Structural and Electronic Properties of Neutral and Ionic (Ga2O3) n

Article pubs.acs.org/JPCC

Structural and Electronic Properties of Neutral and Ionic (Ga2O3)n Clusters with n = 1−10 Amol B. Rahane†,‡ and Mrinalini D. Deshpande*,† †

Department of Physics, HPT Arts and RYK Science College, Nasik, Maharashtra 422 005, India Department of Physics, University of Pune, Pune, Maharashtra 411 007, India

‡

ABSTRACT: The structural and electronic properties of the (Ga2O3)n clusters (n = 1−10) have been studied within the framework of density functional theory. The (Ga2O3)n clusters show the preference for 4-membered (Ga2O2) and 6membered (Ga3O3) rings. For n = 4, the lowest energy configuration appears to be derived from the bulk corundum (α-Ga2O3) configuration. For larger clusters (n = 5−10), the structures evolve around the corundum fragment and are more symmetric with layered configuration. There are 3-, 4-, and 5fold coordinated Ga atoms and 2-, 3-, and 4-fold coordinated oxygen atoms. The (Ga2O3)n structures have similarity to that of the α-Ga2O3 phase, and the average coordination of Ga and oxygen atoms in clusters are lower than the values in the α-Ga2O3. The ionization-induced distortions in the lowest-energy configuration of the respective neutral clusters are small. The isomers with cage configurations lie higher in energy compared with the layered lowest energy structures we have obtained. A sequential addition of a Ga2O3 unit to the (Ga2O3)n cluster initially increases the binding energy, though values of the HOMO−LUMO gap, ionization potential, and electron affinity do not show any systematic variation in these clusters. The bonding characteristics for these clusters is studied using Bader charge analysis and by the electron localization function. With the increase in cluster size, the charge transfer from Ga atoms to oxygen increases toward the value in bulk. The stability of the cluster is dominated by ionic Ga−O interactions with some covalent character between Ga-sp and O-p orbitals.

1. INTRODUCTION Gallium oxide (Ga2O3) is an important wide-band gap semiconductor (4.8 eV) having a wide range of applications from semiconductor lasers and switching memories to hightemperature gas sensors.1−4 In the view of the technological applications of Ga2O3 low-dimensional nanostructures, the studies on Ga2O3 atomic clusters have also been revived.5−9 βGa2O3 has also attracted recent interest as a phosphor host material for applications in thin film, electroluminescent displays.10,11 Because of its chemical and thermal stability, βGa2O3 may emerge as a useful alternative to sulfide based phosphors.12 Gallium oxide can exist in several forms, including α, β, γ, δ, and η.13 Among these polymorphs, β-Ga2O3 with a monoclinic structure is the only thermodynamically stable phase, while the others are metastable, and η-Ga2O3 exhibits the lowest symmetry.13−16 The other metastable states can be prepared, and they have been characterized at ambient pressure and temperature. It is observed to undergo a transition to the hexagonal α-Ga2O3 phase at 4.4 GPa, 1000 °C.15 After quenching to room temperature and pressure, α-Ga2O3 remains in a metastable phase. These different forms of Ga2O3 have different electronic properties. For example, the band gap of the α-Ga2O3, which is isostructural with corundum (α-Al2O3), is 4.98 eV, larger than that of β-Ga2O3.17 β-Ga2O3 emits a wide range of wavelengths from infrared to ultraviolet (UV).4,18,19 In terms of photocatalytic activity, gallium oxide has been shown © 2011 American Chemical Society

to have higher performance than the widely used TiO2 catalyst.20 The nanostructures of Ga2O3 are also found to be in α phase.17 In the form of low-dimensional nanostructures, gallium oxide shows a very high surface to volume ratio, which increases gas-sensing reaction time, while reducing the power requirements associated with heating sensors. These attributes provide advantages to nanostructures over thin films for the gas sensing applications. Small clusters of gallium oxide provide the prototype model to understand the physics and chemistry of formed nanostructures. A few experimental and theoretical studies have been reported on gallium oxide at the cluster level.6−9 Recently, we initiated a systematic study of evolution of the physical and chemical properties of small gallium oxide clusters using density functional theory (DFT) to determine their convergence to the corresponding bulk values. Our initial study on GamOn (m,n = 1,3) clusters reported their structural, vibrational, and electronic properties.6,7 The results of a experimental study by Meloni et al.8 find a very good agreement with the calculated adiabatic electron affinity value for GaO monomer and the Ga−O bond distances in neutral and anionic GaO2. We have also considered both metal-excess Received: October 4, 2011 Revised: December 8, 2011 Published: December 29, 2011 2691

dx.doi.org/10.1021/jp209552a | J. Phys. Chem. C 2012, 116, 2691−2701

The Journal of Physical Chemistry C

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Figure 1. Equilibrium geometries of the (Ga2O3)n, (n = 1−5) clusters with their point group symmetry. The energy of an isomer is given with respect to the energy (taken to be zero) of the lowest energy isomer for a given size. Pink spheres represent Ga atoms, and red spheres represent O atoms.

in the range of n = 1−10. This study will provide a proper support for understanding the nanostructures of gallium oxide as well as in the development of optoelectronic devices. The organization of the paper is as follows: section 2 deals with the computational method used in this work. The results are presented and discussed in section 3. Finally, we present our conclusions in section 4.

and oxygen-excess fragments to investigate the effect of the oxygen/metal ratio on their structural and electronic properties. For Ga2O3, the results of our earlier studies7 using DFT-B3LYP indicate that kite-shaped (C2v) structure is a lowest energy configuration. However, the results at the DFT-B3LYP/MP2/ CCSD(T) levels using flexible one particle basis sets showed that the ground state geometry of Ga2O3− is kite-shaped, while the neutral Ga2O3 prefers the V-shaped geometry.21−23 Our investigations for stoichiometric GanOn reported9 that the structural motif of these small clusters appears to be a rhombus or hexagonal rings with alternate gallium and oxygen atoms. The stability analysis indicates that the larger clusters of GanOn may not be thermodynamically stable. Overall the gallium oxide clusters considered are dominated by ionic metal−oxygen bonds. The ionization induced changes in the structural parameters to be small. However, ordering of the isomeric configuration significantly changes upon the addition of an electron. The present study extends the calculations to the (Ga2O3)n clusters, with n = 1−10 using the density functional theory with plane wave pseudopotential approach. Our aim is to understand the evolution of structural and electronic properties of clusters with the stoichiometry of the bulk Ga2O3 and to determine their convergence to the corresponding bulk values. We report here the results on the equilibrium structure, stability, bonding, electron affinity, and ionization potential of (Ga2O3)n clusters

2. COMPUTATIONAL DETAILS Electronic structure calculations have been performed on neutral and ionic gallium oxide clusters, (Ga2O3)n, with n = 1− 10 using the Vienna ab Initio Simulation Package (VASP)24,25 code. We have performed the first principles spin polarized calculations using the density functional theory. The generalized gradient approximation (GGA) given by Perdew−Bruke− Ernzerhof26 and the projector augmented wave (PAW) method27,28 were used. The computational parameters were taken from our previous studies on GanOn clusters.9 The clusters considered were placed in a cubic supercell with an edge of 24 Å. The cutoff energy for the plane wave was set to 282.8 eV. The calculations were considered to be converged when the force on each ion was less than 0.001 eV/Å, with a convergence in the total energy of about 10−5 eV. Several initial planar and nonplanar diverse configurations of neutral and ionic clusters were considered for these calculations. The choice of the initial geometries was partially dependent upon the 2692



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Figure 2. Equilibrium geometries of the (Ga2O3)n, (n = 6−10) clusters with their point group symmetry. Other details are the same as those in Figure 1.

previous studies of clusters of aluminum oxide,22,29−32 indium oxide,33 and gallium oxide.9,22,34 The stability of the cluster is further verified by performing the calculations with singlet (doublet) or higher spin states depending on an even (odd) number of valence electrons in the cluster. On the basis of our earlier experience, Ga-3d orbitals are included in the core part of the Ga pseudopotential in the subsequent calculations. For comparison, we have also performed the calculations on bulk β- and α-Ga2O3 phases using VASP by keeping the same exchange-correlation functional and energy cutoff as for cluster calculations. For β-Ga2O3 the supercell consisted of two Ga2O3 units, and for α-Ga2O3, the supercell consisted of six Ga2O3 units. We use a 6 × 6 × 6 Monkhorst−Pack35 k-point sampling for Brilluion zone integrations. The calculated lattice parameters within GGA-PBE for β-Ga2O3, a = 12.35 Å, b = 3.07 Å, c = 5.87 Å, and β = 103.7° are consistent with the experimental values14 a = 12.27 Å, b = 3.03 Å, c = 5.80 Å, and β = 103.7°. For α-Ga2O3, the calculated lattice parameters, a = 5.07 Å and c = 13.66 Å agree well with the experimental values15 of a = 4.98 Å and c = 13.43 Å. Our results are also in agreement with previous theoretical calculations by He et al.36 For β-Ga2O3, the Ga atoms have a tetrahedral and octahedral coordination in the lattice, while for α-Ga2O3, gallium ions occupy the octahedral sites. The calculated cohesive energy for β-Ga2O3 and α-Ga2O3 per atom is 5.02 and 4.99 eV, respectively.

3. RESULTS AND DISCUSSION The lowest energy structures along with some low-lying configurations of (Ga2O3)n, (n = 1−10) clusters with their symmetry group are shown in Figures 1 and 2. In this size range (n = 1−10), we find the competition between two structural motifs: the Ga2O2 planar rhombus and the planar or chairlike hexagonal Ga3O3 units. With the increase in cluster size, hollow globular structures were formed by the stacking of fourmembered (Ga2O2) rings. The stability of different isomers of a cluster with a given size depends upon the number of 4- and 6membered rings and their distribution. Such 4- and 6membered rings are also found in nanoparticles of Al2O3, In2O3, GaN, and other compounds in which the metal−oxygen interactions are strongly ionic. The lowest energy configuration of Ga2O3 is a V-shaped configuration (1a in Figure 1). Our result is consistent with previous calculations.21−23 As noted earlier, the DFT-B3LYP/ Gaussian98 calculations predict the ground state to be a kiteshaped configuration. The Ga−O bond-distances for V-shaped configuration are 1.79 Å and 1.67 Å. The Ga−O−Ga bond angle in this configuration is 129.35°. The linear configuration with alternate Ga and O atoms (ΔE = 0.1 eV) and kite structure (ΔE = 0.11 eV) are nearly degenerate isomers with the V-shaped structure. The energy difference between singlet and triplet states of kite configuration is 0.02 eV. The Y-shaped and 3D configurations are well above the V-shaped configuration (ΔE = 1.09 and 1.36 eV, respectively). On the 2693



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Figure 3. Schematic representation of open cage and cage dimer configurations for (Ga2O3)n, (n = 1 − 10) clusters. ΔE represents the energy difference w.r.t. the lowest energy configuration of the respective cluster. Other details are the same as those in Figure 1.

basis of earlier reports,7,23 we have calculated the ionization potential and electron affinity for V- and kite-shaped configurations. The calculated values of the ionization potential (8.52 eV) and electron affinity (4.41 eV) for kite configuration also compare favorably with the reported values. The strong preference for gallium−oxygen alternate bonds together with 3D structure is predicted for (Ga2O3)2. The (Ga2O3)2 prefers a capped windowpane configuration with C2h symmetry. The structure consists of five interconnected 4membered (Ga2O2) rings. The minimum Ga−O bond distance increases from 1.67 to 1.86 Å as compared to the V-shaped, Ga2O3 configuration. The O−Ga−O bond angles for the 3-fold coordinated Ga atoms are 92.84°, and for 4-fold coordinated Ga atoms, they are in the range of 86.08−88.75°. The open cage fullerene configuration with Td symmetry (2b) is 0.43 eV higher in energy than the capped windowpane configuration (2a). In this configuration, four 3-fold coordinated Ga atoms form a tetrahedron, and six 2-fold coordinated O atoms cap its edges. Four units of 6-membered (Ga3O3) rings are observed in this configuration. The O−Ga−O bond angles in the open cage configuration are in the range of 114.83−115.25°. The presence of four hexagons overall decreases the Ga−O interactions, which lowers the stability of the cage configuration. The smaller O−Ga−O angle with a 4-fold coordinated Ga atom in windowpane configuration (2a) appears to facilitate the stronger hybridization of molecular orbitals of the gallium and oxygen atom. In the case of (Al2O3)2, the open cage configuration (Td) is the lowest energy structure, while the

capped windowpane configuration is one of the low-lying configurations.29 The (Ga2O3)3 is a cage-like configuration with Cs symmetry. The addition of a Ga2O3 unit to the (Ga2O3)2 structure distorts the capped windowpane configuration significantly. The added Ga2O3 unit prefers to attach with 3-fold coordinated Ga atoms. We find four planar rhombus and four chairlike hexagonal units in the lowest energy configuration. The minimum Ga−O bond distance is 1.80 Å. The two layered prism configuration (3d in Figure 1) is 0.99 eV higher in energy than the lowest energy structure. In this configuration, all Ga atoms are 3-fold coordinated, and oxygen atoms are 2-fold coordinated. The hollow globular structure (D3d) with six 4-membered (rhombus) and six 6-membered (hexagon) rings consisting of alternating Ga and O atoms is characterized for (Ga2O3)4. This configuration (4a) appears to be derived from the bulk corundum (α-Ga2O3) structure.13 There are six 4-fold and two 3-fold coordinated Ga atoms as well as six 2-fold and six 3fold coordinated O atoms. In this configuration, the O−Ga−O bond angles corresponding to the 3-fold coordinated Ga atoms are around 115.15°, while for 4-fold coordinated Ga atoms ranges from 83.74−162.77°. For 4-fold coordinated Ga atoms, the Ga−O bond distances are in the range of 1.87−2.02 Å, and for 3-fold coordinated Ga atoms, the Ga−O bond distances are 1.82 Å. Note that in the bulk β-Ga2O3, 50% of the Ga atoms are tetrahedrally (4-fold) coordinated, while the remaining 50% of Ga atoms have octahedral (6-fold) coordination. In the bulk αGa2O3 corundum phase, all the Ga atoms are octahedrally coordinated. From our bulk calculations, in β-Ga2O3, for 2694



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and eight 6-membered rings. There are four Ga atoms with 5fold coordination and twelve Ga atoms with 4-fold coordination. The maximum coordination of oxygen atoms is four, similar to that of the bulk corundum structure. For (Ga2O3)9, the lowest energy isomer (9a) has D2d symmetry with two Tshaped units attached to the pyramidal structure of (Ga2O3)8. There are four Ga atoms with 5-fold coordination, twelve Ga atoms with 4-fold coordination, and two Ga atoms with 3-fold coordination. The low-lying configurations with large membered rings (8- and 10-membered) lie higher in energy (more than 1 eV) than the lowest energy structure. For n = 10, a pyramidal structure of (Ga2O3)8 with four T-shaped units (Cs) has the lowest energy (10a). In all, there are three 3-fold coordinated, sixteen 4-fold coordinated, and one 5-fold coordinated Ga atoms. The Ga−O bond distances are in the range of 1.78 to 2.08 Å. A four layered pyramidal cage configuration (10b) with C1 symmetry is nearly degenerate to the lowest energy structure. Overall, for gallium oxide clusters with bulk stoichiometry (Ga2O3)n, in the size range of n = 6−10, we find the strong competition between two structural motifs: the rhombus (Ga2O2) and the planar or chairlike hexagonal (Ga3O3) units. With these two building blocks, the hollow globular configurations that were evolved with a large number of rhombus units may be related with a progression toward the bulk-like behavior. With an increase in cluster size open configurations, with 8- and 10-membered rings, are less preferred over the closed ones. With the presence of a large membered ring, the average coordination of atoms decreases. The lowest energy configurations of clusters with n ≥ 5 prefer the structures that evolve from the corundum fragment configuration (4a) of n = 4. With the increase in cluster size, in the lowest energy configurations, the maximum coordination of Ga atoms increases to five. The tetrahedral arrangement is evidently seen in this size range. Overall, the maximum coordination number of the Ga atom in these clusters is still lower than the bulk phases. The maximum coordination number of O atom is four. All the lowest energy configurations of these clusters in this size range prefer the lowest spin state. From our previous calculations,9 it is observed that the (Ga2O3)n clusters prefer the 3D configurations form n = 2, whereas (GaO)n are planar configurations up to n = 6. The rhombus as well as hexagons are found to be the building blocks for both the series. The higher coordination of Ga and O atoms in (Ga2O3)n clusters enhances the stability as compared to that of (GaO)n clusters. It is observed that the geometries of small gallium oxide clusters are nearly similar to those of aluminum clusters. Sun et al.30 studied the cage and cage dimer configurations for alumina clusters. On the basis of these calculations, we have also considered the cage and cage dimer configurations for (Ga2O3)n clusters in the size range of n = 6−10. It is found that for (Ga2O3)n, the structures with cage fullerenes and cage dimers (combination of small cage fullerenes) are at higher energy than the compact lowest energy configurations obtained in our study. In Figure 3, we have shown the energy difference between the lowest energy configuration and the cage fullerene or cage dimer configuration for a particular n. However, it is found that the cage dimers are favored over the cage fullerene configurations. Also, the energy differences between the lowest energy configuration and the open cage and cage dimer configurations increases with the cluster size. For n = 10, the cages with D3h and Ih symmetry lie higher in energy as

tetrahedral coordinated Ga atoms, the Ga−O bond distances are in the range of 1.87−1.90 Å, and for octahedral coordinated Ga atoms, it is in the range of 1.97−2.03 Å. In the α-Ga2O3 phase for octahedrally coordinated Ga atoms, the Ga−O distances are 1.97 Å and 2.09 Å. The shortening of the bond distances is normally expected with a reduction in the coordination in these clusters. A lower-symmetric configuration (C1) consists of three 4-membered, four 6-membered, and three 8-membered Ga−O rings, which is higher in energy (ΔE = 0.58 eV) than the corundum configuration. Three Ga atoms have 4-fold coordination, while five Ga atoms have 3-fold coordination with oxygen atoms. The minimum Ga−O bond length is 1.80 Å. The O−Ga−O bond angles corresponding to the 3-fold coordinated Ga atoms varies from 92.02−152.72°, while for 4-fold coordinated Ga atoms, they are in the range of 87.0−141.68°. The presence of two 8-membered rings decreases the overall coordination of this configuration. A similar configuration has been obtained as a lowest energy configuration for (Al2O3)4,29 while earlier theoretical study33 has explored the corundum configuration as a lowest energy configuration for (In2O3)4. The lowest energy configuration of (Ga2O3)5 can be viewed as a distorted corundum configuration with a V-shaped Ga2O3 unit. There are six 4-membered, seven 6-membered, and one 8membered rings in this configuration. The minimum bond distance in this configuration is 1.78 Å. The cage dimer configuration (ΔE = 2.16 eV) and cage fullerene configuration (ΔE = 3.1 eV) lies higher in energy than the ground state structure (Figure 3). Recently, Woodley et al.22 investigated the structural and electronic properties of small (X2O3)n, (X = Al, Ga, In) clusters in the range of n = 1−5. Our results of the lowest energy configurations for (Ga2O3)n structures in this size range are consistent with the reported results. The trend of distortion and stacking of 4-membered rings from the corundum configuration continues up to n = 10. In this size range, with the addition of Ga2O3 unit, the clusters evolve around the corundum fragment (4a). Further addition of a Ga2O3 unit to Ga10O15 distorts the cluster significantly. For n = 6, the added Ga2O3 unit prefers to attach to the 3-fold coordinated Ga atom, and it forms a second layer of Ga2O2 units over the perimetric ring of the cluster (6a in Figure 2). The maximum coordination of Ga atoms is 4, while for O atoms, it is 3. The lowest energy isomer of (Ga2O3)7 is bilayered with Cs symmetry. The stacking of Ga2O2 rings facilitates an increase in the coordination number of Ga and O atoms with three Ga atoms 5-fold coordinated, ten Ga atoms 4fold coordinated, and one Ga atom 3-fold coordinated. The O atoms are 2-, 3-, and 4-fold coordinated. The Ga−O bond distances within a layer are 1.86−2.03 Å, and between the two layers, 1.95−2.01 Å. It consist with thirteen 4-membered and fourteen 6-membered rings. As noted earlier, for tetrahedrally coordinated Ga atoms in β-Ga2O3, the Ga−O distances are in the range of 1.87−1.90 Å. The next low-lying configuration (ΔE = 0.82 eV) consists with nineteen 4-membered, nine 6membered rings, and one 8-membered ring (7b). A bilayered configuration (7e) with twelve 4-membered and nine 6membered rings lies higher in energy (ΔE = 1.32 eV). In this configuration, one of the Ga atoms is 6-fold coordinated. Note that the maximum coordination number for Ga atoms in αGa2O3 is 6 and that of oxygen is 4. The lowest energy configuration for (Ga2O3)8 is a three layered pyramidal cage structure with D2d symmetry. Two oxygen atoms are inside the pyramidal cage structure. It consists of twenty-two 4-membered 2695



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where E is the total energy of the system. The binding energy per atom (in eV) for (Ga2O3)n neutral and ionic clusters against the number of atoms is shown in Figure 4. The variation of the average number of the nearest

compared to that of the layered lowest energy configuration (ΔE = 9.67 and 11.72 eV, respectively). It is found that in the open cage fullerene configuration, all the Ga atoms are 3-fold coordinated, and oxygen atoms are 2-fold coordinated. The Ga−O bond lengths are in the range 1.79−1.84 Å, and O−Ga− O bond angles are in the range 118.0−121.9°, while in the cage dimer, the average coordination number for all Ga atoms is around 3.5. The Ga−O bond-lengths corresponding to the 4fold coordinated Ga atoms are in the ranges 1.84−1.99 Å, and corresponding O−Ga−O bond angles are in the range 82.5− 173.6°. The analysis clearly shows that cage fullerene and cage dimer configurations are not favorable in gallium oxide clusters due to the decrease in overall coordination of Ga and O atoms lowering the stability of these open structures. For alumina clusters, also the cage fullerene and cage dimer configurations are not favorable.29 From our previous studies,7,9 it is observed that in small gallium oxide clusters, the ionization induced changes in the structural parameters to be small. However, ordering of the isomeric configuration significantly changes upon the addition of an electron. To study ionization induced changes in structural and electronic properties, we also considered the lowest and some of the low-lying configurations of (Ga2O3)n clusters. It is found that in ionic clusters, the addition or the removal of an electron to the neutral cluster does not induce significant changes in most of the isomers analyzed in this work. The configurational symmetry of the anionic as well as cationic lowest energy structure remains similar to that of the neutral cluster except for n = 1 and 2. For n = 1, the kite-shaped configuration (1c) appears as the lowest energy for both the cationic and anionic Ga2O3. This configuration is well separated at 1.1 eV from the V-shaped configuration in the anionic configuration, while for the cationic case is nearly degenerate (ΔE = 0.08 eV) to the kite-shaped configuration. The results for the anionic cluster are in agreement with the previous study at the DFT-B3LYP and MP2 levels of the theory.23 The addition of the electron increases the Ga−O bond distances in the Ga2O2 ring by around 1−2% and decreases the bond distance of the terminal Ga−O by 2%. For the cationic case, the Ga−O bond distance for the terminal oxygen and Ga−O bond distances associated with the 2-fold coordinated Ga atoms decrease by 1−2%. For (Ga2O3)2 cation, the D4h configuration (2c) appears as the lowest energy. The lowest energy configuration for the neutral case (2a) having C2h symmetry is 0.3 eV higher in energy. The lowest energy configuration of the anion is similar to the neutral lowest energy configuration. The Ga−O bond distances for the neutral clusters are in the range of 1.67−2.06 Å, while that of anionic and cationic clusters are in the range of 1.72−2.09 Å and 1.70−2.05 Å, respectively. It is also found that, for the anionic clusters, the Ga−O bond lengths increase by about 2−3% with respect to the neutral cluster, while the removal of an electron decreases the Ga−O bond lengths by about 1%. The addition or removal of an electron in these clusters is shared more or less equally among the atoms in the cluster. The anionic and cationic configurations prefer the doublet spin state. The stability of these clusters can be discussed on the basis of binding energy per atom (BE) and fragmentation energy (FE). The binding energy per atom is calculated as

Figure 4. Binding energy (eV/atom) for the lowest energy isomers of neutral and ionic (Ga2O3)n clusters with n = 1−10. The calculated bulk cohesive energies (eV/atom) for α- and β-Ga2O3 phases are also shown. The inset presents the average coordination number (CN) for Ga and O atoms for the lowest energy configurations of gallium oxide clusters with n = 1−10 along with the average CN for Ga and O atoms in bulk α- and β-Ga2O3 phases are also shown.

neighbors of Ga and O atoms in the lowest energy isomers is also shown in the inset. With successive addition of Ga2O3 units, there is an increase in the BE and the average coordination of Ga and O atoms. The average coordination increases with n up to n = 4, and it remains constant up to n = 6. The average coordination number again increases at n = 7. The increase in coordination number corresponds to the formation of the layered structure. This indicates that the structures are stabilized with the coordination of four for Ga atoms and three for O atoms. As noted earlier, with the increase in size, some of the Ga atoms prefer the coordination with five oxygen atoms, and oxygen atoms are tetrahedrally coordinated. The average coordination for α-Ga2O3 is 6 for Ga atoms. We have also calculated the BE per Ga2O3 for all the clusters. For n = 10, the BE per Ga2O3 is 22.74 eV, which is lower than the calculated bulk values of the cohesive energy (25.10 eV) in βGa2O3 and (24.95 eV) α-Ga2O3. The BE curves for anionic and cationic clusters show similar nature as that of the neutral clusters. The addition of one more electron enhances the binding energy of anionic clusters, while for the cationic clusters, removal of an electron decreases the binding energy compared to that of the neutral cluster. The stability of the anionic and cationic configuration can be explained on the basis of the analysis of the molecular orbitals. When the electron is added to a neutral (Ga2O3)n cluster, it occupies the lowest unoccupied molecular orbital (LUMO), which has the bonding character. This leads to an enhancement in stability. However, the electron comes out from the lower energy bonding orbital of the neutral cluster, which makes the cationic cluster less stable as compared to the neutral one. Further, the stability of the clusters is also analyzed by calculating their fragmentation energies. The fragmentation energy is calculated as

Eb[(Ga2O3)n ]=( − E[(Ga2O3)n ] + 2nE[Ga] + 3nE[O])/(5n) 2696



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Table 1. Adiabatic and Vertical Values (eV) of the Ionization Potential and Electron Affinity for (Ga2O3)n (n = 1−10) Clusters n system

1

2

3

4

5

6

7

8

9

10

AIP VIP AEA VEA

8.64 8.81 4.29 4.70

8.12 8.52 3.76 3.99

8.25 8.40 3.59 3.96

7.83 7.85 3.69 4.92

7.95 7.84 3.80 4.16

7.60 7.66 4.19 5.05

7.24 7.36 4.29 4.54

7.21 7.33 3.87 3.91

7.11 7.25 3.85 3.88

7.24 7.43 3.81 3.98

neutral and ionic (Ga2O3)n, n = 1−10, clusters are presented in Figure 5. As expected, neutral clusters show a higher value of

ΔE FE[(Ga2O3)n ] = − E[(Ga2O3)n ]+ E[(Ga2O3)(n − 1)]+ E[(Ga2O3)] where E is the total energy of the system. The fragmentation energies for (Ga2O3)n, n = 2−10, associated with the loss of a (Ga2O3) unit are 6.08, 6.73, 6.48, 6.96, 5.01, 6.73, 5.99, 7.90, and 5.64 eV, respectively. It clearly indicates the higher stability against the loss of a Ga2O3 molecule. It is to be noted that fragmentation energies seem to have oscillatory behavior; odd n values have higher fragmentation energies as compared to even n value. In this study, we have calculated the electron affinity (EA) and the ionization potential (IP), which are presented in Table 1. Both the EAs and IPs have considerable importance in the chemisorption. Hydrogen chemisorption on the various gallium oxide polymorphs is being actively performed for various catalytic and surface chemistry applications.37,38 For electronegative adsorbates (e.g., H, OH, and CH3), the charge transfer is away from the cluster, and hence, it is the IP of the cluster that is relevant in determining bond energy. However, for electropositive adsorbates (e.g., Li, Na, and K), the charge transfer should be toward the cluster, and hence, EA is more relevant in determining the bond energy.39 We have therefore calculated the vertical and adiabatic values of EA and IP. The adiabatic electron affinity (AEA) is defined as the energy difference between the anionic and neutral clusters at their own respective optimized geometries. However, vertical electron affinity (VEA) or vertical detachment energy (VDE) is defined as the energy difference between the anionic and neutral clusters with both at the optimized geometry of the anionic cluster. The adiabatic ionization potential (AIP) is defined as the energy difference between the cationic and neutral clusters at their own respective optimized geometries. The vertical ionization potential (VIP) is defined as the energy difference between the cationic and neutral clusters with both at the optimized geometry of the neutral cluster. The vertical and adiabatic EAs and IPs are nearly the same, which indicates that there is not much topological differences between neutral and ionic configurations of (Ga2O3)n clusters. It is observed that VIP decreases and VEA increases with the addition of a Ga2O3 unit in the cluster. After n ≥ 6, the decrease in IP is very small, and the EA also starts decreasing slowly. This is consistent with the trend observed in the binding energy of these clusters. The calculated IP for n = 1 agrees well with the value predicted by Gowtham et al.7 The calculated VEA and AEA values of 4.70 and 4.29 eV, for n = 1, are in agreement with the values 4.47 and 4.34 eV, respectively, given by Archibong et al.23 with the DFT-B3LYP level of the theory. Woodley et al.22 computed the IPs and EAs for (Ga2O3)n, n = 1−5, clusters by DFT method with a local numerical orbital basis set.22 Our calculated values of IPs and EAs are higher than their reported values. The calculated highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO−LUMO) gap for

Figure 5. HOMO−LUMO gap (eV) for lowest energy configurations of neutral and ionic (Ga2O3)n clusters with n = 1−10. The experimental values of the band gaps for α- and β-Ga2O3 phases are also shown. The experimental values are taken from Sinha et al.17 The inset presents the difference between IP and EA on the basis of Koopman’s theorem.

the HOMO−LUMO gap than the anionic cluster and lower value than the cationic configuration. The HOMO−LUMO gap for the lowest energy configurations varies in the range of 1.98−2.55 eV. We have also performed the band structure calculations on the bulk α- and β-Ga2O3. The calculated band gap at Γ-point for the α- and β-Ga2O3 phases are 2.54 and 2.08 eV, respectively. For n = 10, the HOMO−LUMO gap is 2.43 eV, which is approaching toward the bulk value. Note that the experimental band gap17 for the bulk α-Ga2O3 is 4.98 eV, and β-Ga2O3 is 4.8 eV. The underestimation of the calculated values of the cluster HOMO−LUMO gap and the bulk band gap is due to the use of GGA.29,41 It is interesting to see that the behavior of the HOMO− LUMO gap correlates very well with the difference between the ionization potential and the electronic affinity on the basis of Koopman’s theorem. The variation of the difference between IP and EA with the cluster size is shown in the inset of the Figure 5. The nature of both the curves is similar. In bulk Ga2O3, the bonding is mainly ionic.9 In order to understand the nature of bonding in clusters, we have calculated the charge density, total density of states (DOS), and site projected DOS (PDOS) for Ga and O atoms for neutral and ionic clusters. The calculated DOS further provides explanation for the structural evolution with an increase in cluster size n. To understand the systematic evolution with the size of the cluster, we have plotted in Figure 6 the Gaussian broadened electronic spectra for the lowest energy isomers of (Ga2O3)n clusters with n = 1−10 along with bulk α- and βGa2O3 phases. For the small sized clusters, the spectra show 2697



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Figure 6. Total density of states for the lowest energy configurations for (Ga2O3)n (n = 1−10) clusters. The total density of states for the bulk α- and β-Ga2O3 phases are also shown. The Fermi level, given by dotted line, is aligned to zero.

sharp peaks, but with the increase in cluster size, the spectra become broader. The lower energy part of the spectra is dominated by the 2s orbitals of oxygen atoms. The middle part of the spectra consists of hybridized Ga-sp and O-p states. The states from the 4-fold and 5-fold coordinated Ga are more delocalized compared to states from the 3-fold coordinated Ga. The increased coordination of Ga atoms increases the degree of hybridization between Ga-sp with O-p orbitals, which results in shifting the spectra in lower energy region. The states near HOMO arise from the nonbonding 2p orbitals of 2-fold coordinated oxygen atoms. Below these states, there are nonbonding 2p states from 3-fold coordinated oxygen atoms. In the range of n = 6−10, the nature of spectra almost remain the same, which indicates that bonding in these clusters remain almost similar. This is consistent with the earlier observation that the Ga−O bond distances remain nearly the same with the

increase in cluster size. We have also shown the density of states for the bulk β-Ga2O3 and α-Ga2O3 phases. The bulk spectra shows more or less a band like structure, and the various energy bands can be easily noticed. The states near the Fermi level (valence band maximum, (VBM)) consist of the Op orbitals. The Ga-s and Ga-p orbitals shows their appearance, respectively, in the lower and middle part of the valence band along with the O-p states. The O-s states show their presence in the lower energy part of the spectra. The states in the conduction band minimum (CBM) consist mainly of the unoccupied 4s levels of the tetrahedrally coordinated Ga atoms. Because of the presence of the 4-fold coordinated Ga atoms, the spectra for the β-Ga2O3 has a more delocalized nature compared to that of the α-Ga2O3 spectra. Overall, the electronic structure of the clusters is similar to that of the 2698



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Figure 7. Total density of states (DOS) and site projected density of states (PDOS) for associated 4-fold and 3-fold coordinated Ga atoms and 3fold and 2-fold coordinated oxygen atoms for lowest energy and the open cage fullerene configurations for (Ga2O3)4. The Fermi level is aligned to zero.

orbitals decreases the degree of hybridization that results in less stability. To understand the nature of bonding in detail, we have also examined the total charge density, electron localization function (ELF),40 and molecular orbitals. From the analysis of the charge density plots, it is observed that as the coordination of the Ga atom increases, the high charge density around Ga cation distorts the electron cloud around the ion in contact with it causing the polarization. In the lowest energy configuration, the delocalized Ga-4s and Ga-4p significantly alter charge density around oxygen (delocalization of O-p states). This may facilitate the formation of additional chemical bonds (polar covalent character) and further orbital hybridization to form stable configuration. Previous theoretical studies41,42 reported that some degree of covalency is associated with Ga−O bonds in β-Ga2O3. As a representative, we have shown the charge density of (Ga2O3)4 and (Ga2O3)10 clusters in Figure 8a. The localized charge density is evidently seen around O atoms. It is also seen that the charge density associated with oxygen is polarized toward gallium atoms. The small deviation from spherical symmetry around the oxygen suggest the presence of some covalency in the cluster. These remarks are further explained by studying the ELF in these clusters. At higher values of ELF (around 90%), we find that

bulk spectra; the DOS for the (Ga2O3)10 are more closely related to the DOS for β-Ga2O3 than for α-Ga2O3. The calculated DOS and PDOS further provide an explanation for the stability of the cage or cage dimer configurations. As discussed earlier, the corundum fragment configuration consists of six 4-fold coordinated and two 3-fold coordinated Ga atoms, while the open cage configuration consists of all the 3-fold coordinated Ga atoms. In Figure 7, we have presented the DOS and PDOS for the lowest energy corundum fragment (D3d) configuration and open cage fullerene (Oh)(cubic) configuration for n = 4. The total DOS for the corundum fragment configuration shows the delocalized nature near Fermi level as compared to the open cage fullerene configuration. Figure 7 also shows the PDOS for the 4- and 3fold coordinated Ga atoms along with 3- and 2-fold coordinated oxygen atoms. From the PDOS, it is found that the 4s and 4p orbitals of the 4-fold coordinated Ga atom are more delocalized as compared to that of 3-fold coordinated Ga atom. The delocalized Ga-4sp orbitals and 2p orbitals of the 3fold coordinated oxygen atoms enhance the degree of hybridization. The 2p orbitals of 2-fold coordinated oxygen atoms are localized near the Fermi level. In the case of open cage configuration, the localized nature of Ga-4sp and O-2p 2699



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As noted earlier, the geometries of small size gallium oxide clusters are nearly similar to those of aluminum oxide clusters. A present DFT calculations find that the structures of (Ga2O3)n in the size range of n = 1−10 are nearly similar to that of (Al2O3)n clusters except for n = 1, 2, 4, and 10. Similar to that of (Ga2O3)n clusters, the lowest energy configurations of (Al2O3)n show preference for 4-membered Al2O2 and 6membered Al3O3 rings. For the Al2O3 molecule, the lowest energy configuration is kite-shaped, while Ga2O3 shows the preference for V-shaped geometry. For n = 2, (Al2O3)2 is with Td symmetry consisting of four 6-membered rings, while Ga2O3 dimer prefers a capped windowpane configuration with C2h symmetry. The structure consists of five interconnected 4membered (Ga2O2) rings. In alumina clusters, the lowest energy isomers show preference for 4- and 6-membered rings, though in some cases, 8-membered rings are also obtained, while in gallia clusters, the preference for 4-membered and chiral-shaped 6-membered rings are observed. The largest change in the configuration is found at n = 4. The (Ga2O3)4 cluster prefers the compact corundum configuration, while for alumina cluster, the corundum configuration is one of the lowlying configurations. The lowest energy configuration of (Ga2O3)4 consists of three 4-membered, four 6-membered, and three 8-membered rings. In alumina cluster, each oxygen prefers to bind with a maximum number of Al atoms with a large apex angle. The large Al−O−Al angle makes the ring Al3O3 energetically favorable over the Al2O2 unit in small sized clusters. The preference of ring configuration may help to reduce the strain caused by a large sized Al atom. With the increase in size, the electrostatic interaction between Al and O begins to dominate, making the Al2O2 unit more favorable over an Al3O3 ring. From n ≥ 5, the Ga2O3 and Al2O3 structures are nearly similar. The Al−O bond lengths are in the range of 1.68−1.97 Å, which are similar to those found in the amorphous alumina.29 The Ga−O bond lengths are in the range of 1.67−2.06 Å, smaller than that of in α- and β-Ga2O3 phases. The binding energy for (Ga2O3)n, for n = 10, is 4.55 eV/atom, which is slightly smaller than the bulk cohesive energy 5.02 eV/atom for β-Ga2O3 in our calculations with the same pseudopotentials, while for (Al2O3)10 the binding energy is 5.93 eV/atom, compared to the bulk cohesive energy of 6.45 eV/atom for α-Al2O3. This suggests that in this size range, (Ga2O3)n clusters begin approaching the bulk value earlier than the (Al2O3)n clusters. The bonding between Al2O3 and Ga2O3 is predominantly ionic. In these clusters, the charge transfer increases with higher coordination. We have compared the Bader charge transfer from metal ion to oxygen in the lowest energy configurations of Ga2O3 (V-shape) and Al2O3 (kite-shaped) molecular clusters. The charge transfer analysis shows that each one of the two bicoordinated Ga atoms in Ga2O3 gives 1.32e charge to the surrounding O atoms, while in Al2O3 the bicoordinated Al gives 1.76e, and the tricoordinated Al atom gives nearly 2.27e to the surrounding oxygen atoms. For the larger sized clusters, e.g., n = 4, the average charge transfer from the Ga atom is around 1.5e to the surrounding oxygen atom, while the average charge transfer from the Al atom to the surrounding oxygen is around 2.3e. Also, the average extra charge on the oxygen atoms in (Al2O3)4 is around 35−40% more than that in (Ga2O3)4. The more charge transfer from the Al atom to oxygen suggests that the Al−O bond is more ionic compared to the Ga−O bond. This is in accordance with expectation from the differences in the electronegativities of Ga (1.8), Al (1.5), and O (2.44).

Figure 8. (a) Isovalued surfaces of the total charge density at 1/5th of its maximum value; (b) isovalued surfaces of the electron localization function (ELF) at 0.75 of its maximum value for the lowest energy configurations for (Ga2O3)4 and (Ga2O3)10 clusters.

the electrons are localized in basins around O atoms. As the ELF value is decreased to 75% of maximum value, these basins merge into each other suggesting the presence of covalency in the cluster. In Figure 8b, we have shown the typical ELF surfaces for (Ga2O3)4 and (Ga2O3)10 clusters. For n = 4, the high degree of covalency is seen to be associated with Ga−O bonds. This is expected due to lower coordination in this cluster. As the coordination number increases, for n = 10, electrons are localized in basins around O atoms. There is no bond localization region along the maximum number of Ga−O bonds suggesting a mainly ionic bonding in large size clusters. In the neutral configurations, the Bader charges reflect the expected behavior: an increase in coordination leads to greater atomic charges. We have calculated Bader43 charges for some of the lowest and low-lying configurations of (Ga2O3)n clusters. The oxygen charges are relatively higher, indicating the ionic nature of the bonds. For, n = 4 the charge transfer from the 4fold coordinated Ga atom to the surrounding oxygen atoms is around 1.56e. Also the charge gain by the 3-fold coordinated oxygen is around 1.1e. With the increase in cluster size, the charge transfer from Ga to O increases. For n = 10, the charge transfer increases to 1.60e for 4-fold coordinated Ga and 1.66e for 5-fold coordinated Ga and charge gain by oxygen increases to 1.11e for 3-fold coordinated oxygen and 1.18e for 4-fold coordinated oxygen. For comparison, we have calculated the Bader charges for the bulk phases. In bulk α-Ga2O3, the Bader charges on all the Ga atoms are +1.70e and on all the O atoms are −1.13e. In bulk β-Ga2O3, the bader charges on the 4-fold and 6-fold coordinated Ga atoms are, respectively, +1.67e and +1.73e and, on oxygen atoms, around −1.14e. It is seen that the amount of charge transfer from Ga to O is increases with the coordination number. The amount of charge transfer from Ga to O is in the range of 1.60e−1.66e for n = 10, which is comparable to that of β-Ga2O3, but it is still lower than that of α-Ga2O3. 2700



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Walsh et al.33 have studied the structural and electronic properties of (In2O3)n clusters in the same size range using an evolutionary algorithm in the GULP package. The In2O3 clusters favor globular structures and approaching the bulk system at remarkably small cluster size. It is observed that the geometries of gallium oxide clusters are nearly similar to that of indium oxide clusters. Gallium oxide is an important semiconducting oxide with applications in the areas of optics and microelectronics. We hope that small clusters of gallium oxide considered here are reasonable models to study the reactions of dopants and for gaining qualitative insights into the behavior of dopants on different surface sites.

(7) Gowtham, S.; Deshpande, M.; Costales, A.; Pandey, R. J. Phys. Chem. B 2005, 109, 14836. (8) Meloni, G.; Seehan, S. M.; Neumark, D. M. J. Chem. Phys. 2005, 122, 074317. (9) Deshpande, M.; Kanhere, D. G.; Pandey, R. J. Phys. Chem A 2006, 110, 3814. (10) Miyata, T.; Nakatani, T.; Minami, T. J. Lumin. 2000, 87−89, 1183. (11) Xiao, T.; Kitai, A. H.; Liu, G.; Nakua, A.; Barbier, J. Appl. Phys. Lett. 1998, 72, 3356. (12) Hao, J.; Cocivera, M. J. Phys. D 2002, 35, 433. (13) Roy, R.; Hill, V. G.; Osborn, E. F. J. Am. Chem. Soc. 1952, 74, 719. (14) Geller, S. J. Chem. Phys. 1960, 33, 676. (15) Marezio, M.; Remeika, J. P. J. Chem. Phys. 1967, 46, 1862. (16) Edwards, D. F. Handbook of Optical Constants of Solids; Academic Press: New York, 1998; Vol. III. (17) Sinha, G.; Adhikary, K.; Chaudhuri, S. J. Cryst. Growth 2005, 276, 204. (18) Nogales, E.; Mendez, B.; Piqueras, J. Appl. Phys. Lett. 2005, 86, 113112. (19) Song, Y. P.; Zhang, H. Z.; Linn, C.; Zhu, Y. W.; Li, G. H.; Yang, F. H.; Yu, D. P. Phys. Rev. B 2004, 69, 075304. (20) Hou, Y.; Wu, L.; Wang, X.; Ding, Z.; Li, Z.; Fu, X. J. Catal. 2007, 250, 12. (21) Jemmis, E. D.; Giju, K. T.; Leszczynski, J. Electron. J. Theor. Chem. 1997, 2, 130. (22) Woodley, S. M. Proc. R. Soc. A 2011, 467, 2020. (23) Archibong, E. F.; Mvula, E. N. Chem. Phys. Lett. 2005, 408, 371. (24) Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54, 11169. (25) Vienna ab Initio Simulation Package (VASP); Technische Universität Wien: Vienna, Austria, 1999. (26) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (27) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953. (28) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (29) Rahane, A. B.; Deshpande, M. D.; Kumar, V. J. Phys. Chem. C 2011, 115, 18111. (30) Sun, J.; Lu, W. C.; Zhang, W.; Zhao, L. Z.; Li, Z. S.; Sun, C. C. Inorg. Chem. 2008, 47, 2274. (31) Fernandez, E. M.; Borstel, G.; Soler, J. M.; Balbas, L. C. Eur. Phys. J. D 2003, 24, 245. (32) Sierka, M.; Dobler, J.; Sauer, J.; Santambrogio, G.; Brummer, M.; Woste, L.; Janssens, E.; Meijer, G.; Asmis, K. R. Angew. Chem., Int. Ed. 2007, 46, 3372. (33) Walsh, A.; Woodley, S. M. Phys. Chem. Chem. Phys. 2010, 12, 8446. (34) Rahane, A.; Deshpande, M.; Pandey, R. J. Nanopart. Res. 2010, 12, 727. (35) Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, 5188. (36) He, H.; Orlando, R.; Blanco, M. A.; Pandey, R.; Amzallag, E.; Baraille, I.; Rerat, M. Phys. Rev. B 2006, 74, 195123. (37) Collins, S. E.; Baltanas, M. A.; Bonivardi, A. L. Langmuir 2005, 21, 962. (38) Jochum, W.; Penner, S.; Fottinger, K.; Kramer, R.; Rupprechter, G.; Klotzer, B. J. Catal. 2008, 256, 268. (39) Upton, T. H.; Goddard, W. A.; Melius, C. F. J. Vac. Sci. Technol. 1979, 16, 531. (40) Savin, A.; Nesper, R.; Wengert, S.; Fassler, T. F. Angew. Chem., Int. Ed. 1997, 36, 1808. (41) He, H.; Blanco, M. A.; Pandey, R. Appl. Phys. Lett. 2006, 88, 261904. (42) Litimein, F.; Rached, D.; Khenata, R.; Baltache, H. J. Alloys Compd. 2009, 488, 148. (43) Tang, W.; Sanville, E.; Henkelman, G. J. Phys.: Condens. Matter 2009, 21, 084204. (44) Zhou, R. S.; Snyder, R. L. Acta Crystallogr., Sect. B: Struct. Sci. 1991, 47, 617. (45) Fuchs, F.; Bechstedt, F. Phys. Rev. B 2008, 77, 155107.

4. CONCLUSIONS We have studied the structural and electronic properties of (Ga2O3)n clusters with n = 1−10 using the density functional theory. We find a strong competition between two structural motifs: the (Ga2O2) rhombus and (Ga3O3) planar or chairlike hexagons. The (Ga2O3)4 structure appears to be derived from bulk corundum lattice. The open cage or cage dimer configurations are significantly higher in energy than the lowest energy structures. The BE of the clusters increases with the cluster size. The stability of the cluster is dominated by ionic Ga−O interactions with some covalent character between Ga and O orbitals. A comparison of the BE and average coordination of Ga and O atoms with those of β-Ga2O3 and α-Ga2O3 phases shows similarity of atomic structures of clusters with α-Ga2O3. The average coordination of Ga and O atoms are still lower than the average coordination of Ga and O atoms in bulk β-Ga2O3 and α-Ga2O3 phases. With the increase in cluster size, the HOMO−LUMO gap as predicted in earlier studies continues to exhibit an oscillatory behavior. For n = 10, the HOMO−LUMO gap approaches the calculated value of the bulk band gap. We hope that these clusters considered here would offer valuable assistance to future experimental and theoretical studies on gallium oxide nanostructures.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ACKNOWLEDGMENTS We gratefully acknowledge financial assistance from the Department of Science and Technology (DST), Government of India, and University Grants Commission (UGC). We also acknowledge the Department of Physics, University of Pune and the Center for Development of Advance Computing (CDAC), Pune, and Bangalore for providing the supercomputing facilities. We gratefully acknowledge Professor D. G. Kanhere for helpful discussions.

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REFERENCES

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Structural and Electronic Properties of Neutral and Ionic (Ga2O3) n

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