bands and conduction bands of the {111} surface is beneficial for the separation of photogenerated electrons and holes on the {111} surface, which further improves the photocatalytic activity of the {111} surface.

Recent theoretical studies show that the most stable structures for (Al2O3)n clusters (n ⩽ 30) are hollow polyhedral cage and cage-dimer clusters. Density functional theory calculations were performed a comparative study of the medium-sized (Al2O3)n clusters, in which structures and stability are predicted. Medium-sized (Al2O3)n clusters with core–shell structures have high stability and bonding properties, so they may serve as good models for predicting or interpreting novel properties of Al2O3 core–shell nanoparticles.Graphical abstractHighlights► Density functional theory calculations on single-cage and core–shell structures of (Al2O3)n. ► The medium-sized (Al2O3)nn > 40 clusters have the core–shell cage structures. ► The binding energy of (Al2O3)n core–shell clusters increases as the cluster size increases. ► The HOMO–LUMO gap is a useful indicator of the kinetic stability of these core–shell clusters.

A density functional theory (DFT) study concerning the atomistic detail of the interaction between surfactant molecules and II–IV semiconductor nanoparticles is presented. As a corollary effort, we investigated the adsorption of H2O, NaOH and KOH on the (II–IV)n nanostructure with n = 12, 48, 60 under the vacuum and solvent conditions. Different solvent environments like water, methanol and ethanol were considered using a conductor-like screening model (COSMO) method. Results showed that the adsorption reaches a fairly strong due to electrostatic interactions. The strength of interaction is increased in the order of anionic molecule (strong base) > anionic molecule (weak base) > non-ionic molecule, which explains the experimental results clearly. Moreover, the system was found to be more stable under solvent than vacuum environments.

The nature of the interaction of water or ammonia and other base molecules with (ZnS)n clusters with n = 9–60 has been studied by density functional theory. These studies have shown that the most stable structure is the adsorptive molecule towards zinc atom as Lewis acid–base complexes. The strength of interaction between ZnS cluster and adsorptive molecules increases in the order of anionic > non-ionic, which explains the experimental results well. The advantage of using cluster model to describe the interactions between adsorptive molecule and ZnS nanomaterials will provide helpful information to understand experimental phenomena.

In this article, single-crystalline tetrahedral Ag3PO4 microcrystals with exposed {111} facets was successfully synthesized via a facile wet chemical method. The tetrahedral Ag3PO4 with exposed {111} facets showed the highest photocatalytic activity in visible light irradiation among the {111}, {110} and {100} facets. By DFT calculations, it is demonstrated that the surface energy of the {111} facets is higher than that of the {110} and {100} facets. It was found that the largest band gap of the Ag3PO4 {111} surface is likely to suppress the recombination of electron–hole pairs by exploring the electronic structures of the different surfaces of Ag3PO4. Meanwhile, the dispersion between the valence bands and conduction bands of the {111} surface is beneficial for the separation of photogenerated electrons and holes on the {111} surface, which further improves the photocatalytic activity of the {111} surface.