J. Phys. Chem. C 2010, 114, 5741–5744
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Atomic Structure of the Magic (ZnO)60 Cluster: First-Principles Prediction of a Sodalite Motif for ZnO Nanoclusters Baolin Wang,*,† Xiaoqiu Wang,‡ and Jijun Zhao*,§,| Department of Physics, Yancheng Institute of Technology, Jiangsu, 224051, China, Department of Physics, Huaiyin Teachers College, Jiangsu, 223001, China, Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian UniVersity of Technology), Ministry of Education, Dalian 116024, China, and College of AdVanced Science and Technology, Dalian UniVersity of Technology, 116024, China ReceiVed: September 02, 2009; ReVised Manuscript ReceiVed: February 22, 2010
Very recently, mass spectroscopy of ZnO clusters revealed a hitherto unknown (ZnO)60 magic-number cluster with exceptional stability. Using first-principles approaches, we searched the most stable structures of mediumsize (ZnO)n clusters by considering several possible structural motifs. Instead of the previously nominated nested cage for (ZnO)60, we found a sodalite structure via coalescence of (ZnO)12 cages, which was predicted to be a metastable phase in bulk ZnO solid. Due to the smaller influence of surface reconstruction, this sodalite motif is very competitive for larger (ZnO)n clusters up to n ) 96. 1. Introduction Zinc oxide (ZnO) is a versatile material that shows promising performance in a variety of applications such as optoelectronics, spintronics, photovoltaics, photocatalysts, sensors, piezoelectric transducers, and biomedical sciences.1 Under ambient conditions, ZnO crystallizes in the wurtzite (WZ) structure. Under hydrostatic compression, WZ-ZnO transforms to the highdensity rocksalt (RS) phase at a pressure of 9.1 GPa.2 Recent first-principles studies have explored the relative stability of other bulk ZnO polymorphs,3-5 including zinc blende, graphitic (unbuckled wurtzite) or hexagonal (HX), body-centered-tetragonal (BCT), etc. In particular, Bromley’s group4 has predicted a low-density structure via coalescence of (ZnO)12 nanocages, namely, the sodalite (SOD) phase, which is more favorable than the RS-ZnO and HX-ZnO polymorphs and lies only 0.15 eV above the WZ-ZnO. Besides the pressure-induced phase transition in crystalline solids, low-dimensional nanostructures may exhibit new structural phases (probably with novel physical properties). For example, Freeman’s first-principles calculations revealed that the flat graphitic structure is more energetically favorable than the conventionally buckled wurtzite one in the two-dimensional (2D) ultrathin ZnO films.6 For one-dimensional (1D) ZnO nanowires, atomistic simulations also predicted the occurrence of WZ-to-HX structural transformation either in the ultrathin size range (diameter less than 1.3 nm)7 or under external tensile/ elongation loading.8,9 Intuitively, one may anticipate that further reducing the system dimensionality to zero-dimension (0D) would lead to some new structures. It is generally recognized that the atomic structure of a cluster usually deviates from the bulk fragment due to large surfaceto-volume ratio and the consequent surface reconstruction. Currently, experimental information on the structures and * To whom correspondence should be addressed. E-mail:
[email protected] (J.Z.) and
[email protected] (B.W.). † Yancheng Institute of Technology. ‡ Huaiyin Teachers College. § Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education. | College of Advanced Science and Technology, Dalian University of Technology.
stabilities of ZnO clusters is very limited. The time-of-flight mass spectrum of small gas-phase (ZnO)n clusters (up to n ) 20) recorded by Kukreja et al. shows no magic number.10 Meanwhile, first-principles calculations have been carried out to explore the lowest energy structures of ZnO clusters.11-18 The smallest (ZnO)n clusters (n e 7) were found to adopt Zn-O alternating ring configurations,13-16 whereas a ring-to-cage transition at n ) 8 was found.13,15,16 For the medium-sized (ZnO)n clusters with n ) 9-48, our recent studies16,18 suggested that hollow structures with cage and tube-like configurations are the most preferred motif, whereas the onion-like and wurtzite-like structures become more and more favorable with increasing cluster size. However, little is known for the larger (ZnO)n cluster beyond n ) 50. Very recently, time-of-flight mass spectroscopy of zinc oxide clusters produced by laser ablation of bulk zinc peroxide powder revealed relatively high abundance at (ZnO)34, (ZnO)60, and (ZnO)78,19 whereas (ZnO)60 exhibits exceptionally high stability (namely, “magic number”). It is noteworthy that the magic number of 60 monomers was not experimentally observed for semiconductor compound clusters of either II-IV or III-V groups, even though C60 is a famous magic cluster. By analogue to the previous finding of the magic (CdSe)34 cluster with a core-shell structure,20 onion-like nested cage configurations were proposed for those magic ZnO clusters, that is, (ZnO)6@(ZnO)28 for (ZnO)34 and (ZnO)12@(ZnO)48 for (ZnO)60, etc. In this work, by comparing different structural patterns in the medium-sized range we show that the magic-number (ZnO)60 cluster can be interpreted by a (ZnO)12-based sodalite structure rather than the previously proposed nested cage. This theoretical finding, together with the recent experimental observation,19 sheds some light on the growth behavior and relative stability of ZnO nanoclusters and provides indirect evidence for the existence of the new SOD phase in the ZnO nanostructures. 2. Methods First-principles calculations on zinc oxide clusters with up to 96 monomers were carried out with gradient-corrected density functional theory (DFT) implemented in the DMol3
10.1021/jp908472h 2010 American Chemical Society Published on Web 03/05/2010
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Figure 1. Atomic structures of six representative isomers of the (ZnO)60 cluster (data in parentheses are the point group symmetries and the energy differences with regard to the lowest energy D3 sodalite structure): red, oxygen; gray, zinc.
program.21 The generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) parametrization22 was adopted to describe the exchange-correlation interaction. Density functional semicore pseudopotentials (DSPP)22 fitted to all-electron relativistic DFT results, and double numerical basis set including d-polarization functions (DND)21 were employed. The accuracy of this PBE/DSPP/DND scheme has been assessed via testing calculations on the ZnO molecule and wurtzite bulk in our previous works.16,18 Vibrational analysis of the ZnO clusters in their equilibrium configurations has been made to ensure that there are no imaginary frequencies corresponding to the saddle points on the potential energy surface (PES). Due to the large number of atoms, it is very difficult to perform an unbiased global search to determine the lowest energy structures of the (ZnO)n clusters with n > 20. Instead, we obtained a number of candidate structures via “hand-made” construction guided by simple chemical intuition or following those previously proposed structural patterns. 3. Results and Discussion Here we have constructed ∼20 structural isomers for (ZnO)60. Six of them are presented in Figure 1 as representatives. Among all structural isomers considered, a sodalite structure (D3, Figure 1a)4 based on coalescence of eight (ZnO)12 cages via face and edge sharing is the most energetically preferred. Careful examination shows that it is composed of totally 5 (ZnO)2 sharing squares and 13 sharing (ZnO)3 hexagons. Other sodalite isomers with (ZnO)12 cages linked together in different fashions were also considered. For example, a S6 sodalite configuration by seven (ZnO)12 cages with six sharing squares and six sharing hexagons is higher in energy by 5.82 eV. This implies that the SOD-(ZnO)60 cluster tends to maximize the number of sharing faces or the total number of (ZnO)12 building cages. Similar behavior was found for other sized SOD-(ZnO)n clusters, as we will discuss later. In previous theoretical studies,15,16 the (ZnO)12 cluster with Th cage configuration (i.e., truncated octahedron with six quadrangular faces and eight hexagonal faces) was found to possess particularly high stability with regard to the other small (ZnO)n clusters, suggesting that it is
Wang et al. suitable to serve as a building block for constructing ZnO polymorphs in nanoscale and bulk phases. As shown in Figure 1, other metastable structures considered here are energetically less favorable by at least 1.5 eV. The second-lowest energy structure for (ZnO)60 is a capsule-like cage (S6 symmetry, Figure 1b) with 6 (ZnO)2 squares and 56 (ZnO)3 hexagons, satisfying the isolated square rule originally proposed for the BN nanocages.24 It can be achieved from a Th cage of (ZnO)4818 by inserting a (6, 6) armchair ring of alternate ZnO pairs along the 6-fold axis. Moreover, finite-length single-walled ZnO nanotubes25 of different lengths and diameters have been systematically considered and their energies are roughly comparable to each others. As a representative, an ultrathin (3, 3) tube with six and a half repeating unit cells and two octagonal (ZnO)4 rings on the ends is shown in Figure 1d, which is 2.4 eV higher in energy that the lowest energy SOD structure. In addition to the capsule-like and tube-like hollow configurations, we also considered a highly spherical cage (I symmetry, Figure 1f), which consists of 30 squares, 20 hexagons, and 10 decagons. This configuration was previously suggested for the (BN)60 nanocage,26 but it is rather energetically unfavorable by about 9 eV. Inspired by the core-shell structure found for (CdSe)34,20 an onion-like structure by stuffing a (ZnS)12 cage inside a (ZnS)48 cage was recently proposed for (ZnS)60.27 The (ZnS)2 squares of both interior and outer cages are placed in the vertices of two octahedra and are very well aligned, so that both octahedra share the same axis. The same nested (ZnO)12@(ZnO)48 cage with Th symmetry (Figure 1c) was suggested by Dmytruk.19 However, our first-principles calculations show that it is less favorable than the most stable D3 sodalite structure by 1.76 eV. To further compare the ZnO clusters with other II-VI compound clusters, we also investigated the structures of (CdSe)34, (CdSe)60, and (ZnS)60 clusters. In line with previous works,20,27 we found that a (CdSe)6@(CdSe)28 core-shell configuration with C3 symmetry is most favorable for (CdSe)34 and that the energies of the onion-like (ZnS)12@(ZnS)48 and (CdSe)12@(CdSe)48 structures are lower than the corresponding sodalite structures by 2.4 and 2.34 eV, respectively. On the contrary, a similar onion-like cage of (ZnO)6@(ZnO)28 is only a metastable local minimum on the PES and is less favorable than the lowest energy configuration (a capsule-like C3 cage) by 1.76 eV. This indicates that the (CdSe)6 core fit perfectly to the outer (CdSe)28 cage, whereas (ZnO)6 and (ZnO)28 do not match well. The difference in the structural growth pattern between ZnO clusters and the other II-VI compound (like CdSe, ZnSe, and ZnS) clusters can be partially understood by the ionicity of these polar covalent Zn-O, Cd-Se, Zn-S, and Zn-Se bonds, which can be characterized by the electronegativity difference (∆χ) between the two component elements,28 that is, ∆χ ) 1.79 for ZnO, 0.93 for ZnS, 0.9 for ZnSe, and 0.86 for CdSe (under the Pauling definition of electronegativity29). Hence, the chemical bonding in ZnO clusters is more ionic than that in the CdSe, ZnSe, and ZnS clusters. Accordingly, our Mulliken analysis of the (ZnO)60, (CdSe)60, (ZnSe)60, and (ZnS)60 clusters with the same D3 SOD configuration also revealed that the average charge transfer between the cationic and anionic ions is 0.73 electron for ZnO, 0.47 electron for CdSe, 0.33 electron for ZnSe, and 0.25 electron for ZnS, respectively. The stronger ionicity in the ZnO clusters indicates that the existence of Zn-Zn or O-O bonds is energetically unfavorable. The core-shell configurations inevitably contain this kind of bonds, whereas these Zn-Zn and O-O bonds can be avoided in the SOD
Atomic Structure of the Magic (ZnO)60 Cluster structures formed by the (ZnO)12 building cages. In short, the greater ionicity in the ZnO cluster may account for the preference of SOD structures rather than the core-shell configurations. For bulk ZnO crystals, first-principles calculations show that the low-density SOD phase is marginally more stable than the HX-ZnO phase by only 0.01 eV/ZnO and lies 0.15 eV/ZnO above that of WZ-ZnO. Several bulk-like isomers as fragments of wurtzite solid were also constructed for (ZnO)60. The best of them is shown in Figure 1e, which is less energetically preferred than the most stable D3 sodalite structure by 3.07 eV. It can be viewed as a finite-length cylindrical nanowire cutting along the [0001] direction of the WZ-ZnO crystal. However, upon relaxation the regular wurtzite structure of (ZnO)60 is unstable and transforms into the unbuckled wurtzite structure (i.e., graphitic or HX-type). Similar WZ-to-HX transformation was recently observed in the infinite ultrathin ZnO nanowires.7,8 Zhang and Huang pointed out that surface reconstruction is the major driving force for such structural transformation in the ZnO nanostructures.7 In contrast to the WZ-ZnO nanostructures, due to the unique multicage architecture of the SOD structures as well as the high stability of each (ZnO)12 building cage15,16 the surface reconstruction effect is much less pronounced for a complete SOD nanostructure with a suitable number of atoms. For example, on the D3 SOD-(ZnO)60 configuration the Zn-O-Zn bond angles for the surface O vertex range from 86.7° to 91.9° for the smaller angle (within the (ZnO)2 square) and from 105.5° to 115.6° for the larger angle (within the (ZnO)3 hexagon), respectively, which are reasonably close to the angles of 90° and 120° for the SOD-ZnO solid. Meanwhile, the energy difference between the lowest energy SOD-(ZnO)60 structure and the bulk phase of the SOD-ZnO solid is only 0.49 eV per ZnO, which is lower than the typical surface energy of the WZ-ZnO solid (about 0.7-2.0 eV per surface ZnO).30 Therefore, in the 0D ZnO nanoclusters (at least at particular sizes), the SOD motif may prevail over the WZ or HX ones due to the lower influence of surface reconstruction. Other isomer structures generated either from different polymorphic phases (RS, HX, LTA, FAU, BCT-4) of ZnO3-5 or amorphous ZnO solids were also considered but they were all found to be rather energetically unfavorable with regard to the lowest energy SOD structure. To further investigate the relative stability of this SOD motif and to reveal the growth sequence of the ZnO nanoclusters, we have constructed a series of sodalite structures for (ZnO)n (n ) 36, 48, 78, and 96). The lowest energy SOD structures for each size are shown in Figure 2, which consist of 4, 6, 11, and 15 (ZnO)12 cages for (ZnO)36, (ZnO)48, (ZnO)78, and (ZnO)96, respectively. Again, we found that the SOD structures tend to maximize the number of (ZnO)12 building cages. For instance, a Th SOD-(ZnO)96 configuration with 15 cages (shown in Figure 2) is 7.49 eV lower in energy than a SOD isomer of D3 symmetry consisting of 14 building cages. For SOD-(ZnO)78, an S6 isomer with 9 (ZnO)12 cages is 0.89 eV less favorable than the most stable C3 structure (see Figure 2) with 11 cages. Other structural motifs (hollow cage/tube, onion-like, bulk fragment or HX-type, etc.)16-18 were considered for comparison. For each size, we constructed ∼20 isomers. The binding energies (BE) of these (ZnO)n clusters for different structural patterns are plotted in Figure 3. The smaller (ZnO)n clusters with n e 48 favor cage/tube structures, as has already been shown in our previous work.18 For the larger clusters (n g 60), the sodalite structure prevails over the other motifs at the cluster sizes studied
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Figure 2. The most stable sodalite structures for (ZnO)36, (ZnO)48, (ZnO)78, and (ZnO)96 clusters: red, oxygen; gray, zinc.
Figure 3. Binding energies of (ZnO)n clusters per ZnO monomer at selected sizes (n ) 34, 36, 48, 60, 78, 96) for four structural motifs.
(n ) 60, 78, 96); onion-like and HX-type structures also exhibit enhanced relative stability with respect to the hollow cage/tube ones. It seems that the SOD clusters have to be stabilized by a sufficient number of (ZnO)12 building cages. For the energetically unfavorable (ZnO)36 and (ZnO)48 clusters, there are only four and six (ZnO)12 cages, respectively. Note that the SOD phase predicted for bulk ZnO solid4 was not experimentally confirmed yet. The present theoretical results indirectly support the existence of SOD motif at the 0D nanostructures of ZnO. As cluster size further increases (e.g, n > 100), bulk-like WZ structural pattern would eventually become dominant due to the weakening of the surface reconstruction effect. In the future, it would be interesting to explore such a SOD-to-WZ transition. The emergence of the unique SOD structures in the ZnO nanoclusters may result in electronic properties distinctly different from those of the other motifs. We found that these low-density SOD-(ZnO)n clusters exhibit larger electronic gaps compared to those with more compact structural isomers. For example, the theoretical HOMO-LUMO gap of SOD-(ZnO)60 (D3) is 2.035 eV, while it is 1.65 eV for HX-(ZnO)60 and 1.417 eV for onion-like (ZnO)60. For (ZnO)96, the HOMO-LUMO gap is 1.973 eV for the SOD structure and 1.494 eV for the HX isomer. For reference, the band gap calculated for the ZnO solid is 0.895 eV16 (experimental value: 3.37 eV). The gap underestimation is a well-known deficiency of standard DFT, which is even more severe in the case of ZnO systems.31,32 Thus
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the true gaps of the medium-sized SOD-(ZnO)n clusters should be higher (about 4-5 eV). 4. Conclusions To summarize, comparison of a number of isomer structures for ZnO clusters revealed an energetically preferred SOD motif for the medium-sized clusters at (ZnO)60, (ZnO)78, and (ZnO)96. This SOD structure, recently proposed as a metastable phase of bulk ZnO polymorphs, can give a reasonable answer to the magic-number peak at n ) 60 by recent experimental mass spectrum. The SOD-ZnO nanostructures, as a result of selfassembly of (ZnO)12 building cages with very energetically favorable surface, offer a variety of electronic, chemical, and structural possibilities. We hope that this study will stimulate experimental efforts toward the synthesis and confirmation of this type of novel ZnO nanoclusters. Acknowledgment. This work was supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (FANEDD, No. 200421), the National Natural Science Foundation of China (10874052), the Program for New Century Excellent Talents in University of China (NCET06-0281), and the Ph.D. Programs Foundation of Education Ministry of China (20070141026). We thank Prof. Shengbai Zhang and Prof. Zhongfang Chen for stimulating discussions. References and Notes (1) Klingshirn, C. Phys. Status Solidi B 2007, 244, 3027. (2) Desgreniers, S. Phys. ReV. B 1998, 58, 14102. (3) Schleife, A.; Fuchs, F.; Furthmu¨ller, J.; Bechstedt, F. Phys. ReV. B 2006, 73, 245212. (4) Carrasco, J.; Illas, F.; Bromley, S. T. Phys. ReV. Lett. 2007, 99, 235502. (5) Wang, J.; Kulkarni, A. J.; Sarasamak, K.; Limpijumnong, S.; Ke, F. J.; Zhou, M. Phys. ReV. B 2007, 76, 172103. (6) Freeman, C. L.; Claeyssens, F.; Allan, N. L.; Harding, J. H. Phys. ReV. Lett. 2007, 99, 235502. (7) Zhang, L.; Huang, H. Appl. Phys. Lett. 2007, 90, 023115. (8) Wang, B. L.; Zhao, J. J.; Jia, J. M.; Shi, D. N.; Wan, J. G.; Wang, G. H. Appl. Phys. Lett. 2008, 93, 021918.
Wang et al. (9) Kulkarni, A. J.; Zhou, M.; Sarasamak, K.; Limpijumnong, S. Phys. ReV. Lett. 2007, 97, 105502. (10) Kukreja, L. M.; Rohlfing, A.; Misra, P.; Hillenkamp, F.; Dreisewerd, K. Appl. Phys. A: Mater. Sci. Process. 2004, 78, 641. (11) Behrman, E. C.; Foehrweiser, R. K.; Myers, J. R.; French, B. F.; Zandler, M. E. Phys. ReV. A 1994, 49, R1543. (12) Matxain, J. M.; Fowler, J. E.; Ugalde, J. M. Phys. ReV. A 2000, 62, 053201. (13) Matxain, J. M.; Mercero, J. M.; Fowler, J. E.; Ugalde, J. M. J. Am. Chem. Soc. 2003, 125, 9494. (14) Jain, A.; Kumar, V.; Kawazoe, Y. Comput. Mater. Sci. 2006, 36, 258. (15) Reber, A. C.; Khanna, S. N.; Hunjan, J. S.; Beltran, M. R. Eur. Phys. J. D 2007, 43, 221. (16) Wang, B. L.; Nagase, S.; Zhao, J. J.; Wang, G. H. J. Phys. Chem. C 2007, 111, 4956. (17) Zhao, M.; Xia, Y.; Tan, Z.; Liu, X.; Mei, L. Phys. Lett. A 2007, 372, 39. (18) Wang, B. L.; Wang, X. Q.; Chen, G. B.; Nagase, S.; Zhao, J. J. J. Chem. Phys. 2008, 128, 144710. (19) Dmytruk, A.; Dmitruk, I.; Blonskyy, I.; Belosludov, R.; Kawazoe, Y.; Kasuya, A. Microelectronics J. 2009, 40, 218. (20) Kasuya, A.; Sivamohan, R.; Barnakov, Yu. 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. Nat. Mater. 2004, 3, 99. (21) Delley, B. J. Chem. Phys. 1990, 92, 508. (22) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (23) Hamann, D. R.; Schluter, M.; Chiang, C. Phys. ReV. Lett. 1979, 43, 1494. (24) Sun, M. L.; Slanina, Z.; Lee, S. L. Chem. Phys. Lett. 1995, 233, 279. (25) Wang, B. L.; Nagase, S.; Zhao, J. J.; Wang, G. H. Nanotechnology 2007, 18, 345706. (26) Pokropivny, V. V.; Skorokhod, V. V.; Oleinik, G. S.; Kurdyumov, A. V.; Bartnits-kaya, T. S.; Pokropivny, A. V.; Sisonyuk, A. G.; Sheichenko, D. M. J. Solid State Chem. 2000, 154, 214. (27) Spano´, E.; Hamad, S.; Catlow, C. R. A. Chem. Commun. 2004, 864. (28) Phillips, J. C. ReV. Mod. Phys. 1970, 42, 317. (29) URL: http://www.webelements.com/. (30) Diebold, U.; Koplitz, L. V.; Dulu, O. Appl. Surf. Sci. 2004, 237, 336. (31) Van de Walle, C. G. Phys. ReV. Lett. 2000, 85, 1012. (32) Wardle, M. G.; Goss, J. P.; Briddon, P. R. Phys. ReV. Lett. 2006, 96, 205504.
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