can be found from Figure S2 that, the Al charge increases as the size of
cluster grows and tends to flatten out from AlBe9onwards. Note that this varying trend roughly corresponds to that of
coordination number of Al in the AlBen clusters,
suggesting that higher coordination number of impurity atom is
beneficial to intracluster charge transfer in this case. According to
Table 3, the 3s states of Al lose 0.04–0.31 electrons, while the 3p
states get 0.18–2.48 electrons. As for the Be atoms, their 2s orbitals
lose 0.39–0.93 electrons, while the 2p states get 0.22–0.76 electrons.
Hence, the charge transfer within the AlBenclusters is mainly from the 3s orbital of Al and 2s orbitals of Be atoms
to the 3p orbital of Al and 2p orbitals of Be atoms. By contrast, the
contributions from other orbitals of Al and Be are negligible.
The HOMO-LUMO gaps of the AlBen clusters at the
B3LYP level are listed in Table 1 and plotted in Figure S3. From the
figure, there are three obvious peaks at AlBe3,
AlBe5 and AlBe8, indicating relatively
high stability of these three clusters. In particular, the
AlBe8 cluster possesses the largest HOMO–LUMO gap of
2.817 eV, which not only is larger than the experimental gap value of
1.9 eV for the kinetically stable
C60,[47] but also exceeds that of
2.53 eV (computed at the same level) for the chemically inert superatom
Al13–.[48] For
comparison, the HOMO–LUMO gaps of the Ben +1clusters are also depicted in Figure S3. It can be found that
substituting an Al atom for a Be atom enlarges the HOMO–LUMO gaps of
Be8 and Be10 clusters by 0.689 eV and
0.398 eV, respectively, while the Al substitution effect is
insignificant for Be11 and Be13 clusters
and is negative for the other beryllium clusters.
Finally, the evolution of polarizability per atom of
AlBen (n = 1–12) is considered since the
static polarizability is an important measure of electronic properties
of clusters. From the results shown in Figure 4, a turning point atn = 3 can be found, which squares with the geometry
transformation from planar to steroescopic at AlBe3. For
comparison, the polarizability per atom of the lowest-energy
Ben +1 clusters are also given in Figure 4. From
the figure, both curves show generally decreasing trends with increasing
cluster size, and gradually become stable for larger sizes. Besides,
substituting a Be atom in Ben +1 with an Al atom
always brings about a larger polarizability to the doped cluster,
although the Al-substitution effect is less prominent for larger-sized
ones. Hence, the AlBen clusters are more
polarizable compared with their corresponding
Ben +1 clusters. Note that there is a relatively
large polarizability gap between Be6 and
AlBe5, which can be attributed to the large structural
discrepancy between these two clusters since polarizability is sensitive
to the shape of the system.[50]