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Growth Pattern and Electronic Properties of Cluster-Assembled Material Based on Zn12O12: A Density-Functional Study Yongliang Yong, Bin Song,* and Pimo He State Key Laboratory of Silicon Materials and Department of Physics, Zhejiang University, Hangzhou 310027, China ABSTRACT: We report a systematic theoretical study on the growth pattern and electronic properties of Zn12O12-assembled material using density-functional theory within a generalized gradient approximation. Our results show that assembly can form by attaching a Zn12O12 cage on a hexagonal site. A Zn12O12 cage should combine with eight hexagons in adjacent eight Zn12O12 cages, respectively, forming more stable assemblies. As the assembly process continues, we find that the Zn12O12 cages form a new three-dimensional nanoporous ZnO phase with a rhombohedral lattice framework. The Zn12O12 cage structure in the phase is preserved, and the ZnO bond lengths between Zn12O12 monomers are slightly larger than those in the isolated Zn12O12 cage and the bulk wurtzite ZnO phase. The band analysis reveals that this new phase is a semiconductor with large gap value. Because of the nanoporous character of this new phase, it could be used for heterogeneous catalysis, molecular transport, and so on.
1. INTRODUCTION Since the discovery of C60,1 the field of cluster science has been attracting considerable interest both experimentally and theoretically.25 One of the most promising prospects of the field is that the stable size-specific clusters can serve as building blocks for synthesizing nanostructured materials, which are normally called cluster-assembled materials.6 Since the physical, chemical, electronic, optical, and magnetic properties of clusters are found to vary markedly with size and composition, the interest in cluster-assembled materials is largely due to the fact that the quantum confinement and the new topologies lead to novel properties, which could be used in the future for wideranging technological applications. Indeed, several groups are actively pursuing this direction by trying to explore large amounts of magic clusters in beams and assembling them to make the cluster-assembled materials.610 Zinc oxide (ZnO) is one of the most promising wide-band-gap semiconductors for use in short-wavelength photonic,11 highfrequency electronic,12 piezoelectric,13 and high thermal conductivity devices.14 In order to synthesize novel ZnO structures with special properties, a large variety of ZnO nanostructures such as nanowires,15,16 nanotubes,17,18 nanobelts,19,20 and nanoparticles21,22 have been reported, and some of them have been successfully used in, for example, optical devices.23,24 Consequently, as one kind of nanostructure, ZnO clusters have been researched extensively in recent years for understanding their growth and size dependence of properties. Experimentally, ZnO clusters could be prepared and characterized inside mesoporous silica.25 It is reported that ZnO clusters confined in the micropores of zeolites have unique optical properties.26,27 On the theoretical side, several studies, focused on the structure, energetics, stability, and optical properties of small pristine ZnO r 2011 American Chemical Society
clusters, have been performed.2836 In these studies, there is a general agreement that cagelike structures are favored for ZnO clusters as the cluster size increases. Among these cagelike ZnO structures, the Zn12O12 cage with Th symmetry is found to be a magic number cluster with particularly high stability, which can be taken as an ideal building block for synthesizing clusterassembled materials. Recently, Bromley’s group37 has predicted three new low-density nanoporous crystalline phases, via the coalescence of of Zn12O12 nanocages, by using a combination of density-functional theory (DFT) calculation and silicate topologies. However, in comparison with small ZnO clusters, which are extensively studied, the understanding of cluster-assembled materials based on ZnO clusters is less comprehensive. In this paper, we have attempted to understand the initial growth behavior and electronic properties of ZnO clusterassembled materials via nanoscale bottom up approach using a Zn12O12 cage cluster as building block via accurate first-principles calculations. Via calculating the energetics of cagecage coalescence, we find a new phase of ZnO-based nanomaterials. This theoretical finding, together with the recent theoretical observation,37 sheds some light on the growth behavior and electronic properties of ZnO cluster-assembled materials, and provides indirect evidence for the existence of the new ZnObased phase by forming rhombohedral lattice framework.
2. COMPUTATIONAL METHODS All calculations were performed in the framework of DFT, using the DMOL3 program (Accelrys, Inc.).38 The generalized Received: January 25, 2011 Revised: March 9, 2011 Published: March 23, 2011 6455
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The Journal of Physical Chemistry C gradient approximation (GGA) formulated by Perdew, Burke, and Ernzerhof (PBE)39 was employed to describe the exchangecorrelation interaction. Density-functional semicore pseudopotentials (DSPPs)40 fitted to all-electron relativistic DFT results, and double numerical basis set including d-polarization functions (i.e., the DND set) were also selected. The accuracy of the PBE and DND/DSPP combination was tested by following previous studies.30,33,41 During the spin-unpolarized self-consistent calculations, the density and energy tolerances were set to 106 e/ bohr3 and 106 hartree, respectively. The geometric parameters were fully optimized without symmetry constraints. We used a convergence criterion for gradient component set to 103 hartree/bohr and total energy tolerance set to 105 hartree in the geometry optimization. Periodic boundary conditions were employed in the solid-state calculations, and the Brillouin zone was sampled using a 3 3 3 MonkhorstPack grid.42 To generate low energy isomers of Zn12O12 clusters, we used a combination of full-potential linear muffin tin orbital molecular dynamics (FP-LMTO-MD) search and DFT-GGA minimization.43,44 The accuracy of the FP-LMTO-MD method4548 for investigating the cluster structures has been confirmed by previous studies (for example, refs 4953) on small Sin, GanNn, and Gen clusters.
3. RESULTS AND DISCUSSION 3.1. Structure and Energetics of Zn12O12 Clusters. We started this work from investigating the low energy isomers of an isolated Zn12O12 cluster. First, we carried out an initial FPLMTO-MD search to identify a few low-lying isomers of Zn12O12 clusters. In order to perform the systematic search, 240 initial geometric configurations were relaxed. The initial atomic configurations were set up by random selections of atomic positions in three-dimensional space. In the present study, all MT sphere radii for Zn and O were taken as 2.10 and 1.25 au, respectively. The LMTO basis sets included s, p, and d functions on all spheres. In the second step, the low-lying energy structures of Zn12O12 clusters obtained by FP-LMTO-MD calculations were further optimized by using the DMOL3 program with GGA. The structures of the four lowest-lying isomers of Zn12O12 clusters are shown in Figure 1. The lowestenergy structure of Zn12O12, as shown in Figure 1a, is a cage structure (Th symmetry) with six rhombuses and eight hexagons. The lowest-energy cage has two types of ZnO bonds, a longer one (1.981 Å) in rhombuses and the other shorter one (1.880 Å) connecting the neighboring rhombuses. The bond angle in the rhombuses is acute at O (86.4°) and obtuse at Zn (91.0°). The corresponding angles in the hexagons are 108.2 and 129.4°, respectively. The energy gap of the cage we calculated for highest-occupied and lowest-unoccupied molecular orbital (HOMO LUMO) is 2.519 eV. Our DFT-GGA optimization calculations concur with the previous results.2932 The second lowest-energy isomer holds distorted cage structure lying 1.328 eV above the lowest-energy isomer (see Figure 1b). This structure was recently reported by Bromley’s group,37 and our result agrees well with theirs. However, Our DFT-GGA optimization calculations further find that the third lowest-energy isomer is a hitherto unreported distorted cage structure (C1 symmetry) lying only 0.155 eV above the second lowest-energy isomer (see Figure 1c). The second and third lowest-energy structures of Zn12O12 clusters are both distorted cages made primarily out of four- and six-membered rings with one eight-membered ring,
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Figure 1. Structures of the four lowest-lying isomers of Zn12O12. Values in parentheses are relative energies in electronvolts. Red balls represent O atoms, and gray balls represent Zn atoms.
respectively. The large energy separation between the first and the second lowest-energy isomers, and the large HOMOLUMO gap indicate that the Zn12O12 has particularly high stability, indicating that the Zn12O12 cage would be an ideal potential building block to form higher order structures for synthesizing clusterassembled materials. 3.2. Growth Pattern of Clustercluster Coalescence. In this subsection, we consider the initial growth behavior of Zn12O12-assmbled material via the coalescence of Zn12O12 cluster building blocks. Figure 2 shows the evolution of the geometrical structures of (Zn12O12)n (n = 18) assemblies. At first, we examined the Zn12O12 cluster dimer. As shown in Figure 2 (1a), the Zn12O12 cage has two types of edge (linear ZnO) and two different faces (hexagonal Zn3O3 and square Zn2O2). In this work, we have checked all possible dimer interactions (faceface, faceapex, apexside, sideside, and apexapex), and have found that the hexagonal face coalescence is energetically preferred over other coalescences. This is not similar to the cases of cagelike B12N1210 and Zn12S129 clusters, which favor square face coalescence, although their monomers have the same geometric configurations as Zn12O12. The dimer structure is shown in Figure 2 (2a). Our calculations show that the dimerization energy of the dimer structure is 3.88 eV, an increase of at least 0.93 eV in energy with respect to the other coalescence isomers. This means that the system is likely to result in a big minimum of the potential energy surface when the hexagonal face coalescence is taking. This information shows that stable assemblies can be formed by first building the Zn12O12 dimer. It is found that in the interaction region of Zn12O12 dimer, a Zn atom is facing an O atom, forming a ZnO bond. The geometrical parameters of the Zn12O12 dimer are given in Table 1. The ZnO bond lengths between monomers are 2.007 Å, slightly larger than the ZnO bond lengths in a Zn12O12 cage and the bulk wurtzite ZnO phase. The ZnO bond lengths within the interacting ring of the monomer are enlarged about 0.120.21 Å, compared with the values of the isolated Zn12O12 cage. It should point out that the structural deformation of Zn12O12 monomer in dimer is very small, and the distortion mainly occurs in the interaction region, since the values of the hexagonal rings located opposite to the interaction remain very similar to those of the isolated Zn12O12 cage. Thus, the gross geometrical features of the individual Zn12O12 cages are retained in the dimer. In the case of three Zn12O12 monomers being packed, the lowest-energy geometry is linear as shown in Figure 2 (3a). However, the bent structure, as shown in Figure 2 (3b), is only 0.046 eV higher in energy. Thus, the two structures are almost degenerate in energy and can be considered to be the ground state structure. As the number of Zn12O12 monomer increases, the bending feature continues. The most stable (Zn12O12)4 forms a closed planar ring structure (see Figure 2 (4a)). This structure 6456
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Figure 2. The evolution of the geometrical structures of (Zn12O12)n (n = 18) assemblies. Isomeric structures of (Zn12O12)n assemblies are labeled as na, nb, nc, etc., in order of decreasing stability for each assembly size n. Values in parentheses are relative energies (relative to the most stable isomer for each composition) in electronvolts. Red balls represent O atoms, and gray balls represent Zn atoms.
Table 1. Bond Lengths (in Å) in the Most Stable Zn12O12 Dimer as shown in Figure 2 (2a)a
dimer
RMon-Mon
R1
R2
R3
2.007
2.195 (2.007)
1.982 (1.884)
1.961 (1.955)
a
RMon-Mon represents the distance between monomers; R1 is the ZnO distance within the interacting hexagonal ring of the monomer, R2 is the ZnO distance but in the hexagonal ring opposite to the interaction, and R3 is the ZnO distance connecting the interacting ring of the monomer.
can be obtained by capping a Zn12O12 monomer on the side of the structure of (Zn12O12)3, as shown in Figure 2 (3b). We find that the other isomers of (Zn12O12)4 are all higher above 2.0 eV in energy than the most stable structure. As the monomer number continues to increase, the structures of (Zn12O12)n compete at n = 5 and 6. It is found that the planar structures of (Zn12O12)5 and (Zn12O12)6 (Figure 2 (5a) and (6a)) are almost energetically degenerate with the corresponding three-dimensional isomers (Figure 2 (5b) and (6b)). From n = 7, the most stable
configurations hold three-dimensional structures. Though the twodimensional features of the assemblies can be continued as the size n increases, their energies are higher than that of the three-dimensional structures of the corresponding systems (see Figure 2 (7c), (7d), (8b), and (8c)). For (Zn12O12)7, the most stable structure can be obtained by adding a Zn12O12 monomer on side position of the structure (Zn12O12)6 (Figure 2 (6b)). For (Zn12O12)8, the lowestenergy structure 8a can be obtained by capping a Zn12O12 monomer on the top (or bottom) of the structure 7a. From a viewpoint of lowest energy, as shown in Figure 2, the two-dimensional structures are the best for the small (Zn12O12)n assemblies. Therefore, the size at which the three-dimensional structure is formed has great importance for understanding of their growth behavior and reactivity. From n = 5, the threedimensional structure has been found although it is not the most stable. With the size increasing, the Zn12O12 cluster assemblies prefer three-dimensional geometries, and we note that the most stable structures meet the laws of the growth behavior as follows. (1) The lowest-energy geometries of (Zn12O12)n are formed by adding a Zn12O12 monomer on the lowest-energy geometries of 6457
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Table 2. Calculated Binding Energies per ZnO (Eb), Removal Energy (Er), and HOMOLUMO Gap (Eg) for Structures of the (Zn12O12)n Assemblies Shown in Figurre 2 isomer
Eb (eV)
Zn12O12
1a
6.276
(Zn12O12)2
2a
(Zn12O12)3
system
(Zn12O12)4 (Zn12O12)5 (Zn12O12)6 (Zn12O12)7
(Zn12O12)8
Er (eV)
Eg (eV)
6.438
3.880
2.269
3a
6.492
3.879
2.215
3b
6.490
3.835
2.191
4a 5a
6.564 6.570
6.115 3.828
1.916 1.908
5b
6.570
3.814
1.906
6a
6.609
6.326
1.842
6b
6.605
6.609
1.816
7a
6.628
5.862
1.777
7b
6.617
5.337
1.704
7c
6.607
3.828
1.838
7d 8a
6.607 6.654
3.828 6.717
1.838 1.683
8b
6.632
6.329
1.806
8c
6.631
6.276
1.797
2.519
Figure 3. The binding energies (Eb), removal energies (Er), and the HOMOLUMO gaps (Eg) for the lowest-energy structures of (Zn12O12)n (n = 18) assemblies.
(Zn12O12)n1 systems. (2) The more interactions between the adding monomer and the (Zn12O12)n1 assemblies, the more stable for the (Zn12O12)n assemblies. Meanwhile, the interactions must have occurred in the hexagons facing hexagons orientation. The relative stability of the (Zn12O12)n assemblies can be gained by analyzing their energetics. We calculated the binding energies per ZnO (Eb) and removal energy (Er) for the most stable structures of (Zn12O12)n (n = 18). These are defined by Eb ¼ ½EðZn12 O12 Þn 12nEZn 12nEO =12n Er ¼ EðZn12 O12 Þn 1 þ EZn12 O12 EðZn12 O12 Þn where E is the total energy of the corresponding system. The calculated binding energies per ZnO (Eb) and removal energy (Er) are summarized in Table 2. Figure 3 shows the size dependence of Eb and Er for the lowest-energy structures of the (Zn12O12)n (n = 18) assemblies. It is shown that the Eb increases smoothly with the size n increasing and contains minor
Figure 4. One electron levels for the (Zn12O12)n (n = 18) assemblies. The red lines represent unoccupied states, and the black lines represent occupied states.
bumps at the even size. For Er as shown in Figure 3, three peaks at n = 4, 6, and 8 are clearly observed, indicating that these assemblies are relatively stable. We note that in geometric configurations of the (Zn12O12)n (n = 4, 6, and 8) assemblies, every monomer has more hexagons interacting with others than that in adjacent assemblies. It is confirmed that the eight hexagons in one Zn12O12 monomer should combine with eight hexagons in the adjacent eight monomers, forming more stable assemblies. Because the cage structure of Zn12O12 monomers is preserved during the cluster-assembly occurring, it is expected that some unique properties of the isolated Zn12O12 cluster will be retained in the cluster-assembled materials. Figure 3 also shows the HOMOLUMO gap for the lowest-energy structures of (Zn12O12)n (n = 18) assemblies as a function of size. The magnitude of the HOMOLUMO gaps ranges from 2.519 to 1.683 eV (see Table 2). It is found that the HOMOLUMO gaps slightly decrease with the size n increasing. This may be because the HOMO orbitals locate in the interacting region on the Zn12O12 monomers, while the LUMO orbitals mainly remain on the rest O sites of Zn12O12 monomer, and is stabilized though binding adjacent Zn atoms. This can be understood by comparison of the diagrams of the one electron levels for the most stable structures of (Zn12O12)n assemblies given in Figure 4. The assembly of Zn12O12 clusters results in the additional levels. It is found that the decrease of HOMOLUMO gap is mainly due to the increase of the occupied states. As we shall show below, the HOMOLUMO gap will decrease but remain open as the clusters are assembled into three-dimensional crystal materials. 3.3. Electronic Structure and Properties of Zn12O12Assembled Material. Considering that the eight hexagons in one Zn12O12 monomer can combine with eight hexagons in adjacent eight monomers, we may understand a continuation of this assembly process to form a new three-dimensional ZnO phase. In this way, Zn12O12 clusters form a rhombohedral lattice system (R-ZnO), and the space group of this system is R3. It is convenient to express the lattice parameters of the rhombohedral system by using the hexagonal-system parameters. Then the optimized lattice parameters of this system are a = 11.284 Å and c = 6.91 Å. There are six ZnO bonds between any two Zn12O12 monomers with bond lengths of 2.1832.203 Å, and the difference in the bond lengths is very small. The average bond length between the Zn12O12 monomers is about 2.192 Å. The bond lengths inside each Zn12O12 monomer of R-ZnO framework are quite similar to those of the isolated Zn12O12 cluster. This three-dimensional R-ZnO phase is a nanoporous material, as can be observed in Figure 5, but the geometry of the R-ZnO 6458
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phase is different from those of the three nanoporous crystalline phases (SOD-ZnO, LTA-ZnO, and FAU-ZnO) reported by Bromley’s group.37 We have calculated the binding energies and electronic properties of the four nanoporous phases, together with wurtzite ZnO phase (WZ-ZnO), by using the DFTGGA method. The results for binding energy and band gap of various ZnO phases are summarized in Table 3. Obviously, the binding energy per ZnO of the R-ZnO phase is larger than that of
LTA-ZnO and FAU-ZnO phases, indicating that the R-ZnO framework is more stable. Figure 6 shows the partial density of states (PDOS) for the R-ZnO framework, which is compared with that of conventional dense and recent reported nanoporous polymorphs.37 As the cost of calculation increases rapidly with the size of the unit cell, we were able to include only a limited number of the conduction states for larger unit cell phases. Hence, only the lower conduction bands are shown here for the LTA-ZnO and FAU-ZnO structures. Generally, the density of states of all frameworks considered exhibits similar features. The electronic states of the valence band mainly come from the O 2p and Zn 3d states, and the contribution from the Zn 4s and O 2s states is small. Thus, pd hybridization is responsible for the interaction between the Zn and O atoms. Depending on a particular framework of the R-ZnO phase, we may expect to find a different type of the ZnO electronic band structure. In Figure 7, the band structure of the R-ZnO framework is shown. An indirect gap of 1.36 eV is found for the R-ZnO phase. It is well-known that the DFT-GGA calculations systematically underestimate the one-electron band gap. We calculate 0.94 eV (see Table 3) for WZ-ZnO phase, to be compared with
Figure 5. The nanoporous structure of rhombohedral lattice framework assembled by Zn12O12 cages.
Table 3. Calculated Binding Energy per ZnO (Eb) and Band Gap (Eg) for Different ZnO-Based Crystalline Phases Eb (eV)
Eg (eV)
R-ZnO
7.007
1.37
WZ-ZnO
7.217
0.94
SOD-ZnO
7.119
1.22
LTA-ZnO
6.979
1.91
FAU-ZnO
6.880
1.74
species
Figure 7. Band structure for the calculated Zn12O12-based rhombohedral lattice framework.
Figure 6. Total and partial density of states for the representative ZnO polymorphs and Zn12O12-based frameworks. The vertical line indicates the Fermi level. 6459
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The Journal of Physical Chemistry C the experimental value of 3.435 eV. Thus, the true band gap of the R-ZnO phase should be much higher than our theoretical results. Note that the HOMOLUMO gaps of the (Zn12O12)n assemblies are similar to the band gaps of our predicted R-ZnO phase, which might indicate that the cluster-assembled materials remain the basic electronic features of the Zn12O12 monomer.
4. CONCLUSIONS In conclusion, Zn12O12-assembled material has been investigated systematically using DFT within GGA. We began this investigation by trying to determine the lowest-energy structure of Zn12O12 clusters. It is found that the lowest-energy structure of Zn12O12 clusters is a cage structure (Th symmetry) with six squares and eight hexagons. The structure has particularly high stability, indicating that the Zn12O12 cage would be an ideal potential building block for synthesizing cluster-assembled materials. From a viewpoint of lowest energy, assembly can form by attaching Zn12O12 cage on hexagonal site. For the small (Zn12O12)n assemblies, the two-dimensional structures are the best for them; however, as the size n increases, the (Zn12O12)n assemblies prefer three-dimensional geometries. The more interactions between the adding monomer and the (Zn12O12)n1 assemblies, the more stable for the (Zn12O12)n assemblies. It is confirmed that the eight hexagons in one Zn12O12 monomer should combine with eight hexagons in adjacent eight monomers, forming more stable assemblies. As assembly process continues, we find that a new threedimensional ZnO phase, which holds a rhombohedral lattice framework, can be formed. The cage structure of Zn12O12 monomers is preserved in the phase. The R-ZnO phase is more stable than LTA-ZnO and FAU-ZnO phases. The band analysis reveals that the R-ZnO phase is a semiconductor. The gap value is larger than that of WZ-ZnO phase and smaller than that of LTAZnO and FAU-ZnO phases. The R-ZnO phase holding a nanoporous framework, if synthesized, presents opportunities for doping various kinds of atoms or clusters as a means to tailor its electronic structure. We hope this work will encourage experimental efforts toward the synthesis and characterization of such materials based on Zn12O12. ’ AUTHOR INFORMATION Corresponding Author
*Electronic mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by National Basic Research Program of China (973) under Grant No. 2010CB631304. ’ REFERENCES (1) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature (London) 1985, 318, 162. (2) Duncan, M. A., Eds. Advances in Metal and Semiconductor Clusters; JAI: Greenwich, 1993. (3) Theory of Atomic and Molecular Clusters; Jena, P., Khanna, S. N., Rao, B. K., Eds.; Springer: Berlin, 1999. (4) Johnston, R. L. Atomic and Molecular Clusters; Taylor & Francis: New York, 2002. (5) Castleman, A. W., Jr.; Khanna, S. N. J. Phys. Chem. C 2009, 113, 2664 and references therein.
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dx.doi.org/10.1021/jp200780k |J. Phys. Chem. C 2011, 115, 6455–6461
