3.1 Geometrical structures
First, we focus on the geometrical evolution of the AlBen(n = 1–12) clusters. To explore the Al substitution effect on beryllium clusters, the structures of Ben +1 were also obtained on the basis of previous reports[25,26,36] and reoptimized at the B3LYP/aug-cc-pVDZ level. The lowest-energy structures of AlBen along with the corresponding global and local minima of the Ben +1 (n = 1–12) clusters are presented in Figure 1, where their spin multiplicity are also shown. It has been found that all the global minima of AlBen are in doublet states except for AlBe7 corresponding to a quartet state. The symmetry, number of Al–Be bonds, the lowest vibrational frequencies, the shortest Al-Be bond lengths, as well as the HOMO–LUMO gaps of the most stable AlBen (n = 1–12) clusters are listed in Table 1.
The ground state structure of AlBe has a bond length of 2.439 Å and vibrational frequency of 374 cm–1, according well with experimental results (R = 2.395 Å, v = 382 cm–1)[37]and previously reported theoretical results (R= 2.430 Å, v = 385 cm–1;37 R = 2.423 Å,v = 375 cm–1;[38]R = 2.434 Å, v = 379.6 cm–1;[39]). Thus, the B3LYP/aug-cc-pVDZ treatment is considered reliable for predicting the structures of the AlBen clusters. The global minimum of AlBe2 exhibits an isosceles triangular structure with C 2v symmetry, in which the Al–Be and Be–Be bond lengths are 2.302 Å and 2.153 Å, respectively. Note that the Be-Be bond length of AlBe2is shorter by 0.351 Å than that of Be2, indicating that the Be–Be bond strength of Be2 has been enhanced by the attachment of Al atom. Likewise, the Al-Be bond of AlBe2is also shorter than that of AlBe.
The transition from two-dimensional (2D) to three-dimensional (3D) structures occurs at n = 3 in this series. From Figure 1, a tetrahedral configuration (C 3v ) is obtained for AlBe3, where the Al atom caps a equilateral trianglar Be3 unit. In this structure, the Al–Be and Be–Be bond lengths are 2.324 Å and 2.048 Å, respectively. The latter is just equal to that of the lowest-energy structure of Be4. In the case of AlBe4, the most stable structure is a Cs -symmetric trigonal bipyramid with the Al atom at the top site. This structure contains two short Al–Be bonds of 2.339 Å and a long Al–Be bond of 2.721 Å.