Structures, stabilities, and magnetic properties of Cu-doped ZnnOn (n = 3, 9, 12) clusters: A theoretical study

Computational and Theoretical Chemistry 989 (2012) 90–96

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Structures, stabilities, and magnetic properties of Cu-doped ZnnOn (n = 3, 9, 12) clusters: A theoretical study Yongliang Yong, Zhen Wang, Kai Liu, Bin Song ⇑, Pimo He State Key Laboratory of Silicon Materials and Department of Physics, Zhejiang University, Hangzhou 310027, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 27 October 2011 Received in revised form 9 March 2012 Accepted 14 March 2012 Available online 23 March 2012 Keywords: Cu-doped ZnO cluster Electronic structure Magnetic property DFT calculations

a b s t r a c t The structural, electronic, and magnetic properties of Cu-doped ZnnOn (n = 3, 9, 12) clusters have been studied using spin-polarized density functional theory. We firstly investigate the lowest-energy structures of pure ZnnOn (n = 1–13) clusters based on the extensive searching, and identify that the Zn3O3, Zn9O9 and Zn12O12 clusters possess relatively higher stability. Then, these stable clusters are taken as candidates for investigating the effect of Cu-atom doping. Three doping modes, that is, substitutional, exohedral, and endohedral doping, are considered. It is found that the substitutional mono- and bi-doped clusters are the most stable among doped clusters. The HOMO–LUMO gaps of the doped clusters are all reduced due to the p–d hybridization caused by the Cu-atom doping. For the monodoped clusters, all isomers have a magnetic moment of 1 lB, which is mainly contributed by the Cu 3d and Cu-surrounding O 2p states. However, for the bidoped clusters, the ground states have zero magnetic moment with the spins on the Cu atoms being either antiferromagnetically coupled or completely quenched, except for Cu2ZnO3 cluster. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Dilute magnetic semiconductors (DMSs), obtained by doping suitable impurities in conventional semiconductors, have become a focus of great attention as a potential semiconductor-compatible magnetic component for spintronic applications [1]. Several semiconductors (e.g., TiO2, AlN, GaN and ZnO) have been found to exhibit ferromagnetism when doped with transition metal impurities. Among these semiconductors, ZnO attracts most interest since it is predicted as one of the most promising materials for room-temperature DMSs [2], in addition to its promising performance in a variety of applications such as optoelectronics, sensors, transducers, photovoltaics, and photocatalysts [3–5]. Recently, Cu-doped ZnO has been investigated as an ideal DMS from both theories [6–9] and experiments [10–16], since the ZnO doped with the intrinsically nonmagnetic Cu atoms exhibits pronounced DMS properties. For example, the Curie temperature (TC) of Cu-doped ZnO is well above room temperature, and the nonmagnetic Cu atoms can avoid troublesome problems as to whether ferromagnetic ordering arises from the magnetic ions actually substituting in the lattice or from the secondary magnetic phases or magnetic precipitates. Since the growth of thin films can be viewed as deposition or coalescence of clusters [17], the clusters can often be pro-

⇑ Corresponding author. Tel./fax: +86 571 87951328. E-mail address: [email protected] (B. Song). 2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2012.03.011

duced to model various surface sites and defects. Furthermore, with current miniaturization trends continuing, minimum device features will soon approach the size of atomic clusters. Thus, clusters are believed to play an important role in retaining ferromagnetism in DMSs [18]. The DMS Zn0.93Mn0.07S clusters of about 2.5 nm diameter were successfully synthesized inside a glass matrix [19]. Interests of both fundamental research and potential applications of ZnO-based DMSs stimulate the synthesis of novel ZnO nanostructures with special properties. Cluster, as a particular state of matter, exhibits novel properties due to its size effect and large surface/volume ratio, and constitutes a bridge between small molecular systems and the bulk materials. Moreover, since the properties of clusters can be manipulated by changing the shape, size and composition, it is possible to use clusters as building blocks to design cluster-based materials with desired electronic properties. For these aims, ZnO clusters have been extensively studied experimentally [20–24] and theoretically [25–36]. The theoretical studies showed that the smallest ZnnOn (n 6 7) clusters are found to adopt Zn–O alternating ring-like structures, whereas a ring-to-cage transition at n = 8 is found. For the medium-sized ZnnOn (n > 8) clusters, the cage or tube structures are the most stable motif. Since cluster has an open structure, doping is easier to achieve than that in bulk and film. Recently, the doped ZnO clusters have attracted many attentions due to their potential technological applications. Several theoretical calculations have been mainly performed on transition metals (TM)-doped Zn12O12 cluster [37–42] and carbon-doped ZnnOn (n = 3–10, 12) clusters [43,44]. For example, when Zn12O12

Y. Yong et al. / Computational and Theoretical Chemistry 989 (2012) 90–96

cluster doped with a single Co [37,40], Fe [40,41] and Mn [39,40] atom, respectively, the doped cluster carry a magnetic moment of 3 lB, 4 lB, and 5 lB, respectively, which is equivalent to that of corresponding free atom. Doping with two Co sites leads to ferromagnetically coupled Co moments, whereas the Zn12O12 cluster doped with two Fe or Mn atoms favors the antiferromagnetic state. Nagare et al. [43] have systematically studied carbon-doped ZnnOn (n = 3– 10, 12) clusters using density functional theory. They predicted that the clusters doped with one carbon induce magnetic moment of 2 lB in all cases. When they doped with two C atoms, the Zn2C2, Zn3OC2, and Zn7O5C2 clusters favor antiferromagnetic state, whereas the others favor ferromagnetic state. These results mean that the ZnO clusters are capable of sustaining ferromagnetism, which should be good candidates for developing nanoscaled DMSs. Further, the origin of the observed ferromagnetism of Cu-doped ZnO thin films still remains controversial, whether it is an intrinsic or extrinsic property of the materials. The study of the doped ZnO clusters may offer a platform to understand finite size effect on magnetic properties and the origin of ferromagnetism due to Cu doping. In this work, we present a systematical theoretical investigation on the geometries, electronic structures, and magnetic properties of ZnnOn (n = 3, 9, 12) clusters doped with one or two Cu atoms. As for the small ZnnOn (n = 2–13) clusters, it is found that the Zn3O3, Zn9O9 and Zn12O12 clusters possess relatively higher stability as we discuss below. To the best of our knowledge, only Chen and Wang [40] and Ganguli et al. [42] were involved in the investigations of the Cu-doped ZnO clusters using density functional theory, but limited to substitutional Cu-doping in a Zn12O12 cluster.

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results [50–54]. To our knowledge, no experimental bond length and dipole moment data are available for ZnO molecule. Meanwhile, we note that a bond length of 1.719 Å for ZnO molecule is also in agreement with the results (1.695–1.730 Å) of previous theoretical studies [25,26,29,31]. Hence we believe that the PBE/DNP/ ECP combination used here would reproduce the general features of pure ZnnOn and Cu-doped ZnnOn clusters. To generate the low-energy isomers of ZnnOn clusters, we use a combination of full-potential linear-muffin-tin-orbital moleculardynamics (FP-LMTO-MD) search and DFT-GGA minimization [55,56]. The accuracy of the FP-LMTO-MD method [57–60] for investigating the cluster structures has been confirmed by previous studies (for example, Refs. [61–65]) on small Sin, GanNn, Gen clusters. In the present study, all MT sphere radii for Zn and O are taken as 2.10 and 1.25 a.u., respectively. The LMTO basis sets include s, p, and d functions on all spheres. In order to perform the systematic search for the lowest-energy structures of ZnnOn clusters, depending on the cluster size, 60–300 initial geometric configurations as seeds are relaxed until the local minimum of the total energy is found. Then, the low-lying energy structures for each cluster size obtained by FP-LMTO-MD calculations are further optimized by DMOL3 program with GGA. To make sure the obtained lowest-energy structures are real local minima, normal-mode vibrational analysis implemented in the DMOL3 program is applied. All of the energy minima obtained for the lowest-energy ZnnOn and Cu-doped ZnnOn clusters have no imaginary frequencies.

3. Results and discussion 2. Computational methods

3.1. Structures and stability of pristine ZnnOn clusters

In this work, all calculations are performed using the spinpolarized density functional theory (DFT) implemented in the DMOL3 program (Accelyrs Inc.) [45,46]. The generalized gradient approximation formulated by Perdew, Burke, and Ernzerhof (PBE) [47] is employed to describe the exchange–correlation energy functional. Relativistic effective core potentials (ECPs) [48,49] and double numerical basis set supplemented with d-polarization functions (i.e., the DNP set) are selected for all atoms. Self-consistent field procedures are performed with a convergence criterion of 10 6 a.u. on the energy and electron density. The geometries are fully optimized without any symmetry constraints. We use a convergence criterion of 10 3 a.u. on the gradient and displacement and 10 5 a.u. on the total energy in geometrical optimization. To check the reliability of the current PBE/DNP/ECP combination, ZnO and CuO molecules are, respectively, analyzed as a test. Their bond lengths, binding energies, vibrational frequencies, and dipole moments are shown in Table 1. The calculated results of ZnO and CuO molecules are in good agreement with experimental

The lowest-energy and some low-lying structures of ZnnOn (n = 2–13) clusters are shown in Fig. 1. The symmetries, bond lengths, bond angles, binding energies, and HOMO–LUMO gaps for the lowest-energy structures are summarized in Table 2. Our calculation results show that the lowest-energy geometries for ZnnOn (n = 2–7) clusters form open Zn–O alternating ring-like structures. This is especially interesting in view of the fact that these ring-like structures are building blocks for large size clusters. When the cluster size n is greater than 7, the cagelike and tube structures are found to be most favorable. The lowest-energy structures of ZnnOn (n = 2–13) clusters we obtained are in good agreement with previous theoretical studies [25–29] in dimensions for geometric parameters such as symmetry, Zn–O bond length, –O–Zn–O and – Zn–O–Zn bond angles. Furthermore, our calculated electronic properties of these clusters such as HOMO–LUMO gaps are also agree with the reference works [26,29,37,39]. Table 3 shows the detailed comparison for lowest-energy structures of ZnnOn (n = 3, 9, 12) clusters, since the same features are found in all ZnnOn (n = 2–13) clusters. To identify the relative stability of the clusters, we analyze the energetics and electronic properties of the lowest-energy structures of ZnnOn clusters. It is found that the binding energy (Eb) as shown in Table 2 and plotted in Fig. 2, rises monotonically with cluster size increasing and contains two minor bumps at n = 9 and 12. The Eb increases with cluster size n rapidly up to 4, and the size dependence of the Eb becomes smooth at n = 5–13. The second difference in energy defined by D2E = E(Znn 1On 1) + E(Znn+1On+1) 2E(ZnnOn) are shown in Fig. 2. Maximum peaks for D2E are found at n = 3, 9, and 12, which indicates that the ZnnOn clusters with n = 3, 9, and 12 are more stable than their neighboring clusters. The HOMO–LUMO gaps (see Table 2) for the lowest-energy structures of ZnnOn clusters are also plotted in Fig. 2. It is found that the HOMO–LUMO gaps are sensitive to the cluster size, however, the gaps for Zn3O3, Zn9O9 and Zn12O12 clusters are all larger than 2.0 eV. Thus, our calculations

Table 1 Bond lengths (d), binding energies (Eb), vibrational frequencies (xe), and dipole moments (DM) for ZnO and CuO molecules.

a

c d e

DM (Debyes)

726.9

5.312

Method

d (Å)

Eb (eV)

ZnO

PBE/ECP/ DNP Experiment

1.719

1.922

...

1.61 ± 0.04

769

...

PBE/ECP/ DNP Experiment

1.729

3.547

659.6

4.235

CuO

b

xe (cm 1)

Molecule

Ref. Ref. Ref. Ref. Ref.

[50]. [51]. [52]. [53]. [54].

1.724

a

c

d

2.85 ± 0.15

b

c

640

4.45 ± 0.30e

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Y. Yong et al. / Computational and Theoretical Chemistry 989 (2012) 90–96

Fig. 1. The lowest-energy and some metastable structures of ZnnOn (n = 2–13) clusters. Values in parentheses are relative energies in eV. Red balls represent O atoms, and gray balls represent Zn atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 2 The symmetries, bond lengths, bond angles, binding energies per ZnO (Eb), and HOMO–LUMO gaps (Eg) for the lowest-energy structures of ZnnOn (n = 2–13) clusters. n

Symmetry

Zn–O (Å)

–O–Zn–O (°)

–Zn–O–Zn (°)

Eb (eV)

Eg (eV)

2 3 4 5 6 7 8 9 10 11 12 13

D2h D3h D4h D5h D6h D7h D4d C3h C2 Cs Th Cs

1.910 1.840 1.807 1.793 1.785 1.781 1.862–2.260 1.894–2.032 1.884–2.214 1.885–1.982 1.864–1.959 1.774–2.000

104.6 149.2 169.3 178.8 176.0 172.7 92.6–158.3 93.5–135.6 90.5–143.7 93.9–134.9 90.9–129.4 90.4–143.2

75.4 90.8 100.7 109.1 116.0 121.2 83.5–111.8 84.4–108.1 82.3–115.0 87.5–113.1 86.4–108.2 86.4–122.9

3.871 5.109 5.541 5.472 5.714 5.724 5.804 5.864 5.900 5.987 6.121 6.086

1.252 2.913 3.051 3.166 3.143 3.284 2.524 2.127 2.199 2.089 2.542 2.079

Table 3 The symmetries, bond lengths, bond angles, and HOMO–LUMO gaps for the lowestenergy structures of ZnnOn (n = 3, 9, 12) clusters compared with previous theoretical works. Symmetry

Zn–O (Å)

–O–Zn–O (°)

–Zn–O–Zn (°)

Eg (eV)

Zn3O3

D3h D3h D3h

1.840 1.826 1.850

149.2 146.3 148.3

90.8

2.913 2.74a 2.901

C3h

1.894–2.032

84.4– 108.1

C3h

1.89–1.99

C3h

1.902–2.039

93.5– 135.6 93.1– 130.7 93.1– 135.9

83.7– 107.2

2.188

Th

1.864–1.959

90.9– 129.4

86.4– 108.2

2.542

Thb Th

1.89–1.99b 1.864–1.964

90.6– 129.3

86.6– 108.2

Zn9O9

Zn12O12

91.8

Eb Eg

4

Energy (eV)

Species

6

Δ 2E 2

0

2.127 2.11a

-2 0

2

4

6

8

10

12

14

Cluster size n Fig. 2. The binding energies per ZnO (Eb), second difference of cluster energies (D2E), and HOMO–LUMO gaps (Eg) as a function of size for ZnnOn (n = 1–13) clusters.

2.47b 2.751

Unless otherwise specified, the results on the first row in the table for different ZnnOn (n = 3, 9, 12) cluster are from our calculations, whereas the results on the second and third row are from referential works [25] and [29], respectively. a Reference value [26]. b Reference value [39].

show that the Zn3O3, Zn9O9 and Zn12O12 clusters possess relatively higher stability. From the analysis of D2E for ZnnOn (n = 2–13) clusters, Wang et al. [29] found that ZnnOn (n = 9, 12) clusters are more stable than their neighboring clusters, while the more stable ZnnOn clusters of n = 3, 6, 9, 12 are predicted by Al-Sunaidi et al. [27]. From the analysis of removal energy and fragmentation energy, Reber

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et al. [26,37] indicated that Zn3O3 and Zn12O12 clusters are very stable species. Our results agree well with these reports, which further support that our calculations are validity. 3.2. Cu-monodoped ZnnOn (n = 3, 9, 12) clusters Having identified the stable clusters, we firstly focus our study on the Cu-monodoped ZnnOn (n = 3, 9, 12) clusters. To search for the most energetically favorable configurations of the Cu-monodoped ZnnOn (n = 3, 9, 12) clusters, three doping modes (i.e., substitutional, exohedral, and endohedral doping) and numerous possible doping sites are considered. The calculated results are presented in Table 4, and the lowest-energy structures of Cu-monodoped ZnnOn (n = 3, 9, 12) clusters are shown in Fig. 3. To examine the reasonable of the approach that the structures of the Cu-doped ZnnOn clusters could be obtained from the corresponding pure ZnnOn structures. We have systematically investigated the structures of CuZn2O3 clusters, as an example, using FP-LMTO-MD search and DFT-GGA minimization. 50 initial geometric configurations as seeds are optimized using FP-LMTO-MD, and then further optimized by using DMOL3 program with GGA. The lowest-energy and metastable structures of CuZn2O3 clusters are shown in Fig. 4. It is found that the lowest-energy structure of CuZn2O3 cluster is a planar ring-like structure, according with the result obtained from that of the pure structure. As for substitutional doping, we find that substitution of Zn atom by Cu is energetically more favorable than substitution of an O atom in ZnnOn clusters. For Cu-monodoped Zn3O3 clusters, as shown in Fig. 3, isomer 3A and 3B still remain in the two-dimensional ring-like structure with the Cu–O bonds of 1.812 Å and 1.802 Å, respectively. However, for isomer 3C, the Zn3O3 ring structure is greatly broken because of the central doping. For Cumonodoped Zn9O9 and Zn12O12 clusters, the energetically favorable configurations of substitutional doped clusters retain the cage forms. However, the substitution induces a little structural change, that is, the replacement introduces a change in bond lengths of the clusters. For example, for isomer 9A, the average Cu–O bond length is 1.94 Å and shows a little change from that of the average Zn–O bond length (1.97 Å) without Cu doping. As shown in Fig. 3, clearly, the exohedral doping results in significant structural distortion. The Cu atom allocates on the surface of the corresponding cluster, and is bound to one Zn atom and one O atom, respectively. For the endohedral doping, we note that it does not lead to structural change. The Cu atom locates in the center of the corresponding cage. From the analysis of Eb, it is found that the ZnnOn clusters can improve their stabilities by substitutionally doping a Cu atom. For exohedral and endohedral doped isomers that have the same chemical compositions, the Eb of the exohedral doped isomers are always larger than these of the corresponding endohedral doped ones, indicating that exohedral doped isomers are more energetically favorable.

Table 4 The symmetries, binding energies per atom (Eb), HOMO–LUMO gaps (Eg), total magnetic moments (ltot), and local magnetic moments of Cu atom (lCu) for the lowest-energy structures of Cu-monodoped ZnnOn (n = 3, 9, 12) clusters. Species

Symmetry

Eb (eV)

Eg (eV)

ltot (lB)

lCu (lB)

3A 3B 3C 9A 9B 9C 12A 12B 12C

Cs C1 Cs Cs C1 C3h Cs C1 Th

2.694 2.464 2.352 2.985 2.868 2.788 3.088 2.989 2.978

0.692 0.861 0.811 1.158 0.721 0.143 1.175 0.683 0.302

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

0.336 0.427 0.419 0.498 0.482 0.113 0.541 0.519 0.500

Fig. 3. The lowest-energy structures of Cu-monodoped ZnnOn (n = 3, 9, 12) clusters. Red balls represent O atoms, gray balls represent Zn atoms, and blue balls represent Cu atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. The lowest-energy and some metastable structures of CuZn2O3 clusters. Values in parentheses are relative energies in eV. Red balls represent O atoms, gray balls represent Zn atoms, and blue balls represent Cu atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

It is interesting to note that all Cu-monodoped ZnnOn clusters can retain a magnetic moment of about 1 lB (see Table 4). From the analysis of Mulliken population, we find that the magnetic moment is mainly contributed by the 3d orbital component of Cu atom and the 2p orbital components of the Cu-surrounding O atoms. These results are very similar to Cu-monodoped bulk ZnO phase [6,8]. Ye et al. [6] and Ferhat et al. [8] predicted that a total magnetic moment of about 1 lB per supercell, respectively, and the local magnetic moments mainly concentrate on Cu atom and its surrounding O atoms. It can be seen from Table 4 that the local magnetic moment of Cu atom increases generally with the cluster size increasing. For different doping modes of each cluster size, the local magnetic moment of Cu atom is found to be different, which indicates that the local magnetic moment of Cu atom is dependent on the geometry of the clusters. Similar behavior was found in other transition metal-atoms doped Zn12O12 cluster [37,39,40]. For example, for Mn-monodoped Zn12O12 cluster [39], the substitutional-doping makes the Mn atom have a magnetic moment of 4.78 lB, and the different sites of endohedral-doping make the Mn atom have magnetic moments of 4.87 lB and 4.65 lB, respectively. It should be pointed out, however, for the magnetic TM atom-doped ZnO clusters, that the total magnetic moment mainly arises from the TM atom, whereas the contribution of the O atoms surrounding TM atom is quite little, which is quite different from the case of Cu-doping. As can be seen from Table 4, the

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HOMO–LUMO gaps of Cu-monodoped ZnnOn clusters are usually much smaller than those of the corresponding pure ZnnOn clusters. To understand this, we have examined the total and partial density of states (PDOSs) from the contribution of different orbitals components. Fig. 5 gives the PDOS of pure and Cu-doped Zn9O9 clusters as an example, since the same features are found in all the Cumonodoped ZnnOn clusters. The electronic states near the Fermi level are mainly from p and d states with only little contribution from s states. Therefore, the p–d hybridization is believed to be responsible for the reduction of HOMO–LUMO gaps because of the addition of Cu atom. Note that the net spin (spin-up minus spin-down) is detected from the PDOSs, which is in complete agreement with the analysis of Mulliken population. 3.3. Cu-bidoped ZnnOn (n = 3, 9, 12) clusters We then investigate Cu-bidoped ZnnOn (n = 3, 9, 12) clusters. The fully optimized lowest-energy structures are shown in Fig. 6, and the calculated results are presented in Table 5. We only consider substitutional and exohedral doping for a Zn3O3 cluster because of the small inner space. For the substitutional Cu-bidoped Zn3O3 cluster, the ferromagnetic (FM) and antiferromagnetic (AFM) states have the same geometry as shown in Fig. 6(3D). However, the structure with FM state is more stable than that with AFM state by 0.1 eV in energy. A total magnetic moment of 2 lB is found in ferromagnetic Cu-bidoped Zn3O3 cluster. For Cu-bidoped bulk ZnO with various Cu concentrations, theoretical calculations also predicted that the FM configuration with a total magnetic moment of 2 lB per supercell is ground state structure [6,9]. For the exohedral Cu-bidoped Zn3O3 cluster (Fig. 6(3E)), it is found to have zero magnetic moment with the spins on Cu atoms being completely quenched. Although we have considered all possible locations of two Cu atoms in Zn9O9 cluster, the three lowest-energy structures of Cubidoped Zn9O9 clusters have zero magnetic moment, and there is 18

(a)

(b)

9

PDOS (electrons/eV)

0

-9

-18 18

(c)

(d)

9

0

-9

-18

-4

-2

0

2

-4

-2

0

2

Energy (eV) s s

p p

d d

sum sum

Fig. 5. Total and partial density of states (spin-up and spin-down) for (a) substitutionally, (b) exohedrally, (c) endohedrally Cu-monodoped Zn9O9 and (d) pure Zn9O9 clusters. The vertical line indicates the Fermi level.

Fig. 6. The lowest-energy structures of Cu-bidoped ZnnOn (n = 3, 9, 12) clusters. Red balls represent O atoms, gray balls represent Zn atoms, and blue balls represent Cu atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 5 The symmetries, the Cu–Cu distances (d), binding energies per atom (Eb), and HOMO– LUMO gaps (Eg) for the lowest-energy structures of Cu-bidoped ZnnOn (n = 3, 9, 12) clusters. Species

Symmetry

d (Å)

Eb (eV)

Eg (eV)

3D 3E 9D 9E 9F 12D 12E 12F

C2 C1 C1 C1 Cs C1 C1 C2h

2.662 2.340 2.391 2.518 2.705 2.482 2.514 2.166

2.844 2.480 3.031 2.878 2.800 3.116 2.973 2.904

0.767 1.783 0.710 1.393 0.613 0.534 1.364 1.544

not FM or AFM state in existence. The geometrical structure of isomer 9D is similar to that of pristine Zn9O9 cluster except for some local deformations, which mainly occurs around Cu atoms. The exohedral doping process results in evident structural distortion as shown in Fig. 6(9F). For endohedral doping, the cage of Zn9O9 cluster is not large enough to envelop two Cu atoms, so that one Cu atom moves to the cage surface (see Fig. 6(9E)). For substitutional Cu-bidoped Zn12O12 cluster, it is found that the ground state of the cluster is AFM state with the Cu–Cu distance of 2.482 Å, and no other states exist. Our result is different from that of previous study [40]. Chen and Wang [40] reported that the ground state of the substitutional Cu-bidoped Zn12O12 cluster is a para-magnetic (PM) state, and the FM state is only higher 0.186 eV in energy. The disagreement is attributed to the different Cu–Cu distance in the ground state structures. They reported a Cu– Cu distance of 3.133 Å, which is much larger than our results. The AFM ground states were also found in Fe- and Mn-bidoped Zn12O12 cluster, in which Fe and Mn atoms have the same doping sites as Cu atoms [39–41]. For exohedral doping, the lowest-energy structure is shown in Fig. 6(12F). Two Cu atoms in the structure are located on the surface of the Zn12O12 cluster, which is similar to that of isomer 9F. For endohedral doping, the lowest-energy geometry of Cu-bidoped Zn12O12 cluster, as shown in Fig. 6(12E), has C2h

Y. Yong et al. / Computational and Theoretical Chemistry 989 (2012) 90–96

symmetry, which is very different from that of Mn-bidoped Zn12O12 cluster [39]. It is found that exohedral and endohedral Cu-bidoped Zn12O12 clusters have zero magnetic moment with the spins on Cu atoms being completely quenched, which is consistent with that of exohedral and endohedral Cu-bidoped ZnnOn (n = 3, 9) clusters. It is interesting to compare the Cu-bidoped ZnnOn clusters with different doping modes. We find that the substitutional isomers have the largest binding energy per atom among the isomers of the same cluster size, which indicates that they are the most stable ones. The total binding energies of isomers 9F and 12F are lower 1.553 eV and 1.781 eV than those of isomers 9E and 12E, respectively. This may imply that endohedral doped isomers would easily transform into other stable configurations if their surrounding environment is changed, even though they are stable local minima. It can be seen clearly that the HOMO–LUMO gaps of the Cu-bidoped ZnnOn clusters are much smaller than that of corresponding pristine ZnO clusters. The exohedral doped isomers of Zn3O3 and Zn9O9 clusters have larger gaps among different doping modes while the endohedral doped isomer of Zn12O12 has the largest HOMO–LUMO gap. The ground states of the Cu-bidoped ZnnOn cluster have zero magnetic moment with the spins on the Cu atoms being either antiferromagnetically coupled or completely quenched, except for Cu2ZnO3 cluster. As mentioned above, the FM state of Cu2ZnO3 cluster is ground state, and has a total magnetic moment of 2 lB. For the substitutional Cu-bidoped ZnnOn (n = 9, 12) clusters, the Cu pair has a clear tendency of forming cluster (see Table 5), which may induce the disappearance of ferromagnetism. Ma et al. [66] experimentally proved that a ZnO:Cu film in which copper exists in clusters is not ferromagnetic even for clusters as small as CuO4. The exohedral and endohedral doping processes are not conductive to the generation of magnetism in ZnO clusters. This may indicate that Cu-bidoped ZnnOn clusters are not effectively useful for developing DMSs.

4. Summary The structural, electronic, and magnetic properties of Cu-doped ZnnOn (n = 3, 9, 12) clusters have been studied using spin-polarized density functional theory. We firstly investigate the lowest-energy structures of pure ZnnOn (n = 1–13) clusters based on the extensive searching, and identify that the Zn3O3, Zn9O9 and Zn12O12 clusters possess relatively higher stability. Then, these stable clusters are taken as candidates for investigating the effect of Cu-atom doping. The main findings are summarized as follows: (i) For the pure ZnnOn (n = 1–13) clusters, ring structures are most stable for cluster size n = 2–7, while cage or tube structures become energetically favorable for n = 8–13. Calculated results show that Zn3O3, Zn9O9 and Zn12O12 clusters possess relatively higher stability. (ii) The substitutional, exohedral, and endohedral doping with Cu atoms can enhance the stability of the clusters. It is found that the substitutional mono- and bi-doped clusters are the most stable. The HOMO–LUMO gaps of the doped clusters are all reduced due to the p–d hybridization, which are caused by the Cu-atom doping. (iii) For the monodoped clusters, all isomers have magnetic moments of about 1 lB, which is mainly contributed by the Cu 3d and Cu-surrounding O 2p states. However, for the bidoped clusters, the ground states have zero magnetic moment with the spins on the Cu atoms being either antiferromagnetically coupled or completely quenched, except for Cu2ZnO3 cluster.

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Acknowledgments This work was supported by the National Basic Research Program of China (973) under Grant No. 2010CB631304, and the National Natural Science Foundation of China (No. 11074214) and the Ministry of Science and Technology of China.

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