Figure 2. Size dependence of binding energies per atom (Eb ), dissociation energies (ΔE ), and the second difference in energy (Δ2E ) for the lowest-energy AlBen and Ben+ 1 (n = 1–12) clusters at the CCSD(T)/aug-cc-pVDZ level.
In addition, the Eb curve of AlBen shows two turning points at n = 3 and n = 8, indicating relatively high stability of AlBe3 and AlBe8. This is more clearly reflected in varying trends of ΔE and Δ2E . As shown in Figure 2b, the ΔE curve of AlBen has two distinct peaks at AlBe3 and AlBe8, indicating that these two clusters are less likely to lose a Be atom. As for Ben +1, two local maximum ΔE values appear at Be4 and Be10 because they are magic clusters and possess unique stability according to spherical jellium model (SJM)15 . A similar situation can be found in the evolution of Δ2E values. From Figure 2c, the curves of Δ2E have particular peaks at n = 3 andn = 8 for AlBen , and at n = 3 andn = 9 for the Ben +1 series. Combining all the results given above, it can be concluded that AlBe3and AlBe8 have special stability among the AlBen clusters as do Be4 and Be10 in the Ben +1 system.
The stability of the AlBen clusters is also examined in terms of adsorption energy of Al, i.e. , the energy released when an Al atom is attached to a pure Ben cluster, which can be expressed as
The E ad values of AlBenwere also obtained by using the CCSD(T)//B3LYP and B3LYP methods, and the results are collected in Table S1 and plotted in Figure 3. From the figure, the two methods yield consistent results, and there are two obvious dips at AlBe3 and AlBe8 in both curves. These dips denote that a lot of energy is released when an Al atom is adsorbed by either Be3 or Be8cluster. From Table S1, all the E ad values are negative, indicating that the adsoption of Al on Ben is a favorable process. Besides, AlBe8 exhibits the largest E advalue (-4.132 eV at CCSD(T) level and -3.872 eV at B3LYP level), so the impurity Al atom is tightly bound to the host Be8cluster.