Background: The majority of complex and advanced materials contain nanoparticles. The properties of these materials depend crucially on the size and shape of these nanoparticles. Wulff construction offers a simple method of predicting the equilibrium shape of nanoparticles given the surface energies of the material.Results: We review the mathematical formulation and the main applications of Wulff construction during the last two decades. We then focus to three recent extensions: active sites of metal nanoparticles for heterogeneous catalysis, ligand-protected nanoparticles generated as colloidal suspensions and nanoparticles of complex metal hydrides for hydrogen storage.Conclusion: Wulff construction, in particular when linked to first-principles calculations, is a powerful tool for the analysis and prediction of the shapes of nanoparticles and tailor the properties of shape-inducing species.

Catalysis development relies on the predictive abilities of the rational approaches provided by the study of complex reaction networks through density functional theory, DFT. DFT constitutes a robust framework to study reaction networks on metal surfaces with the required accuracy. However, the problem of accuracy remains a challenge for materials where self-interaction severely affects the proper description of their electronic structures. Among practical approaches to address the problem, the Hubbard U corrected DFT has emerged as the most attractive tool in terms of resources balance that can allow the investigation of intricate reaction networks. Even if applying the DFT+U approaches in catalysis has reached some consensus, extensive benchmarks have not been performed. We have precisely done this benchmark against available experiments and hybrid (more accurate) functionals and seen that the dependence of thermodynamics and kinetics for redox steps with the U parameter is different, thus being impossible to fit both with the same value of U (hence preventing the universality of the functional). The origin of this dependence can be traced back to the different electron localization between the initial, transition, and final states and points to the need of obtaining reaction profiles with geometry dependent U to reach adequate accuracy required for understanding and engineering.

Milling corundum nanoparticles: High-purity corundum (α-Al ₂ O ₃ ) nanoparticles could enable applications such as more stable catalyst supports or precursors for high-strength ceramics. Milling of corundum only produces micrometer-scale particles, and direct synthesis from other aluminum oxides that would be likely starting materials, such as γ-Al ₂ O ₃ , fails because of the high activation barrier for converting the lattice structure of these cubic close-packed oxides. Amrute et al. show that ball milling of boehmite, γ-AlOOH, created ∼13-nanometer-diameter corundum nanoparticles of high purity through a mechanically induced dehydration reaction and by the effect of milling impacts on the surface energy of the particles. Science , this issue p. 485

Self-consistent density functional calculations of the hydroxylated (0001) corundum surfaces are presented. It is demonstrated that the hydroxylated surfaces are the most stable under most, but not all, conditions. Hydroxylation significantly lowers the surface free energy of α-alumina. The stability of the hydrated surface resolves the discrepancies between the morphology of the α-alumina (0001) surface observed under ultra-high vacuum, and at ambient conditions. A method for the calculation of the equilibrium surface stoichiometry is proposed. The proposed approach provides a valuable connection between theoretical calculations and experiments with metal oxides.

A systematic approach to study the phase stability of ${\mathrm{L}\mathrm{i}\mathrm{B}\mathrm{H}}_4$ based on ab initio calculations is presented. Three thermodynamically stable phases are identified and a new phase of $Cc$ symmetry is proposed for the first time for a complex hydride. The x-ray diffraction pattern and vibrational spectra of the $Cc$ structure agree well with recently reported experimental data on ${\mathrm{L}\mathrm{i}\mathrm{B}\mathrm{H}}_4$. Calculations of the free energy at finite temperatures suggest that the experimentally proposed $P{6}_{3}mc$ phase is unstable at $T>0\mathrm{K}$.