Structural stabilities and electronic properties of Mg28-nAln clusters: A first-principles study

Structural stabilities and electronic properties of Mg28-nAln clusters: A first-principles study Bao-Juan Lu,1,2 Xiao-Tian Li,1 Yu-Jun Zhao,1,3 Zhao-Yi Wang,1 and Xiao-Bao Yang1,3,a 1Department of Physics, South China University of Technology, Guangzhou 510640, People’s Republic of China 2School of Electronics and Information Engineering, Guizhou Industry Polytechnic College, Guiyang 550008, People’s Republic of China 3Key Laboratory of Advanced Energy Storage Materials of Guangdong Province, South China University of Technology, Guangzhou 510640, People’s Republic of China


INTRODUCTION
Bimetallic clusters 1 continue to be attractive due to their unexpected stabilities and extraordinary electronic properties, with a variety of applications in catalysis, 2 optics 3 and spintronic. 4 In comparison with pure clusters, the properties of bimetallic clusters vastly rely on the chemical compositions, 5 cluster size 6,7 and the detailed atomic structures, crucial for the regulation in practice. For instance, in the Ag 3-x Au x (x=03), the binding energies of CO increase with increasing the number of Au atoms, and the sd energy gap was found to become smaller by increasing the Au content in the case of anionic clusters. 8 Note that bimetallic clusters display not only magic size but also magic compositions, 9 characterized by the relatively high stability. Among Ni 13-n Ag n (n=013) clusters, the magic composition NiAg 12 exhibits the unique properties including the high coordinated structure and the total magnetic moment of zero, as well as maximum HOMOLUMO gap. 4 Aluminum is a light-weight and low-cost metal material, while Al clusters and doped-Al clusters have been widely investigated. 10 The mixed metal systems of magnesium and aluminum are lighter and cheaper than other Albased alloy, 11,12 having superiorities in the development of new materials for hydrogen storage. 13 Based on the density functional theory (DFT), small stable MgAl clusters such as MgAl 4 14 and Mg 4 Al 4 15 were theoretically investigated. Osorio and co-workers discussed the potential energy surface of Mg x Al y (x, y=14) and found that MgAl 4 , Mg 2 Al 4 and Mg 4 Al 4 present high stabilities. 16 From the famous magic cluster of Al 13 , previous theoretical studies were also focused on the structural and electronic properties of hydrogenated MgAl 12 clusters. [17][18][19][20] According to a spherical jellium 21 which the electronic configuration of clusters approaches a closed shell, magic clusters have the valence electron count of 2,8,18,20,34,40. . . . The neutral and anionic MgAl n (n=320) have been carried out by the combination of the Particle Swarm Optimization (CALYPSO) [22][23][24] method and the time-dependent DFT calculation, 25 indicating that the MgAl 6 cluster shows high stability due to the magic number of 20. Expected stabilities were found in Mg 2 Al 5 -, Mg 3 Al 11 with 20 and 40 valence electrons. 12 However, Mg 3 Al 7 -, MgAl 11 and Mg 2 Al 11 non-magic clusters exhibit unexpected stabilities, 12 revealing that applications of the jellium model may be inapplicable in some cases of the MgAl clusters.
Probing the ground state structures of bimetallic clusters is more complex than the corresponding pure clusters, due to the existence of homotops 26 which have the same number of total atoms, component and geometrical structures, but different in the atom arrangement. 5 With the increasing of the bimetallic cluster size, the number of homotops increases rapidly. 27 For the medium and large bimetallic clusters, the structure prediction will become time-consuming because of numerous possible candidates. Paiva et al. focused on probing the most stable candidates of MgAl clusters of the total atoms number up to 55. 11 They predicted the 10 lowest energy structures for given chemical component using the genetic algorithm of Gupta potential function and re-optimized these structures with the DFT calculation. The investigation exposed that the atomic arrangement of MgAl clusters has a tendency of core-shell segregation. 3 In this paper, taking 28-atom as an example, we perform a detailed investigation of the medium size MgAl clusters with the congruence check. Here, we consider two initial morphologies, the pure Mg 28 and Al 28 clusters reported in the literatures. In order to probe the stable structures, the candidates of MgAl clusters are from the substitution by Al atoms on Mg atoms of the pure Mg 28 cluster and vice versa, followed by the re-optimization using the first-principles calculations. This task is complicated for 28-atom bimetallic clusters because of the large number of equivalent homotops. We adopt the molecular eigen-subspace projection function (EPF) 28 method to screen non-equivalent homotops and study the geometries, structural evolution and electronic properties of 28-atom MgAl clusters. For comparison, the CALYPSO method is used to conduct a global structure search for some given components.

CALCULATION METHODS
We performed the calculations of MgAl cluster based on DFT method, as implemented in the Vienna ab initio simulation package (VASP). [29][30][31][32] The projector augmented wave (PAW) method was adopted and the exchange-correlation functional was formulated by PerdewBurkeErnzerhof (PBE) within the generalized gradient approximation (GGA).The energy cutoff was set to be 350 eV for the plane wave basis set, and the converged criteria of the force on each atom was fixed on 0.01 eV/Å, with a K mesh of 1 × 1 × 1. In order to eliminate the interactions of two neighbor clusters, the vacuum distances were set to be more than 10 Å. We considered the valence electron configuration of 3s 2 for Mg atoms, and 3s 2 3p 1 for Al atoms.
In order to describe the structural stabilities of a binary alloy cluster, we have calculated a mixing enthalpy which is defined as: 6,33 The total energy of the MgAl cluster noted by E(Mg 28n Al n ) is compared to the energy of the stable structures of pure Mg 28 and Al 28 cluster, while χ and 1χ denote the percentage of Al and Mg atoms, respectively. A negative value of mixing enthalpy indicates a favorable mixing tendency. When we used the CALYPSO method to predict structures, 34,35 at least 1000 isomers were probed on the same molecular formula to achieve a lower energy structure, and the 30 lowest energy isomers were further optimized to predict the ground state structure.

Initial structures
To obtain the possible stable alloy clusters, we start from the stable structures of Mg 28 cluster 36 and Al 28 cluster 37,38 with MgMg distances of 3.07 Å and AlAl distances of 2.70 Å, respectively. We choose two systems of pure Mg 28 clusters: one is the stable structure reported in the literature as shown in Figures 1(a); the other one is given in Figures 1(b) where the four atoms in the middle of the cluster have a smaller offset position. Brown and blue balls represent Mg and Al atoms, respectively. The following diagrams have the same marks. The Mg atoms of these two Mg 28 initial structures are gradually replaced by Al atoms at various possible positions with n=14. Based on the symmetry of cluster structure, the isomers of MgAl clusters are screened with the congruence check and reoptimized by theoretical calculations. Note that the alloy clusters in Figs. 1(b) show relatively high stability. Thus, we use the Mg 28 structure shown in Figs. 1(b) for the possible alloy clusters. Similarly, we create initial Mg 28-n Al n (n=2427) structures with Mg-substituting of the stable structure of Al 28 shown in Figs. 1(c).
According to the congruence check, the total number of MgAl isomers reaches 8712 when the number of Al atoms n=5, and 8614 when the number of Mg atoms is 5, therefore the traversal calculation is no longer used. We analyze the structural evolution of Mg 28-n Al n (n=14, 2427) and conduct over 20 different isomers as starting geometries for MgAl clusters with n=513, 15,17,19,21,23. The CALYPSO method is also used to conduct a global structure search for n=25, 7,10,11,14,20,22,24,26.

Structures of Mg 28-n Al n (n=1−6) clusters
The lowest energy structure and some representative isomers of Mg 28-n Al n (n=1, 2) clusters are displayed in Figure Figs. 2(b), the most stable structure is greatly deformed compared with the Mg 28 cluster, having the two Al atoms in the central position adjacent to each other. Two Al atoms are located in the internal of alloy cluster for the third and fourth isomers, which are 0.312 eV and 0.329 eV higher than the most stable structure. From high energy structures, the more Al atoms are located on the surface, the worse system stability. Figure 3 shows the lowest energy structures of the Mg 28-n Al n clusters with n=36. Our results indicate that these four optimized structures have large deformations compared with the initial structures. Mg 25 Al 3 has been found that three Al atoms are adjacent in the center of the cluster, with two AlAl distances of 2.727 Å and 2.816 Å. In Mg 24 Al 4 , four Al atoms are aggregated into a tetrahedral structure with AlAl bonds from 2.711 Å to 2.888 Å, while Mg 23 Al 5 has an additional Al atom capping Al 4 group, forming a double tetrahedron structure with AlAl distances in the ranges of 2.6823.024 Å. Mg 22 Al 6 is based on the structure of Mg 23 Al 5 , capping an additional Al atom on the double tetrahedral structure with AlAl distances in the ranges of 2.6823.024 Å. Thus, in the lowest energy structures of the Mg 28-n Al n (n=36) clusters, Al atoms tend to occupy the central position of the alloy cluster forming a tetrahedral structure. Al atoms prefer to be adjacent since the AlAl bond is stronger than the MgAl interaction.

Mixing properties
The mixing enthalpies of the MgAl clusters for the entire component have been computed as Figure 6 shown. In the same component series, the maximum negative value of the mixing enthalpy implies the most stable cluster. 4   The alloy configurations by replacing atoms with the congruence check can be a method of researching alloy clusters.

Electronic properties
In the following, we focus on electronic properties of Mg 24

CONCLUSION
In summary, we have investigated bimetallic MgAl clusters using the density functional theory. The calculations reveal that Al atoms prefer to gather around the center of the clusters, while Mg atoms segregate to the surface, leading to a core-shell like structure. The mixing enthalpies of structures are found to be negative for all components, illustrating that these MgAl alloy clusters are energetically favorable against the phase segregation. The five systems Mg 24 Al 4 , Mg 21 Al 7 , Mg 14 Al 14 , Mg 26 Al 2 and Mg 27 Al 1 present outstanding stabilities and the charge distributions around the Fermi level of these clusters prefer to be around the Al atoms. These may play a guiding role in the research of the MgAl alloy stability under the finite size and the development of new functional materials.