1 Department of Basic Education, Qinghai University, Xining 810016, China
2 Department of Physics, Nanyang Normal University, Nanyang 473061, China
[Keywords] MAln (M=F, Cl) clusters;Geometrical structures;Electronic properties
  1. Introduction
In the past few decades, small aluminum clusters have always been a research hotspot, not only because they can provide a model system for the detailed study of the Al-based alloy in traditional material industry, but also it has wide applications in advanced material technology1-6. Pramann et al.7probed the structures of CoAln-1 (n =8-17) cluster using the photoelectron spectra (PES). Rao et al.8 studied the nature bond of CAln cluster using density functional theory (DFT) computations and pointed out that the C atom shows different bonding behavioral characteristics in CAlnclusters according to different size and electronic state. Wang et al.9 studied the minimum structures of NAln (n =2-12) cluster by using DFT with generalized gradient approximation (GGA). They concluded that NAl7 is found to have particularly high stability. Guo10 used DFT method to investigate the geometries and electronic properties of phosphorus-doped aluminum PAln (n =2-12) cluster. They found that P atom occupying a peripheral position is ground state geometry. Xing et al.11 studied growth behavior and the electronic properties of MgAln (n =3-20) clusters, the result of which shown that the Al6Mg cluster has a good stability in accord with the jellium model predictions. Alcantar-Medina et al.12 studied the structural and electronic properties of Aln and MAln clusters (n =2-14, M=Li, Na o K), the result of which has shown that the Al7+1, Al13-1, Al2,6,13M-1 clusters are closed shell structures.
Although, no matter pure Aln or Aln clusters doped with other different elements have been studied extensively in the last decades, surprisingly, both theoretical and experimental studies on the structure, stability and electronic properties of MAln (M=F, Cl) clusters have not been reported yet. So far as we know, there are only three theoretical studies on the geometries and properties of AlF, AlCl13, Al7X0,-1, Al13X1,2,12-1(X=F, Cl, Br)14, MX and MX2(M=Al11-Al15, X=F, Cl, Br, I)15 have been reported. In order to further understand the geometrical structure and electronic properties of MAln (M=F, Cl) clusters and enrich our understanding of aluminium -based clusters, we have carried out computational studies on a series of MAln (M=F, Cl; n =3-15) clusters.
  1. Computation methods
All structures of MAln (M=F, Cl; n =3-15) clusters are predicted using the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) structure prediction method16-18. The obtained isomers within 2.0 eV of the global minimum are further optimized using B3LYP method with 6-311+G(d) basis set, as implemented in Gaussian 09 program package19. The B3LYP/6-311G+G(d) method has been successfully used to study many heteroatom-doped aluminum clusters20-22. During the calculation, six electronica states with different multiplicities, i.e. the singlet, doublet, triplet, quartet, quintet and sextet states for MAln (M=F, Cl; n =3-15) are considered. In addition, we do frequency analysis on all optimized structures. If imaginary frequency occurs in any frequency analysis process, in order to ensure the optimized structure state is a local minimum on the potential energy surface, we will adjust the intramolecular coordinates according to the molecule’s vibration direction, and then, redo optimization until the imaginary frequency disappears.
The frequency ω(cm-1) and bond length r(Å) of Al2, F2, Cl2, AlF and AlCl are calculated to verify the accuracy of this calculation. The experimental data23-27 and results are presented inTable 1 . The results show that that the ω and r calculated from the B3LYP functional are consistent with experimental results well. So the B3LYP functional is adopted in the current work.
  1. Results and discussions
  2. Structures
The lowest-energy structures of MAln (M=F, Cl;n =3-15) cluster as shown in Figs. 1 and 2. The symmetries and spin multiplicities are listed in Table 2 .
As shown in Fig. 1 , only the FAl3 cluster has a planar structure with Cs symmetry. Starting from n≥4, the ground state structures of FAln have stereoscopic structure. The FAl4 is obtained when F atom is capped on the top of triangular pyramid. The FAl5 show a similar structure to the most stable structure of PAl5, MgAl5, and AsAl510, 28, 29. The FAl6 is a derived geometry of FAl5cluster after one F atom is capped on it, which resembles the most stable cluster PAl610. When one Al atom is capped on the bottom of FAl6, the FAl7 is generated, which is similar to the most stable cluster of Al7F14. The FAl8 can be considered as one Al atom being capped on triangle face of FAl7 structure and FAl9is viewed as one Al atom being capped on the FAl8structure. The stereoscopic structure of FAl10 is a generated by capping one F atom on the top of a bicapped hexahedron Al10. The FAl11 is obtained when one F atom is capped on a capped pentaprism Al11 cluster. The FAl12 is the derived geometry of FAl11structure after one F atom is capped on it. The cubic form FAl13 in which one Al atom encapsulated into the Al cage is generated when one F atom is capped on the top of FAl12. On the basis of FAl13, two derived structures (FAl14 and FAl15) can be obtained by capping the surface of FAl13 with different amounts of Al atoms (1 and 2). The structures of FAl12-15 are similar to those of Al12-15X(X=F, Cl, Br and I)15clusters, respectively. For ClAl3-15 clusters, it is clearly see that the most stable ClAln clusters at n >3 favour the stereoscopic structure, and most of them are similar to the corresponding FAlnclusters except n =10. This could be because of the similar electronic structure that both fluorine and chlorine atoms have.
From the results, for the ground state structures of MAln (M=F, Cl; n =3-15) clusters, we can find something interesting. On the one hand, except n =3, the ground state MAln clusters favor the 3D structures. The M atom tend to occupy the surface position of the aluminium clusters, and one Al atom encapsulated into the Aln cage when the number of cluster goes to 12. This is similar to the growth pattern of Aln P, Aln X(X=F, Cl, Br and I), Aln Mg, and Aln As clusters10, 14, 28, 29. On the other hand, one Al atom capped MAln-1 structures for different sized MAln clusters is the dominant growth behavior.
  1. Relative stabilities
In order to discuss the relativity stabilities and size-dependent properties of MAln (M=F, Cl; n =3-15) clusters, the average binding energy (Eb ), and the second-order energy differences (Δ2E ) are calculated. The theoretical results are listed in the Table 2 . The Eb and Δ2E equations are read [30]:
(1)
(2)
The change curves of Eb andΔ2E for MAln (M=F, Cl;n =3-15) clusters are plotted in Fig. 3 (a)-(c) . From theFig. 3(a) , it’s easy to find that, the curves of FAln and ClAln clusters show the similar trajectory. When n = 7, one peak is found for FAln and ClAln clusters, respectively. This means that the clusters FAl7 and ClAl7 are more stable than their neighboring clusters. In addition, the Eb of Aln+1 clusters are smaller obviously than those of FAln and ClAlnclusters, indicates that the stabilities of pure aluminum cluster with dopant atoms doping go down. Fig. 3(b) shows theΔ2E for MAln (M=F, Cl) clusters. The two curves are almost exactly the same. Three remarkable peaks at n = 5, 7 and 14 are found for FAln and ClAln clusters, which indicates the ground state of FAl5, FAl7, FAl14, ClAl5, ClAl7 and ClAl14 clusters have more stronger relative stabilities than their neighbors. This feature also occurs separately in chemical hardness. Fig. 3(c) gives the curves of the HOMO-LUMO energy gap Egap of ground state FAln and ClAln clusters. We can find that the Egap of FAln and ClAln cluster shown a similar oscillation tendencies. When n = 3, 5, 7, 9, 11, 13 and 15, seven peaks are found for FAln and ClAln clusters, respectively, indicates that the ground state of FAl3,5,7,9,11,13,15 and ClAl3,5,7,9,11,13,15 clusters have more stronger relative stabilities than their neighbors. This can be due to the closed-shell configuration of F and Cl atom.
Therefore, according to the above mentioned analysis, one can easily conclude that the FAl7 and ClAl7clusters are the most stable clusters among the studied MAln (M=F, Cl; n =3-15) clusters, which may make them as the most suitable building block for new functional materials.
  1. Charge transfer
NBO analysis is a useful tool to understand the localization of the charge in the cluster’s structure. To understand the charge transfer within the clusters further, here we calculated the natural charge population (NCP) and natural electron configurations (NEC) of the lowest-energy MAln (M=F, Cl; n =3-15) clusters, which are presented in the Table 3 . As shown, one can find that F and Cl atom possess negative -0.75 ~ -0.82e and -0.47 ~ -0.58e charges, respectively. It shows that the charges transfer from the Al frame to M(M=F, Cl) atom, that is to say, F or Cl atom is an electronic acceptor in all studied MAln(M=F, Cl) clusters. The reason is the electronegativity of M(M=F(3.98), Cl(3.16)) atom is much larger than Al(1.61) atom31, and thus the M(M=F, Cl) atom has stronger ability to attract electrons. In addition, it can be found from the NEC results that 2s state of F and 3s state of Cl lose a number electron, the 2p state of F and 3p state of Cl gain a certain amount of electron. Namely, there is an internal electron transfers from 2s state to the 2p state for F atom and from 3s states to the 3p state for Cl atom. This phenomenon indicates that there is asp hybridization in the M(M=F, Cl) atom.
  1. Chemical hardness
The chemical hardness (η ) is an important factor in chemical stability. According to principle of maximum hardness (PMH) proposed by Pearson31, the η is rigorously defined as follows:
(3)
where and
The values of η , IP and EA for lowest-energy MAln (M=F, Cl; n =3-15) clusters are calculated with above formulas and summarized in Table 4. To compare the results, the η curves of MAln (M=F, Cl) and Aln+1 28, 29 clusters are plotted in Fig. 4 . From Fig. 4 , one can safely conclude that, the curves of FAln and ClAln clusters have the same changing tendency. When n = 3, 5, 7, 9, 11, 13 and 15, seven peaks are found for FAln and ClAln clusters, respectively. This means that the clusters FAl3,5,7,9,11,13,15 and ClAl3,5,7,9,11,13,15 have stronger η than their neighboring clusters. This finding is consistent with the koopmans’ analysis of chemical hardness, in which a hard molecule has a largeEgap and a soft molecule has a smallEgap 30. Another obvious conclusion is that, the η of Aln+1 clusters are higher than those of MAln (M=F, Cl) clusters, which indicates that doping of F, Cl atom can lower the η of aluminum clusters.
  1. Polarizabilities
The polarizability analysis is a useful tool to understand the static property of clusters. The size-dependent property of mean polarizability <α>, and polarizability anisotropies Δα of the most stable MAln (M=F, Cl; n =3-15) clusters can be found in the Fig. 5(a, and b) . The <α> and Δα equations are as following form:
(4)
(5)
ajj(j=x, y, z) in Eq. (4)- Eq. (5) represents the integral parts of ploarizability tensors for MAln (M=F, Cl; n =3-15) clusters.
From the Fig. 5(a) , we can safely conclude that, the <α> values of MAln (M=F, Cl) clusters increased slowly with cluster number. It means that the electronic cloud of MAln clusters is affected by external electric field easily and the optical nonlinearity in MAln clusters is enhanced obviously. Also, it is found that the <α> value of ClAln cluster is larger than that of FAln cluster. It illustrates that the ClAln are more stable than FAln . This result is in good agreement with the minimum polarizability principle (MPP) theorem32,33. In Fig. 5(b) , a similar trend of Δα changes is observed in the MAln (M=F, Cl) clusters with the exception ofn =6, 10 and 12. For FAln cluster, three local peaks are found at n =3, 10 and 15. This result indicates that FAl3, FAl5 and FAl10 clusters possess dramatically enhanced chemical stability. For ClAln cluster , the local peaks are found at n =3, 6, 9, 12 and 15, which implies that ClAl3, ClAl6, ClAl9, ClAl12 and ClAl15 clusters are more stable than their neighbors.
  1. Conclusion
In summary, by using B3LYP/6-311G+G(d) basis set of DFT method, we study the geometric structure, stability, charge transfer, chemical hardness, and polarizability of MAln(M=F, Cl; n=3-15) clusters. The results show that, the most stable structures of MAln clusters favor 3D structures when n > 3. The MAl7(M= F, Cl) clusters have stronger stability in the studied FAln and ClAln clusters, respectively. The internal charges in MAln clusters transfer from Al frame to M atom. The doping of F, C atom reduce the η of aluminum clusters.
  1. Acknowledgement
This work was supported by the National Natural Science Foundation of China (Nos. 11274235 and 11304167), and Universities Key Scientific Research Project of Henan Province (16A430023).