Figure 1. Ground-state geometries of the host Ben +1clusters (1 n 12) on the left side. The lowest-energy structures of the AlBen clusters (1 n 12) on the right. In the bottom, the global minimum structures of Ben +1 (n = 5, 6, 11, and 12) are shown. Ben -g represents a global minimum and the Ben -l represents a local minimum and the multiplicity of each structure is displayed in parentheses. Be atoms are shown as yellow spheres while Al atoms in pink color.
It can be noticed that, from AlBe to AlBe4, the larger structure can be obtained by attaching a Be atom to the smaller one. As for AlBe5, the lowest-energy structure prefers aCs -symmetric cap-like configuration, which looks similar to a metastable structure of Be6(Be6-l in Figure 1). The Al-Be1 and Al-Be2 bond lengths of AlBe5 are 2.610 Å and 2.274 Å, respectively, and the Be–Be bond lengths vary from 1.992 Å to 2.167 Å. The lowest-lying state of AlBe6 has a pentagonal bipyramidal geometry of C 2 symmetry. It can be obtained by attaching a Be atom to AlBe5 from the opposite side of the Be1 atom, which accordingly shortens the Al-Be1 bond by 0.127 Å. Just like the case of AlBe5, the ground state of AlBe6 has a similar configuration to that of a local, but not global, minimum of Be7. The most stable structure of AlBe7 presents a bicapped octahedral structure, which can be obtained by either duplicating the Be2 atom of AlBe6 or substituting an Al for the top Be atom in the global minimum of Be8 (Be8-g ). Note that a similar structure with a spin multiplicity of 2 was also obtained for AlBe7, whereas it is 4.47 kcal/mol less stable than the quartet state.
As can be seen from Figure 1, each structure of the AlBen (n = 8-12) series could be generated by attaching a Be atom to that of AlBen -1. The lowest-energy structure of AlBe8 can also be regarded as a result of substituting an Al atom for a Be atom in Be9-g . A 16-faced deltahedron was identified to be the most stable structure of AlBe9. Obviously, this structure can be obtained by an additional Be atom face-capping the bottom of AlBe8. Meanwhile, it quite resembles the global minimum structure of Be10. The ground-state structure of AlBe10 bears strong resemblance to that of Be11. It can be considered derived from AlBe9 by twinning the top Be1 atom of the latter. The global minimum of AlBe11 presents a capsule geometry derived from a local minimum structure (Be12-l ) of Be12 instead of the icosahedral Be12-g . On the other hand, face-capping the AlBe10polyhedron can also generate the structure of AlBe11. Meanwhile, the introduction of the Be5 atom leads to lengthened Be1–Be3 distance (from 2.095 Å to 3.102 Å), so the Be1–Be3 bond is broken in AlBe11. The most stable structure of AlBe12 can be regarded as the result of attaching a Be (Be8) atom to AlBe11, accompanied by broken Be4-Be6 and Be4-Be7 bonds. In this group of structures, the Al–Be bond lengths range from 2.285 Å to 2.505 Å and the Be–Be bond lengths are 2.044–2.220 Å.
Table 1. Symmetry Point Groups, the Number of Be–Al Bonds (N), the Shortest Be–Al Bond Lengths (R Be-Al, in Å), the Lowest Vibrational Frequencies (v , in cm-1), and the HOMO–LUMO Gaps (in eV) of the Lowest-energy AlBen (n = 1–12) Clusters.