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