To obtain insight into the structure and surface stoichiometry of copper-based catalysts in commercially important chemical reactions such as the oxygen-assisted water-gas shift reaction, we perform density-functional theory calculations to investigate the relative stability of low-index copper oxide surfaces. By employing the technique of “ab initio atomistic thermodynamics,” we identify low-energy surface structures that are most stable under realistic catalytic conditions are found to exhibit a metallic character. Three surfaces are shown to have notably lower surface free energies compared to the others considered and could be catalytically relevant; in particular, under oxygen-rich conditions, they are the ${\mathrm{Cu}}_2\mathrm{O}\left(110\right):\mathrm{Cu}\mathrm{O}$ surface, which is terminated with both Cu and O surface atoms, and the ${\mathrm{Cu}}_2\mathrm{O}\left(111\right)\text{−}{\mathrm{Cu}}_{\mathrm{CUS}}$ surface, which contains a surface (coordinatively unsaturated) Cu vacancy, while for the oxygen-lean conditions, the ${\mathrm{Cu}}_2\mathrm{O}\left(111\right)$ surface with a surface interstitial Cu atom is found to be energetically most favorable, highlighting the importance of defects at the surface.

As a first step towards gaining microscopic understanding of copper-based catalysts, e.g., for the low-temperature water-gas shift reaction and methanol oxidation reactions, we present density-functional theory calculations investigating the chemisorption of oxygen, and the stability of surface oxides on $\mathrm{Cu}\left(111\right)$. We report atomic geometries, binding energies, and electronic properties for a wide range of oxygen coverages, in addition to the properties of bulk copper oxide. Through calculation of the Gibbs free energy, taking into account the temperature and pressure via the oxygen chemical potential, we obtain the $(p,T)$ phase diagram of $\mathrm{O}∕\mathrm{Cu}\left(111\right)$. Our results show that for the conditions typical of technical catalysis the bulk oxide is thermodynamically most stable. If, however, formation of this fully oxidized surface is prevented due to a kinetic hindering, a thin surface-oxide structure is found to be energetically preferred compared to chemisorbed oxygen on the surface, even at very low coverage. Similarly to the late $4d$ transition metals (Ru, Rh, Pd, Ag), sub-surface oxygen is found to be energetically unfavorable.

The layered semiconductor SnSe is one of the highest-performing thermoelectric materials known. We demonstrate, through a first-principles lattice-dynamics study, that the high-temperature $Cmcm$ phase is a dynamic average over lower-symmetry minima separated by very small energetic barriers. Compared to the low-temperature $Pnma$ phase, the $Cmcm$ phase displays a phonon softening and enhanced three-phonon scattering, leading to an anharmonic damping of the low-frequency modes and hence the thermal transport. We develop a renormalization scheme to quantify the effect of the soft modes on the calculated properties, and confirm that the anharmonicity is an inherent feature of the $Cmcm$ phase. These results suggest a design concept for thermal insulators and thermoelectric materials, based on displacive instabilities, and highlight the power of lattice-dynamics calculations for materials characterization.