3.1 Geometrical structures
First, we
focus
on the geometrical evolution of the AlBen(n = 1–12) clusters. To explore the Al substitution effect on
beryllium clusters, the structures of Ben +1 were
also obtained on the basis of previous
reports[25,26,36] and reoptimized at the
B3LYP/aug-cc-pVDZ level. The lowest-energy structures of
AlBen along with the corresponding global and
local minima of the Ben +1 (n = 1–12)
clusters are presented in Figure 1, where their spin multiplicity are
also shown. It has been found that all the global minima of
AlBen are in doublet states except for
AlBe7 corresponding to a quartet state. The symmetry,
number of Al–Be bonds, the lowest vibrational frequencies, the shortest
Al-Be bond lengths, as well as the HOMO–LUMO gaps of the most stable
AlBen (n = 1–12) clusters are listed in
Table 1.
The ground state structure of AlBe has a bond length of 2.439 Å and
vibrational frequency of 374 cm–1, according well
with experimental
results
(R = 2.395 Å, v = 382
cm–1)[37]and previously reported theoretical results
(R= 2.430 Å, v = 385
cm–1;37 R = 2.423 Å,v = 375
cm–1;[38]R = 2.434 Å, v = 379.6
cm–1;[39]). Thus, the
B3LYP/aug-cc-pVDZ treatment is considered reliable for predicting the
structures of the AlBen clusters. The global
minimum of AlBe2 exhibits an
isosceles
triangular structure with C 2v symmetry, in
which the Al–Be and Be–Be bond lengths are 2.302 Å and 2.153 Å,
respectively. Note that the Be-Be bond length of AlBe2is shorter by 0.351 Å than that of Be2, indicating that
the Be–Be bond strength of Be2 has been enhanced by the
attachment of Al atom. Likewise, the Al-Be bond of AlBe2is also shorter than that of AlBe.
The transition from two-dimensional (2D) to three-dimensional (3D)
structures occurs at n = 3 in this series. From Figure 1, a
tetrahedral configuration (C 3v ) is
obtained for AlBe3, where the Al atom caps a equilateral
trianglar Be3 unit. In this structure, the Al–Be and
Be–Be bond lengths are 2.324 Å and 2.048 Å, respectively. The latter is
just equal to that of the lowest-energy structure of
Be4. In the case of AlBe4, the most
stable structure is a Cs -symmetric trigonal
bipyramid with the Al atom at the top site. This structure contains two
short Al–Be bonds of 2.339 Å and a long Al–Be bond of 2.721 Å.