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

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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)

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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)

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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

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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

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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),

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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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