As discussed above, there is a counterpart for each lowest-energy structure of AlBen in the minimum structures of their corresponding Ben +1 cluster. Besides, as can be seen in Table 1, the number of Al–Be bonds in AlBen increases with the increasing cluster size and reaches a maximum value of six. It implies that the impurity Al atom is able to bond with six Be atoms at most. These rules may help to identify the low-lying structures of larger Al-doped Ben clusters.
The comparison between AlBen and other Al-doped clusters shows how the relative size of impurity atom affects the structural evolution of the whole system. For example, the impurity Al atom always occupies an external position of the host clusters in AlBen and AlBn [40] until n = 12, while it gets trapped in the host cage from n = 6 onwards in AlLin [41] and AlNan ,[42,43] and fromn = 9 onwards in the AlTin ,[44]AlScn ,[45]AlPbn ,[46] and AlYn [47] clusters. These structural distinctions can be related to the size difference of the dopant atom versus the host atom. To be specific, the impurity Al atom (1.25 Å)[48] has larger atomic radius than those of B (0.85 Å) and Be (1.05 Å) atoms, which hinders it from entering the Bn or Ben cages. In contrast, a framework constituted by larger host atoms such as Li (1.45 Å), Na (1.80 Å), Ti (1.40 Å), Sc (1.60 Å), Pb (1.80) and Y (1.80 Å) can accommodate the dopant Al atom.