Structural Growth Sequences and Electronic Properties of Zinc Oxide

Mar 9, 2007 - The lowest-energy structures of (ZnO)n are then selected from a number of structural isomers via DFT optimization. For small clusters (n...
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J. Phys. Chem. C 2007, 111, 4956-4963

Structural Growth Sequences and Electronic Properties of Zinc Oxide Clusters (ZnO)n (n)2-18) Baolin Wang,*,†,‡,§ Shigeru Nagase,*,† Jijun Zhao,| and Guanghou Wang§ Department of Theoretical Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan, Department of Physics, Huaiyin Institute of Technology, Jiangsu 223001, People’s Republic of China, National Laboratory of Solid State Microstructures and Department of Physics, Nanjing UniVersity, Nanjing 210093, People’s Republic of China, and State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams School of Physics and Optoelectronic Technology and College of AdVanced Science and Technology, Dalian UniVersity of Technology, Dalian 116024, People’s Republic of China ReceiVed: October 5, 2006; In Final Form: January 13, 2007

The structural and electronic properties of (ZnO)n (n ) 2-18) clusters are studied using gradient-corrected density-functional theory (DFT). The starting structures are generated from empirical genetic algorithm simulations or handmade constructions with chemical intuition. The lowest-energy structures of (ZnO)n are then selected from a number of structural isomers via DFT optimization. For small clusters (n ) 2-7), ring structures were found to be the most stable. Three-dimensional cage and tube structures become energetically preferable for larger clusters (n ) 9-18), and the competition between cage and tube structures leads to the alternative appearance of these two types of structures as global minima. The size evolution of electronic properties for zinc oxide clusters from ring toward cage or tube is discussed.

1. Introduction Zinc oxide (ZnO) is an important semiconducting and piezoelectric material with a wide band gap of 3.37 eV and a large exciton binding energy of 60 meV. It has attracted considerable attention because of the unique combination of material properties and wide range of applications to transducers, varistors, transparent conductors, transparent UV protection films, chemical sensors, solar cells, and so on.1-5 Many methods have been developed to synthesize ZnO nanostructures, such asnanowires,6-18 nanotubes,19-23 nanocages,24,25 nanoparticles,26-30 and nanoflowers.31,32 In particular, Wang’s group has successfully fabricated the freestanding single-crystal nanobelts,33 nanosprings,34 nanorings,35 nanobows,36 and nanohelices37 by bending or folding polar-surface-dominated nanobelts of ZnO, which could be used as nanoscale sensors, transducers, and resonators. In spite of the recent efforts of production of ultrathin nanoparticles, nanowires, nanotubes, and nanocages, the atomic structures of clusters, wires, and tubes formed by ZnO are still not clear.13,14,18,27-29 It is well known that the transition from small clusters to bulk solids involves substantial size-dependent structural reconstruction as well as variations in physical and chemical properties. It would be interesting to elucidate how the bulklike wurtzite structure is formed in ZnO nanostructures with increasing size and to investigate the bonding nature, stability and electronic properties such as highest-occupied molecular orbital (HOMO)-lowest-unoccupied molecular orbital (LUMO) gaps of ZnO nanostructures. On the theoretical side, accurate first-principle calculations on (ZnO)n clusters were limited to relatively smaller size * Corresponding author. Email address: [email protected], [email protected]. † Institute for Molecular Science. ‡ Huaiyin Institute of Technology. § Nanjing University. | Dalian University of Technology.

(n < 10).38-42 The study of larger (ZnO)n clusters (n > 10) were only based on chemical intuition,43 and their lowest-energy structures remain unclear. Therefore, an unbiased search of the global minimum structures using the first-principle method is essential to extend our theoretical knowledge to the mediumsized (ZnO)n clusters, where the transition from molecular behavior to bulklike behavior is expected to occur. Moreover, the structural, electronic properties and bonding character of (ZnO)n clusters are of key importance in understanding the growth mechanism of ZnO-based materials and the usage of low-dimensional ZnO nanostructures for nanoscale materials and devices. In this work, we focus on (ZnO)n clusters with n ) 2-18. An exhaustive search has been performed using densityfunctional theory (DFT) to find the global minimum structure for each cluster size. A crossover from ring to cage/tube structure is found for n ) 8, which was predicted previously in ref 41. Coexistence and competition of two structural growth patterns, i.e., cage structures vs tube structures, are found in the size range of n ) 9-18. The electronic properties of clusters and the correlation with atomic structures and sizes are discussed. 2. Theoretical Method In this work, electronic structure calculations and geometry optimization on (ZnO)n (n ) 2-18) clusters were performed using DFT implemented in the DMol package.44 The generalized gradient approximation was adopted to describe the exchangecorrelation interaction with the parametrization by Perdew, Burke, and Enzerhof (PBE).45 Density functional semi-core pseudopotentials (DSPP)46 fitted to all-electron relativistic DFT results, and double numerical basis set including d-polarization functions (DND)44 were employed. Spin-unpolarized selfconsistent field (SCF) calculations were carried out with a convergence criterion of 10-6 au. for total energies. Geometry optimization was performed using the Broyden-FletcherGoldfarb-Shanno (BFGS) algorithm with a convergence cri-

10.1021/jp066548v CCC: $37.00 © 2007 American Chemical Society Published on Web 03/09/2007

Growth Sequences and Electronic Properties of (ZnO)n terion of 2 × 10-3 au. for the maximum force and 5 × 10-3 Å for the maximum displacement. To conduct an unbiased search of the global minimum structures of ZnO clusters, we combined an empirical genetic algorithm (GA) simulation47,48 with DFT geometry optimization. In the GA simulation, the potential-energy surface (PES) is divided into a number of regions to find a locally stable structure to represent each region. The minima obtained from GA simulation were further optimized at the PBE/DND level. The GA approach has been successfully applied to the geometry optimization of atomic clusters48 in our previous works. In the GA global optimization, the PES of (ZnO)n is approximated by an empirical pairwise potential of Born-Mayer form50 fitted for bulk zinc oxide solid, which predicted the existence of stable spheroid structures of (ZnO)n clusters.38 In addition, we constructed a number of candidate structures of (ZnO)n following some “handmade” structural rules by simple chemical intuition. For all the low-energy structures considered in this work, we found that ZnO clusters prefer Zn-O alternating arrangement. Similar phenomena were found for ZnO clusters by other authors (see refs 41 and 43) and for other II-VI and III-V binary compound clusters.51-61 Hence candidate structures containing Zn-Zn or O-O bonds were eliminated. For each cluster size, 24 structures were generated from either GA search or handmade construction, and they were used as input structures for DFT optimization. With the scheme described above, the lowest-energy structures of (ZnO)n up to n ) 18 have been obtained at the PBE/DND level. The efficiency and validity of the present hybrid scheme were demonstrated in our previous works.47,48 The details of GA are described in our early publication.48 Vibrational frequency calculations and normalmode analyses were then performed on the lowest-energy structures to confirm that they are true minima and to simulate the infrared (IR) spectra. 3. Lowest Energy Structures of Zinc Oxide Clusters 3.1. (ZnO)n (n ) 2-7). The lowest-energy structures and some representative metastable structures obtained for (ZnO)n are presented in Figure 1 for n ) 2-7, Figure 2 for n ) 8-12, and Figure 3 for n ) 13-18, respectively, together with the relative energies with respect to the lowest-energy structures. The most essential results of this work are summarized in Table 1. For diatomic ZnO molecule, the theoretical bond length, binding energy, and vibration frequency at PBE/DND level are 1.73 Å, 2.121 eV, and 664.9 cm-1, respectively. At the same PBE/DND level of theory, the binding energy for the wurtzite solid of ZnO was also calculated using a hexagonal supercell of 108 atoms. The calculated binding energy of 7.33 eV per ZnO agrees well with the experimental data of 7.52 eV per ZnO.62 The calculated Zn-O bond length is 2.005 Å, the ZnO-Zn (or O-Zn-O) bond angles are 109.3°, Mulliken charge on Zn and O is 0.762. The present PBE calculations yield a Γ-point band gap of 0.895 eV, similar to 0.77 eV from previous all-electron local spin-density approximation (LDA) calculations.63 The calculated phonon frequencies at Brillouin zone center for ZnO wurtzite solid are 97, 279, 446, and 553 cm-1, which can be assigned to E2L, B1L, E2H, and A1L modes, respectively. These agree reasonably well with previous LDA results of 91, 261, 440, and 560 cm-1 and experimental values of 100, 438, and 584 cm-1 at 7 K for E2L, E2H, and A1L modes, respectively.49 Therefore we believe that the PBE/DND scheme used here can reproduce the general structural properties and chemical bonding for ZnO nanostructures, though the calculated band gaps are significantly lower than the experimental values.

J. Phys. Chem. C, Vol. 111, No. 13, 2007 4957 The lowest-energy structure found for (ZnO)2 is a rhombus (2a, D2h) with bond length of Zn-O ) 1.914 Å and bond angle of -O-Zn-O ) 103.8°. This structure is 0.752 eV more stable than the linear chain structure (2b). The lowest-energy structure of (ZnO)3 is a hexagon ring (3a, D3h) with bond length of Zn-O ) 1.850 Å and bond angle of -O-Zn-O ) 148.3°. It is 2.461, 3.029, 3.157 eV more stable than a zigzag chain (3b, C1,), a rhombus plus chain (3c, Cs), and 3-dimension structure (3d, C2V), respectively. The lowest-energy structure found for (ZnO)4 is a octagonal ring (4a, D4h) with bond length of Zn-O ) 1.810 Å and bond angle of -O-Zn-O ) 169.7°, which is 2.454 and 3.614 eV more stable than a NaCl-like structure (4b, Td) and a zigzag chain (4c, C1), respectively. Several low-energy structures of (ZnO)5 are shown in Figure 1. The ring structure (5a, D5h) is 2.437 and 2.452 eV more stable than a three-dimensional bowl structure (5b, Cs) and a tetragonal bipyramid structure (5b, Cs), respectively. The average Zn-O bond length of 5a is 1.795 Å and the bond angle for -O-Zn-O is between 178.5 and 178.7°, approaching 180°. In the ring structures (also see 3b and 4c), a strong trend toward an O-Zn-O angle of 180° is found as cluster size increases. It is noticeable that the chain-ring structure (5e, Cs) and the structural isomers C4V (5d) and C2V (5f) with higher symmetry and the higher coordination number are 5.01, 3.70, and 5.28 eV less stable than the most stable one 5a, respectively. A planar ring is obtained for (ZnO)6 (6a, D6h) as the lowestenergy structure. 6a is 0.734 eV more stable than a tube (6b, D3d), which is the thinnest tube following the so-called squares-hexagons route and can be viewed as the embryo of wurtzite structure of ZnO crystal. The planar triple rings (6c, C2h) and bowl (6c, Cs) are 0.951 and 2.048 eV less stable than 6a, respectively. It is noteworthy that the planar structures containing three rings, in which two rings are linked together by a small square, are metastable for (ZnO)6 to (ZnO)12. For (ZnO)8, the triple-rings-based planar structure becomes the most stable, as discussed below. Interestingly, the similar planar triplering structures were found for (BN)n clusters,51 which are energetically very close to the most stable ring structures for n ) 6-15. For (ZnO)7, a planar ring (7a, D7h) was found to be most stable. It is 0.293, 0.301, 0.335, and 0.596 eV more stable than the three-dimensional triple rings (7b, C1) and the twodimensional cagelike structures (7c, Cs, and 7d, C1), and the three-dimensional triple rings structure (7e, C2V), respectively. Other three-dimensional structures such as the cage-like ones (7f, 7h, 7k) and bowl-like ones (7g, 7i, 7j) are energetically unfavorable. It is rather surprising that 7f is unstable despite its high C3V symmetry. It should be pointed out that the energy differences between the most stable ring structures and the metastable threedimensional cage/tube structures are drastically reduced as the clusters become larger. For (ZnO)6, the energy difference between planar and three-dimensional structures is 0.734 eV, whereas such energy difference drops down to only 0.293 eV for (ZnO)7. In addition, the Zn-O bond length shrinks as the ring size increases, i.e., from 1.914 Å for (ZnO)2 to 1.783 Å for (ZnO)7 (see Table 1). These suggest that there is a tendency of forming three-dimensional structures as cluster size increases. The present ringlike configurations as lowest-energy structures for smallest (ZnO)n clusters with n ) 2-7 agree with previous results obtained in ref 41. 3.2. (ZnO)n (n ) 8-12). The low-energy structures obtained for (ZnO)8 to (ZnO)12 are shown in Figure 2. For (ZnO)8, a planar triple-ring structure (8a, C2h) is the most stable. This

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Figure 1. Lowest-energy and metastable structures of (ZnO)n (n ) 2-7). Values in parentheses are relative energies in eV. Blue ball, Zn atom; red ball, O atom.

finding is different from previous results at level of B3LYP,41,43 which predicted that the tubelike structure is most stable. The metastable structure (8b, D4d) from this work can be viewed as a tube built by two “parallel” (ZnO)4 rings linked together by (ZnO)2 rings, which is only 0.015 eV less stable than 8a. The three-dimensional structure (8c, S4) of (ZnO)8, which consists of (ZnO)2 and (ZnO)3 rings, is 0.261 eV less stable than 8a. It can be viewed as a cage structure, where each face is formed by (ZnO)2 and (ZnO)3 rings with a certain rotation. It contains (ZnO)2 rings at the top and the bottom. In total, six rhombuses and four hexagons are found in the 8c structure. Three cagelike structural isomers (8d, 8f, and 8h) are energetically less favorable than 8a by 0.368, 0.512, and 1.803 eV, respectively. The ring (8e), bowl (8g), and planar (8i) structures are 0.458, 0.789, and 1.825 eV less stable than 8a, respectively. Our results in Figures 1 and 2 clearly show competition between monocyclic rings and cagelike structures for the medium-sized (ZnO)n clusters. For smaller clusters with

n ) 2-7, ring structures with Dnh symmetry are more stable than cagelike structures. As cluster size increases, the energy difference between rings and cages becomes small, i.e., 2.454 eV for (ZnO)4, 2.437 eV for (ZnO)5, 0.734 eV for (ZnO)6, and 0.301 eV for (ZnO)7. Eventually, the cage-based structural pattern becomes dominant and a crossover from ring to cage configuration was found at (ZnO)8. For (ZnO)8 and (ZnO)9, the symmetric tubes (8b and 9b) are 0.458 and 1.232 eV more stable than ring structures, respectively. Similar competition between ring and cage was found for BN,51-53 GaN,54 AlN,55,56 CdSe,60 and CdTe61 clusters. For BN clusters,51 the (BN)9 and (BN)10 cages are roughly as stable as the ring isomers of the same sizes, while the (BN)11 cage is more stable than the(BN)11 ring. Meanwhile, the crossover from ring to cage occurs at n ) 6 for (AlN)n55,56 and n ) 8 for (GaN)n.54 For (CdSe)n60 and (CdTe)n61 clusters, the cagelike configurations emerges at n ) 4 and 5, respectively. The present calculations indicate that the critical size for ring-to-cage crossover in (ZnO)n is n ) 8. For (ZnO)8,

Growth Sequences and Electronic Properties of (ZnO)n

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Figure 2. Lowest-energy and metastable structures of (ZnO)n (n ) 8-12). Values in parentheses are relative energies in eV.

a delicate balance between two opposite tendencies was found. On one hand, rings are favored because of the linearity of the O-Zn-O bonds. On the other hand, three-dimensional structures are favored because of the achievement of higher coordination. For (ZnO)9, the three-dimensional spherical structure (9a, C3h) consisting of (ZnO)2 and (ZnO)3 rings is the most stable. The (ZnO)3 blocks may be envisioned as caps of a polyhedron joined by a ring formed by (ZnO)2 and (ZnO)3 units. The ring is formed by the alternating arrangement of one (ZnO)3 unit and two joined (ZnO)2 units. There are six rhombuses and five hexagons in 9a. It should be noted that similar B-N alternating cages were found for BN clusters.52,53 The tube structure (9b, D3h) consisting of three hexagons is 0.243 eV less stable than 9a. 9b may be constructed by adding an extra (ZnO)3 ring to 6b. The cagelike structures (9c and 9d) are 0.507 and 0.528 eV less stable than 9a, respectively. The planar triple-ring structure (9e) has relatively higher energies. For (ZnO)10, the cage structure (10a, C2) consisting of seven (ZnO)2 and four (ZnO)3 rings is most stable. This result is different from a recent study43 that predicted a lowest-energy C3 structure with six (ZnO)2 and six (ZnO)3 rings. In our

calculation, the corresponding structure (10b) is 0.231 eV higher in energy than 10a. 10c with C2h symmetry is 0.411 eV less stable than 10a, while the tube isomer (10d) consisting of two (ZnO)5 and the planar three-ring structure (10e) are energetically unfavorable. For (ZnO)11, the cage structure (11a, Cs) with six (ZnO)2 and seven (ZnO)3 rings is the most stable, as found in a recent study.43 11a can be constructed by removing a ZnO molecule from the most stable structure (12a) of (ZnO)12. The threedimensional structures such as 11b and 11d are 0.868 and 2.146 eV less stable than 11a, respectively. The planar triplering structure (11c) is 2.107 eV less stable than 11a. For (ZnO)12, the most stable structure (12a, Th) is based on six (ZnO)2 and eight (ZnO)3 rings decoration of the truncated octahedron in which all Zn and O vertices remain equivalent. The tetragonal rings satisfy the isolated rule, as do BN fullerenes. The metastable tubelike structures consisting of three (ZnO)4 (12b), four (ZnO)3 rings (12c), and two (ZnO)6 rings (12e) are 1.427, 1.833, and 2.506 eV less stable than 12a, respectively. The cage structures with eight (ZnO)2 units and the planar structures (12d, 12f, and 12 g) were also found for (ZnO)12. A careful examination reveals that decorations of (ZnO)12 based

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Figure 3. Lowest-energy and metastable structures of (ZnO)n (n ) 13-18). Values in parentheses are relative energies in eV.

TABLE 1: Bond Lengths, Bond Angles, BE per ZnO, HOMO-LUMO Gap (∆) of the Lowest-Energy Structures of (ZnO)n (n ) 2-18) n

symmetry

Zn-O (Å)

-O-Zn-O (deg)

-Zn-O-Zn (deg)

BE (eV)

∆ (eV)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

D2h D3h D4h D5h D6h D7h C2h C3h C2 Cs Th C1 Cs C3h Td C1 S6

1.914 1.850 1.810 1.795-1.796 1.788-1.789 1.782-1.783 1.785-2.042 1.902-2.039 1.877-2.117 1.890-2.057 1.864-1.964 1.780-2.070 1.880-2.038 1.887-1.995 1.926-1.959 1.885-2.045 1.887-1.994

103.8 148.3 169.7 178.5-178.7 175.6-176.0 172.2-172.6 82.9-176.2 93.1-135.9 90.2-143.8 88.8-134.9 90.6-129.3 89.1-157.5 94.4-133.9 90.7-133.8 91.6-130.5 91.9-131.2 90.7-134.7

75.9 91.4 99.9 108.7-109.3 115.1-116.4 120.7-121.2 99.1-121.7 83.7-107.2 82.2-115.6 83.1-113.8 86.6-108.2 84.5-122.8 83.9-113.3 87.1-118.2 86.5-112.5 82.5-121.9 85.6-116.4

4.082 5.358 5.792 5.918 5.950 5.958 6.010 6.128 6.162 6.248 6.372 6.334 6.370 6.440 6.460 6.426 6.486

1.261 2.901 3.124 3.291 3.303 3.441 3.735 2.188 2.266 2.154 2.751 2.182 2.133 2.417 2.325 2.109 2.401

on hexagonal faces can be constructed by hexagonal rings and are rhomboidal rather than square in shape, that is, the bond angle is acute at O (86.6°) and obtuse at Zn (90.6°). The

corresponding angles in the six-membered rings are 108.2 and 129.3°, respectively, with significant nonplanarity (“buckling”) of the hexagons. The sides of the rhombuses are relatively long

Growth Sequences and Electronic Properties of (ZnO)n (1.964 Å), but the edges shared by two adjacent hexagons are short (1.866 Å) as in borazine. Similar results were also found for (BN)12,53 in which the rhomboidal angle is acute at N (83°), obtuse at B (95°), and the B-N bond length is 1.54 Å. The bond angles in the six-membered rings are 109 and 127°, and the bond length is 1.46 Å. 3.3. (ZnO)n (n ) 13-18). The lowest-energy and representative metastable structures obtained for (ZnO)n (n)13-18) are presented in Figure 3. The lowest-energy structure (13a, C1) found for (ZnO)13 can be understood as a consequence of (ZnO)12 by face-capping one ZnO molecule on the (ZnO)12 cage. The cage structure (13d) based on six (ZnO)2 and nine (ZnO)3 rings is 1.169 eV higher in energy than 13a, although it was predicted to be the most stable in a recent study.43 This discrepancy may be due to the different choice of computational methodology. To validate our result, we have constructed some cage structures based on six (ZnO)2 and nine (ZnO)3 rings as initial guesses. Upon optimization, these structures transform into 13b, 13c, and 13e, which are less energetically preferred. For (ZnO)14 and (ZnO)15, we successfully reproduced the previously predicted lowest-energy structures (14a and 15a).43 As shown in Figure 3, 14a is based on six (ZnO)2 and ten (ZnO)3 rings, connected by two tetragonal rings, while the 15a cage structure with C3h symmetry consists of six (ZnO)2 and eleven (ZnO)3 rings that satisfy the isolated tetragonal rule. Therefore, 15a is more stable than 14a. It is interesting to note that the metastable structures of (ZnO)14, (ZnO)15, and (ZnO)17 (14b, 15b, and 17b) are based on the incomplete cage of (ZnO)16 (16a). For example, 15b can be view as removing one ZnO molecule from 16a, while 17b is formed by face-capping one ZnO molecule on 16a. This implies that (ZnO)16 is a magicnumber cluster with relatively high stability. Similar to (ZnO)12, the most stable Td structure of (ZnO)16 (16a) is based on an underlying framework, which has six (ZnO)2 rhombuses and twelve (ZnO)3 hexagonal rings, in which each rhombus is completely surrounded by hexagons. In the initial Oh structure there are two distinct sites, one belonging to two hexagons and a square and another at the junction of three hexagons. In the decorated structure, O and Zn atoms occupy two distinct sites, compatible with reduced Td symmetry that has been observed for (BN)16.53 The side lengths of the rhombuses are long (1.959 Å), but the edge lengths shared by two adjacent hexagons are short (1.926 Å), as in borazine. The rhomboidal angle is acute at O (86.5°) and obtuse at Zn (91.6°). The corresponding angles in the six-membered rings are 104.2, 112.5, 118.7, and 130.5°, respectively. It is interesting to note that the isoenergetic structure of (ZnO)16 (16b) is the perfect cage with C3V symmetry that also has six (ZnO)2 rhombuses and twelve (ZnO)3 hexagonal rings, satisfying the isolated rule. The same isoenergetic case is also observed for the lowest energy (18a) and first low-lying isomer (18b) of (ZnO)18. In Figure 3, 17c is constructed by capping one additional ZnO molecule on the distorted structure (16b) of (ZnO)16. Similarly, 17d is constructed by capping two additional ZnO units on the most stable structure (15a) of (ZnO)15. It is interesting to find that removal of one ZnO unit from 18a leads to the most stable structure (17a) of (ZnO)17. 18a and 18b are nearly degenerate in energy, 18b being only 0.002 eV higher than 18a. 18a can be view as an armchair (3, 3) nanotube and 18b as a zigzag (3, 0) tube. Perfect cages were also found for (ZnO)18. For example, 18c consists of 7 isolated four-membered rings, 12 six-membered, and 1 eightmembered ring, while 18d consists of 6 isolated four-membered rings and 14 six-membered rings. 18e and 18f have two

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Figure 4. (a) BE per ZnO, (b) second-order difference of totally energy (∆2En ) En+1 + En-1 - 2En), and (c) HOMO-LUMO gap calculated for (ZnO)n.

interconnected tetragonal rings and eight-membered rings. These cage structures are also close to 18a in energy. The lowest-energy structures of (ZnO)n (n)9-18) follow cage and tube structural growth patterns with stacks of small subunits (ZnO)2 and (ZnO)3 that form spheroid structures. Perfect cage and tube structures are the most stable for (ZnO)12, (ZnO)15, (ZnO)16, and (ZnO)18. Similar structures have also been found for medium-sized BN, AlN, GaN, ZnS, and CdO, clusters.51-59 The structural similarity for (BN)n, (AlN)n, (GaN)n, (ZnO)n, (ZnS)n, and (CdO)n (n ) 10-18) suggests that formation of cages with four- or six-membered rings is the dominant growth pattern of the medium-sized II-IV and III-V compound clusters. On the other hand, tubular structures are metastable for (ZnO)n (n ) 9-18), suggesting that ZnO nanotubes somehow resemble C or BN nanotubes As the cluster becomes larger, hollow cage structures become less favorable and the stuffed fullerene cages are expected to emerge as the precursor of nanocrystalline structures, as found for medium-sized Si64 and CdSe65 nanoclusters. In the present work, stuffed fullerene cages and bulklike structures were not observed for (ZnO)18 yet. To search for the structures other than cages, we constructed some compact and bulklike structures as initial guesses, such as the stuffed fullerene cages and fragments of bulk. Upon geometry optimization, these structures transform to hollow cage or some unstable compact structures with the higher energies. 4. Electronic Properties of Zinc Oxide Clusters For the most stable structures of (ZnO)n, the binding energies per ZnO (BE) are plotted in Figure 4a as a function of n. BE increases rapidly with increase in cluster size n from 2 to 6 and becomes constant for n ) 7-18. The second-order differences of total energies defined by ∆2En ) En+1 + En-1 - 2En are plotted in Figure 4b, which are sensitive to the relative stability of clusters. Local maximum peaks for ∆2E were found at n ) 9, 12, 15, and 16, indicating that these size of clusters are more stable than their neighboring clusters. In Figure 4c, we present the energy gap between the HOMO and LUMO for the lowest-energy structures of (ZnO)n (n ) 2-18). Usually the clusters with larger HOMO-LUMO gaps are more stable and chemically inert. Relatively larger HOMO-LUMO gaps were

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Figure 5. Simulated IR spectra for (ZnO)n (n ) 2-9, 12, 15, 16, 18).

found for the ring structures of small (ZnO)n (n ) 2-8), similar to previous results for small (GaN)n clusters.54 For the larger clusters (n ) 9-18) with cage and tubular structures, their HOMO-LUMO gaps are insensitive to the cluster size and structure. The coincidence between the maximum peaks for ∆2En and HOMO-LUMO gap for n ) 12, 15, and 16 suggests that the relative high stability of the cluster size is dominated by electronic effects instead of geometric effects. For the (ZnO)n and (BN)n cage configurations that satisfy the isolated rhombus rule, we compare the characteristics of chemical bonding. The electronegativity difference between O (3.4) and Zn (1.6) is larger than that between N (3.0) and B (2.0). In other words, ZnO may have more pronounced ionic character than BN. The ionic character of ZnO and BN leads to the analogous growth sequence. On the other hand, the different electronegativity difference (1.8 for Zn and O vs 1.0 for B and N) is partially responsible for difference in the details of cluster structures. For example, the critical size for ring-tocage crossover is n ) 8 for (ZnO)n and n ) 11 for (BN)n. The charge transfer between Zn and O in small ring clusters (n ) 2-8) is smaller than that in cage structures, suggesting that small ring clusters have less ionic character. For the other II-VI compound clusters like CdSe and CdTe, their electronegativity differences are relatively smaller, i.e., about 0.86 between Cd and Se and 0.4 for Cd and Te. Alternating ringlike and cagelike configurations were also observed in those CdSe and CdTe clusters60,61 of different sizes, similar to present results for ZnO clusters. The simulated IR spectra of (ZnO)n (n ) 2-9, 12, 15, 16,18) are presented in Figure 5. For smaller (ZnO)n (n < 8) with ring structures, the dominant peak of IR spectra shift from 550 cm-1 for (ZnO)2 to 830 cm-1 for (ZnO)7, while it comes back to 650 cm-1 for (ZnO)8 with triple-ring structure, close to the vibrational frequency of 664.9 cm-1 for diatomic ZnO molecule. Therefore, the small clusters with ring structures are somewhat moleculelike. For larger clusters with n ) 9, 12, 15, 16, and 18, the dominant IR peaks are located at 570-590 cm-1. For comparison, the computed vibrational frequencies for ZnO solid in wurtzite structure are 97, 279, 446, and 550 cm-1 and the experimental values for the wurtzite crystal are 100,

438, and 584 cm-1 for E2L, E2H, and A1L modes, respectively.49 The predicted trend in IR spectra of (ZnO)n clusters will be helpful in future experiments. 5. Conclusion The main findings from density functional calculations of (ZnO)n (n)2-18) are summarized as follows: (i) Ring structures are most stable for n ) 2-7, while cage and tube structures become dominant for n ) 9-18. A crossover from ring to cage/tube structure was found for n ) 8. (ii) The perfect cage and tube structures were found in (ZnO)12, (ZnO)15, (ZnO)16, and (ZnO)18, which satisfy six isolated rhomboidal rings rule, and they have relatively higher binding energies and larger HOMO-LUMO gaps. These magicnumber clusters are similar to (BN)n clusters of the same size. (iii) The HOMO-LUMO gap and charge transfer between Zn and O are not sensitive to cluster size, which are rather dominated by the local coordination. (iv) Vibrational spectra are helpful to distinguish between rings, cages, tubes, and bulklike structures. Ring structures show a strong peak at around 550-760 cm-1, while the cage and tube structures show strong peaks at around 570-590 cm-1. Acknowledgment. This work was supported by the Grantin-Aid for Scientific Research on Priority Area and Next Generation Super Computing Project (Nanoscience Program) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, the National Natural Science Foundation of China (Grant Nos. 10372045, 10474030, and 90206033), the National Climbing Project of China, the Foundation for the Author of National Excellent Doctoral Dissertation of China (FANEDD, No.200421), and Program for New Century Excellent Talents in University of China. References and Notes (1) Wang, Z. L.; Kong, X. Y.; Ding, Y.; Gao, P. X.; Hughes, W. L.; Yang, R. S.; Zhang, Y. AdV. Funct. Mater. 2004, 14, 944; Wang, Z. L. Mater. Today 2004, 7, 23 and references therein. (2) Tang, Z. K.; Wang, G. K. L.; Yu, P.; Kawasaki, M.; Ohtomo, A.; Koinuma, H.; Segawa, Y. Appl. Phys. Lett. 1998, 72, 3270.

Growth Sequences and Electronic Properties of (ZnO)n (3) Wu, Y.; Kind, H.; Weber, E.; Russo, R.; Yang, P. Science 2001, 292, 1897. (4) Choy, J. H;. Jang, E. S.; Won, J. H.; Chung, J. H.; Jang, D. J.; Kim, Y.W. AdV. Mater. 2003, 15, 1911. (5) Kind, H.; Yan, H.; Law, M.; Messer, B.; Yang, P. AdV. Mater. 2002, 14, 158. (6) Ye, C. H.; Fang, X. S.; Hao, Y. F.; Teng, X. M.; Zhang, L. D. J. Phys. Chem. B 2005, 109, 19758. (7) Zhang, Y.; Wang, N.; Gao, S. Chem. Mater. 2002, 14, 3564. (8) Valyssieres, L. AdV. Mater. 2003, 15, 464. (9) Wang, Y. W.; Zhang, L. D.; Wang, G. Z.; Peng, X. S.; Chu, A. Q.; Liang, C. H. J. Cryst. Growth 2002, 234, 171. (10) Lyu, S. C.; Zhang, Y.; Ruh, H.; Lee, H. J.; Shim, H. W.; Suh, E. K.; Lee, C. J. Chem. Phys. Lett. 2002, 363, 134. (11) Li, S. Y.; Lee, C. Y.; Tseng, T. Y. J. Cryst. Growth 2003, 247, 357. (12) Tian, Z. R.; Voigt, J. A.; Liu, J.; Mckenzie, B.; Mcdermott, M. J. J. Am. Chem. Soc. 2002, 124, 12954. (13) Wang, X. D.; Ding, Y.; Summers, C. J.; Wang, Z. L. J. Phys. Chem. B 2004, 108, 8773. (14) Zhang, D. F.; Sun, L. D.; Yin, J. L.; Yan, C. H.; Wang, R. M. J. Phys. Chem. B 2005, 109, 8786. (15) Xu, L. F.; Guo, Y.; Liao, Q.; Zhang, J. P.; Xu, D. S. J. Phys. Chem. B 2005, 109, 13519. (16) Zhang, H.; Yang, D. R.; Ma, X. Y.; Du, N.; Wu, J. B.; Que, D. L. J. Phys. Chem. B 2006, 110, 827. (17) Kuo, C. L.; Kuo, T. J.; Huang, M. H. J. Phys. Chem. B 2005, 109, 20115. (18) Yin, M.; Gu, Y.; Kuskovsky, I. L.; Andelman, T.; Zhu, Y.; Neumark, G. F.; O’Brien, S. J. Am. Chem. Soc. 2004, 126, 6206. (19) Zhang, X. H.; Xie, S. Y.; Jiang, Z. Y.; Zhang, X.; Tian, Z. Q.; Xie, Z. X.; Huang, R. B.; Zheng, L. S. J. Phys. Chem. B 2003, 107, 10114. (20) Kong, X. Y.; Ding, Y.; Wang, Z. L. J. Phys. Chem. B 2004, 108, 570. (21) Yu, H. D.; Zhang, Z. P.; Han, M. Y.; Hao, X. T.; Zhu, F. R. J. Am. Chem. Soc. 2005, 127, 2378. (22) Hu, J. Q.; Li, Q.; Meng, X. M.; Lee, C. S.; Lee, S. T. Chem. Mater. 2003, 15, 305. (23) Wu, D.; Huang, L. D.; Wang, Q. J.; Zhao, X. N.; Li, A. D.; Chen, Y. F.; Ming, N. B. Mater. Chem. Phys. 2006, 96, 51. (24) Gao, P. X.; Wang, Z. L. J. Am. Chem. Soc. 2003, 125, 11299. (25) Fan, H. J.; Scholz, R.; Kolb, F. M.; Zacharias, M.; Gosele, U. Solid State Commun. 2004, 130, 517. (26) Ischenko, V.; Polarz, S.; Grote, D.; Stavarache, V.; Fink, K.; Driess, M. AdV. Funct. Mater. 2005, 15, 1945. (27) Antony, J.; Chen, X. B.; Morrison, J.; Bergman, L.; Qianga, Y. Appl. Phys. Lett. 2005, 87, 241917. (28) Mahamuni, S.; Borgohain, K.; Bendre, B. S.; Leppert, V. J.; Risbud, S. H. J. Appl. Phys. 1999, 85, 2861. (29) Pesika, N. S.; Hu, Z.; Stebe, K. J.; Searson, P. C. J. Phys. Chem. B 2002, 106, 6985. (30) Zhang, W. H.; Shi, J. L.; Wang, L. Z.; Yan, D. S. Chem. Mater. 2000, 12, 1408. (31) Gao, X. D.; Li, X. M.; Yu, W. D. J. Phys. Chem. B 2005, 109, 1155. (32) Pan, Z. W.; Dai, Z. R.; Wang, Z. L. Science 2001, 291, 1947; Bai, X.D.; Gao, P. X.; Wang, Z. L. Appl. Phys. Lett. 2003, 82, 4806. (33) Jiang, C. L.; Zhang, W. Q.; Zou, G. F.; Yu, W. C.; Qian, Y. T. J. Phys. Chem. B 2005, 109, 1361. (34) Kong, X. Y.; Wang, Z. L. Nano Lett. 2003, 3, 1625. (35) Kong, X. Y.; Ding, Y.; Yang, R. S.; Wang, Z. L. Science 2004, 303, 1348.

J. Phys. Chem. C, Vol. 111, No. 13, 2007 4963 (36) Hughes, W. L.; Wang, Z. L. J. Am. Chem. Soc. 2004, 126, 6703. (37) Gao, P. X.; Ding, Y.; Mai, W. J.; Hughes, W. L.; Lao, C. S.; Wang, Z. L. Science 2005, 309, 1700. (38) Behrman, E. C.; Foehrwiser, R. K.; Myers, J. R.; French, B. R. Phys. ReV. A 1994, 49, R1542. (39) Zandler, M. E.; Behrman, E. C.; Arrasmith, M. B.; Myers, J. R.; Smith, T. V. THEOCHEM 1996, 362, 215. (40) Lu, X.; Xu, X.; Wang, N. Q.; Zhang, Q.; Ehara, M.; Nakatsuji, H. Chem. Phys. Lett. 1998, 291, 445. (41) Matxain, J. M.; Fowler, J. E.; Ugalde, J. M. Phys. ReV. A 2000, 62, 053201. (42) Jain, A.; Kumar, V.; Kawazoe, Y. Comput. Mat. Sci. 2005, 36, 258. (43) Matxain, J. M.; Mercero, J. M.; Fowler, J. E.; Ugalde, J. M. J. Am. Chem. Soc. 2003, 125, 9495. (44) DMOL is a DFT program distributed by Accelrys, Inc. Delley, B. J. Chem. Phys. 1990, 92, 508; J. Chem. Phys. 2000, 113, 7756. (45) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (46) Hamann, D. R.; Schluter, M.; Chiang, C. Phys. ReV. Lett. 1979, 43, 1494. (47) Zhao, J. J.; Xie, R. H. J. Comput. Theor. Nanosci. 2004, 1, 117 and references therein. (48) Wang, B. L.; Zhao, J. J.; Chen, X. S.; Shi, D. N.; Wang, G. H. Phys. ReV. A 2005, 71, 033201; Wang, B. L.; Zhao, J. J.; Chen, X. S.; Shi, D. N.; Wang, G. H. Phys. ReV. A 2005, 72, 023204. (49) Serrano, J.; Romero, A. H.; Manjon, F. J.; Lauck, R.; Cardona, M.; Rubio, A. Phys. ReV. B 2004, 69, 094306. (50) Nyberg, M.; Nygren, M. A.; Pettersson, L. G. M.; Gay, D. H.; Rohl, A. L. J. Phys. Chem. 1996, 100, 9054. (51) Matxain, J. M.; Ugalde, J. M.; Towler, M. D.; Needs, R. J. J. Phys. Chem. A 2003, 107, 10004. (52) Strout, D. L. J. Phys. Chem. A 2001, 105, 261. (53) Seifert, G.; Fowler, R. W.; Mitchell, D.; Porezag, D.; Frauenheim, T. Chem. Phys. Lett. 1997, 268, 352. (54) Zhao, J. J.; Wang, B. L.; Zhou, X. L.; Chen, X. S.; Lu, W. Chem. Phys. Lett. 2006, 422, 170. (55) Wu, H. S.; Zhang, F. Q.; Xu, X. H.; Zhang, C. J.; Jiao, H. J. J. Phys. Chem. A 2003, 107, 204. (56) Costales, A.; Blanco, M. A.; Francisco, E.; Pandey, R.; Pendas, A. M. J. Phys. Chem. B 2005, 109, 24352. (57) Matxain, J. M.; Irigoras, A.; Fowler, J. E.; Ugalde, J. M. Phys. ReV. A 2001, 64, 013201. (58) Hamad, S.; Catlow, C. R. A.; Spano, J E.; Matxain, M.; Ugalde, J. M. J. Phys. Chem. B 2005, 109, 2703. (59) Matxain, J. M.; Mercero, J. M.; Fowler, J. E.; Ugalde, J. M. J. Phys. Chem. A 2003, 107, 9918. (60) Troparevsky, M. C.; Kronik, L.; Chelikowsky, J. R. Phys. ReV. B 2001, 65, 033311. (61) Bhattacharya, S. Kr.; Kashirsagar, A. P. Phys. ReV. B 2007, 75, 035402. (62) Jaffe, J. E.; Snyder, J. A.; Lin, Z.; Hess, A. C. Phys. ReV. B 2000, 62, 1660. (63) Usuda, M.; Hamada, N.; Kotani, T.; van Schilfgaarde, M. Phys. ReV. B 2002, 66, 125101. (64) Yoo, S.; Zhao, J. J.; Wang, J. L.; Zeng, X. C. J. Am. Chem. Soc. 2004, 126, 13845; Wang, J. L.; Zhou, X. L.; Wang, G. H.; Zhao, J. J. Phys. ReV. B 2005, 71, 113412; Zhao, J. J.; Wang, J. L.; Jellinek, J.; Yoo, S.; Zeng, X. C. Eur. Phys. J. D 2005, 34, 35. (65) Kasuya, A.; Sivamohan, R.; Barnakov, Y. A.; Dmitruk, I. M.; Nirasawa, T.; Romanyuk, V. R.; Kumar, V.; Mamykin, S. V.; Tohji, K.; Jeyadevan, B.; Shinoda, K.; Kudo, T.; Terasaki, O.; Liu, Z.; Belosludov, R. V.; Sundararajan, V.; Kawazoe, Y. Nature Mat. 2004, 3, 99.