Structures and Electronic Properties of the SiAun (n = 17â20) Clusters

Article pubs.acs.org/JPCA

Structures and Electronic Properties of the SiAun (n = 17−20) Clusters Huai-Wen Yang,† Wen-Cai Lu,*,†,‡ Li-Zhen Zhao,† Wei Qin,† Wen-Hua Yang,† and Xu-Yan Xue† †

College of Physical Science and Laboratory of Fiber Materials and Modern Textile, Growing Base for State Key Laboratory, Qingdao University, Qingdao, Shandong 266071, China ‡ State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, Jilin 130021, China S Supporting Information *

ABSTRACT: The structures and electronic properties of the SiAun (n = 17−20) clusters are systematically investigated using DFT calculations. The result shows that doping with silicon would significantly change the structures of the gold clusters. For the SiAun (n = 17−20) clusters, the lowest-energy structures exhibit shell-like cage configuration in which the dopant Si atom binds to the cage surface and one Au atom skips to the top of the Si atom forming a SiAu5 or SiAu6 subunit except SiAu19, which is a tetrahedron-like structure with a protruding Au atom. The Au atoms of the SiAun (n = 17−20) clusters carry different partial charges due to their different locations.

1. INTRODUCTION Gold clusters have attracted great attention in the past decade for their special catalytic effect.1 Because of the strong relativistic effect, the gold clusters exhibit fascinating structures as the size increases. Because the properties of the clusters are intimately related to their structures, a great amount of research has been performed on searching for the structures of pure gold clusters both in experiment and in theory.2−6 It is known that the gold clusters have planar structures at n = 1−13 and turn from 2D to 3D at the size of 13 but transform to hollow cages at 16−18.7,8 Aun exhibits a perfect tetrahedral structure at n = 20,4,9 a tube structure when n = 24, and a fullerene-cage at n = 32.10−13 Recently, doped gold clusters have attracted increasing interest intrigued by their tunable catalytic properties and potential application in biomedicine and nanodevices.14−16 When doped with other elements, gold clusters reveal intriguing structures and properties.17−26 Combining the PES spectra with the DFT calculations, Wang et al. have investigated the structures of MAu16− (M = Ge, Sn, Fe, Co, Ni, Ag, Zn, In, Cu) clusters and found that all the lowest-energy structures are the cage-like, endohedral for Cu, Fe, Co, Ni, Ag, and Zn and exohedral for Ge and Sn elements.27−30 Using the DFT calculations, Brahm et al. studied the electronic and magnetic properties of the GdAu15 cluster, and the result was that the most stable GdAu15 structure is a cage with the Gd atom in the center having the magnetic moment 7 μB and the gap is up to 1.31 eV, showing it may be a good candidate for cancer therapy.31 The lowest-lying structures and magnetic properties of M@Au24 (M = V, Cr, Mn, Fe, Co, and Ni) were investigated by Yang et al., and the result showed the 3d transition metal atoms can be encapsulated stably into the tube without significantly perturbing the atomic and electronic structures and while also retaining the magnetism of the dopant atom.32 The study of the MAu16 clusters by Fa et al. showed that the Cu, Li, © 2013 American Chemical Society

and Na atoms can be stably encapsulated in the Au16 cage, whereas K prefers to adsorb at the surface or outside of the cage.33 Jayasekharan et al. also discovered that the dopant atoms of MAu32 (M = Li, Na, K, Rb, Cs) are inclined to locate in the center of the fullerene-like cage.34 Silicon is an important element in the field of semiconductor and nanoelectronics. The system of Si−Au clusters is subjected to much focus on the structural search and electronic properties due to the adding degree of freedom in the stoichiometry. Gold clusters doped with silicon have exhibited special structures that are distinctly different from other dopant elements forming exohedral or endohedral configurations.35 Combining the experimental PES study and the DFT calculations, Wang et al. showed that the SiAu16− cluster is a cage and the silicon dopant is capped by a gold atom dangling over the silicon atom.27 Sun et al. also found that for the neutral SiAu16 cluster, the best structure is that the Si atom binds to the exterior surface of the Au16 cage with a gold atom dangling on top of the silicon.36 On the basis of the DFT study, the most stable structures of AuSin (n = 1−16) clusters were studied by Wang et al. and Chuang et al., respectively.37 With the experimental PES and theoretical DFT method, Pal et al. investigated the MAun− (n = 5−8, M = Si, Ge, Sn) clusters and proposed that the evolution of SiAun− structures is from 3D to quasi-2D to 3D structures.38 Majer et al. got the photoelectron spectra of the anions SiAun− (n = 2−56) clusters.39 Cao et al. verified the best SiAu4− structure is an aurosilane with a Td symmetry, and Majumder found the SiAu4 cluster shows an extraordinary stability among the SiAun (n = 1−8) clusters.40,41 Among the doped gold clusters, the SiAun system is special and exhibits fascinating structures that are quite different from Received: January 15, 2012 Revised: January 31, 2013 Published: February 1, 2013 2672

dx.doi.org/10.1021/jp3004807 | J. Phys. Chem. A 2013, 117, 2672−2677

The Journal of Physical Chemistry A

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pure gold clusters. To our knowledge, the SiAun (n = 17−20) clusters have not been studied yet. The structures of the Aun (n = 17−20) clusters are very typical: Au17 and Au18 exhibit hollow cages, whereas the Au19 and Au20 are tetrahedral structures. In this work, we systematically investigated the SiAun (n = 17−20) structures using the DFT calculations. In section 2, we briefly outlined the computation method used. The discussions on the SiAun (n = 17−20) structures and the electronic properties were presented in section 3. The last section is the conclusions.

Figure 1. Typical low-lying isomers of the SiAu17 cluster and the relative energies in electronvolts calculated at (1) PBEPBE/ {Au:LANL2DZ; Si:6-31G(d)}(black) and (2) PAW-PBE, in VASP (red).

2. COMPUTATIONAL METHODS The SiAun (n = 17−20) clusters were optimized on the basis of the DFT-PBE method with a DND (double numerical basis plus d-polarization function) basis set in the DMol3 module of the Materials Studio Program,42−44 in which the convergence criterions we used were 2.0 × 10−5 Ha, 0.004 Ha/Å, and 0.005 Å for energy, maximum force, and maximum displacement, respectively. These low-energy candidates from DMol3 calculations were further reoptimized using the PBEPBE functional42 in the Gaussian 09 software package.45 The basis sets were LANL2DZ46 for gold, which contains a scalar relativistic effective core potential, and a standard 6-31G(d) basis set for silicon. In Gaussian 09, the convergence criterions of 1.0 × 10−6 Ha, 0.00045 Ha/Å, and 0.0018 Å were adopted for energy, maximum force, and maximum displacement, respectively. We also performed frequency calculations for all the lowest-energy SiAun isomers which were confirmed to be energy minimum structures. The total energies of the SiAun (n = 17−20) isomers included the corrections of the zero-point vibrational energy (ZPVE). The structures were also calculated in the VASP47 program with PBE method and PAW potential considering the L-S coupling as comparison. The adsorption energies, HOMO−LUMO (highest occupied molecular orbital−lowest unoccupied molecular orbital) gaps, NBO bond orders,48 and IR spectra were analyzed.

tetrahedron-like structure with the silicon atom binding on the surface and becoming one part of the lateral arris. The Si atom is coordinated with four Au atoms. However, the energy is 0.316 eV higher than that of the SiAu17a. The SiAu17c is a tetrahedron-like structure with a protruding Au atom forming a SiAu5 subunit. But the unit is different from that of the SiAu17a, and the protruding Au atom could form Au−Au bonds with two neighboring Au atoms. The isomer that the silicon atom binds on the surface like the SiAu18b or SiAu19b is not very favorable in energy, whereas the SiAu17c is better in energy than SiAu17b in VASP considering the L-S coupling. Figure 2 shows three low-lying isomers of the SiAu18 clusters. Similar to the SiAu17 clusters, the lowest-energy SiAu18a is a

Figure 2. Typical low-lying isomers of the SiAu18 cluster and the relative energies in electronvolts calculated at (1) PBEPBE/ {Au:LANL2DZ; Si:6-31G(d)}(black) and (2) PAW-PBE (red).

3. RESULTS AND DISCUSSION Geometries. The original configurations of SiAun clusters were constructed mainly by (1) adding one silicon atom on the surface or into the center of the stable pure Aun clusters’ isomers, (2) replacing the gold atom of the pure Aun+1 clusters by a silicon atom, and (3) replacing one gold atom of pure Aun isomers by a Si−Au dimer. The stable structures of the silicon and aluminum clusters were also considered in constructing the SiAun clusters. From our calculations, three typical low-lying energy isomers of the SiAun (n = 17−20) clusters are obtained: cage structure with a dangling gold atom; tetrahedron-like structure with a protruding gold atom; and tetrahedron-like structure with the silicon atom binding on the surface. The exact coordinates and some other isomers are in the Supporting Information (Figure S1−S4). Figure 1 shows the low-lying energy isomers of the SiAu17 clusters. As depicted, the three isomers are distinctly different from the pure Au17 cluster of the hollow cage shape. The lowest-energy structure SiAu17a exhibits a shell-like cage in which the silicon atom binds to exosurface as a part, and one gold atom skips out the cage dangling on top of the silicon atom forming a SiAu5 subunit just like a four-arris pyramid. In the SiAu5 subunit, the dangling Si−Au bond length is 2.295 Å, about 0.16 Å less than other Si−Au bonds, whereas the dangling Au atom could not form a bond with neighboring Au atoms. The second low-lying energy isomer SiAu17b is the

shell-like cage with a dangling Au atom forming a SiAu5 subunit. It could be regarded as adding one Au atom to the bottom of the SiAu17a cage. The dangling Si−Au bond length is 2.291 Å, whereas the SiAu18b is the tetrahedron-like structure with a protruding Au atom like the SiAu17c. It is lower in energy than the SiAu18c with the silicon atom binding on the surface, but they are very competitive with each other because the energy difference is less than 0.1 eV. As shown in Figure 3, the structure also changes as the number of gold atoms increases. The lowest-energy isomer of the SiAu19 cluster has evolved to a tetrahedron-like structure with a protruding Au atom at the level of PBEPBE in Gaussian

Figure 3. Typical low-lying isomers of the SiAu19 cluster and the relative energies in electronvolts calculated at (1) PBEPBE/ {Au:LANL2DZ; Si:6-31G(d)}(black) and (2) PAW-PBE (red). 2673



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comparison. The results are listed in Table 1. After the clusters are doped with Si, the average binding energies per atom become larger than that of the corresponding pure Au clusters, indicating that doping with Si atom could enhance the stability of the Au clusters. For further evaluating the relative stability, the doping energy (Ed) defined as Ed = ESi + EAun − ESiAun has been calculated as shown in Table 1. The Ed of the SiAu17 is the largest, up to 4.963 eV and that of the SiAu20 is the least, which proves in reverse that the Au20 is more stable than others. The clusters’ reactive stabilities and properties are revealed in the HOMO−LUMO gap. The gaps of the lowest-energy pure Au clusters and SiAun (n = 17−20) were calculated and listed in Table 1. In our calculations, the gap of the tetrahedral Au20 cluster is up to 1.89 eV at PBEPBE/LANL2DZ in Gaussian 09 and 1.85 eV at PBE/DND with the semicore DFT method in DMol3, matching well with the experiment result of 1.78 eV (or 1.818 eV).9 From Table 1, we can see that after doping with silicon, their energy gaps change little except for the SiAu20. The HOMO−LUMO gaps of the SiAu17 and SiAu19 are very small and only slightly larger than 0.1 eV due to having one unpaired electron, so they exhibit more metallic properties, whereas the gaps of SiAu18 and SiAu20 without unpaired electron are about 1 eV, showing their good semiconductor properties, and the electrons can be easily excited by infrared and visible light spectra. Figure 5 is the absorption spectra of

09, whereas the cage SiAu19c is most favored using the PAWPBE method implemented in VASP. The pure Au19 is a perfect truncated tetrahedron configuration. The SiAu19a could be viewed as the Si atom replaces the middle Au of the lateral arris of the pure Au19 cluster, and the original Au atom skips on top of the Si atom. It has a very perfect C2v symmetry. Like SiAu18b and SiAu17c, the five Au atoms around the silicon atom form a SiAu5 deformed subunit, which is different from that in the cage structure. The length of the protruding Si−Au bond is 2.385 Å, which is longer than that of the cage structure, whereas the distance between the protruding Au and the neighboring two are both 2.997 Å, which is in range of forming Au−Au bonds. SiAu19b is similar to SiAu18c and it could be obtained by putting a Si atom on the surface of pure Au19. Unlike SiAu17a and SiAu18a, the energy of the cage SiAu19c is higher than that of the tetrahedron-like SiAu19a and SiAu19b. However, the energies of the SiAu19 isomers are very close, and they are expected to be competitive structures. Figure 4 shows the three typical low-lying isomers of the SiAu20 cluster. The energy order of the isomers is like SiAu18.

Figure 4. Typical low-lying isomers of the SiAu20 cluster and the relative energies in electronvolts calculated at (1) PBEPBE/ {Au:LANL2DZ; Si:6-31G(d)}(black) and (2) PAW-PBE (red).

The cage structure SiAu20a with a dangling Au atom becomes more stable than the other two isomers. There are six Au atoms around the Si atom forming a SiAu6 subunit beside the dangling Au atom. The isomer is with a Cs symmetry. The dangling Si− Au bond is 2.299 Å, 0.25 Å less than the other five Si−Au bonds. And the tetrahedron-like structure with a protruding Au is also more stable than that of the silicon atom binding on the surface. For the SiAun (n = 17−20) clusters, the growth pattern is from cage to tetrahedron to cage. SiAu17,18,20 exhibit shell-like cages with a dangling Au atom, whereas the SiAu19 cluster prefers a tetrahedron-like structure with a protruding Au atom. All the four lowest-energy structures have SiAun (n = 5 or 6) subunits. We further analyzed the electronic properties in detail in the following section. Electronic Properties. To determine the relative stability of the SiAun (n = 17−20) clusters, the average binding energies per atom were calculated by using Eb = (ESi + nEAu − ESiAun)/(n + 1), where ESi and EAu are the energies of free single Si and Au atoms, respectively, and ESiAun is that of the SiAun clusters. The binding energies of the pure Aun (n = 17−20) are also given for

Figure 5. Absorption spectra of the SiAu20 and Au20 clusters calculated at PBEPBE/{Au:LANL2DZ; Si:6-31G(d)}. The spectra were calculated with the TD-DFT method using 30 unoccupied orbitals.

the Au20 and SiAu20 clusters calculated with the TD-DFT method. The absorption peak of the SiAu20 appears in the visible region and has a red shift compared with that of the Au20. And the absorption in the infrared region is obviously enhanced. Therefore, the SiAu20 cluster could be used in photothermal therapy and expected as a good candidate for biomedicine and cancer therapy.14−16,31 To study the interaction of the dopant silicon atom with the Aun clusters, the NBO (natural bond orbital) charges were calculated and shown in Table 2. We can see the natural charges and the Mulliken charges are very different. For the silicon atom, the results are just the opposite. The NBO charges should be more accurate in analyzing the electron configurations according to the computational method. Figure

Table 1. Calculated Average Binding Energies per Atom for Lowest-Energy Isomers of SiAun and pure Aun (n = 17−20) Clusters Defined by Eb = (ESi + nEAu − ESiAun)/(n + 1), Doping Energy Ed = ESi + EAun − ESiAun, HOMO−LUMO Gap (Egap)a Eb/eV Ed/eV Egap/eV a

Au17

SiAu17

Au18

SiAu18

Au19

SiAu19

Au20

SiAu20

2.093

2.252 4.963 0.115

2.132

2.267 4.698 0.993

2.163

2.266 4.220 0.133

2.209

2.279 3.683 0.971

0.108

1.109

0.130

1.890

Calculated at PBEPBE/{Au:LANL2DZ; Si:6-31G(d)}. 2674



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Table 2. Calculated Natural and Mulliken Charges on the Silicon Atom (QSinatr, QSiMull) and the Dangling Gold Atom (QAunatr, QAuMull), Bond Length between the Silicon and the Dangling Gold Atom (BSi−Au), Total Dipole Moments (D),a Calculated Bond Order between the Silicon Atom and the Dangling Gold Atom (BOSi−Au), and Average Bond Order for Other Si−Au Bonds (BOave) for the SiAun (n = 17 − 20) Clustersb SiAu17 SiAu18 SiAu19 SiAu20 a

QSinatr (au)

QAunatr (au)

QSiMull (au)

QAuMull (au)

BSi−Au (Å)

D (Debye)

BOSi−Au

BOave

−0.253 −0.260 −0.213 −0.291

0.175 0.188 0.129 0.191

0.962 0.912 1.141 1.152

−0.637 −0.640 −0.791 −0.512

2.295 2.291 2.385 2.299

1.073 1.210 0.788 0.920

0.228 0.904 0.201 0.885

0.143 0.569 0.133 0.479

Calculated at PBEPBE/{Au:LANL2DZ; Si:6-31G(d)}. bCalculated at PBEPBE/LANL2DZ.

moments of the SiAun (n = 17−20) clusters were calculated and listed in Table 2. The dipole moments are very large for the existence of the dangling Au atom. They are mainly along the direction of the dangling Si−Au dimer. The infrared (IR) vibrational spectrum reflects the information of the geometrical structure. Figure 7 shows the

6 shows the exact distributions of the natural charges. In the SiAun (n = 17−20), the Si atom carries negative charges,

Figure 6. Natural charges of SiAun (n = 17−20) calculated at PBEPBE/{Au:LANL2DZ; Si:6-31G(d)}. Figure 7. IR spectra of SiAun (n = 17−20) calculated at PBEPBE/ {Au:LANL2DZ; Si:6-31G(d)}.

whereas the Au atoms have different charges depending on their locations. The Au atoms around the cage have positive charges in which the dangling Au atom has the largest, and the other Au atoms inside have negative or zero charges. The charge inclines to transfer to the inside atoms from the surface Au atoms. This may enrich the properties of the SiAun clusters. For SiAu20a, the charges on the dangling Au and its neighboring Si are +0.191 and −0.291, respectively. Among the four clusters, the dangling Au atom of SiAu20 carries the largest positive charge. This obvious ionic character may have some possible applications, such as catalysis and targeting therapy. The NBO bond order is also calculated, which could indicate the type and the strength of the bond, and the Wiberg bond index matrix in the NAO basis is adopted. In the calculation we used the same basis set LANL2DZ for both Si and Au and the clusters are still the optimized structures with the basis set {Si/ 6-31G(d); Au/LANL2DZ}. As shown in Table 2, only the bond order of the Si−Au bond is listed because they are much larger than that of the Au−Au bond, showing that the Si−Au interaction is much stronger than that of the Au−Au bond. In the SiAun (n = 17−20) clusters, the bond order of the Si and the dangling Au atom is larger than that of the other Si−Au bonds, so the covalence interaction between the dangling Si− Au is suggested. For SiAu18 and SiAu20, the NBO bond orders are much larger than that of SiAu17 and SiAu19; thus the Si−Au interaction is stronger in SiAu18 and SiAu20. The dipole

IR vibrational spectra of the lowest-energy SiAun (n = 17−20) clusters. Except for SiAu19, the spectra of the other three clusters are nearly the same for their similar structures: there are two main IR peaks, one is in the range 100−180 cm−1, which is due to the vibration of the gold atoms; the other is in the range 350−500 cm−1, causing by the vibration of the silicon atom along the dangling Si−Au direction. Obviously, the intensity of the second peak is much stronger than the former. For SiAu20, the second peak has a big red shift and intensity decreasing compared to the SiAu17 and SiAu18. This is because the subunit turns from SiAu5 to SiAu6. The SiAu19 has one more peak which is in the range 250−300 cm−1, corresponding to the vibration of the silicon atom in the direction vertical to dangling Si−Au bond, and the intensity is stronger than the other two peaks. For SiAu18 and SiAu20, a vibration mode also occurs at 250−300 cm−1, but the intensity is very weak. In addition, all the lowest-energy SiAun (n = 17−20) have some small peaks less than 100 cm−1 due to the vibration of the gold atoms. We have calculated the anionic isomers for SiAun a, b, and c (n = 17−20) with DFT-PBE in VASP. The results show that the lowest-energy neutral cluster structures at DFT-PBE are also favored for anionic species, and the cage SiAu19c− is more 2675



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Notes

favorable than other two isomers. It seems that there is little change in shape by adding one extra electron for the present studied clusters’ size 17−20. Figure 8 shows the calculated electronic density of states (DOS) for the best structures of the anionic SiAu17,18,19,20

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 21273122, 21203105 and 11104152).

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Figure 8. DOS of the lowest-lying isomers of the anionic SiAu17,18,19,20 clusters at PAW-PBE.

clusters, and the other DOS for the isomers are in the Supporting Information (Figure S5). The Fermi energy level is set to zero. The electronic DOS is intimately related to the interaction of the atomic lattice. And the DOS of the isomers are obviously different from each other. In Figure 8, though the SiAu17a−, SiAu18a−, SiAu19c−, and SiAu20a− have similar structural motifs as the cage structure with a dangling gold atom, their DOS behaviors are remarkably different due to the difference of the electrons. These properties might be compared with future experimental photoelectron spectra to determine the structures of SiAu17−20 clusters.

4. CONCLUSIONS The structures and electronic properties of the SiAun (n = 17− 20) clusters were systematically investigated by the DFT calculations. The results show that doping with silicon could significantly change the structures of the gold clusters. For the SiAun (n = 17−20) clusters, the SiAu17,18,20 exhibit shell-like cage structures with an Au atom dangling on top of Si that is embedded on the cage surface, much different from pure Au clusters. The dopant Si atom with the neighboring Au atoms forms a SiAu5,6 unit. The SiAu19 cluster prefers a tetrahedronlike structure with a protruding Au atom, where the protruding Au atom on Si forms Au−Au bonds with other two neighboring Au atoms. The SiAu20 has a calculated gap of about 1.0 eV, which may be a good candidate for biomedicine. By the population analysis, we find that the gold atoms around the cage carry positive charges and the others have negative or no charges. The IR spectra and DOS have a strong relationship to the structures, and these characteristic peaks may be used as a signature for experimental identification of the configuration.

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ASSOCIATED CONTENT

S Supporting Information *

Figures showing the isomers of SiAun (n = 17−20), DOS of the low-lying isomers of SiAun (n = 17−20) clusters, and atomic coordinates of SiAun (n = 17−20). Complete ref 45. This information is available free of charge via the Internet at http:// pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

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