We address the formation of the energetically most favourable single oxygen vacancies in ceria nanoparticles (CeO₂)_n focusing on their size dependence. We study a series of structures with increasing number of CeO₂ units (n = 21, 30, 40 and 80) that, according to well tested interatomic-potential calculations, approach the global minima for these particle sizes. The structures thus obtained are refined by means of density functional (DF) methods, modified by the on-site Coulomb correction. Subsequent DF calculations are performed to quantify and analyse the depletion of atomic O from the nanoparticles that results in the formation of a vacancy O_vac. We show that (i) removal of a low- (two-)coordinate O atom from ceria species requires the lowest energy, in line with evidence from other metal oxides; (ii) the depletion of such O atoms from the nanoparticles is strongly facilitated compared to extended (even irregular) surfaces; (iii) increase of the particle size is accompanied by a dramatic decrease of the O_vac formation energy, implying that at certain sizes this energy should reach a minimum; (iv) the size dependence of the O_vac formation energy is driven by the electrostatics, thus enabling the prediction of the most easily removable O atoms by analysing the distribution of the electrostatic potential in the pristine stoichiometric (vacancy-free) ceria systems. Our findings provide a key to rationalize the observed spectacularly enhanced reactivity of ceria nanostructures.

Aims. We model the synthesis of molecules and dust in the inner wind of the oxygen-rich Mira-type star IK Tau by considering the effects of periodic shocks induced by the stellar pulsation on the gas and by following the non-equilibrium chemistry in the shocked gas layers between 1 R ⋆ and 10 R ⋆ . We consider a very complete set of molecules and dust clusters, and combine the nucleation phase of dust formation with the condensation of these clusters into dust grains. We also test the impact of increasing the local gas density. Our derived molecular abundances and dust properties are compared to the most recent observational data.Methods. A semi-analytical formalism based on parameterised fluid equations is used to describe the gas density, velocity, and temperature in the inner wind. The chemistry is described by using a chemical kinetic network of reactions and the condensation mechanism is described by a Brownian formalism. A set of stiff, ordinary, coupled differential equations is solved, and molecular abundances, dust cluster abundances, grain size distributions and dust masses are derived.Results. The shocks drive an active non-equilibrium chemistry in the dust formation zone of IK Tau where the collision destruction of CO in the post-shock gas triggers the formation of C-bearing species such as HCN and CS. Most of the modelled molecular abundances agree well with the latest values derived from Herschel data, except for SO2 and NH3, whose formation may not occur in the inner wind. Clusters of alumina, Al2O3, are produced within 2 R ⋆ and lead to a population of alumina grains close to the stellar surface. Clusters of silicates (Mg2SiO4) form at larger radii (r> 3R ⋆ ), where their nucleation is triggered by the formation of HSiO and H2SiO. They efficiently condense and reach their final grain size distribution between ~6 R ⋆ and 8 R ⋆ with a major population of medium size grains peaking at ~200 Å. This two dust-shell configuration agrees with recent interferometric observations. The derived dust-to-gas mass ratio for IK Tau is in the range 1–6 × 10-3 and agrees with values derived from observations of O-rich Mira-type stars. Conclusions. Our results confirm the importance of periodic shocks in chemically shaping the inner wind of AGB stars and providing gas conditions conducive to the efficient synthesis of molecules and dust by non-equilibrium processes. They indicate that the wind acceleration will possibly develop in the radius range 4–8 R ⋆ in IK Tau.

A chiral catalyst from the ligand 1,1′-bis(diphenylphosphino)ferrocene (dppf) anchored to the inner walls of the mesoporous support MCM-41 and co-ordinated to Pd^II has been shown to exhibit a degree of regioselectivity and enantiomeric excess, in the allylic amination of cinnamyl acetate, which is far superior to that of its homogeneous counterpart or that of a surface-bound analogue attached to a non-porous silica.

We review the growing role of computational techniques in modelling the structures and properties of nano-particulate oxides and sulphides. We describe the main methods employed, including those based on both electronic structure and interatomic potential approaches. Particular attention is paid to the techniques used in searching for global minima in the energy landscape defined by the nano-particle cluster. We summarise applications to the widely studied ZnO and ZnS systems, to silica nanochemistry and to group IV oxides including TiO₂. We also consider the special case of silica cluster chemistry in solution and its importance in understanding the hydrothermal synthesis of microporous materials. The work summarised, together with related experimental studies, demonstrates a rich and varied nano-cluster chemistry for these materials.