2. Methods
The lowest-energy structures of the AlBen(n = 1–12) clusters were identified by using two methods, for
both of which the spin multiplicity of 2 and 4 were taken into account.
In the first one, a large number of AlBengeometries were manually built on the basis of those of pure beryllium
clusters.[16] We
have obtained various structures where the impurity Al atom is either
attached to each possible site of the Ben cluster
or used to substitute one Be atom of the host
Ben +1 cluster. In the second one, a stochastic
search procedure[2]was used to make sure that all the global minimum structures have been
found. This procedure can generate structures randomly, and hence
facilitates a thorough exploration of unknown isomers. With this method,
a great number of starting geometries were obtained at the B3LYP/LANL2DZ
level. Afterwards, much more hunts were performed in the region of these
structures to do an intensive search until no new minima appeared. Then,
all the possible initial structures obtained from these two methods were
optimized with subsequent frequency analysis at the B3LYP/aug-cc-pVDZ
level to identify the lowest-energy ones.
To examine the energetic and electronic properties of the
AlBen clusters, single-point calculations were
performed by using both B3LYP and CCSD(T) methods with the aug-cc-pVDZ
basis set. Natural bond orbital (NBO) analysis[33]was carried out at the B3LYP/aug-cc-pVDZ level. At the same
computational level, the spherically averaged polarizability (α) of
AlBen were calculated, which is defined as the
mean value of diagonal terms of the polarizability matrix, namely,
All calculations were carried out by using the GAUSSIAN
09[34] program
package. Dimensional diagrams of the molecular structures and orbitals
were generated with the GaussView program.[35]
RESULTS AND DISCUSSION