# First-Principles Studies on the Structural and Electronic Properties of As Clusters

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{n}(n = 2–24) are investigated. The size-dependent physical properties of neutral clusters, such as the binding energy, HOMO-LUMO gap, and second difference of cluster energies, are discussed. The supercluster structures based on the As

_{8}unit and As

_{2}bridge are found to be dominant for the larger cluster As

_{n}(n ≥ 8). Furthermore, the possible geometric structures of As

_{28}, As

_{38}, and As

_{180}are predicted based on the growth pattern.

## 1. Introduction

_{n}clusters has focused on small-sized clusters with n ≤ 5 [12,13,14,15,16,17]. For example, Wang et al. [12] utilized high-resolution photoelectron spectroscopy to study the electronic vibration and spin orbit of As

_{4}. Bennett et al. [13] have measured the appearance potentials and ion translational energies for the As

_{1}, As

_{2}, and As

_{3}ions formed by the dissociative resonance capture of As

_{4}. Lippa et al. [14] have probed the electron affinities of As

_{n}(n = 1–5) using photoelectron spectra in 1998. Brumbach and Rosenblatt [15] have investigated the vibrational modes of As

_{4}with Raman spectroscopy. Yonezo [16] designed a high-temperature nozzle assembly for gas-electron diffraction to determine the structure of As

_{4}. Jeffrey et al. [17] measured the ionization potentials (IPs) for As

_{n}(n = 1–5) using gas-phase charge-transfer reactions. No experimental data are available for As

_{n}with n ≥ 6 right now.

_{n}(n = 1–16) and their anions. Their results showed that the even-numbered neutral As

_{n}species are more stable than the odd-numbered clusters, but the even-numbered anionic As

_{n}species are less stable than the odd-numbered species. Liang et al. [19] probed the electronic structure and property of neutral and charged arsenic clusters As

_{n}

^{(+1,0,−1)}(n = 2–8). At the B3LYP/6-311+G(d) theoretical level, Guo [20] investigated the geometries and energies for neutral and charged As

_{n}(n = 2–15) clusters, and reported their relative stability, ionization potential, and electron affinity. Baruah et al. [23] using a generalized gradient approximation (GGA) to explore the geometry, vibrational modes, and polarizabilities, as well as the infrared and Raman spectra of fullerene-like arsenic cages with n = 4, 8, 20, 28, 32, 36, and 60. Zhao et al. [22] investigated the structures and electronic properties of As

_{n}clusters with even-numbered As

_{n}(n = 6–28) using density functional theory (DFT) with the Perdew–Burke–Ernzerhof functional and a doubled numerical basis set with d-polarization functions(PBE/DND) scheme and found that the supercluster structures based on As

_{4}, As

_{6}, and As

_{8}units, and the As

_{2}bridge were dominant for the larger As

_{n}with n ≥ 14.

_{n}clusters, all the results are always most of the artificial speculation studies to investigate the structure of clusters in certain symmetries. In this work, we have performed a genetic algorithm (GA) incorporated with density functional theory (DFT) calculations to explore the structures and electronic properties of As

_{n}(n = 2–24) neutral and charged clusters. After we have determined the growth pattern of As

_{n}clusters, the possible geometric structures of As

_{28}, As

_{38}, and As

_{180}are predicted based on the growth pattern. We also discussed the size-dependent physical properties of neutral clusters such as the binding energy, HOMO-LUMO gap and second difference of cluster energies.

## 2. Computational Methodology

_{n}clusters, we combined a genetic algorithm (GA) simulation with local optimization at the Dmol

^{3}level [24,25,26,27,28,29]. The fundamental aim in GA is to divide the potential-energy surface (PES) into a number of regions and find the locally stable isomers in each region. In the GA program, we generated 15 As

_{n}(n = 3–12) and 20 As

_{n}(n = 13–24) initial populations to ensure that we could find the local minimum. Any population can be chosen as parents to generate their child cluster according to a crossover operation. In addition, there was a possibility of a 30% mutation rate for a single parent to produce child alone. The child cluster was optimized with Dmol

^{3}, and then compared with its parent in energy. The child with lower energy replaced its high-energy parent. The whole process of genetic algorithm with 2000 iterations was to ensure we got the lowest energy structure.

_{n}(n = 2–24) clusters was performed using DFT with the Perdew–Burke–Ernzerhof (PBE) [24] exchange-correlation functional and an all-electron basis set of the double-numerical-plus-d-polarization (DND) type, as implemented in the Dmol

^{3}[25] package. A self-consistent field calculation kept the accuracy with an energy convergence for 10

^{−6}a.u., and the forces for 2 × 10

^{−3}a.u. There was no symmetry restriction for geometry optimization.

_{n}(n = 2–24) cluster, we saved ten energetically lower isomer structures for further electronic structure calculations, which were performed using the Vienna Ab-initio Simulation Package (VASP) codes. The Kohn–Sham equations were solved variationally in a plane wave basis set using the projector-augmented-wave (PAW) method. The exchange-correlation energy was described by the functional of Perdew, Burke, and Ernzerhof (PBE) based on the generalized gradient approximation (GGA). The energy cutoff was set to be 400 eV and the vacuum space was set to be at least 14 Å to separate the interactions between the neighboring slabs. Only the Gamma k-point was used to sample the Brillouin zone for the geometry and electronic structure calculations. All structures were fully relaxed by Gaussian smearing and electronic structure calculations by tetrahedron smearing method until the convergence criteria (with the force less than 0.02 eV/Å and the energy less than 10

^{−5}eV). Although each structure of As

_{n}(n = 2–24) cluster was further optimized by VASP, the energy sequencing of each cluster was basically unchanged.

## 3. Results and Discussions

#### 3.1. As_{n} (n = 2–8) Clusters

_{2}cluster (2a in Figure 1) is 2.103 Å through experimental measurement [30]. In our calculation the distance between the As atoms was 2.118 Å, which is closer to the experimental data compared with the 2.142 Å calculated using PBE/DND methods [22].

_{3}cluster, the energy of the structure with C

_{2v}symmetry (3a in Figure 1) was the global minimum. It was an isosceles triangle structure with a top angle of 65.14° and side length of 2.325 Å. It was energetically lower than the linear chain structure with D∞h symmetry (3b in Figure 1), in which structure, the bond length was 2.204 Å.

_{4}with T

_{d}symmetry (4a in Figure 1) was a regular tetrahedron, which was consistent with the previous reports [18,19,20]. Its energy was much lower than other isomorphic configurations. The energy of the rectangular structure with D

_{2h}symmetry (4b in Figure 1) was 0.605 eV/atom higher than that of the ground state and the chain structure with C

_{2}symmetry (4c in Figure 1) was energetically higher than the rectangular structure.

_{5}had C

_{2v}symmetry (5a in Figure 1) and it may be considered as adding an atom in the cross section of a dihedral formed by four atoms. It had 0.07 eV/atom less energy than the rectangular pyramid structure with D

_{4h}symmetry (5b in Figure 1) and 0.142 eV/atom less than the planar structure with D

_{5h}symmetry (5c in Figure 1).

_{3h}symmetry (6a in Figure 1) was the ground-state structure for As

_{6}and was only 0.005 eV/atom lower than the benzvalene type with C

_{2v}symmetry (6b in Figure 1) and 0.117 eV/atom lower than the dihedral angle structure of six atoms with C

_{2v}symmetry (6c in Figure 1). The side length was 2.522 Å and the edge length was 2.559 Å. Our ground state was consistent with the result calculated by B3LYP/6-311+G(d) [20] or PBE/DND methods [22]. However, the structure 6b in Figure 1 was found to be the lowest energy by Liang [19] using MP2(full)/g-31G(d) methods and Bai [21] using B3LYP/DZP++ methods. As the outer shell structure of As is 3s

^{2}3p

^{3}, we think our results are reasonable as the completely three-coordination structure (6a in Figure 1) must be more stable than the structure with two two-coordinations (6b in Figure 1).

_{7}, the ground-state structure with C

_{2}v symmetry (7a in Figure 1) could be derived from the trigonal prism of As

_{6}by edge-capping with an additional As atom. This low-energy structure is also predicted in Refs. [19,20,21]. Its energy was lower than the structure with Cs symmetry (7b in Figure 1) by 0.008 eV/atom and the structure with Cs symmetry (7c in Figure 1) by 0.053 eV/atom.

_{2v}symmetry was obtained as the lowest energy structure for As

_{8}, as seen from 8a in Figure 1. It was energetically lower than the structure with C

_{2v}symmetry (8b in Figure 1) by 0.038 eV/atom and the structure with Cs symmetry (8c in Figure 1) by 0.048 eV/atom. We also checked the cage structure with O

_{h}symmetry cut from the bulk phase reported by Baruah [23], and we found that it was 0.64 eV energy higher than our ground state structure.

_{n}(n = 2–8) clusters, we find that As

_{2}was a one-dimensional bridge, As

_{3}was a two-dimensional isosceles triangle and As

_{4}became a three-dimensional tetrahedron. When n was larger than 3, the two-dimensional cluster structure, such as 4b and 5c in Figure 1, sorts more and more backward energetically. We can conclude that the structure of small As clusters tends towards a three-dimensional cage structure and it was not stable for a 2-D planar structure.

#### 3.2. As_{n} (n = 9–18) Clusters

_{9}with C

_{s}symmetry (9a in Figure 2) could be regarded as being derived from a cage-like As

_{8}structure by attaching an As atom at one side. The isomers (C

_{2v}) with a higher symmetry (9b,c in Figure 2) were less stable based on our VASP calculations. It also hinted to us that the ground structure of As

_{8}might be a stable cluster with a magic number. From further calculations, we found that the cage-like As

_{8}structures unit served as the primary building unit for forming the As clusters with larger sizes.

_{2v}) of As

_{10}consistd of the cage structure of 8a in Figure 1 that was edge-capped by each As atom. After relaxation, the upper bond broke to form two four-atom cages and an As

_{2}bridge. The structure 10b in Figure 2 was a new structure discovered by our GA global searching. The structure obtained by Zhao [22] is structure 10c in Figure 2, whose energy was higher than 10b in Figure 2 by 0.006 eV/atom and 10a in Figure 2 by 0.009 eV/atom.

_{11}was 11a in Figure 2 which was formed on the base of As

_{10}with an As atom added above the As

_{2}dimer and linked with an As

_{8}cage. It was more stable than the 11b in Figure 2 isomer with C

_{s}symmetry by 0.008 eV/atom and 11c in Figure 2 isomer by 0.04 eV/atom with C

_{s}symmetry in energy.

_{12}, the structure with D

_{3d}symmetry was confirmed to be the lowest energy structure among all the structural candidates considered. The highly-symmetric structure was shaped of two As

_{8}cages that share a four-atom plane. From another point of view, the ground-state structure of As

_{12}was a layered structure of three layers of atoms (3 + 6 + 3). Such a nice structure was energetically lower than 12b in Figure 2 with C

_{1}symmetry by 0.023 eV/atom and 12c in Figure 2 with C

_{s}symmetry by 0.025 eV/atom.

_{13}carefully, we also found two As

_{8}cages. Different from As

_{12}, the two cages jointly owned a three-atom plane. It had 0.008 eV/atom less energy than the structural 13b in Figure 2 (C

_{1}) and 0.009 eV/atom less than the structure 13c in Figure 2 (C

_{s}).

_{14}with Cs symmetry could be considered to be composed of an As atom link to the three-atom plane on one side of the As

_{13}(13a in Figure 2). The less stable isomer 14b was a distorted structure of 14a, which was energetically higher by 0.011eV/atom. The 14c was a structure without an As

_{2}dimer bridge, it was linked by As

_{8}cage with an As

_{6}cage and had 0.032 eV/atom more energy than 14a in Figure 2.

_{15}with C

_{s}symmetry was composed of two connected cages (As

_{8}and As

_{7}). The other two candidates 15b in Figure 2 with C

_{s}symmetry and 15c in Figure 2 with C

_{s}symmetry were less stable than the ground-state structure by 0.005 eV/atom and 0.025 eV/atom in energy, respectively.

_{8}cage and a downward As

_{8}cage connected to form a new structure as the ground state of As

_{16}(16a in Figure 2 with C

_{2h}symmetry). It was more stable than the C

_{2}-symmetry isomer 16b in Figure 2 and the C

_{s}-symmetry isomer 16c in Figure 2 by 0.05 eV and 0.08 eV in energy. Although structural 16c in Figure 2 contained an As

_{8}cage and an As

_{2}bridge, the As

_{6}cage in the structure led to the overall energy as being higher than other two isomers.

_{17}(17a in Figure 2) with C

_{s}symmetry was built by As

_{8}and As

_{7}units with an As

_{2}bridge in the middle. The two C

_{s}-symmetry isomorphic structure 17b,c in Figure 2 were also formed by the As

_{8}and As

_{7}units with different orientation connections.

_{18}(18a in Figure 2) with C

_{2v}symmetry was formed by two identical As

_{8}units and an As

_{2}bridge in the middle. Our structure was exactly the same as that in Ref. [22]. Two slightly higher energy isomers (18b in Figure 2) with C

_{2h}symmetry and 18c in Figure 2 with C

_{2v}symmetry were combined by the same units as 18a in Figure 2 with different orientations, and they were energetically higher than 18a in Figure 2 by 0.05 eV and 0.35 eV energy. The calculations showed that the structure with As

_{8}unit and As

_{2}bridge in the middle was more stable than other cage structures. We also generated one As

_{18}structure cut from bulk phase and the energy was 3.17 eV higher than the ground state. So, we think the chain structure with As

_{8}units and an As

_{2}bridge is much more important for middle-sized As

_{n}clusters.

#### 3.3. As_{n} (n = 19–24) Clusters

_{19}(19a in Figure 3) with C

_{s}symmetry could be regarded as an As atom added into one side of As

_{18}. Therefore, As

_{19}(19a in Figure 3) could be considered as the combination of As

_{8}-As

_{2}-As

_{8}-As

_{1}. The isomers of As

_{19}(19b,c in Figure 3) with only C

_{1}symmetry were both built up by two identical As

_{8}units and an As

_{3}bridge. Due to the distortion of the structures, they had 0.008 eV/atom and 0.009 eV/atom higher energy than 19a in Figure 3.

_{20}was predicted to be C

_{1}symmetry, as shown in 20a in Figure 3. It could be regarded as an As

_{8}cage link with an As

_{10}cage joined by an As

_{2}bridge. As

_{20}(20a in Figure 3) could be considered as the combination of As

_{8}-As

_{2}-As

_{10}. Zhao [22] predicted the optimal combinations for the As

_{20}is super-clusters of As

_{4}-As

_{2}-As

_{8}-As

_{2}-As

_{4}. The energy of As

_{20}(20a in Figure 3) we got based on the genetic algorithm was energetically lower than the structure 20b in Figure 3 with C

_{2v}symmetry. A distorted structure 20c in Figure 3 originated from 20a in Figure 3 also appeared in our calculations. After the calculations with VASP, two isomers showed 0.006 eV/atom and 0.053 eV/atom higher energy than 20a in Figure 3. This result shows the super-clusters of As

_{4}-As

_{2}-As

_{8}-As

_{2}-As

_{4}did not have much of an advantage.

_{21}, the most stable structure (21a in Figure 3) could be regarded as an As atom link to the As

_{10}cage of As

_{20}(20a in Figure 3). Two other isomers (21b,c in Figure 3) were constituted by an As

_{8}cage and an irregular As

_{11}structure linked with an As

_{2}bridge. They were energetically higher than 21a in Figure 3 by 0.011 eV/atom and 0.017 eV/atom.

_{22}with C

_{s}symmetry are formed with two symmetrical As

_{10}cages in the As

_{20}units and an As

_{2}bridge in the middle. The isomers were two kinds of super-clusters (22b in Figure 3, As

_{6}-As

_{2}-As

_{8}-As

_{2}-As

_{4}and 22c in Figure 3, As

_{4}-As

_{2}-As

_{8}-As

_{8}), and they were stretched by more units compared to the ground-state structures (22a in Figure 3). Although we could find stable As

_{8}and As

_{4}units in isomers, they each had 0.02 eV and 0.09 eV higher energy than 22a in Figure 3. According to previous findings, it can be found that the second lower energy As

_{10}cage 10b in Figure 2 will be favorable if the structure is composed by an As

_{8}unit connected with an As

_{2}bridge.

_{23}(23a in Figure 3) with C

_{2v}symmetry seemed to be four As

_{8}cages linked to each other to share the three-atom plane, and the bottom edge of the middle two cages were broken. At the same time, we could also regard 23a in Figure 3 as a super-cluster of As

_{8}-As

_{2}-As

_{3}-As

_{2}-As

_{8}. The other two candidates, 23b in Figure 3 with C

_{s}symmetry and 23c in Figure 3 with C

_{1}symmetry, were less stable than the structure 23a in Figure 3 by 0.008 eV/atom and 0.021 eV/atom in energy, respectively.

_{24}with C

_{s}symmetry (24a in Figure 3) was built by three units (an As

_{4}cage and two identical As

_{8}cages), connecting the neighboring structure with an As

_{2}bridge. Zhao [22] considered that the optimal combinations of the super-clusters As

_{24}are As

_{6}-As

_{2}-As

_{8}-As

_{2}-As

_{6}(24b in Figure 3) with C

_{2v}symmetry. DFT calculations show that the ground-state structure of As

_{24}we get based on the genetic algorithm weare the combinations of As

_{8}-As

_{2}-As

_{8}-As

_{2}-As

_{4}, which was energetically lower than the structure 24b in Figure 3 by 0.018 eV/atom. Besides, we also gained another high symmetric structure with C

_{2v}symmetry (24c in Figure 3) that was constituted by three As

_{8}units. However, its energy was 0.025 eV/atom higher than the ground state structure (24a in Figure 3). We could realize from this result that the lowest energy structures of larger As clusters not only have the combination of As

_{8}units but also needed an As

_{2}bridge in the middle of adjacent units.

#### 3.4. As_{n} (n = 2–24) Charged Clusters

_{n}(n = 2–24) charged clusters. Theoretically, it was easy to simulate a cationic or anionic cluster by adjusting the total electrons from the neutral cluster. From Figures S2 and S3, we could know the lowest energy structures of charged clusters (n = 2–4) were almost the same as with neutral cases. For As

_{8}clusters, 8a in Figure 1 structures were quite stable even in cationic or anionic cases and it was the cluster with the magic number. For other As

_{n}(n < 16) clusters, the isomers changed the energy sequence as the system changed the electron numbers. It was interesting to find that the structures for As

_{n}(15 < n < 24) clusters were quite stable whatever attachment of extra electron to the neutral or losing of an electron from the neutral cluster.

#### 3.5. As_{n} (n = 28, 38, 40, 180) Clusters

_{28}, As

_{38}, and As

_{40}based on the above findings. The structural size evolution and electronic properties of arsenic clusters indicated that the clusters combined by an As

_{2}bridge and an As

_{8}cage had lower energy than their isomers and showed more stability in each local size-dependent range. Here we have to emphasize that As

_{4}and As

_{6}units were not dominant for the larger As

_{n}cluster, which was different from Zhao’s result [22]. Furthermore, different sizes of fullerene cage structure isomers were also calculated to compare with our ground state structures in energy, and their energies were far more than units-linked one-dimensional structures. Given this understanding, we constructed As

_{28}as As

_{8}-As

_{2}-As

_{8}-As

_{2}-As

_{8}and As

_{38}as As

_{8}-As

_{2}-As

_{8}-As

_{2}-As

_{8}-As

_{2}-As

_{8}in all possible ways. The structures we calculated of As

_{28}are listed along with the increase of energy in Figure 4. The lowest energy structure of As

_{28}with C

_{2v}symmetry (Figure 4a) had 0.05 eV less energy than the structure with C

_{s}symmetry (Figure 4b) and 0.10 eV less than the structure with C

_{2v}symmetry (Figure 4c). In addition to considering structure growth in the one-dimensional direction, we also calculated the longitudinal growth mode. Three isomers Figure 4c,e,f were all with C

_{s}symmetry and energetically higher than the lowest energy structure a with 0.08 eV, 0.35 eV, and 0.40 eV, respectively. Besides, the other two semi-ring isomers Figure 4g,h had 0.44 eV and 0.70 eV energy higher than the ground state structure. Compared with the bulk truncated structure of As

_{28}, the lowest energy structure of As

_{28}was 0.16 eV/atom lower.

_{38}with C

_{2v}symmetry (Figure 5a) and its isomers are listed in Figure 5. We could find that the structure of Figure 5a was a continuation of As

_{8}, As

_{18}, and As

_{28}clusters, and all of them were constructed with As

_{8}cages in the same direction with As

_{2}bridges. The structural isomers Figure 5b with C

_{2v}symmetry and Figure 5c with C

_{2h}symmetry could be regarded as one-dimensional chain structures, the same as Figure 5a. Their respective energies were 0.10 eV and 0.22 eV higher than Figure 5a. The C

_{2v}isomer Figure 5d could be regarded as a two-dimensional structure that has four As

_{8}cages held in four directions and all of them point to the center. The energy of this structure was highest in our calculation with 1.11 eV higher energy than a. Compared with the bulk truncated structure of As

_{38}, the lowest energy structure of As

_{38}was 0.156 eV/atom lower. We could find that the structures did not change previous growth tendencies even with increasing the size of the clusters.

_{40}can form ring and fullerene cage structures, we also studied the structures of As

_{40}. The structures we calculated of As

_{40}are listed along with the increase of energy in Figure 6. We found that the lowest energy structure of As

_{40}with C

_{1}symmetry (Figure 6a) and its isomers Figure 6b (0.42 eV energy higher) with C

_{s}symmetry both were one-dimensional chain structures. Three isomers Figure 6c,d,e could all be regarded as two-dimensional structures and energetically higher than the lowest energy structure a with 0.014 eV/atom, 0.044 eV/atom, and 0.09 eV/atom, respectively. Seemingly stable three-dimensional fullerene cage isomers Figure 6f with D

_{5d}symmetry and Figure 6g with D

_{5d}symmetry were 0.194 eV/atom and 0.226 eV/atom higher in energy than the lowest energy structure.

_{180}cluster based on the As

_{8}units and As

_{2}bridge, which is shown in Figure 7. The HOMO-LUMO gap of As

_{180}was 1.868 eV and the binding energy per atom was −2.901 eV.

#### 3.6. Electronic Properties of As_{n} Clusters

_{n}(n = 2–24) clusters are shown in Figure 8a. In the size range of n = 12–24, the binding energy increased smoothly with weak odd-even oscillation properties. This result can be related to the evolution of the ground-state from cage-like structure to cage-link structure at n = 12. Besides, the binding energy of As

_{8}was a peak value in the small size of n = 3–11, and this suggests the ground structure of As

_{8}would be a vital growth unit in larger structures. Our next calculation also proved the conjecture.

_{n}(n = 2–24) clusters. As is known, the cluster with the larger energy gap is more stable and easier to prepare. As the largest energy gap of As

_{4}is 4.06 eV, it is the most prominent species in arsenic vapor, leading to a number of experimental and theoretical studies on As

_{4}clusters. Although the gaps of As

_{n}clusters from n = 5–10 change smoothly, we also observe the gap of As

_{8}is highest locally, which points out that the stability of As

_{8}was higher than the neighboring cluster. The HOMO-LUMO gap was higher for As

_{n}(n = 4, 6, 8, 12, 14, 16, 18, 20, 22, and 24) than their adjacent structures. The atoms in these even-numbered sequences were all three-coordination and eight-electron structure. The odd-numbered clusters were unable to achieve this condition, so they were less stable than the odd-numbered species.

^{2}E = E(n + 1) + E(n − 1) − 2E(n). Figure 8c describes how the second-order differential energy changed with the increase of atom number and it shows good odd–even oscillation properties. The second-order difference of cluster energies of even-numbered clusters were all higher than their adjacent odd-numbered clusters. Therefore, we could draw the conclusion that even-numbered clusters were more stable than their neighboring odd-numbered clusters. Above all peaks for Δ

^{2}E, three local maximum peaks were found at n = 4, 8, and 18, where As

_{n}(n = 4, 8, and 18) clusters were chemically stable.

## 4. Conclusions

_{n}(n = 2–24). The ground-state structures of As

_{n}clusters change from two to three dimensional after n = 3. Arsenic clusters followed a structural growth pattern starting from n = 8 and the structures of As

_{n}(n = 9–24) clusters could all be regarded as evolving from the ground state structure of an As

_{8}unit and an As

_{2}bridge. The binding energy of As

_{n}(n = 2–24) clusters had a periodic step-like behavior, and the size-dependent HOMO-LUMO gap and second-order difference of cluster energies exhibited obvious even–odd alternations with several magic numbers. Based on the growth pattern concluded from small As

_{n}clusters, the possible superstructures of As

_{28}, As

_{38,}As

_{40}, and As

_{180}were discussed.

## Supplementary Materials

_{n}(n = 2–24) neutral clusters, Figure S2: Low energy isomers of As

^{+}

_{n}(n = 2–24) cationic clusters, Figure S3: Low energy isomers of As

^{-}

_{n}(n = 2–24) anionic clusters.

## Author Contributions

## Funding

## Conflicts of Interest

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Sample Availability: Samples of the compounds are available from the authors. |

**Figure 1.**Lowest-energy and isomorphic structures for As

_{n}(n = 2–8) clusters. The relative total energies are in eV.

**Figure 2.**Lowest-energy and isomorphic structures for As

_{n}(n = 9–18) clusters. The relative total energies are in eV.

**Figure 3.**Lowest-energy and isomorphic structures for As

_{n}(n = 19–24) clusters. The relative total energies are in eV.

**Figure 4.**Lowest-energy and isomorphic structures for As

_{28}clusters. The relative total energies in eV.

**Figure 5.**Lowest-energy and isomorphic structures for As

_{38}clusters. The relative total energies are in eV.

**Figure 6.**Lowest-energy and isomorphic structures for As

_{40}clusters. The relative total energies in are eV.

**Figure 8.**(

**a**) Average binding energies (

**b**) HOMO-LUMO Gaps and (

**c**) second-order difference of cluster energies of As

_{n}clusters.

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**MDPI and ACS Style**

Yan, J.; Xia, J.; Zhang, Q.; Zhang, B.; Wang, B.
First-Principles Studies on the Structural and Electronic Properties of As Clusters. *Materials* **2018**, *11*, 1596.
https://doi.org/10.3390/ma11091596

**AMA Style**

Yan J, Xia J, Zhang Q, Zhang B, Wang B.
First-Principles Studies on the Structural and Electronic Properties of As Clusters. *Materials*. 2018; 11(9):1596.
https://doi.org/10.3390/ma11091596

**Chicago/Turabian Style**

Yan, Jialin, Jingjing Xia, Qinfang Zhang, Binwen Zhang, and Baolin Wang.
2018. "First-Principles Studies on the Structural and Electronic Properties of As Clusters" *Materials* 11, no. 9: 1596.
https://doi.org/10.3390/ma11091596