A study of the (ZrO2)n (n = 1 ÷ 11) clusters by density functional theory

Abstract. To reveal the origin of the (ZrO2)n (n = 1 ÷ 11) cluster stability and to study the structural trends in the zirconium oxide neutral cluster distribution, (ZrO2)n clusters have been constructed and calculated employing Density Functional Theory (DFT). In this work, we calculate the formation energy, electronic structures, stabilities and Raman spectra for varying isomers of (ZrO2)n clusters. The total binding energy of the cluster (ZrO2)n indicates that energies of stabilization does not decrease monotonically with increasing size and the energies change very slow from n = 5. The results of the calculated Raman spectra of the clusters (ZrO2)n were compared with the experimental data. We also consider anionic clusters and analyze the both the neutral and anionic clusters (ZrO2)n. This calculation results are useful for studies on nanometer-sized photocatalysts.

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92 HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1059.2018-0033 Natural Sciences 2018, Volume 63, Issue 6, pp. 92-99 This paper is available online at A STUDY OF THE (ZrO2)n (n = 1 ÷ 11) CLUSTERS BY DENSITY FUNCTIONAL THEORY Nguyen Minh Thuy and Nguyen Phuong Lien Faculty of Physics, Hanoi National University of Education Abstract. To reveal the origin of the (ZrO2)n (n = 1 ÷ 11) cluster stability and to study the structural trends in the zirconium oxide neutral cluster distribution, (ZrO2)n clusters have been constructed and calculated employing Density Functional Theory (DFT). In this work, we calculate the formation energy, electronic structures, stabilities and Raman spectra for varying isomers of (ZrO2)n clusters. The total binding energy of the cluster (ZrO2)n indicates that energies of stabilization does not decrease monotonically with increasing size and the energies change very slow from n = 5. The results of the calculated Raman spectra of the clusters (ZrO2)n were compared with the experimental data. We also consider anionic clusters and analyze the both the neutral and anionic clusters (ZrO2)n. This calculation results are useful for studies on nanometer-sized photocatalysts. Keywords: Zirconium, clusters, absorption, Raman frequency, Density functional theory. 1. Introduction Zirconium ZrO2 is an important ceramic materials with high melting point, low thermal conduction and high ionic conductivity, so that ZrO2 possesses excellent thermal, dielectric, mechanical, chemical and biocompatibility properties [1, 2]. Zirconium is also a useful catalysis or an important support material for catalysis, having acidic and alkaline properties. The zirconium nanoparticles will be widely applied in high-performance structural engineering ceramics and catalyst industry. The lack of understanding on the electronic structure and catalytic activity of metal oxides particles and surfaces is still under debate. Many studies have been carried out on zirconium oxide clusters to correlate their properties with those of the bulk. For efficient and cost effective applications of nanomaterials based on ZrO2, their structural and physical properties are required at molecular and atomic scale. Due to complexity and very high cost of equipment, only limited experiments have been conducted to characterize required properties at nanoscale. This led to computational modeling and simulation of various structures and properties of ZrO2 based on atomistic and continuum approaches [3]. A study of small metal oxide cluster reactivity as a function of cluster size can help us to find which role played by each of these properties in cluster activity. In all applications, surface properties are of major importance [3]. Received July 25, 2018. Revised August 6, 2018. Accepted August 14, 2017. Contact Nguyen Minh Thuy, e-mail address: thuynm@hnue.edu.vn A study of the (ZrO2)n (n = 1 ÷ 11) clusters by density functional theory 93 In this work the structures, stabilities and properties of small zirconium oxide clusters (ZrO2)n (n = 1÷11) are studied by density functional theory calculations. We calculate the formation energy, electronic structures and stabilities for varying configuration of (ZrO2)n (n = 1÷11) clusters. By comparing with experimental investigation, a theoretical analysis by computer simulation is expected to clarify varies effects in detail [4, 5]. With this aim, DFT semi-core pseudopotentials (DSPP) method within the framework of density functional theory (DFT) [6, 7] has been adopted in this work. We calculate the Raman modes of the zirconium oxide clusters (ZrO2)n (n = 1÷11) and their anions. The calculation results have been compared with the experimental and other calculated results. 2. Content 2.1. Computational methodology The structures and stabilities of (ZrO2)n (n = 1÷11) clusters are calculated using DFT. Geometry optimizations with full relaxation of all coordinates are done for these clusters in attempt to find the global minimum on the cluster potential hypersurface of each cluster size. Calculations of total energy and electronic structure were carried out using the DMOL3 package within the framework of DFT. The Perdew – Burke – Ernzerhof (PBE) parameterization of the generalized gradient approximation (GGA) [5] was adopted for the exchange-correlation potential. The atomic orbital was specified by double numerical plus polarization (DNP) and the core electrons were described by DFT semi-core pseudopotentials (DSPP). The Zirconium 4s, 4p, 4d, 5s and 5p; the Oxygen 2s, 2p and 3d electrons were treated as part of the valence states. Cut off element values for the Zr and O were chosen for fine calculation and were assumed equal for both, is 10.2 Å. The self- consistent field (SCF) convergence criterion is set to 1 × 10-6 Ha for the total energy. A 0.005 Ha/Å smearing was applied to the system to facilitate convergence of the electronic structure. The point symmetry group of the resulting clusters is determined with the tolerance of 0.001 Å. Total density of state (DOS) and projected DOS (PDOS), adsorption energy, charge transfer, Raman modes calculations was performed. 2.2. Results and discussion 2.2.1. Stability of the (ZrO2)n clusters (n = 1÷11) There are many stable isomers corresponding to different local minima (LM) on the cluster potential hypersurface for each cluster size [8]. The most stable isomers (the global minima (GM) on the cluster potential surface) are found from a number of different optimized configurations. We have considered many different structures for each cluster size. We built 2, 4, 12 different configurations for n = 1, 2, 3 respectively. For the n > 3, the DFT energy calculation predicted that the lowest energy configuration is the boomerang arrangement or close - rigid ion model [9]. Many of the local minima found for the larger size clusters (n > 4) can be constructed from smaller local minima clusters and they are in a good agreement with report [9]. The most stable configurations of the neutral (ZrO2)n clusters are shown in Figure 1. In order to quantify the relative stabilities of these clusters, we have calculated the average total binding energies Eb(n) for the most stable (ZrO2)n configurations for cluster size n = 1÷11. Figure 2 shows the binding energy per ZrO2 unit as a function of n. Eb(n) is a measure of average energy per ZrO2 unit and indicates the stability of a particular cluster in terms of the (ZrO 2)n. Nguyen Minh Thuy and Nguyen Phuong Lien 94 All clusters (n > 1) have positive Eb and are stable with respect to a single ZrO2 unit. Eb(n) approaches that of the bulk phase structure while the cluster size increases. The Eb(n) is defined by        22 n n b nE Zr nE O E Zr O E n n    where E (Zr) = -1938,145 eV, E(O) = -2040.678 eV are the energies of a Zr and O atom, respectively (when they were as separate atoms and not bonding to other atoms). The energies of the GM clusters are shown from figure 2 as a function of cluster size n. Figure 1. The most stable configurations of the neutral (ZrO2)n clusters for n = 1÷11. Light blue and red indicate zirconium (Zr) and oxygen (O) atoms, respectively Table 1. The binding energy per ZrO2 unit of the neutral (ZrO2)n clusters Cluster size n Eb(n)(eV) 1 17.78 2 19.80 3 20.64 4 21.10 5 21.60 6 21.84 7 22.03 8 22.30 9 22.48 10 22.53 11 22.53 1 2 3 4 5 6 7 8 9 10 11 A study of the (ZrO2)n (n = 1 ÷ 11) clusters by density functional theory 95 Figure 2.The binding energy per ZrO2 unit of the neutral (ZrO2)n clusters The average total binding energies Eb(n) for the most stable form in each cluster size does not rise monotonically as the cluster increases in size. There is a slight increase in these energies from n = 5. As can be seen from this graph, the binding energy differences between clusters of a larger size tend to be smaller. 2.2.2. Properties of the neutral and anionic (ZrO2)n clusters for n = 8 Considering the different geometry configurations of the (ZrO2)n clusters can clarify the structures and growth modes of the large size clusters, what related to the final bulk phase structure ZrO2. As shown in Figure 2, the larger size (ZrO2)n clusters (n > 8) have only a slight increase of the average binding energies, so we choose (ZrO2)8 clusters for the more detail configuration research. Figure 3. The relaxed configurations of the neutral (ZrO2)8 clusters and labeled 8x X, where X indicate its symmetry point group and x are the isomers of neutral (ZrO2)8 clusters 8a C 1 8b C 1 8c C i 8d C 1 8e C 1 8f C 1 8g C 1 8h D2d Nguyen Minh Thuy and Nguyen Phuong Lien 96 We have built 12 different (ZrO2)8 typical cluster structures and charged them with -1 (e). After geometry optimizing, these neutral (ZrO2)8 clusters configurations are divided into typical two groups. Group I consists of fourconfigurations (8a, 8b, 8c, 8d) in which there are one or two terminal O atoms. The 8b and 8d structure each have one terminal O atom. The 8a and 8c structure each have two terminal O atoms binding to inverse Zr atoms in opposite corners. In these structures, there are some three – fold coordinated O atoms and almost all of Zr atoms have four - foldcoordination. Group II includesfourconfigurations (8e, 8f, 8g, 8h) in which all structures have no terminal O atom. All optimized configurations of (ZrO2)8 cluster are shown in Figure 3. Anion configurations are structurally similar to neutral configurations and differences are not much. The point symmetry group of the relaxed clusters is determined with the tolerance of 0.001Å. The symmetry group of neutral (ZrO2)8 clusters was predicted to be C1 for the 8a, 8b, 8d, 8e, 8f, 8g structures, Ci for the 8c structure, and D2d for the 8h structure. * Density-of-state (DOS) calculation Figures 4 and 5 show the DOS for the neutral and their anionic (ZrO2)8 clusters. In the anionic (ZrO2)8, the extra electron enters the predominantly Zr – 4d state based on LUMO of neutral (ZrO2)8, which should evolve into the conduction band of the bulk. The HOMO of the neutral (ZrO2)8 clusters derives primarily from O – 2p state and should evolve into the bulk valence band. At higher energy from 0 eV there is a relatively board band of O - 2p state that are hybridized with Zr - 4d state. There is a clear peak in the O - 2p state ranging from -0.5 to 5eV is seen for the group I clusters, reflecting the local environment of terminal O atoms in configurations of the group I. These terminal O atoms can be related to some states in the gap, which are likely to affect the photocatalytic properties of ZrO2 clusters. Figure 4. Total density-of-states (DOS) for neutral (ZrO2)8 clusters corresponding group I configurations (8a, 8b) and group II configurations (8e, 8f) A study of the (ZrO2)n (n = 1 ÷ 11) clusters by density functional theory 97 Figure 5 shows that the DOS of anionic (ZrO2)8 clusters tend to shift to lower energy, however the DOS structures for the neutral and anionic (ZrO2)8 clusters do not change significantly. Figure 5. Total density-of-states (DOS) for the structure 8a corresponding to the neutral (left) and anionic (right) (ZrO2)8 clusters * HOMO-LUMO energy Energy difference between HOMO and LUMO orbital is called as energy gap (Eg) which is an important stability for structures. Thus, we have calculated the HOMO (EHUMO), LUMO (ELUMO) energies, and the energy gap Eg (=EHUMO - ELUMO), of all clusters in order to elucidate the electronic properties. In general, there is a direct relation between the stability and Eg of the clusters, and a larger Eg implies a higher stability of a particular system. Table 2 shows the calculated HOMO and LUMO energies of the neutral and the anionic (ZrO2)n cluster, in eV unit. Table 2. Calculated HOMO and LUMO energies of the neutral and the anionic (ZrO2)n cluster (EHUMO, ELUMO, (EHUMO - ELUMO) = Eg, eV) Structure Neutral clusters Anionic clusters EHOMO ELUMO Eg EHOMO ELUMO Eg 8a -5.927 -3.291 2.636 -1.312 -0.624 0.688 8b -5.884 -3.309 2.575 -2.786 -0.852 1.934 8c -5.927 -3.291 2.636 -3.222 -0.618 2.604 8d -5.603 -3.109 2.494 -2.623 -0.493 2.130 8e -6.384 -3.046 3.338 -3.09 -0.272 2.818 8f -6.373 -3.033 3.340 -3.089 -0.298 2.791 8g -6.449 -3.845 2.604 -3.096 -0.931 2.165 8h -6.359 -2.985 3.374 -2.914 -0.474 2.440 The result from Table 2 shows that the calculated Eg values range from the visible (2.494 eV) to ultraviolet region (3.374 eV). The calculated Eg of the n = 8 cluster is smaller than the Eg of the calculated bulk monoclinic, cubic and tetragonal ZrO2 phases (3.5 to 4.7 eV) [10]. This trend could lead to design of suitable materials for photocatalytic applications of ZrO2 clusters. Nguyen Minh Thuy and Nguyen Phuong Lien 98 * Vibrational properties We have initially calculated Raman spectra for neutral (ZrO2)n clusters. All calculations use the same condition with room temperature (300 K) and incident light wavelength 488nm. As can be seen from Figure 6, the prominent Raman (or infrared) peaks are observed mainly in two regions. Region I has wavenumber values ranging from 0 to 250 cm -1 , which has peaks assigned to O – O bondstretching vibrations. Region II has a wavenumber values range of 400 to 900 cm-1, which has peaks assigned to Zr - O bond stretching vibrations [11]. For the group I configurations, the sharp peaks ranging from 600 to 900 cm -1 observed may correspond to terminal O (the Zr-O vibration [12]). Figure 6. The calculated Raman spectra for the neutral (ZrO2)8 clusters At present, there is no direct method for measuring the structure and properties of small clusters by experimental study. The author of [12] investigated infrared spectra of zirconia nanoparticles prepared by the precipitation method and compared the experiment result with theoretical IR spectra. Cubic zirconia has only one IR active peak at 480 cm -1 , the IF spectra at a low region between cubic and tetragonal zirconia are very close. The peaks of 500 - 600 cm -1 for the cubic-like clusters (8g, 8h configurations in Figure 2) could be ascribed to the characteristic vibration mode of cubic zirconia. Vibration frequencies between 600 - 700 cm -1 were assigned to Zr-O vibrations in the Zr-O-Zr-O ring [12]. 3. Conclusion We have studied the stability, structural, electronic properties of the neutral and anionic (ZrO2)n clusters, where n = 1÷11 by using DFT. We have observed that the structure and the size of the clusters have main effects on the stability, electronic and other properties of these clusters structures. The stability of the clusters increases as the cluster size grows. The initial calculations of Raman spectra show the influence of terminal O atoms to the peaks of the Raman spectra. The calculated HOMO - LUMO energy gap Eg values range from the visible to ultraviolet regions. This property could lead to design of suitable materials for photocatalytic applications of ZrO2 clusters. A study of the (ZrO2)n (n = 1 ÷ 11) clusters by density functional theory 99 Acknowledgements. This work was supported by the Vietnamese National Foundation for Science and Technology Development (NAFOSTED) under Grant N 103.02-2017.328. A part of this work was performed at the Environment Physics Project’s Laboratory at the General Physics Division of the Department of Physics, Hanoi National University of Education. REFERENCES [1] R.G. Luthardt, M. Holzhüter et al.. 2002. Reliability and Properties of Ground Y-TZP- Zirconia Ceramics. Dent Res., 81(7), pp. 487-491. [2] B.M. Weckhuysen and D.E. Keller. 2003. 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