SinV₂ (n = 1 - 8) clusters: a dft investigation on their dissociation behaviors

66 HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1059.2017-0056 Chemical and Biological Science 2017, Vol. 62, Issue 10, pp. 66-73 This paper is available online at SinV2 + (N = 1 - 8) CLUSTERS: A DFT INVESTIGATION ON THEIR DISSOCIATION BEHAVIORS Nguyen Thi Minh Hue 1,2 , Nguyen Cao Khang 3 , Pham Thuy Duong 1 , Le Huy Nguyen 1 and Ngo Tuan Cuong 1,2 1 Faculty of Chemistry, Hanoi National University of Education 2 Center for Computational Science, Hanoi National University of Education 3 Faculty of Physics, Hanoi National University of Education Abstract. The method of density functional theory using B3P86/6-311+G(d) functional/basis set have been performed for searching stable structures and preferable dissociation channels of the doubly vanadium-doped silicon cationic clusters SinV2 + (n = 1 - 8). The dissociation energies of the cation clusters SinV2 + into smaller atoms, cations and clusters have been determined for the first time. This results show that the SinV2 + clusters have a priority for the decomposition of one vanadium atom/cation along with smaller clusters, and that the Si5V2 + is the most stable species among the investigated clusters. Keywords: Vanadium-doped silicon clusters, density functional theory, dissociation. 1. Introduction Over the past decades, silicon clusters have been preserved to be the mainstay objects of study owing to their potential application, and much research effort has been directed towards the field. [1-6] While pure silicon clusters have been known in the form of non- magnetic states, their incorporating with transition metals shall make them stable in high spin states due to the unpaired electrons they possess [7-10]. Vanadium is a transition metal that possess three unpaired electrons in its 3d sub-shell. The doping of a vanadium atom into silicon clusters of small sizes SinV + have been investigated recently, by both experimental and theoretical work, for their geometrical structures [9, 11, 12]. That is, clusters of interest could be generated by an introduction of laser ablation to the cluster sources. Then the technique of Infrared Multiple Photon Dissociation (IR-MPD) could be applied to obtain vibrational spectra for the clusters in gas phase, and their structural assignment in detail would be done by a combination with quantum chemical calculations. The method of density-functional theory (DFT) can be used to optimize the geometry, Received October 27, 2017. Revised December 15, 2017. Accepted December 22, 2017. Contact Ngo Tuan Cuong, e-mail address: cuongnt@hnue.edu.vn SinV2 + (n = 1 - 8) clusters: a dft investigation on their dissociation behaviors 67 compute the electronic energies of different isomers of clusters from this the most stable isomer of each cluster size could be predicted. Then vibrational spectra obtained by theoretical calculations could help to deduce structures of specific cluster-size [13-14]. In another work, vanadium-doped small silicon anionic clusters, SinV (-) and SinV2 (-) (n = 3 - 6), have also been investigated by anion photoelectron spectroscopy in combination with theoretical calculation. The vertical detachment energies (VDEs) and adiabatic detachment energies (ADEs) of these clusters as well as their geometries have been determined [15]. In our recent theoretical work, the doubly V-doped silicon clusters in their cationic form SinV2 + upto six Si atoms (n = 1 - 6) have been investigated for their stable geometries [16]. However, their stabilities associating with their dissociation behaviors have not been studied yet. What happens to the doubly vanadium-doped cationic silicon clusters upon receiving certain amount of energies, that is, would the clusters dissociate a V atom/cation or would they fragment a dimer? Being motivated by this enquiry, this research is done for answering it. 2. Content 2.1. Computational methods In order to investigate the dissociation behavior of doubly vanadium-doped cationic silicon clusters SinV2 + (n = 1 - 8), the searching for the most stable isomers of Sin 0/+ , SinV 0/+ and SinV2 + (n = 1 - 8) is needed. And we have used the method of density functional theory (DFT) which is implemented in the Gaussian 09 program [17-21] for all of our calculations. The stable geometrical structures of the cluster Sin, SinV 0/+ and SinV2 + have been determined as follows. Firstly, we have optimized all the possible geometries of the pure silicon clusters Sin (n=1-8), following by frequency calculations to confirm the stable structures. Secondly, one and two V atoms have been attached at different positions in the lowest energy lying isomers of the Sin clusters forming new input geometrical structures of the SinV 0/+ and SinV2 + (n = 1 - 8) clusters. These structures then have been re-optimized, also followed by frequency calculations for their stable isomers. The optimized geometries of the investigated clusters are illustrated in Figures 1-3 in associating with their point groups and electronic states. The B3P86/6-311+G(d) combination of functional and basis set has been employed [7, 16] since it is good for the calculation of silicon clusters doped with transition metals. From the calculation results the electronic energies with zero point energy corrections, relative energies between isomers for each cluster stoichiometry. After identifying the most stable isomers of each cluster size of the Sin, Sin + , SinV 0/+ and SinV2 + (n = 1 - 8), the dissociation energies of the SinV2 + (n = 1 - 8) cluster have been evaluated. 2.2. Results and discussion 2.2.1. Geometrical structures * Geometrical structures of neutral SinV 0/+ clusters (n = 1 - 8) By using the computational method that is described in Section 2, the most stable isomer for each cluster stoichiometry is found, and represented in Table 1. Nguyen Thi Minh Hue, Nguyen Cao Khang, Pham Thuy Duong, Le Huy Nguyen and Ngo Tuan Cuong 68 Si1V1 0/+ : The hetero-diatomic Si1V1 0/+ clusters belong to the C∞v point group. Si2V1 0/+ : The most stable isomers of this cluster size have an isosceles triangle which is in C2v point group and associating with the electronic state 4 B1, 5 B1 for neutral and cationic cluster, respectively. Si3V1 0/+ : The most stable isomer of the Si3V + cluster has a tetrahedral shape with the three Si atoms forming the base plane and the V atom locating on its top. This structure associates with 5 and 6 unpair electrons, respectively for the neutral and cationic form. Si4V1 0/+ : In the most stable isomer of the Si4V 0/+ cluster, the 4 Si atoms form a rhombous and the V atom is out of the Si4 base plane, forming the distorted tetrahedral pyramid. This structure belongs to the Cs point group associating with the 6Aꞌ and 5Aꞌ electronic states, respectively for the neutral and cationic cluster. Si5V1 0/+ : In the most stable isomer of the Si5V 0/+ cluster, four of the five Si atoms form a rhombous while the remaining Si atom and the V atoms cape on different side of the Si4 base plane forming the distorted octahedral. The molecule belongs to the symmetry group Cs with the electron state 4 A" and 5 A", respectively. Si6V1 0/+ : Six Si atoms and the one V atom arrange in a pentagonal bipyramidal associating with the Cs point group and the 4Aꞌ, 5Aꞌ electronic states, respectively. Si7V 0/+ : Seven Si atoms forming a 3D structure which is on the way forming the tetragonal antiprism of the Si8 cluster, while the V atom capes onto one of its faces. This structure associates with the 4 A, and 5 A electronic states, respectively. Si8V + : Eight Si atoms forming a distorted cube or a tetragonal antiprism as it is in the pure silicon Si8 cluster, while the V atom locates on one of its faces. This structure belongs to the C1 point group and associates with the 4 A, and 5 A electronic state, respectively. Si1V1, C∞v Si1V1 + , C∞v Si2.V1, C2v, 4 B1 Si2.V1 + , C2v, 5 B1 Si3V1, C1, 6 A Si3V1 + , C1, 7 A Si4.V1, Cs, 6A’ Si4.V1 + , Cs, 5A’ Si5V1, Cs, 4A’’ Si5V1 + , Cs, 5A’’ Si6V1, Cs, 4A’ Si6V1 + , Cs, 5A’ Si7V1, C1, 4 A Si7V1 + , C1, 5 A Si8V1, C1, 4 A Si8V1 + , C1, 5 A Figure 1. Geometrical structures of SinV1 0/+ cluster (n = 1 - 8) * Geometrical structures of SinV2 + clusters (n = 7 - 8) The geometrical structures of SinV2 + clusters up to six Si atoms (n = 1 - 6) have been reported in our previous work [16]. Hereafter we would like to report the stable isomers of the two cluster compositions, namely Si7V2 + and Si8V2 + . SinV2 + (n = 1 - 8) clusters: a dft investigation on their dissociation behaviors 69 Cluster Si7V2 + For Si7V2 + cluster size, many isomers with different spin multiplicities have been found whose geometries are illustrated in Figure 2. Many of them contain a pentagonal bipyramid with two atoms cape outside of the bipyramid. In the energetically low-lying isomers of the Si7V2 + cluster one of the two V atoms positions at one of the top vertices of the pentagonal bipyramid and the other V atom locates on one of the faces oppositely to the first V atom. The pentagonal bipyramid of the Si5V2 + cluster [16] still preserve in this cluster size. The most stable isomer of Si7V2 + could be described as such: six of the seven Si atom and one of the two V atom form the pentagonal bipyramid with the V at the top of it. The remaining Si and V atoms cape onto different faces of the petagonal bipyramid. This structure though preserves the pentagonal bipyramid as it does in the Si6V2 + cluster but it does not simply grow from the most stable isomer of the previous cluster size. It associates with the spin multiplicity of 8 and the C1 point group. A (C1, 8 A, 0.00 eV) B (C1, 2 A, 0.01 eV) C (C1, 8 A, 0.06 eV) D (C1, 8 A, 0.23 eV) E (C1, 6 A, 0.31 eV) F (C1, 8 A, 0.39 eV) G (C1, 10 A, 0.42 eV) H (C1, 10 A, 0.55 eV) I (C1, 8 A, 0.57 eV) J (C1, 10 A, 0.65 eV) K (Cs, 6A’, 0.84 eV) L (C1, 8 A, 0.93 eV) Figure 2. Geometrical structures, symmetry point groups, electronic states and relative energies between isomers of the Si7V2 + cluster Cluster Si8V2 + For Si8V2 + cluster size, many isomers with different spin multiplicities have been found, whose geometries are illustrated in Figure 3. The most stable isomer of Si8V2 + arise from the distorted cube or tetragonal anti- prism structure of the Si8 pure cluster with the two V atoms caping on neighboring faces of the cube. It also associate with the spin multiplicity of 8 and the C1 point group. Nguyen Thi Minh Hue, Nguyen Cao Khang, Pham Thuy Duong, Le Huy Nguyen and Ngo Tuan Cuong 70 A (C1, 8 A, 0.00 eV) B (C1, 4 A, 0.26 eV) C (C1, 6 A, 0.27 eV) D (C1, 6 A, 0.37 eV) E (C1, 2 A, 0.41 eV) F (C1, 2 A, 0.77 eV) G (C1, 4 A, 1.03 eV) H (C1, 4 A, 1.15 eV) Figure 3. Geometrical structures, symmetry point groups, electronic states and relative energies between isomers of the Si8V2 + cluster 2.2.2. Possible dissociation processes of the SinV2 + clusters (n = 1 - 8) From the electronic energies of the most stable isomers of the clusters, taking into account the zero point energy corrections, we compute the dissociation energies of the studied clusters into small clusters by the possible separation channels. The dissociation energy of a cluster is the difference between sum of the electronic energies of the forming species and the electronic energy of the parent cluster. The SinV2 + clusters would have seven dissociation channels that are the most possible: SinV2 +  Sin-1V2 + + Si (1) SinV2 +  SinV + + V (5) SinV2 +  Sin-1V + + SiV (2) SinV2 +  Sin + V2 + (6) SinV2 +  SinV + SiV + (3) SinV2 +  Sin + + V2 (7) SinV2 +  SinV+ V + (4) The dissociation energy corresponding to each of the above processes is shown in the Table and Figure 4. Calculation results which are presented in Tables and Figure 4 show that: The first direction, namely the dissociating of SinV2 + cluster into a Si atom, is the most difficult one due to its highest separation energy. The (4) and (5) pathways that produce one V/V + atom/ion are the most likely ones though they are in competition with the channels that fragment the V2 or V2 + dimers, namely the (6) and (7) channels. In most of the fragmentation channels, we would see that the Si5V2 + cluster has the highest dissociation energies. In other words, this is the most stable cluster among the investigated clusters SinV2 + (n = 1 - 8). This cluster possesses a pentagonal bipyramidal geometry with the two V atoms sitting on the base plane and being separated by a Si atom. This isomer of Si5V2 + associates with the spin multiplicity of two or it has only one unpaired electron. It is also seen that the Si3V2 + cluster has high dissociation energies as compared to the other clusters. Therefore this cluster which is in a triangular bipyramid is also a stable cluster among the cluster studied. SinV2 + (n = 1 - 8) clusters: a dft investigation on their dissociation behaviors 71 Table 1. Energy of the dissociation channels of the SinV2 + clusters calculated at the B3P86/6-311+G(d) level of theory Cluster Composition/Dissociation Channel (1) (2) (3) (4) (5) (6) (7) n = 8 12.77 5.05 5.83 3.23 3.56 4.68 5.48 n = 7 12.22 4.61 4.53 3.84 3.08 3.16 4.86 n = 6 11.99 5.06 4.92 3.10 3.20 3.38 5.35 n = 5 13.51 6.00 6.01 3.71 3.87 4.86 6.77 n = 4 12.55 5.92 5.67 3.29 3.30 3.80 5.61 n = 3 12.73 5.38 4.60 3.89 4.18 4.48 6.42 n = 2 12.84 5.22 5.22 2.66 3.46 5.14 6.70 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 10 12 14 Si n V + 2 1 2 3 4 5 6 7 E n e rg y , e V Figure 4. Dissociation energy of the SinV2 + clusters for the channels (1)  (7) 3. Conclusion The method of density functional theory using B3P86/6-311+G(d) functional/basis set have been performed for searching stable structures and preferable dissociation channels of the doubly vanadium-doped silicon cationic clusters SinV2 + (n = 1 - 8). The results of the work are as follows: The geometries of stable isomers of the SinV 0/+ , SinV2 + clusters are determined. The clusters of small size (n = 1, 2) have flat structures, larger clusters (n = 3 - 8) possess spatial structures. The most stable isomer for each cluster stoichiometry has high spin multiplies, ranging from 4 to 8. The energies of many dissociation channels of the cationic clusters SinV2 + (n = 1 - 8) into smaller atoms, cations and clusters have been determined. The results show that the SinV2 + clusters prefer to dissociate one vanadium atom/cation along with smaller clusters. Nguyen Thi Minh Hue, Nguyen Cao Khang, Pham Thuy Duong, Le Huy Nguyen and Ngo Tuan Cuong 72 Acknowledgement. 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