Figure 1

Potential energies of ${\mathrm{Al}}_2$ (a) and ${\mathrm{Al}}_4$ (b)–(i) clusters calculated by MBTB-S method (solid line). Energies denoted by crosses come from the $\mathrm{PBE}0∕\mathrm{MG}3$ data set. The structures of the clusters are specified by geometry numbers in the supporting material (Ref. 11): (a) 1–10, the dimer; (b) 1–8, short bridge approach of $\mathrm{Al}$ to ${\mathrm{Al}}_3$; (c) 9–16, on top approach of $\mathrm{Al}$ to small triangle; (d) 17–24, threefold approach of $\mathrm{Al}$ to small triangle; (e) 25–33, long bridge approach of $\mathrm{Al}$ to ${\mathrm{Al}}_3$; (f) 34–41, dimer-dimer approach; (g) 42–50, on top approach of $\mathrm{Al}$ to large triangle; (h) 51–60, threefold approach of $\mathrm{Al}$ to large triangle; (i) 61–66, reaction path for conversion of tetrahedron to rhombus.Reuse & Permissions

Figure 2

The same as in Fig. 1 but for ${\mathrm{Al}}_3$ (a)–(f), and ${\mathrm{Al}}_7$ (g)–(k). The points are (a) 1–9, sideways approach of $\mathrm{Al}$ to small dimer; (b) 10–19, sideways approach of $\mathrm{Al}$ to medium dimer; (c) 20–28, sideways approach of $\mathrm{Al}$ to large dimer; (d) 29–39, oblique approach of $\mathrm{Al}$ to large dimer; (e) 40–47, equilateral triangles; (f) 48–57, linear approach of $\mathrm{Al}$ to small dimer; (g) 1–11, approach of $\mathrm{Al}$ to small octahedron; (h) 12–22, approach of $\mathrm{Al}$ to large octahedron; (i) 23–31, large trimer approaching large tetramer; (j) 32–40, small trimer approaching small tetramer; (k) 41–46, approach of $\mathrm{Al}$ to small octahedron along the perpendicular bisector of a bond.Reuse & Permissions