Unraveling Special Structures and Properties of Gold-Covered Gold

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Unraveling Special Structures and Properties of Gold-covered Gold-core Cage on Au Nanoparticles 33-42

Li-Xia Zhao, Meng Zhang, Hong-Yu Zhang, Xiao-Juan Feng, and You-Hua Luo J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b08923 • Publication Date (Web): 18 Nov 2015 Downloaded from http://pubs.acs.org on November 19, 2015

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The Journal of Physical Chemistry

Unraveling Special Structures and Properties of Gold-covered Gold-core Cage on Au33-42 Nanoparticles Li-Xia Zhao,* Meng Zhang, Hong-Yu Zhang, Xiao-Juan Feng, You-Hua Luo*

Department of Physics, East China University of Science and Technology, Shanghai 200237, China

*Corresponding authors. E-mail: [email protected] (Zhao, L. X.); [email protected] (Luo, Y. H.)

ACS Paragon Plus Environment


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ABSTRACT: New low-energy atomic structures and properties of

medium-size gold nanoparticles （Au33-42） are studied, where the atomic positions of gold atoms are obtained on the basis of the generic formulation of shell and core concept. Hollow cage, tube-like, double-layered flat, fcc-like, and close-packed configurations are predicted. Relativistic density functional theory optimization indicated that low-symmetry stuffed configurations are all lower in energy than the others. Further analysis of the optimized structures of Au33-42 nanoparticles shows that these gold cores are all four-atom tetrahedral structures and similar to each other, only the number and positions of gold atoms at the surface of gold core are different. Compared with structure and electronic properties, Au33-42 nanoparticles have different structure stabilities and chemical activities. But they are all hybridization of sp and d electron. The obtained information forms the basis for future chemisorption studies to unravel the catalytic effects of gold nanoparticles.


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INTRODUCTION As we all know, the catalytic properties of gold nanoparticles （Au NPs） is remarkably different from chemical inert of the bulk phases.1-4 As one of the key factors to understand the intriguing characterizations, all kinds of structures and properties of Au NPs have been studied. It is found that small-sized gold clusters Au3 to Au13 exhibit 2D planar structures and the even-odd effect with enhanced structural and chemical stabilities at odd-numbered

clusters.5-9

configurations.5-7Au16-19

prefer

Au14-15 the

have

pyramid-based

the bulk

close-flat fragment

structures in addition to the Au20.10-13 It is especially mentioned that the fragment structure of Au16, with the same Td symmetry as Au20, is found to be strongly favored over all the other isomers, showing its high stability and chemical inert with a large HOMO-LUMO gap11. Next, Au20 has the pyramid-tetrahedral structure with an extremely large energy gap, which is even greater than that of C60.14-17 Au21-23 adopt fcc-like structure owing to the high stability of tetrahedral Au20.18 Meanwhile, a structural transition from fcc-like to tubular configuration occurs at Au24, and the tubular motif continues at Au27 and Au28. However, at Au25 and Au26, a double-layered flat structure and a pyramid-based structure are found respectively. Importantly, an icosahedral Au32 hollow cage configuration is computed to be especially stable.19-21 This perfect Ih structure, referred as “golden fullerene”, can be constructed from the C60 as a template. For



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Au33-35, cage-like structures are also found to be lower in energy than other isomers.20 But, Au38, Au44, Au55, Au56, and Au58 probably exhibit stuffed fullerene structures.22-26 Recently, a large hollow tube-like Au42 is predicted as a new ground-state configuration.21 In addition, an Au50 cage and an icosahedral Au72 cage have been predicted to be the lowest-energy structures with extra stability.26-28 These studied results show strong competition between cage-like, tube-like, and space-filled isomers in the medium-size Au NPs. So, the overall growth sequence of those systems is rather complicated and requires very careful examination. Despite these theoretical predictions, there is still no experimental evidence up to now for them. The electronic properties such as EA and PDOS show sensitivity to cluster geometry, which might be helpful for distinguishing those structural motifs experimentally. Because of the sheer number of possible atomic arrangements, structural determination for larger gold clusters becomes increasingly more challenging, and global minimum searches are more essential. The aim of the current study is to explore the systematic structural evolution and properties of Au NPs: Au33-42. The obtained structures reveal generic structural motifs and structural trends for gold clusters in this size range, which will be valuable for future studies of their catalytic characterizations.


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COMPUTATIONAL METHODS To identify the lowest-energy configurations of Au33-42, all kinds of initial structures are obtained by different approaches as follows: first, close-packed configurations are obtained from the basin-hopping method using Sutton-Chen29 and Glue potentials30; second, the configurations from the previous studies20,21,25 are considered; third, isomers are constructed by adding or removing gold atoms on golden fullerene Au3220,21 and icosahedral Au42 25 etc.; fourth, the core-shell structures are generated with a different number of Au-core. These methods are effective ways to produce more than one hundred initial structures for relativistic density functional theory (RDFT) optimization. In the DFT calculations31-32 based on relativistic semi-core pseudopotential33

within

generalized

gradient

approximation

(DSPP/GGA), Perdew-Burke-Ernzerhof correlation functional (PBE)34 is employed. A double numerical basis set including d-polarization functions (DND) is chosen to carry out the electronic structure calculation. Spin-unrestricted self-consistent field calculations are done with a convergence criterion of 10-5 a.u. on the total energy and the electron density. Furthermore, convergence criteria of 0.002 hartree/Å and 0.005Å are used on the force parameters and the displacement parameter in the geometry optimization respectively. Vibrational frequency analysis has structures without imaginary frequencies. All computations are carried



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out in the DMol3 package. 35,36

30b. 0, C1 , 0

30c. 0, D6h, 1.630

31a. 4, C1, 2.683

31b. 0, C5v , 0

31c. 0, Cs, 3.612

32a. 4, C1, 0.920

32b. 0, Ih, 0

30a. 4, C1 ,0.941

32c. 0, D6h, 1.794

Figure 1. Low-energy structures of Au30-32, with the number of gold-atom core, the symmetries, and the relative energies (eV) calculated at the GGA/PBE/DND level.

Using the optimization approach described above, a lot of structures for each size of Au33-42 NPs have been examined, such as hollow cage, tube-like, double-layered flat, fcc-like, close-packed configurations etc.. These isomers have strong competitions and can be grouped into three structural growth motifs, that is, space-filled, cage-like, and tube-like structures (shown in Fig.1 and Fig.2). In Fig.1, the lowest energy structures of Au30-32 are found to be hollow cages, which is in agreement with ones of previous research20-21. The results confirm that the current ACS Paragon Plus Environment

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computational scheme is exact for the medium-sized gold clusters. The accuracy of this method has also been checked in previous researches 26-27, 37. RESULTS AND DISCUSSION In Fig.2, eight isomers of Au33 are obtained by DFT optimization, including one cage-like, one tube-like, and six core-shell structures. The most stable configuration is found to be a core-shell structure with a four-atom tetrahedral core and without any symmetry (33a shown in Fig.2). It is very different from Au30-32 (shown in Fig.1). Furthermore, in previous research, the lowest energy structure of Au33 is found to be cage-like.21 In our optimization, the cage-like isomer 33b is also obtained, but it is higher in energy than the lowest energy structure by 0.087 eV. The cage-like isomer is similar to the structure of icosahedral Au32, with one more atom added to the top of hollow cage of Au32.20,21 The tube-like configuration can be considered to be resulted from adding one gold atom on tube-like structure of Au3238 , which is also higher in energy than this 33a by 1.221 eV. When the cluster size reaches 34, the most stable structure motif is the same as the Au33. The lowest energy isomer of Au34 is space-filling with four gold atoms in the core and obtained by adding one gold atom to the similar structures of Au33. The cage-like configuration is obtained by add one gold atom to the 33b, its energy is 0.373 eV higher than that of the



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33a. 4, C1, 0

34a. 4, C1, 0

35a. 4, C1, 0.00

36a. 4, Cs, 0

37a. 4, C1, 0

33b. 0, C2v , 0.087

34b. 0, D2h, 0.373

35b. 0, C1, 1.804

36b. 0, C1, 1.520

37b. 0, C1, 4.080

33c. 0, Cs, 1.221

34c. 0, C3v , 1.393

35c. 0, C1, 3.960

36c. 0, D2d, 1.051

37c. 0, C1, 4.519


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38a. 4, C1, 0

39a. 4, C1, 0

40a. 4, C1, 0

41a. 4, C1, 0

42a. 4, C1 , 0

38b. 0, C2h, 0.912

39b. 0, C1, 1.213

38c. 0, D6d, 1.427

39c. 0, Cs, 1.770

40b. 0, C1, 1.210

40c. 0, C1, 2.296

41b. 0, C5v, 0.807

41c. 0, C1, 2.091

42b. 0, D5d ,3.096

42c. 0, D2h, 3.100

Figure 2. Low-energy structures of Au33-42, with the number of gold-atom core, the symmetries, and the relative energies (eV) calculated at the GGA/PBE/DND level.



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most stable structure 34a. Another tube-like isomer is higher in energy than the most stable state by 0.226 eV. Then it is less stable in the structure than the lowest energy isomer. For Au35 to Au41, their lowest energy isomers are similar each other and can be considered to be resulted from adding one or two gold atoms on the stable structures of the last sizes obtained. Note that the lowest energy structure of Au35-41 have 4 gold atoms in the core, which is more stable than the cage-like and tube-like isomers. A large hollow tube-like Au42 has been predicted as a new ground-state configuration25. However, our result is very different from the previous one (in Fig.2). The space-filling isomer with four-atom core is more stable than the hollow tube-like structure, which is lower in energy than the 42b by 3.096 eV. Both structures are also optimized by GGA/PBE/DND with all electron relativistic core treatment. The core-shell configuration is still lower in energy than the hollow tube-like one by 0.353 eV. Furthermore, the space-filling isomer with one-atom core is also more stable than the hollow tube-like configuration, because it is 1.490 eV lower than that one in energy. In the growth of gold clusters around the present size range, the global minimum structures are found to exhibit low-symmetry core-shell configurations with containing a four-atom tetrahedral core . Surprisingly, the most stable structures of Au33-35 and Au42 are


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demonstrated to be hollow cage-like and hollow tube-like respectively in the previous study.21,25 The obtained structures reveal generic structural motifs and structural trends for Au33-42, which may be used as a guide to construct low-energy candidate configurations for gold clusters with larger sizes. The stabilities of neutral clusters can be evaluated by their binding energies per atom (Eb) and second differences in energies ( ∆2 E ). The Eb and ∆2 E of gold clusters are calculated according to the following definitions: E b (Au n ) = [nE (Au) − E (Au n )] / n ,

∆2 E (Au n ) = E (Au n −1 ) + E (Au n +1 ) − 2 E (Au n ) ,

where E(Au), E(Aun), E(Aun-1), and E(Aun+1) represent the total energies of the most stable Au, Aun, Aun-1, and Aun+1 clusters, respectively. Larger average binding energies and larger second differences would indicate a cluster being more stable and is not easy to dissociate. The Eb and ∆2 E of gold clusters are presented in Fig.3 as a function of their sizes. Note that the average binding energies of Au33-42 range from 2.385 eV to 2.497 eV and have not obvious change. The same result is found in Au21-28. The ∆2 E of gold clusters calculated are obviously larger at Au32, Au35, Au37, Au39, and Au41, and thus these clusters have special stability compared to their neighboring ones. It is to be noted that the curves has obvious odd-even change, which is consistent with the change tendency



of Au2-26 clusters suggested by Li et al..7,11

Binding energies per atom and second differences (eV)

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Binding energies per atom second difference in energies

4 3 2 1 0 -1 -2 -3 -4 32

34

36

38

40

42

Cluster Size n

Figure 3. Binding energies per atom and second differences in energies of Au33-42 clusters.

The

highest-occupied

molecular

orbital

(HOMO)

and

the

lowest-unoccupied molecular orbital (LUMO) gap, having relations with the relative chemical reactivity of clusters, is of much importance in theoretical researches. It is found that systems with larger HOMO-LUMO gap are more stable in chemical reactivity. In our work, the eigenvalues of HOMO and LUMO shells of the lowest-energy structures for Au33-42 clusters are calculated, and the results are displayed in Table 1. Thus, the HOMO-LUMO gap are obtained and shown in Fig.5. For Au33-35 clusters, their gaps are larger than others. The large gaps ensure reactive stability. Therefore, Au34, with special stability in structure, also has a large reactive stability. Au38 and Au40 have the higher values of gap than their ACS Paragon Plus Environment

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neighbours. Au39 has the lowest gap in energy, corresponding to its highest chemical reactivity. Among the studied clusters, those with full HOMO shells and empty LUMO shells are energetically favorable. It is found that the electronic structures of Au34 and Au38 are fully filled in HOMO and unfilled in LUMO (shown in Table 1), and those are of exactly closed shells, consistent with its special chemical stability. Au34 have also largest HOMO-LUMO gaps of 1.07eV.

1.2

1.0

Egap (eV/Atom)

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0.8

0.6

0.4

0.2

0.0 32

34

36

38

40

Cluster Size n

Figure 4. HOMO-LUMO gaps (Egap) of Au33-42 clusters.


42


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Table 1. Eigenvalues and occupation on highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) for Au33-42 clusters.

Eigenvalue(eV)

Occupation(100%)

Cluster size HOMO

LUMO

HOMO

LUMO

33

-4.933

-4.127

0.615

0.004

34

-5.256

-4.191

1.000

0.000

35

-5.481

-4.507

0.997

0.231

36

-4.697

-4.391

0.594

0.133

37

-4.821

-4.442

0.508

0.060

38

-4.602

-4.193

1.000

0.000

39

-4.996

-4.577

0.941

0.421

40

-4.994

-4.386

0.907

0.101

41

-5.186

-4.807

0.922

0.419

42

-4.973

-4.671

0.716

0.215

The lowest-energy structures of anionic Au33-42 clusters are also searched by the same method. Their lowest energy structures are similar to neutral ones and those of Au33-35- are in agreement with the experimental results.39-40 The photoelectron spectrum (PES) measurement suggests that Au33-35- exhibit core-shell type structures with featuring a four-atom tetrahedral core. In Fig.5, the electron affinities (EAs) of Au33-42 are shown. According to our calculated results, the EA of Au34 (3.390 eV) is close to the experimental data (3.45 eV).39 Also, it is found


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that the EA value of Au38 (5.848 eV) is the largest and that of Au42 (0.247 eV) is the smallest among those of Au33-42 clusters, indicating that Au38 is likely to get an electron to form Au38-, whereas Au42 is not.

6

5

4

EA (eV)

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3

2

1

0 32

34

36

38

40

Cluster Size n

Figure 5. Electron affinity (EA) energies of Au33-42 clusters.


42


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Table 2. Structure, symmetry, charge, and average bond length of the core for Au33-42 clusters and pure Au4 cluster.

Cluster size

Structure

Symmetry of core

Charge of

core

Average bond length of core(Å)

33

D2d

0.466

2.822

34

Td

0.419

2.778

35

D2d

0.388

2.771

36

D2d

0.446

2.785

37

Td

0.442

2.797

38

D2d

0.466

2.791

39

Td

0.423

2.810

40

Td

0.383

2.817

41

Td

0.379

2.821

42

D2d

0.382

2.824

4

D2h

0

2.717


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Figure 6. Partial density of states (PDOS) of s, p, d, f and Sum orbitals for Au33-42 NPs. Feimi level is set at zero on the energy axis.



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In the Au33-42 nanoclusters, the lowest energy structures are the spaced-filled isomers with four gold atoms in the core, which can be explained by maximizing charge transfer. The structure, symmetry, charge, and average bond length of the core for Au33-42 clusters are calculated and shown in the Table 2. The results show that, comparing with two dimensions structure of pure Au4 cluster, it is three dimensions and has high symmetry in the core of gold cage. The gold cage could change the structure of other clusters, which should be studied in the near future. The Mulliken charges of gold atoms in the core are near +0.100 and are much higher than the gold atoms on the shell (near + 0.050), which is due to the maximizing charge transfer. The charge transferring from the central atoms to the peripheral atoms is much higher than one from the peripheral atoms to the peripheral atoms in order to maximize the value. The average bond length of Au-Au in the core is near 2.800 Å and is a little higher than one of the pure Au4 cluster (2.717 Å). It is said that the interaction force of Au-Au in the core is weaker than one of the pure Au4 cluster, which may be due to the gold cage. To further compare with the future experimental characterization, we have computed the partial densities of states (PDOS) of the global minimum structure of Au33-42 NPs and show it in Fig.6. Careful examinations show that space-filling structure possesses relatively broad d-bandwidth, which due to its low-symmetry. Another noticed finding is


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that three peaks with a little overlap of s, p, and d orbitals emerge at the vicinity of Fermi level, which indicates hybridization of s, p and d electron in these cases and the situations of Au33-42 NPs are somewhat located in the area of the major valence band. SUMMARY In summary, we investigated the atomic structures and properties of medium-size gold NPs （Au33-42）of hollow cage, tube-like, double-layered flat, fcc-like, and close-packed configurations by relativistic density functional theory calculation. We revealed such Au NPs favor similar core-shell configurations with four gold atoms in the core, which indicates that one has to examine all the possibilities and to optimize them at a first-principle level in order to find the lowest energy configurations of all Au NPs within the structural pattern of core-shell. We further examined electronic properties of these NPs, which show Au34 has the highest chemical stability with the biggest gap and Au38 is the easiest getting an electron to form Au38-. The PDOS shows hybridization of s, p and d electron in the studied NPs. These principles should be applicable to larger systems, which will benefit the design of nanomaterial on experiment.



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ACKNOWLEDGMENTS This work is financially sponsored by Natural Science Foundation of Shanghai (No. 15ZR1409600 and 12ZR1407000), National Natural Science Foundation of China (No. 11304096 and 11204079), and Fundamental Research Funds for the Central Universities of China (WM.1514320).

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