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GEOMETRIES OF SinV2+ CLUSTERS (n = 1-6): A DFT INVESTIGATION
Abstract
The geometries of SinV2+ clusters (n = 1 – 6) have been determined for the first
time by the method of density functional theory using B3P86/6-311+G(d) level of theory. Spin multiplicities of the clusters vary significantly with their stoichiometries, being from 2 to 8.
Keywords: Silicon cluster doped vanadium, density functional theory (DFT)
1. INTRODUCTION
Silicon clusters remains the mainstay objects of study owing to their potential
application. Over the past decade, significant research effort has been directed towards the
synthesis and characterization of silicon clusters. [1-6] It is shown in literature that pure
silicon clusters possesses low spin states and are non magnetic type of materials. Transition
metal atoms are magnetic owing to their non-fully filled d obitals. Therefore doping
transition metal atoms into silicon clusters are hopefully to create clusters which have
profilic magnetic properties [7-10]. The introduction of laser ablation cluster sources has
made experimental study of small silicon clusters possible. The fragmentation behavior of
silicon cluster has attracted attention from the first observations of silicon cluster in
molecular beams. Many researches on the small cationic silicon clusters doped with
transition metals, for instance copper and vanadium SinCu+ and SinV+ (n=6-8), have been
performed for their geometrical structures. It has recently been shown that infrared
multiple photon dissociation (IR-MPD) of complexes of metal clusters with rare gas atoms
is a suitable experimental technique to obtain vibrational spectra for clusters in gas phase.
In principle, we can determine the geometry of the cluster of small size dispersed in an
inert gas environment based on the IR or Raman spectrum.
In order to determine in more detail geometries of the clusters, such experimental
investigation need to be complemented by theoretical chemistry calculations. The method
of density-functional theory (DFT) can be used to optimize the geometry, compare the
electronic energies of different isomers of clusters from this the most stable isomer of each
1
cluster size could be predicted. Then vibrational spectra obtained by theoretical
calculations could help to deduce structures of specific cluster-size [11-13].
This study has been motivated by the purpose of finding the most stable isomers of
SinV2+ (n = 1-6) cation clusters which are not yet available in literature, that would initiate
successive work on the silicon clusters doped with vanadium.
2. METHOD OF CALCULATION
The method of density functional theory (DFT) which is implemented in the Gaussian
09 software [14,15] has been used for our investigation of the vanadium doped silicon
cationic cluster SinV2+ (n = 1-6).
The B3P86/6-311+G(d) functional/basis set combination has been employed for our
calculations [16-18]. The optimization calculations which are followed by frequency
calculations have been done for searching minima of the clusters. These functional and
basis set have been proved suitable for optimization and frequency calculations for silicon
clusters [7-9]. Geometries, relative energies are deduced from these calculations.
The searching for minima of each cluster stoichiometry has been performed as
following description. For the smallest cluster Si1V2+, all the possible geometrical
structures associated with all possible spin multiplicities is considered as input structures
which are then optimized to minima. Into stable structures obtained one Si atom is added to
all plausible positions to form many input structures of the Si2V2+ cluster, which are then
re-optimized to their minima. This procedure is repeated until the Si6V2+ cluster.
3. RESULTS AND DISCUSSION
The number of possible geometrical isomers associating with different spin
multiplicities is large for binary systems. In fact our extensive search for structural isomers
resulted in besides the global minimum a large variety of local minimum structures and
spin configurations for each stoichiometry – many of which are close in energy. The results
on searching for minima of SinV2+ clusters with n=1-6 are displayed in Figs. 1-6. In the
following, we denote each structure as n.x, in which n stands for number of Si atoms in
cluster SinV2+ and x is labeled as A, B, C, D, E and so on for isomers with increasing order
of energy.
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3.1. Si1V2+ cluster
1A(Cs, 2A’, 0.00 eV) 1B(C2V, 8A2, 0.47 eV) 1C(C2V, 10B1, 0.68 eV)
1D(Dh, 2S+1=6, 0.71 eV)1E(C2V, 6A1, 0.80 eV)
1F(Dh, 2S+1=10, 1.31 eV)
1G(Dh, 2S+1=8, 1.59 eV) 1H(Dh, 2S+1=4, 2.14 eV) 1I(Dh, 2S+1=2, 5.35 eV)
Figure 1. Geometries of global and local minima of Si1V2+ cluster
We started our work with searching for stable isomers of Si1V2+ clusters. Two geometries
have been considered which are triangular and linear. The most stable isomer is 1A (C s, 2A’, 0.00 eV) which is in the lowest spin state for this cluster could be. Several electronic
states with this triagular structure have also found by our calculations : 1B(C2V, 8A2, 0.47
eV), 1C(C2V, 10B1, 0.68 eV), 1E(C2V, 6A1, 0.80 eV). The linear structure is less stable than
the triangular one regardless the electronic states they possess: 1D(Dh, 2S+1=6, 0.71 eV),
1F(Dh, 2S+1=10, 1.31 eV), 1G(Dh, 2S+1=8, 1.59 eV), 1H(Dh, 2S+1=4, 2.14 eV),
1I(Dh, 2S+1=2, 5.35 eV).
3.2. Si2V2+ cluster
2A(C2v, 8A2, 0.00 eV) 2B(C2v, 4B1, 0.30
eV)2C(Cs, 8A”, 0.36
eV)
2D(C2v, 6A1, 0.39 eV)
3
2E(Cs, 2A”, 0.42 eV) 2F(C2v, 10A1, 0.78
eV) 2G(C2v, 10B1, 1.08
eV)
2H(Cs, 8A’, 1.26 eV)
2I(C2v, 2A1, 1.99 eV)2J(Cs, 8A’, 1.99 eV)
2K(Cv, 2.68 eV)
Figure 2. Geometries of global and local minima of Si2V2+ cluster
Many stable isomers of the Si2V2+ cluster have been found by our calculations. The most
stable one is 2A (C2v, 8A2, 0.00 eV) which is a non-proper tetrahedral in C2V point group
having 7 unpaired electrons. Several different electronic states for this structureare found
higher in energy: 2B(C2v, 4B1, 0.30 eV), 2D(C2v, 6A1, 0.39 eV), 2F(C2v, 10A1, 0.78 eV),
2G(C2v, 10B1, 1.08 eV), 2I(C2v, 2A1, 1.99 eV). The next motif of structure is a Y shape, and
two electronic states in this motif are found by our calculations: 2C(Cs, 8A”, 0.36 eV) and
2E(Cs, 2A”, 0.42 eV). The trapezoid and linear structures are found in higher energies:
2H(Cs, 8A’, 1.26 eV), 2J(Cs, 8A’, 1.99 eV) and 2K(Cv, 2.68 eV).
3.3. Si3V2+ cluster
3A(C1, 4A, 0.00 eV) 3B(Cs, 8A”, 0.13 eV)3C(Cs, 8A”, 0.29 eV)
4
3D(C1, 6A, 0.32 eV) 3E(Cs, 4A”, 0.44 eV) 3F(C1, 6A, 0.49 eV)
3G(C1, 8A, 0.57 eV)3H(Cs, 10A”, 1.01 eV)
3I(Cs, 6A’, 1.24 eV)
Figure 3. Geometries of global and local minima of Si3V2+ cluster
For the Si3V2+ cluster, the triangular bipyramidal structure with the two V atoms on the
tops having 3 unpaired electrons is the most stable isomer for the Si3V2+ cluster.
Associating with this structures two other electronic states have been found lying 0.32eV
(3D, C1, 6A) and 0.57 eV (3G, C1, 8A) above the ground state. There are two isomers found
in planar trapezoid structure: 3B(Cs, 8A”, 0.13 eV) and 3I(Cs, 6A’, 1.24 eV). Several
isomers in triangular bipyramidal structure with two neighboring V atoms have also been
found by our calculation, namely 3C(Cs, 8A”, 0.29 eV), 3E(Cs, 4A”, 0.44 eV), 3F(C1, 6A,
0.49 eV) and 3H(Cs, 10A”, 1.01 eV).
3.4. Si4V2+ cluster
4A(Cs, 6A’, 0.00 eV)4B(C1, 6A, 0.09 eV)
4C(Cs, 6A’, 0.30
eV)
4D(Cs, 8A”, 0.36 eV)
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4E(Cs, 8A’, 0.48 eV)4F(C1, 8A, 0.52 eV) 4G(C2V, 4A1, 0.79
eV)
4H(C2V, 8A1, 0.80 eV)
4I(Cs, 10A’, 1.00 eV)4J(Cs, 4A”, 1.35 eV)
4K(C2V, 2B2, 1.70
eV)
Figure 4. Geometries of global and local minima of Si4V2+ cluster
11 isomers of Si4V2+ cluster have been found by our calculations and all of them are
3-dimentional structures. The most stable isomer 4A (Cs, 6A’, 0.00 eV) grows from the
lowest energy isomer of Si3V2+ cluster with additional Si atom caped onto one of the faces
of the triangular bipyramidal. It has 5 unpaired electrons. The next energetically lowest
isomer 4B(C1, 6A, 0.09 eV) lies at barely 0.09 eV above the ground state. It has the same
spin multiplicity of 6 but differs only in symmetry, being C1, while the most stable isomer
is in Cs point group. Several other low-energy isomers have been found and all of them
have similar motif of structure in which the four Si atoms form a tetrahedral and the two V
atoms capes on faces or edges of the Si4 tetrahedral: 4C(Cs, 6A’, 0.30 eV), 4D(Cs, 8A”, 0.36
eV), 4E(Cs, 8A’, 0.48 eV), 4F(C1, 8A, 0.52 eV), 4G(C2V, 4A1, 0.79 eV), 4H(C2V, 8A1, 0.80
eV) and 4I(Cs, 10A’, 1.00 eV).
3.5. Si5V2+ cluster
6
5A(Cs, 2A’, 0.00eV) 5B(Cs, 8A”, 0.99 eV) 5C(Cs, 4A’, 1.23eV) 5D(Cs, 10A”, 1.34eV)
5E(Cs, 6A’, 1.40 eV) 5F(C1, 6A, 1.48 eV)5G(Cs, 10A’, 1.76
eV)
Figure 5. Geometries of global and local minima of Si5V2+ cluster
Seven isomers have been found for Si5V2+ cluster and all of them possess a
pentagonal bipyramid. The isomers differ in the positions of two V atoms. In the most
stable isomer (Cs, 2A’, 0.00eV) the two V atoms locate on the base plane and far apart from
each other. It has only one unpaired electrons and belongs to the Cs point group. The
isomer 5D(Cs, 10A”, 1.34eV) has the same positions of the two V atoms but differs in the
number of unpaired electrons. The isomers having the two neighboring V atoms on the
base plane of the pentagonal bipyramid are less stable: 5B(Cs, 8A”, 0.99 eV), 5C(Cs, 4A’,
1.23eV), 5E(Cs, 6A’, 1.40 eV), and 5G(Cs, 10A’, 1.76 eV). The isomer 5F(C1, 6A, 1.48 eV)
in which one of the two V atoms locates on the top and the other V atom on the base plane
of the pentagonal bipyramid is also found less stable:
3.6. Si6V2+ cluster
7
6A(C2V, 8A2, 0.00eV) 6B(C1, 6A, 0.08eV) 6C(C2V, 8A2,
0.26eV)
6D(C1, 6A, 0.76eV)
6E(Cs, 4A”, 0.79eV)6F(CS, 6A’, 0.80eV)
6G(C1, 10A, 0.81 eV)6H(C2V, 4A1,
0.98eV)
6I(CS, 4A’, 1.01eV)6J(C1, 6A, 1.11eV) 6K(Cs, 4A”, 1.25
eV)
6L(C2v, 6A1,
1.34eV)
6M(C2V, 10A1,
1.50eV)
6N(Cs, 10A’, 1.59eV) 6O(Cs, 10A”,
1.86eV)
6P(Ci, 2Au, 2.05eV)
Figure 6. Geometries of global and local minima of Si6V2+ cluster
For Si6V2+ cluster we have found 16 isomers. They could be categorized into three
motifs of structure. In the first motif, seven of the eight atoms form a pentagonal bipyramid
and the other atom capes on face or edge of the bipyramid. The most stable isomer 6A(C2V, 8A2, 0.00eV) is of this motif in which one V on the base plane and the other V atom capes
onto the Si-Si edge next to the V atom of the base plane. It is in high spin state with 7
unpaired electrons. This motif of structure is also found in several other isomers, namely
6B(C1, 6A, 0.08eV), 6C(C2V, 8A2, 0.26eV), 6E(Cs, 4A”, 0.79eV), 6F(CS, 6A’, 0.80eV),
8
6G(C1, 10A, 0.81 eV), 6H(C2V, 4A1, 0.98eV), 6J(C1, 6A, 1.11eV), 6K(Cs, 4A”, 1.25 eV),
6L(C2v, 6A1, 1.34eV), 6M(C2V, 10A1, 1.50eV), 6N(Cs, 10A’, 1.59eV), and 6O(Cs, 10A”,
1.86eV). In the second motif of structure, six of the eight atoms form an octahedron and
the two other atoms cape on its faces. Isomer 6D(C1, 6A, 0.76eV) belongs to this motif. The
isomers 6I(CS, 4A’, 1.01eV) and 6P(Ci, 2Au, 2.05eV) belong to the third motif of structure,
that is a distorted cube of Si6V2+ and they are both rather less stable.
4. CONCLUSION
A series of calculations using density functional theory (DFT) employed rather
high level of theory B3P86/6-311+G(d) have been performed for searching the global as
well as local minima of the SinV2+ clusters (n = 1-6), which are not yet available in
literature. Relative energies of the many isomers for each stoichiometry of the clusters
have been determined.
Acknowledgement: ……
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