Figure 1

Compact structures of $\mathrm{Au}/\mathrm{MgO}(001)$ (a),(b) Square pyramid of 30 atoms. (c),(d) Rectangular pyramid of 40 atoms. In (b),(d) surface atoms of the pyramids are represented by small spheres, so that inner atoms are visible. (e) fcc cluster of 31 atoms—a truncated octahedron in (111) epitaxy with the MgO. (f),(g) Noncrystalline structures—icosahedral and decahedral fragments of 32 atoms, respectively. (h) Fcc truncated octahedron of 34 atoms, in (001) epitaxy with the substrate. (i) Icosahedral hollow cage. (j) ${\mathrm{D}}_{6h}$ hollow cages. (k) Truncated octahedral hollow cage. (l) Bilayer structure.Reuse & Permissions

Figure 2

Substrate-stabilized cages. (a) Rectangular pyramidal cage of 38 atoms, obtained by removing the two inner atoms of the compact pyramid of Fig. 1b. In the right column, bottom view of this cluster, where O and Mg atoms are small spheres, to show the basal layer of the cage. This plane consists of 20 atoms, of which 14 belongs to its perimeter, and 6 (in white) belong to its inner part. (b) Rectangular open cage of 32 atoms obtained by removing six basal atoms from (a). (c) Square open cage of 25 atoms. (d) Rectangular cage with distorted basal plane—in the right column, the three atoms in white are in bridge positions between neighboring oxygens.Reuse & Permissions

Figure 3

(a) Energy difference $\Delta E$ (in eV) between cage structural motifs and the best compact structures, depending on size $N$. Negative values of $\Delta E$ correspond to cage structures that are more stable than compact structures of the same size. Open pyramidal cages correspond to open symbols. Four series of open pyramidal cages are considered—with $4\times 4$, $5\times 4$, $6\times 4$, and $5\times 5$ basis (open circles, upward triangles, diamonds, and downward triangles, respectively). Full symbols correspond to other cage motifs: closed pyramidal cages with (001) basis (full circles); icosahedral cages (full squares); closed pyramidal cages with distorted basis (full triangles). (b) Second difference in the energy ${\Delta }_{2}E$ (in eV, see text) vs size $N$. Positive peaks single out the most stable sizes.Reuse & Permissions