3.2.1 Stability
The relative stability of different sized AlBenclusters can be discussed on the basis of binding energy per atom (Eb ), dissociation energy (ΔE ), and the second difference in energy (Δ2E ), where
These energetic properties, calculated at the CCSD(T)//B3LYP and B3LYP levels, are listed in Table S1 in supporting information. From the table, the B3LYP method overestimates binding energies and dissociation energies by 0.103–0.254 eV and 0.147–0.387 eV, respectively, when compared with the CCSD(T) results. Nevertheless, theEb and ΔE values obtained by both methods show consistent trends. Besides, the B3LYP results of Δ2E accord well with those at the CCSD(T) level, and the differences are 0.033 eV–0.240 eV.
To explore the Al-substitution effect on the stability of bare beryllium clusters, the above-mentioned quantities of Ben +1were also calculated according to the following equations,
For comparison, the size dependence of these energetic properties for the lowest-energy AlBen and Ben+ 1 (n = 1–12) clusters are plotted in Figure 2. It is known that small bumps and dips in theEb curve are indicative of relative stability and reactivity for corresponding clusters, respectively. From Figure 2a, theE b values of AlBen and Ben +1 increase sharply first, then, both curves reach a plateau from n = 3 to n = 5 and then rise again as cluster size grows. It is noted that the Eb value of an AlBen cluster is larger by 0.033–0.324 eV than that of its corresponding Ben +1 cluster, suggesting that the substitution of an Al arom for a Be atom in Ben +1 can enhance the intracluster binding force.