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.