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First Principles Study on Sino (N=14-18) and Si10-Mom(M=1-8) Clusters

Zhu Yuhong and Li Baoxing*

Department of Physics, Hangzhou Normal University, Hangzhou 310036, China

*Corresponding Author:
Li Baoxing
Department of Physics
Hangzhou Normal University
Hangzhou 310036, China
Tel: 086 571 28865282
E-mail: [email protected]

Received date: February 26, 2014; Accepted date: May 05, 2014; Published date: May 14, 2014

Citation: Y. H. Zhu, B.X. Li (2014) First Principles Study on SinO (n=14-18) and Si10-mOm(m=1-8) Clusters. J Theor Comput Sci 1: 113. doi:10.4172/2376-130X.1000113

Copyright: © 2014 Baoxing L, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Combining the full-potential linear–muffin–tin–orbital molecular-dynamics (FP-LMTO-MD) and the Amsterdam Density Functional (ADF) with TZ2P basis set in conjunction with self-consistent-field (SCF), we have studied the geometric features and stabilities of the SinO (n=14-18) clusters.. The total binding energy Etot, gap of HOMO (highest-occupied molecular orbital)-LUMO (lowest-unoccupied molecular orbital) Eg, dipole moment μ and total constant volume heat capacity Cv(tot) were also calculated. The results show that the one dopant oxygen atom tends to occupy the edge or the surface position in the middle size silicon clusters (Sin, n=14-18). To further understanding the evolutionary tendency of the physical characteristics for the Si-O clusters with different composition, the Si10-mOm (m=1-8) clusters were also studied using the same methods. It was found that the structures of the Si10-mOm (m=1-8) clusters evolve from compact three dimensions to chain-like with increasing of the O proportion. The binding energy curve of Si10-mOm clusters with different m shows a dip at m=6, which suggests that an optimal proportion of O and Si atoms may exist in the Si10-mOm(m=1-8) clusters.


Si-O clusters; Stable structure; Bonding energy


Silicon and its oxides are important materials because of their wide application potential, such as light-emitting materia, [1-3] solar energy [4] and catalyst [5]. With the deeply understanding of the physical properties of the silicon oxide materials, more new application fields have been developed [6,7]. For example, the SiOx-based resistive switching behavior provides a new use for traditional SiOx materials [8]. In addition, the Si-O compounds are found to be very abundant in most dusty media in space, and thus important in astrophysical processes such as star and planet formation [9]. All these (potential) applications are closely related to the structures of these compounds, therefore a systematical study would be of great importance.

In recent years, the oxide silicon was investigated in both experiment [1,4,5,10-13] and theory [10-21] for its broad prospect in the application. Desjardin and co-workers [1] studied oxidation of Si (111)-(7×7) surface by STM. They found that the low coverage O2 molecules absorbed on the surface could form more stable structures at room temperature. Very recently, Kinahan et al. [4] revealed the quantitative relationship between the coverage of site-specific oxygen and a decrease of the Si (111)-(7×7) surface stress in tensile by the same method. Wang et al. [5] studied the Si3Oy clusters using anion photoelectron spectroscopy and ab initio calculation. They presented that the Si3O4 may be a model structure for oxygen defect sites in bulk SiO2.

On the other hand, the features of the Si-O clusters are the key points in the study of the Si-O systems. Kinds of Si-O clusters such as SimOn (m, n=1-8) [10,11], SinOn (n=3-5) [12], SimOn (m=1-5, n=1, 2m+1) [14], SinOn (n>=5) [17], Si6On (n=1-12) [19], Si7On (n=1-14) [20] and SiOn (1<n≤6) [21] were studied by first principle calculations. Many new possible structures of these clusters were drawn and numerous unfamiliar features of them were investigated. Based on the quantum-mechanical calculations, Zhang et al. [10] studied the O-ratio-dependent features of the SimOn (m,n=1-8) clusters. They found that energetically the most favorable small Si-O clusters have O atomic ratios at about 0.6. James [12] found that the structure of the ground state Si3O3 cluster is planar and the lowest energy structures of Si4O4 and Si5O5 are non-planar rings. Lu and coworkers [17] obtained the results that the binding energies of SimOn(m=1-5, n=1, 2m+1) clusters increase with the number of oxygen atoms, and the dissociation energies of these clusters are strong relative to the O and Si atoms ratio in one cluster. In addition, some researches focused on the (SiO2)n nanoclusters [15,16,18]. A number of ringed, tube-like, cage shape, columnar and disk-like nanostructures based on SiO2 unit were illustrated in detail.

We studied oxygen molecule and one O atom adsorption on Sin (n<=13) clusters by the FP-LMTO-MD method [22-25] and ADF program [26] and the lowest energy structures for these clusters were given [13,27]. The calculated results show that there is a potential barrier of dissociative chemisorption of O2 when the Si clusters have more than four atoms. Moreover, it is found that the edge or the surface of the host Si clusters is the favorable adsorption sites for one O atom.

In this work, we investigated one oxygen atom adsorption on the middle size silicon clusters (Sin, n=14-18) and the Si10-mOm (m=1-8) clusters using combination of the FP-LMTO-MD and ADF program. Our main purpose is to find the lowest energy structures of these clusters, and to explore the geometry and physical properties in the evolutionary procedure of the Si-O clusters with various compositions. Some new the lowest energy structures for these Si-O clusters were found. The total binding energy for Si10-mOm (m=1-8) clusters decrease, and then increase with the increasing of the ratio of Si:O.


The initial structures of the SinO (n=14-18) clusters are constructed through an oxygen atom being absorbed on the positions of the lowest energy silicon clusters [28] which are given by previous studies. Geometrical optimization algorithm is performed on the initial structures without any symmetry constraints by the FP-LMTO-MD method. For the Si10-mOm (m=1-8) clusters, a huge number of initial atomic conformations are randomly sampled within a real threedimensional box, or cage, or ball structure. Moreover, several chainlike initial structures of the Si10-mOm (m=1-8) clusters are also prepared.

After that, we choose the three lowest energy structures of each Si-O clusters in two types as candidates and re-optimize these selected structures by using the ADF program [26] version (2007.01) with TZ2P [29] basis set in conjunction with self-consistent -field (SCF). The TZ2P basis using in ADF is an all-electron basis with triple-zeta quality for valence region. The frozen-core approximation for the inner-core electrons is used. The orbitals up to 2p for silicon and 1s for oxygen are kept frozen. An accessional STOs (Slater Type Orbitals) basis set including s, p, d, f, and g-type is used to fit the molecular density and hence to present the Coulomb and exchange potentials more accurate. The combined self-consistent-field (SCF) is converged to a value of 10-6. For both two types’ clusters, the frequencies of them are computed using numerical differentiation of gradients in slightly displaced geometries.

Furthermore, the cationic and anionic clusters corresponding to each neutral candidate are also calculated. Using the ADF program, such calculations can be performed by altering the charge state in the input file for a given cluster.

Results and Discussions

Existing imaginary frequencies indicate that the given molecular structure is unstable. Our calculated results show that there are no imaginary frequencies in the energy minima structures for both two types’ Si-O clusters. It suggests that our obtained the lowest energy structures are stable.

SinO (n=14-18) clusters

The three lowest energy structures for the SinO (n=14-18) clusters are shown in Figure 1. The number 0 and the sign +, - in parentheses represent the neutral, cationic and anionic clusters respectively. The three isomers are labeled as a, b and c in order of decreasing stability. For example, (0,-) a indicates that the labeled structures are the most stable structure for neutral and anionic clusters. The calculated results for each neutral SinO (n=14-18) cluster are listed in Table 1, which include the total binding energy (Etot, in eV), electron affinity (EA, in eV), ionization potential (IP, in eV), the gap of HOMO-LUMO (Eg, in eV), dipole moment (μ, in Debye), and total constant volume heat capacity (Cv(tot), in cal/mol•K).


Figure 1: The lowest binding energy structure of the SinO (n=14-18) clusters. The number 0 and the sign +, - in parentheses represent the neutral, cationic and anionic clusters, respectively. The letters a, b and c mean the stable order for three isomers.

Structure Etot (eV) EA (eV) IP (eV) Eg(eV) µ Cv
Si14oa -69.58 2.61 6.76 1.30 1.03 71.38
Si14ob -69.35 2.61 6.94 1.40 1.20 72.00
Si14oc -69.34 2.48 7.00 1.69 1.02 71.98
Si15oa -74.90 1.60 8.11 1.85 2.37 76.92
Si15ob -74.17 2.66 7.11 1.56 0.42 76.51
Si15oc -74.06 2.44 7.23 1.78 2.19 76.74
Si16oa -78.72 2.86 6.58 0.94 0.84 80.73
Si16ob -78.65 2.78 6.48 0.72 1.27 80.99
Si16oc -78.49 2.81 6.68 0.92 0.91 80.87
Si17oa -83.45 3.05 7.13 1.21 0.72 86.54
Si17ob -83.44 2.90 6.86 1.27 0.12 86.72
Si17oc -83.06 2.63 6.53 1.08 1.55 86.85
Si18oa -87.61 2.51 6.79 2.03 3.25 92.28
Si18ob -87.58 2.50 6.72 1.54 4.47 91.64
Si18oc -87.54 3.08 7.01 1.05 1.96 93.21

Table 1: The total binding energy (Etot, in eV), electron affinity (EA, in eV), ionization potential (IP, in eV), the gap of HOMO-LOMO (Eg, in eV), dipole moment (µ, in Debye), and total constant volume heat capacity (Cv(tot), in cal/mol K), for the three lowest energy structures of SinO (n=14-18) clusters.

For the Si14O cluster, their isomers are formed by an O atom being adsorbed to different sites of the ground state Si14 cluster [6,28]. The Si14O(0)a structure with Cs symmetry lies 0.23eV energetically below the Si14O(0)b structure. Both of the structures Si14O(0)b and the Si14O(0) c have C1 symmetries. The energy difference between them is only 0.01eV. Our calculated result shows that the largest energy difference between the adsorption structures with the same host Si structure can be up 0.8 eV.

For Si15O isomers, the symmetries of the lowest two binding energy Si15O clusters are both C2, while for third one is C3. The most and second stable structures of them are formed by the second lowest energy structure of pure Si15 cluster [28] absorbing an impurity oxygen atom at the different edge sites for a Si triangular pyramid unit. While, for the third stable Si15O cluster, the O atom connects three Si atoms to form a triangular pyramid and lays on the apex site of the pyramid, as shown in Figure 1. The similar absorbed sites of O atom also can be found in other SinO (n=14-18) clusters (shown in the Figure 1 and 2). The energy of the cluster Si15O (0)a is about 0.73eV and 0.84eV more stable than Si15O(0)b and Si15O(0)c , respectively.


Figure 2: The lowest binding energy structure of the Si10-mOm (m=1-8) clusters. The numbers present the Si and O atomic number in cluster.

The three lowest binding energy structures of Si16O cluster are C2 symmetries. Comparison of the structures for the Si16 [6,28] and Si16O cluster shows that the impure O atom will result in the compact pure cluster becoming loose. The distortion arising from the O atom doping is more significant for Si16O clusters than for other SinO (n=14,15,17 and 18)clusters.

The three Si17O clusters shown in the Figure 1 are Cs symmetries, which are formed by one O atom being absorbed to the lowest and the third lowest Si17 clusters [6,28]. The difference of binding energy for the first and second stable structures is only 0.01eV. For the third stable isomer, the absorbed O atom leads the two ends of the pure Si17 cluster slightly bend to the center.

For the Si18O isomers, the O atom performs as a trigonal facecapping atom. The symmetries for three lowest binding energy clusters are C3, C2 and C3 in energy order. After the O atom is adsorbed, slight distortion occurs in the host silicon structures. The energy difference of three low-lying isomers of pure Si18 cluster is about 0.26 eV [6]. The absorption O atom reduces the difference to less than 0.07 eV. Hence, the three structures of Si18O clusters can be regarded degenerate energetically.

Our calculated results reveal that the impurity oxygen atom is favorable to adsorb on the edge or surface site of the middle-size silicon clusters, the same phenomena also has been found in small-size SinO (n=1-13) clusters [27]. The Si atom with 3s23p2 electronic configurations, trends to through sp3 hybridization forming covalent bonds with other atoms. Meanwhile, the 2s22p4 O atom has lone electron pair of p orbital besides two p single electrons and probably forms two or three bonds with neighboring atoms in the mixed clusters. This is the main reason why the doped oxygen atom usually occupy the surface or edge site to form three or two bonds in the SinO clusters (the analyses in details see our previous study [13,27]).

For the adsorption structures with edge-capping O atom, O atom bridges two Si atoms by two bonds, in which the lengths are from 1.64 to 1.79Å. The bond angles of the Si-O-Si are from 90.5 to 116.1 degree. For the surface adsorption, the O-Si bond lengths are around 1.83 Å and slightly longer than bonds in the edge-adsorption’s case. Compared with the Sin (n=14-18) clusters [6,28], the structures of the SinO clusters become loose. We think the main reason is that the parts of charges transfer from the surrounding Si atoms to doped O atom and the covalent bonds are formed between them.

The ionic clusters corresponding to the above neutral SinO (n=14- 18) candidates with larger binding energies are also studied. The calculated results indicate that the neutral and ionic clusters show similar geometrical configurations and different stability orders. It is found from observing the positions of all atoms for a given SinO cluster that the differences of coordinates for the ionic and neutral clusters are less than 0.2Å. Such small difference is hardly to distinguish from the structural figures. So we use the same structure to describe the ionic and neutral cluster with similar motif. As shown in the Figure 1, the three lowest binding energy ionic and neutral Si14O clusters have same energetic orders. While, when n>14, the energetic orders of ionic and of neutral SinO clusters are different. The energy gaps between HOMO and LUMO (Egs) of ionic and of neutral SinO clusters are also different. For example, for example, for the three Si17O isomers at the lowest energy state, the Egs of the neutral clusters are 1.21eV, 1.27eV and 1.08eV, while 0.23 eV, 0.36eV and 0.39eV for cationic isomers and 0.44 eV, 0.31eV and 0.32eV for anionic ones, respectively. We speculate that the electronic redistributions due to add or reduce one electron may contribute to the energy order and Eg changes.

We have also investigated the magnetism properties of the neutral and ionic SinO (n=14-18) clusters. It is found that the neutral clusters with even number of electrons have no magnetic moment because all the electrons are paired together in their respective molecular orbitals, whereas all the ionic clusters with odd number of electrons have the total magnetic moment of 1.0 lμB, which is trivial, due to one unpaired electron. In addition, Mulliken population analyses imply that about 0.62e to 0.66e charge transfer from the silicon atoms to the oxygen atom.

Si10-mOm (m=1-8) clusters

Zhang and co-workers reported that the binding energies per O atom for Si6On (n=1-12) increased with the numbers of O atoms at first, and then decreased when n>8 [19]. The similar tendency also was found in Si7On (n=1-14) clusters [20]. The structural feature of SimOn clusters strongly depend on the ratio of component Si and O atoms [14,19,20]. For small SimOn clusters, the structural motif will transit from a disk-like structure to a double-oxygen-bridged rod structure [19].

In order to explicitly explore how the different ratio of Si:O effect on the structural evolution properties and physical characteristics for the SiO mixed clusters, the SimO10-m (m=1-8) clusters are studied. The initial structures of them are given by unbiased global search (details see the method). More than 4000 candidates for each SimO10-m clusters with different m are calculated, and the most stable structures of them are shown in the Figure 2. For all clusters, the bond lengths of O-O, Si-O and Si-Si fall between 1.52-1.65 Å, 1.67-1.71 Å and 2.31-2.95 Å, respectively. The shortest Si-O bond is the single Si-O bond in Si3O7 cluster.

For Si9O cluster, the O atom is adsorbed on the edge site of the lowest energy Si9 cluster [30], which excellently agrees with our previous results using different method [27]. To our knowledge, the ground-state structure of Si8O2 cluster has never been reported up to now. The Si8O2 cluster has Cs symmetry. It looks like a silicon crown being adorned with two O atoms jewels. When m≥3, the Si3O3-ring and Si2O2-rhombus structures formed in the ground state SimO10-m clusters. With the ratio of O atom further increasing, the SimO10-m clusters trend to form the chain-like conformation. Our calculated lowest energy structures of Si7O3, Si6O4, Si5O5, Si4O6 and Si3O7 are in agreement with the findings of other groups [14,19,20]. The most stable structure for Si2O8 cluster consists of the two SiO3 rhombuses and one Si2O2 rhombus buckled-chain structure. The computation of frequencies shows that the structure Si2O8 is stable because no imaginary frequencies exist. We also calculated the SiO9 clusters. The structures are unstable, therefore, the dissociated SiO9 cluster does not be listed.

The Si4O6 cluster is the most stable in all the Si10-mOm (m=1-8) clusters. The chain-like Si4O6 cluster with D2 symmetry is formed by three Si2O2-rhombuses sharing with two Si atoms. The lengths of Si-O bonds in the cluster are different. The lengths of Si-O bonds connecting the two ends Si atoms are 1.73 Å, which are longer than the other –bonds’ lengths (about 1.68 Å). Mulliken population analyses imply that the some charge transfer from silicon atoms to oxygen atoms. For neutral Si4O6 cluster, the dipole moment is zero due to symmetrical structure.

Figure 3 plots the total binding energies Etot (Si10-mOm) versus the number of oxygen atoms. As opposed to the linear curve of the nitrogen atom and aluminum atom doped to Si clusters [31,32], the curve for the Si-O mixed cluster shows a valley. With the number O atom increasing, the Etot (Si10-mOm) decreases linearly when 1≤m≤6, and then goes up when m > 6. This is to say that the lowest binding energy structure for Si10-mOm cluster with the ratio of 0.6 for O component, which is similar to the findings by Zhang’s in the SimOn (m, n=1-8) clusters [14]. On the one hand, comparing the Si10-mOm clusters, there is a tendency that the structures of the Si10-mOm clusters evolve from compact three dimensions to chain-like with increasing of the proportions for O components. On the other hand, the symmetries of these clusters increase with O when m≤6. Therefore, the energetic valley may suggest that the stability of the mixed Si-O clusters depends on the cooperation of the composition and structural properties.


Figure 3: The total energies of the Si10-mOm (m=1-8) clusters Etot (eV) versus the atom number of O atom m.

The second different energyΔ2E (eV) is a sensitive quantity to reflect the stability of clusters. It is defined as Δ2E (Si10-mOm)= Etot (Si10-(m-1) O m-1)+ Etot (Si10-(m+1) O m+1) -2 Etot (Si10-mOm) . TheΔ2E have the largest value at m=6, also indicates that the Si4O6 cluster is more stable than their neighboring clusters (Figure 4). In addition, the Δ2E also displays an even/odd alternating pattern as a function of cluster size. The clusters with even oxygen atoms present higher stability.


Figure 4: The second different energies of the Si10-mOm (m=1-8) clusters Δ2E (eV) versus the atom number of O atom m.

The energy gaps Eg between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) are showed in Figure 5. The highest peak occurs again at the Si4O6 cluster. The energy gaps also display a certain even/odd alternating pattern as a function of cluster size. All the evidences mentioned above suggest that the ratio 4:6 is the optimal proportion for the stability of the Si10-mOm (m=1-8) clusters. Chu et al. found that when O ratio reaches to about 60% in a small Si-O clusters, the energy gaps of the clusters present the biggest value [11]. Such result is a convincing evidence to support our conclusion.


Figure 5: The energy gaps Egs (eV) between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) of Si10-mOm (m=1-8) clusters.

Furthermore, it is found that the rhombus Si2O2 unit is a basic structure of ground Si-O clusters [5,11,33,34]. Two rhombus Si2O2 units will buckle with each other by sharing a central Si atom to form a stable chain-like configuration. Such structural patterns are usually found in ground state Si-O clusters [5,11,13,19,20]. In other word, to form the stable buckled rhombus Si-O chain, for each added Si atom needs two O atoms more. This may be the reason why the Si-O clusters with even oxygen atoms possess lower binding energy.

The heat capacities of the clusters are computed based on the ideal gas approximation omitting the electronic contribution. The heat capacity Cv is related to the number of degrees of freedom (DoF) of the cluster system. In ideal gas model, the nonlinear cluster with n atoms has 3 translational, 3 rotational and 3n-6 vibrational DoF. The molar heat capacity of the n-atom cluster is [3+3+2(3n-6)]•R/2, where R is the ideal gas constant. For Si10-mOm (m=1-8) clusters, the Cv(tot) equals to 27R (≈53.6 cal/mol•K). In our calculation, Si9O cluster shows the largest heat capacity 45.4 cal/mol•K. The smaller Cv(tot)s with respect to the theoretical values may due to the inactivation of some vibrational DoFs. According to the ideal gas model, the heat capacity of the cluster only relates to its atom number. Thus, the Si10-mOm clusters would have similar value of the Si10-mOm cluster. However, it is interesting that the Cv(tot) of Si10-mOm cluster decreases gradually with the proportions of O atomic increases (See Figure 6). Observing the structural evolution of Si10-mOm clusters, it is found that the structures of these clusters vary radically with the increasing of the ratio for oxygen: the whole structure for silicon-rich clusters transfer to the fragments consisted for oxygenrich clusters. We assume that such structural changes may contribute to the decreasing of Cv with increasing of the O component’s ratio for the Si10-mOm clusters.


Figure 6: The total constant volume heat capacity (cal/mol•K) of Si10-mOm (m=1-8) clusters.


The SinO(n=14-18) and Si10-mOm(m=1-8) clusters are investigated systemically by using the FP-LMTO-MD and the ADF with TZ2P basis set in conjunction with SCF. The calculated results suggest that the edge and surface adsorption structures are the favorable structures for the middle size silicon clusters doped an oxygen atom. For Si10-mOm (m=1-8) clusters, their structures evolve from compact three dimensions to chain-like with increasing of the proportion of O. The Si4O6 cluster has the lowest bonding energy and the largest Δ2E. It suggests that the conclusion which the small silicon-oxygen clusters have the optimal ratio of 0.6 for O component [14] is still correct in the Si10-mOm (m=1-8) clusters. Whether the bigger Si-O clusters still have such optimal O ratio needs further study.


The Natural Science Foundation of Zhejiang Province (Grant No. Y6100098) the Science Foundation of Zhejiang Province Department of Education (Grant No. Y201018280) and the Science Foundation of Hangzhou Normal University (Grant No. 2010QN03) supported this work.


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