J. Phys. Chem. C 2010, 114, 13035–13038
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MgO-Supported Gold Cages Identified by Their Vibrational Modes: First-Principles Simulations Wei Fa,*,†,‡ Jian Zhou,†,§ Xiaowei Li,†,‡ and Jinming Dong*,†,‡ Group of Computational Condensed Matter Physics, National Laboratory of Solid State Microstructures, Nanjing UniVersity, Nanjing 210093, China, Department of Physics, Nanjing UniVersity, Nanjing 210093, China, and Department of Material Science and Engineering, Nanjing UniVersity, Nanjing 210093, China ReceiVed: March 26, 2010; ReVised Manuscript ReceiVed: June 13, 2010
The structural and vibrational properties of the MgO-supported gold clusters, AuN (N ) 25-41), have been investigated by using the first-principles calculations. It is found that they indeed prefer the open pyramidal hollow (OPH) cages in this size range, showing distinctly different vibrational spectra from other adsorbed isomers. The spectra can provide a fingerprint signal to accurately identify their characteristic OPH structures. More interestingly, it is found that each of these OPH cages has its own breathing-like mode, whose frequency depends on cluster size, following approximately a linear variation with its inverse effective radius, which may be tested by the future Raman measurements. I. Introduction Bulk gold is the most inert metal in the periodic table. However, nanometric gold aggregates dispersed on the oxide supports have displayed the exceptional catalytic activities, triggering the so-called “gold rush” for understanding their electronic and chemical properties.1-6 Undoubtedly, it is needed to characterize atomic structures of gold nanoparticles both experimentally and theoretically. Previous studies revealed that the free gold clusters AuN exhibit a variety of fascinating geometrical structures, e.g., planar ones up to about N ) 12,7-11 anionic cages for N ) 16-18,12,13 bulk-fragment pyramidal structures for N ) 19-23,14-19 possible tubular cages at N ) 24 and 26,10,20,21 and gold fullerene at N ) 32.22,23 The unique structural behavior of these free AuN was attributed to the relativistic effects, as well as the possible metal aromaticity.9,17,22,24 When supported, the clusters are likely to distort and possibly undergo fundamental structural changes. Recent years have witnessed increased interest in the supported gold clusters, in which more attention has been paid to understand their catalytic activities that are influenced by cluster morphology, electronic structure, charge state, the metal-oxide surface, and so on.25-32 In contrast to the known structures of the free gold clusters identified by the experiments in juxtaposition with the quantummechanical calculations, those of the supported gold clusters have not been well-established yet. Previous theoretical simulations have shown that the tetrahedral Au20 is extremely robust and likely to survive when supported on both perfect and defective MgO surfaces.33,34 However, cluster geometries and dimensionalities may be changed via substrate manipulations. For example, it is found that there is a dimensionality crossover from three-dimensional optimal cluster geometries on MgO (100) to energetically favored two-dimensional structures on the metal-supported films. When adsorbed on thin MgO films supported on Mo(100), the pyramidal isomer of Au20 becomes * To whom correspondence should be addressed. E-mail:
[email protected] (W.F.);
[email protected] (J.D.). † Group of Computational Condensed Matter Physics, National Laboratory of Solid State Microstructures, Nanjing University. ‡ Department of Physics, Nanjing University. § Department of Material Science and Engineering, Nanjing University.
less stable than the planar one.35 Moreover, a recent densityfunctional theory (DFT) study revealed that the gold clusters on the MgO (001) surface prefer new open pyramidal hollow (OPH) cage structures in the size range between 23 and 42 atoms, which have no counterpart in the gas-phase gold clusters.36 This new family of the supported gold cage clusters is interpreted to be stabilized by the combined effects of the Au-Au and Au-oxide interactions. Due to their lowcoordinated hollow configurations, these gold cage clusters are of great interest both experimentally and theoretically since they provide a possibility to design novel endohedral gold clusters with dopants in them, offering a chemical versatility for finely tuning their electronic properties. Despite their potential applications, the OPH golden cage supported on the MgO (001) surface are only found by the aforementioned DFT calculations, which adopt the traditional energy criterion to judge their stability. Up to now, there is still no experimental evidence for these supported gold cages. On the other hand, the spectroscopic tool, especially the vibrational spectra, can be used to well-identify the geometric structures of both free and supported gold clusters. For example, the infrared measurements were reported to characterize the supported gold clusters.27,37 Therefore, it is interesting and important to make numerical simulations on the geometrical structures and corresponding vibrational spectra of the supported gold clusters on the MgO surface, in order to find a possible fingerprint signal to be used in future experiments for identifying unambiguously their OPH cage structures. In this paper, we report our first-principles calculations on the structural and vibrational properties of the gold clusters supported on the MgO (001) surface in the size range from 25 to 41. It is found that there indeed exist the isomer-specific vibrational spectra to distinguish the OPH golden cages from other adsorbed isomers, e.g., the compact ones containing at least one inner atom or closed cages, such as the golden fullerene Au32. More interestingly, these supported gold cages are found to possess a Raman-active breathing-like mode, whose frequency decreases with increasing cluster size, showing an approximate linear variation with the inverse effective radius. Our results indicate how the supported OPH cage gold clusters can be
10.1021/jp1027383 2010 American Chemical Society Published on Web 07/09/2010
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practically detected by their vibrational spectra in future experiments. We describe our computational details in section II and present our results and discussions in section III. Some concluding remarks close the paper in section IV. II. Computational Methods Our first-principles calculations are carried out using the Vienna ab initio simulation package (VASP) code38 with exchange and correlation energy corrections, included through a spin-restricted generalized gradient approximation in the Perdew-Burke-Ernzerhof formulation.39 The ion-electron interaction is described by the highly accurate full-potential projected augmented wave method40,41 with Γ-point sampling of the Brillouin zone. The 5d10 and 6s1 orbitals of gold atom are treated as valence orbitals, and a plane-wave cutoff of 300 eV is employed. Self-consistent-field calculations are done with a convergence criterion of 10-6 eV on total energy. Several geometrical candidates are considered for each size, which include the low-lying structures in the gas phase, available structures in the literature such as the OPH cages,36 and compact structures constructed in fcc (111) or (001) epitaxy to maximize the cluster-support interaction. Depending on the size and shape of gold clusters, the MgO (001) surface is modeled by a two-layer-thick slab in a (6 × 6) or (7 × 5) surface unit cell, which is thick enough to reproduce the characteristics of the bare MgO surface and obtain converged results for the energetics of adsorbed gold clusters with respect to the number of layers.42,43 The first MgO layer is held to be fixed, while the second MgO layer and the adsorbed gold clusters are fully relaxed until the maximum forces on each atom were smaller than 2 meV/Å. The replicated slabs are periodically separated in the direction perpendicular to (001) surface by a vacuum region of 18 Å. The harmonic approximation is used in the frequency calculations with 0.01 Å displacements, in which two MgO (001) layers are frozen for saving the computational time. We have calculated the vibrational spectra of the supported Au4 and Au32 when the MgO vibrations are also included, from which it is found that there are small frequency shifts compared to those without including the substrate. Taking the supported OPH Au32 as an example, it has a breathing-like mode at 80.2 cm-1, which is slightly blueshifted to 81.2 cm-1 if the MgO substrate is frozen. The vibrational density of states (VDOS) are obtained by broadening the calculated stick spectra with a Gaussian line shape function of 3 cm-1 full width at half-maximum. The first-order resonant Raman intensity in the Stokes process is calculated following the standard formula given in refs 44 and 45. The reliability of the current computational scheme has been checked by benchmark calculations on the gold dimer. For the Au2, the calculated binding energy of 2.476 eV, bond length of 2.516 Å, and vibration frequency of 179.5 cm-1 are consistent with the experimental data of 2.28 ( 0.10 eV, 2.47 Å, and 191 cm-1, respectively,46 and also with previous DFT results of 2.43 eV, 2.55 Å, and 173 cm-1 by Wang et al.47 III. Results and Discussions Our numerical results show that except for the supported Au34, the OPH golden cages are the most energetically favorable structures on the MgO (001) surface in size range between 25 and 41 atoms, which are in good agreement with the previous DFT calculations.36 The ground-state structures of AuN (N ) 25-41) on the MgO (001) surface we obtained are the same as those given in ref 36. For example, the OPH Au25 cage (isomer 1) with 12 gold atoms lying on the oxygen sites is lower in
Figure 1. VDOS of substrate-supported OPH golden cages and their isomers: (a) Au25 and (b) Au32. Their corresponding geometries are shown in the right panel. If the cluster has a breathing-like mode, its frequency has been listed in parentheses and its schematic diagram has also been illustrated, in which the directions and amplitudes of the atom displacements are depicted by the corresponding vectors. Gold, magnesium, and oxygen atoms are represented by the yellow, green, and red balls, respectively. Only one-layer MgO (001) are shown for clarity.
energy by 0.948 eV than the pyramid-based bulk fragment structure (isomer 2) with 10 gold atoms on the oxygen sites, and also by 1.038 eV than the double-layered flat cage (isomer 3) with 7 gold atoms on the oxygen sites (see Figure 1a), although the latter two are far more stable than the OPH cage by at least 1 eV in the gas phase. As another example, the free OPH Au32 cage is well separated from the lowest-energy icosahedral cage by 2.67 eV. When deposited on the MgO (001), however, the Au-MgO interactions reverse the situation: the OPH Au32 cage (isomer 1) with 14 gold atoms on the oxygen sites prevails itself by 0.582 eV over the Ih Au32 cage (isomer 2) with only 4 gold atoms on the oxygen sites (see Figure 1b). Our results of the support Au32 are consistent with those in ref 36, which has found that isomer 1 is lower than isomer 2 by 0.53 eV. The high stability of the OPH golden cages AuN (N ) 25-41) on the MgO (001) surface is judged according to the energy criterion, which lacks experimental evidence to date. Now, we study the vibrational properties of the gold clusters deposited on the MgO (001), paying more attention to their relationship with the cluster’s geometrical structures in order to find the isomer-specific spectra. Figure 1 also shows the VDOS for different isomers of the supported Au25 and Au32, from which it is clearly seen that each isomer has its own VDOS since the vibrational frequencies are sensitive to structures and bonding. As shown in Figure 1a, the three different isomers of Au25 have remarkably different VDOS. The supported OPH Au25 cage exhibits a more well-defined spectrum owing to its complete square cage motif, while its isomers 2 and 3 show a more continuous distribution in the calculated spectra. Taking the supported Au32 as another example, the VDOSs of its OPH and icosahedral Au32 cages are obviously different (see Figure 1b). The former VDOS spans a much wider frequency range with more peaks since the former with a lower symmetry has more inequivalent bonds than the latter. It is known from our calculations that there are also the obvious differences between the VDOSs of the supported OPH golden cage and its other AuN isomers in a size range from 25 to 41 atoms. Considering that these OPH cages contain only tens of gold atoms, their VDOSs with many peaks are much richer than that the bulk gold with two peaks.48 However, owing to their common structural origin from the pyramidal clusters in fcc (001) epitaxy by removing the inner atoms, the supported OPH
MgO-Supported Gold Cages
Figure 2. Size evolution of the breathing-like mode frequency (ωBLM) j ), shown by the filled and and the inverse effective cluster radius (1/R open circles, respectively, for the supported OPH AuN. The inset j , in which the blue line illustrates the dependence of ωBLM on the 1/R is the linear fit.
golden cages have some similar features in their VDOS. For example, they have almost the same highest vibration frequency, lying in a narrow range of 172-178 cm-1, which is usually larger than those of other isomers as illustrated in Figure 1. Since the high-frequency vibration modes come from the relative movements of the nearest neighbor atoms, they can present information about the bond length and strength in crystals. For example, the highest vibration frequency of the supported OPH Au25 cage is 13.3 cm-1 higher than that of its double-layered flat cage isomer (isomer 3), reflecting a fact that the former average bond length (2.774 Å) is smaller than the latter one (2.827 Å). The VDOS profile of the supported OPH golden cages shows some similarity, suggesting that it is possible to find characteristic vibrational modes that could be distinguished from those of other isomers in the future infrared or Raman experiments. As is well-known, a Raman-active breathing mode is the characteristic one of the cage or tubular structures, as found in the carbon fullerenes and nanotubes.49 The so-called golden fullerene, i.e., the free Ih Au32, also has a breathing mode at 90.4 cm-1, which is slightly blue-shifted to 92.1 cm-1 when supported on the MgO (001) surface (see Figure 1b). In fact, the latter should be referred to as the breathing-like mode since the substrate brings changes to the directions and amplitudes of its vibrational vectors, especially those close to the MgO surface. For the double-layered flat cage isomer of Au25, its breathing-like mode lies at 94.5 cm-1 in the free state, which is destroyed by the substrate due to its asymmetrical soft-landing. Because of their special hollow cage structures located in fcc (001) epitaxy with the substrate, it is expected to find such a breathing or breathing-like mode for the supported OPH gold clusters that could be tested in future Raman measurements. The characteristic breathing-like mode is easily found by examining all the vibrational modes for each supported OPH golden cage, which is especially obvious for the complete square and rectangular open cages at N ) 25, 32, 39, and 41, showing the atomic movements along the radial directions for the most gold atoms. The frequency evolution of the breathing-like mode (ωBLM) vs cluster size for the supported OPH AuN is shown in Figure 2, from which it is seen clearly that the ωBLM decreases systematically with increasing cluster size. Considering that the frequency of the radial breathing mode is inversely proportional to the diameter of the carbon nanotube, it is naturally interesting
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Figure 3. The calculated first-order resonant Raman intensities in the Stokes process for the breathing-like mode and the highest-frequency mode of the OPH Au25 supported on the MgO surface versus the excitation energy. Here, E-74 denotes the optical transition energy from the seventh valence energy level (-7) to the fourth conduction one (4). EBL and EH are the phonon energies of the breathing-like and highest-frequency modes, being 0.011 and 0.021 eV, respectively.
to explore the influence of spatial distributions of the OPH AuN on the ωBLM. Since there is no exact and unique definition on its radius, we instead have calculated the average distance of each atom in an OPH cluster to its mass center, which is referred j ). By plotting the inverse R j (1/R j ) vs to as its effective radius (R cluster size in Figure 2, it is found that its size evolution is similar to that of ωBLM, reflecting that the effective cluster radius can be used to estimate roughly the magnitude of ωBLM. As illustrated in the inset of Figure 2, a linear formula of ωBLM ) j + C2 can be obtained to roughly fit the ωBLM variation C1/R j for all the calculated supported OPH AuN. with the inverse R The two coefficients in the formula are found to be C1 ) 388.43 cm-1 · Å and C2 ) -0.34 cm-1 · Å, respectively. We note that the coefficient C1 for the supported OPH AuN is bigger than the corresponding one in the single-walled gold nanotubes (about 169.4 cm-1 · Å),50 but much smaller than that in the single-walled carbon naotubes (about 1072 cm-1 · Å),51 which means that the bonds of support OPH AuN are “harder” than those of the gold nanotubes, but much “softer” than the covalent bonds of the carbon nanotubes. Finally, we should mention that there exists a deviation from the linear variation with the inverse radius of small-diameter carbon nanotubes,52 which is induced by the curvature effect and tube’s chirality. Similarly, the approximate j for linear variation behaviors of the ωBLM with the inverse R the OPH AuN imply that other structural factors, such as the curvature effect and substrate, would also play roles in their breathing-like modes. As a promising technique to characterize the structures of nanosized materials, the resonant Raman spectroscopy is expected to be useful to probe the existence of supported OPH golden cages and test our theoretical results. Figure 3 has shown the calculated first-order Stokes resonant Raman spectra for the breathing-like mode and highest-frequency mode of the supported OPH Au25. It is seen clearly from Figure 3 that the intensity of the breathing-like mode is much larger than that of the highest-frequency mode due to a strong electron-phonon coupling of the former, indicating that the breathing-like mode of the supported OPH golden cage could be easily detected in the future resonant Raman experiments. IV. Conclusion We have calculated the structure-dependent vibrational spectra of the supported gold clusters on the MgO (001) surface in size range from 25 to 41 atoms. It is found that the overall VDOS spectra exhibit distinctive features among different isomers for each size, which could be used to distinguish the OPH cages
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from other isomers with different motifs. Especially, each OPH cage has its characteristic breathing-like mode due to its hollow cage structure, whose frequency decreases with increasing the cluster size, thus offering a possibly powerful experimental tool to identify its geometrical structure. A linear fit formula of ωBLM j - 0.34 can be roughly obtained, which can well ) 388.43/R describe the relationship between the breathing-like mode frequency and the inverse effective radius for the supported OPH golden cages. Our theoretical results can be tested by future infrared and Raman spectra. Acknowledgment. The authors acknowledged financial support from the State Key program for basic researches of China through grant Nos. 2006CB921803 and 2009CB929504. W.F. also acknowledged support from the Natural Science Foundation of China under grant No. 10704032 and the Research Fund for the Doctoral Program of Higher Education RFDP20070284055. We thank Profs. R. Ferrando and A. Fortunelli for providing us the coordinates of gold clusters on the MgO (001) surface published in ref 36. References and Notes (1) Haruta, M.; Yamada, N.; Kobayashi, T.; Iijima, S. J. Catal. 1989, 115, 301. (2) Haruta, M.; Tsubota, S.; Kobayashi, T.; Kageyama, H.; Genet, M. J.; Delmon, B. J. Catal. 1993, 144, 175. (3) Haruta, M. Catal. Today 1997, 36, 153. (4) Valden, M.; Lai, X.; Goodman, D. W. Science 1998, 281, 1647. (5) Bond, G. C.; Thompson, D. T. Catal. ReV.-Sci. Eng. 1999, 41, 319. (6) Ha¨kkinen, H.; Abbet, S.; Sanchez, A.; Heiz, U.; Landman, U. Angew. Chem., Int. Ed. 2003, 42, 1297. (7) Furche, F.; Ahlrichs, R.; Weis, P.; Jacob, C.; Gilb, S.; Bierweiler, T.; Kappes, M. M. J. Chem. Phys. 2002, 117, 6982. (8) Ha¨kkinen, H.; Yoon, B.; Landman, U.; Li, X.; Zhai, H.-J.; Wang, L.-S. J. Phys. Chem. A 2003, 107, 6168. (9) Ha¨kkinen, H.; Moseler, M.; Landman, U. Phys. ReV. Lett. 2002, 89, 033401. (10) Xing, X.; Yoon, B.; Landman, U.; Parks, J. H. Phys. ReV. B 2006, 74, 165423. (11) Johansson, M. P.; Lechtken, A.; Schooss, D.; Kappes, M. M.; Furche, F. Phys. ReV. A 2008, 77, 053202. (12) Bulusu, S.; Li, X.; Wang, L.-S.; Zeng, X.-C. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 8326. (13) Yoon, B.; Koskinen, P.; Huber, B.; Kostko, O.; von lssendorff, B.; Ha¨kkinen, H.; Moseler, M.; Landman, U. ChemPhysChem 2007, 8, 157. (14) Li, J.; Li, X.; Zhai, H.; Wang, L.-S. Science 2003, 299, 864. (15) Fa, W.; Luo, C.; Dong, J. Phys. ReV. B 2005, 72, 205428. (16) Bulusu, S.; Zeng, X. C. J. Chem. Phys. 2006, 125, 154303. (17) Apra`, A.; Ferrando, R.; Fortunelli, A. Phys. ReV. B 2006, 73, 205414. (18) Gruene, P.; Rayner, D. M.; Redlich, B.; van der Meer, A. F. G.; Lyon, J. T.; Meijer, G.; Fielicke, A. Science 2008, 321, 674. (19) Tian, D.; Zhao, J. J. Phys. Chem. A 2008, 112, 3141.
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