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
- 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.
- 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.
- Results and discussions
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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).