Two-dimensional growth mode of thiolate-protected gold nanoclusters Au28+4n(SR)20+2n (n = 0–8): compared with their one-dimensional growth mode

Pengye Liu a, Wenhua Han a, Mengke Zheng a and Wen Wu Xu *ab
aDepartment of Physics, School of Physical Science and Technology, Ningbo University, Ningbo 315211, China. E-mail: xuwenwu@nbu.edu.cn
bLaboratory of Clean Energy Storage and Conversion, Ningbo University, Ningbo 315211, China

Received 21st July 2020 , Accepted 16th September 2020

First published on 17th September 2020


Abstract

In this paper, six new atomic structures of thiolate-protected gold nanoclusters, i.e. Au32(SR)20, Au40(SR)26, Au48(SR)30, two Au56(SR)34, and Au60(SR)36, are predicted. Considering these six newly predicted structures and six previously predicted or crystallized Au28(SR)20, Au36(SR)24, Au44(SR)28, Au52(SR)32, and Au60(SR)36 altogether, the two-dimensional (2D) growth mode of Au28+4n(SR)20+2n (n = 0–8) nanoclusters is completely presented to compare with their one-dimensional (1D) growth mode. In Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes, the same number of gold-core atoms with different morphologies can be seen. Furthermore, the growth of the gold cores occurs via sequential fusion of one tetrahedral Au4 unit by sharing one gold atom. In addition, density functional theory calculations show that these six newly predicted gold nanoclusters following the 2D growth mode have relative energies very close to those of their isomeric structures following the 1D growth mode, large highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO–LUMO) gaps, and all-positive harmonic vibration frequencies, indicating their high stabilities. Therefore, the complete presentation of the 2D growth mode of Au28+4n(SR)20+2n (n = 0–8) is beneficial not only for a better understanding of the structural growth of gold nanoclusters, but also for a theoretical guidance on the prediction of new stable structures for experimental confirmation.


Introduction

The one-dimensional (1D) growth of Au28+4n(SR)20+2n (n = 0–8) has gained sustained attention in recent years.1–8 Many theoretical and experimental efforts have been devoted to achieve a better comprehension of this 1D growth mechanism. Based on the structures of crystallized Au28(SR)20 and Au36(SR)24 nanoclusters,1,2 the structural evolution pathway, i.e. Au28(SR)20 + [Au8(SR)4] → Au36(SR)24 + [Au8(SR)4] → Au44(SR)28, was identified as a sequential addition of a common structural motif [Au8(SR)4], resulting in the successful structure prediction of Au44(SR)28.3 The predicted Au44(SR)28 was experimentally confirmed by X-ray crystallography later.4 Thereafter the crystal structure of Au52(SR)32 obtained in 2015 first demonstrated a double-helical Au32 core composed of ten tetrahedral Au4 units and five tetrahedra were connected by vertex sharing within each helix.5 Such similar double-helical superstructures can also be seen in the Au14 core of Au28(SR)20, Au20 core of Au36(SR)24, and Au26 core of Au44(SR)28 nanoclusters.6 In addition, the structure of Au52(SR)32 can be viewed as the addition of a common structural motif, [Au8(SR)4], on Au44(SR)28, also obeying the structural evolution among Au28(SR)20, Au36(SR)24, and Au44(SR)28. Therefore, the generic growth pattern underlying this sequence of Au28(SR)20, Au36(SR)24, Au44(SR)28, and Au52(SR)32 nanoclusters can be viewed as fusing two highly stable tetrahedral Au4 units with the double-helical cores by sharing two gold atoms, suggesting their 1D growth mode. According to this 1D structural evolution pathway, the structures of longer Au60(SR)36, Au68(SR)40, and Au76(SR)44 nanoclusters were obtained theoretically.6 Recently, an atomic structure of Au56(SR)34 was experimentally determined to have a double-helical Au35 core, within which one helix has one more tetrahedral Au4 unit than the other.7 The double-helical Au35 core in Au56(SR)34 can be viewed as fusing one tetrahedral Au4 unit with one helix of the double-helical Au32 core in the Au52(SR)32 nanocluster by sharing one gold atom. Therefore, the Au56(SR)34 nanocluster, also obeying the 1D structural evolution, can be viewed as an intermediate structure between Au52(SR)32 and Au60(SR)36 nanoclusters. Following the same way, three intermediate structures, i.e. Au32(SR)20 between Au28(SR)20 and Au36(SR)24, Au40(SR)26 between Au36(SR)24 and Au44(SR)28, and Au48(SR)30 between Au44(SR)28 and Au52(SR)32, were theoretically predicted.8 When considering these crystallized and predicted structures mentioned above altogether, the Au28+4n(SR)20+2n (n = 0–8) nanoclusters following the 1D growth mode can be completely presented, as shown in Fig. 1 and S1.
image file: d0nr05439a-f1.tif
Fig. 1 One-dimensional (red arrow) growth of Au28+4n(SR)20+2n (n = 0–8) nanoclusters and two-dimensional (green arrow) growth of Au28+4n(SR)20+2n (n = 0, 2, 4, 6, and 8) nanoclusters. The dotted squares in red denote several “missing” gold nanoclusters. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity. * denotes the experimentally crystallized structure.

With the rapid increase in the number of isomeric structures of thiolate-protected gold nanoclusters, structural isomerism for thiolate-protected gold nanoclusters has become increasingly common.9 It is no exception for Au28+4n(SR)20+2n (n = 0–8) nanoclusters. A new Au52(SR)32 isomer has been shown to have the same number of gold-core atoms but different morphology compared with Au52(SR)32 following the 1D growth mode.10 This behavior can also be seen in the predicted Au28(SR)20 isomer.9 Inspired by the structures predicted for Au28(SR)20 and the crystallized Au52(SR)32 isomer, three new isomeric structures of Au36(SR)24, Au44(SR)28, and Au52(SR)32 were predicted.11 Among them, the Au36(SR)24 isomer was experimentally confirmed. In addition, another Au36(SR)24 isomer was predicted to have the same core as the newly crystallized isomer.8 Considering these isomers altogether, a two-dimensional (2D) growth mode was identified among Au28+4n(SR)20+2n (n = 0, 2, 4, and 6) nanoclusters. Recently, an isomeric structure of Au60(SR)36 obeying the 2D structural evolution was predicted by removing 6 four-coordinated μ4-sulfido motifs in crystallized Au604-S)6(SR)36.12,13

For convenience, Au28+4n-1D-Iso1 and Au28+4n-2D-Iso2/Iso3 (n = 0–8) are used to represent the Au28+4n(SR)20+2n (n = 0–8) isomers following 1D and 2D growth modes, respectively, as shown in Fig. 1 and S1. When comparing the Au28+4n-1D-Iso1 (n = 0–8) nanoclusters with Au28+4n-2D-Iso2/Iso3 (n = 0, 2, 4, 6, and 8) nanoclusters, one can see that there are several “missing” gold nanoclusters (Fig. 1 and S1), i.e. Au28+4n-2D-Iso2/Iso3 (n = 1, 3, 5, and 7). Therefore, in order to completely present the 2D growth of Au28+4n(SR)20+2n (n = 0–8) nanoclusters, six new atomic structures of thiolate-protected gold nanoclusters, i.e. Au32-2D-Iso2, Au40-2D-Iso2, Au48-2D-Iso2, Au56-2D-Iso2, Au56-2D-Iso3, and Au60-2D-Iso2, are predicted to fill some vacant spaces. Density functional theory (DFT) calculations show that these six newly predicted gold nanoclusters with the 2D growth mode have relative energies very close to those of their isomeric structures with the 1D growth mode, large highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO–LUMO) gaps, and all-positive harmonic vibration frequencies, indicating their high stabilities.

Results and discussion

First, we focus on the structures of predicted Au28-2D-Iso2 and crystallized Au36-2D-Iso2 nanoclusters.9,11 Based on the grand unified model (GUM),14,15 the Au20 core of Au36-2D-Iso2 can be viewed as fusing two tetrahedral Au4 with the Au14 core of Au28-2D-Iso2 by sharing two gold atoms. Therefore a new Au17 core can be obtained by fusing one tetrahedral Au4 with the Au14 core of Au28-2D-Iso2 by sharing one gold atom or removing one tetrahedral Au4 from the Au20 core of Au36-2D-Iso2 (Fig. 2). Since the Au17 core has the same Au14 structure (highlighted by wine color in Fig. 2) as Au28-2D-Iso2, two [Au(SR)2], one [Au2(SR)3], and one [Au4(SR)5] can bind with the Au17 core to form the Au17[Au(SR)2]2[Au2(SR)3][Au4(SR)5] structure. Similarly, since the Au17 core has the same Au14 structure (highlighted by wine color in Fig. 2) as Au28-2D-Iso1, the Au17[Au(SR)2]2[Au2(SR)3][Au4(SR)5] structure can further bind with two [Au2(SR)3] and one [Au3(SR)4] to form the complete structure of Au32-2D-Iso2 (Fig. 2). It can be seen that the protection motifs of Au32-2D-Iso2 can be obtained from Au28-1D-Iso1 and Au28-2D-Iso2.
image file: d0nr05439a-f2.tif
Fig. 2 Structural prediction of Au32-2D-Iso2. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity.

Similarly, a new Au23 core can be obtained by fusing one tetrahedral Au4 on the Au20 core of Au36-2D-Iso3 by sharing one gold atom or removing one tetrahedral Au4 from the Au26 core of Au44-2D-Iso2 (Fig. 3).11 Then the protection motifs on the Au23 core can be obtained from Au28-1D-Iso1 and Au44-2D-Iso2, resulting in the structural prediction of Au40-2D-Iso2. Following the same way presented in Fig. 2 and 3, other four new structures of Au48-2D-Iso2 (Fig. S2), Au56-2D-Iso2 (Fig. S3), Au56-2D-Iso3 (Fig. S4), and Au60-2D-Iso2 (Fig. S5) can also be obtained.


image file: d0nr05439a-f3.tif
Fig. 3 Structural prediction of Au40-2D-Iso2. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity.

Considering these six new structures and previously predicted or crystallized gold nanoclusters altogether, the 2D growth of Au28+4n(SR)20+2n (n = 0–8) nanoclusters can be completely presented, as shown in Fig. 4. In Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes, the same number of gold-core atoms with different morphologies can be seen. Furthermore, the growth of the gold cores occurs via sequential fusion of one tetrahedral Au4 unit (highlighted in blue color in Fig. 4) by sharing one gold atom. When the value of n reaches 5 (Au48-2D-Iso2), the 2D evolutionary pathway breaks into two. In addition, based on the GUM,14,15 the gold cores of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes can be viewed as several tetrahedral Au4 elementary blocks fusing or packing together. The isomeric mechanism of the gold cores can be understood as the same number of elementary blocks with different packing modes.9


image file: d0nr05439a-f4.tif
Fig. 4 One-dimensional (red arrow) and two-dimensional (green arrow) growth of Au28+4n(SR)20+2n (n = 0–8) nanoclusters. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity. * denotes the experimentally crystallized structure.

It was also noted that the gold core in Au28+4n(SR)20+2n (n = 0–8) nanoclusters can be described by the recently developed new polyhedral approach, in which the gold core is constituted of several tetrahedral Au4 and octahedral Au6 blocks.16,17 The average Au–Au distance in a tetrahedral Au4 block and the average Au–Au distance between two neighboring tetrahedral Au4 blocks in the gold cores of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes were calculated, as shown in Fig. 5. The calculated average Au–Au distance in a tetrahedral Au4 block is within the range of 2.80–2.90 Å, close to the Au–Au distance in bulk gold, that is, 2.88 Å. While the calculated average Au–Au distance between two neighboring tetrahedral Au4 blocks is within the range of 3.0–3.15 Å, the “holes” are closely related to octahedral units.16,17 Therefore, the gold cores of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes are composed of several compact tetrahedral Au4 blocks fusing together, with octahedral Au6 blocks among them.


image file: d0nr05439a-f5.tif
Fig. 5 Average Au–Au distance in the tetrahedral Au4 unit and the average Au–Au distance between two neighboring tetrahedral Au4 units in the gold cores of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes.

With the obtained 6 structures, density functional theory (DFT) calculations using the Gaussian 09 program package were performed to obtain the electronic properties of these clusters.18 Specifically, the Perdew–Burke–Ernzerhof (PBE) functional, the all-electron basis set 6-31G* for H and S, and effective-core basis set LANL2DZ for Au were adopted.19 In order to avoid prolonged computational time, the R groups were substituted by H atoms in all calculations. However, it should be noted that the ligand effects are very important for the properties of thiolate-protected gold nanoclusters.20 As shown in Table 1, the computed relative energies and HOMO–LUMO gaps of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes are quite close, suggesting the likelihood of high chemical stabilities of the predicted structures. The computed harmonic vibrational frequencies of these 6 nanoclusters were all positive, indicating that the 6 structures are local minima on the potential energy surfaces. In addition, the second-difference energies of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with 1D and 2D growth modes are computed via E = [E(n+2)E(n+1)] − [E(n+1)E(n)], in which E(n) denotes the energy of Au28+4n(SR)20+2n (n = 0–8) nanoclusters, as shown in Fig. 6. The zigzag curves of the second-difference energies show that the Au28+4n(SR)20+2n (n = 0–8) nanoclusters for odd n are less stable than those with an even n. This behavior can be understood from the lower symmetry of the core with an odd number of tetrahedral Au4 blocks in the Au28+4n(SR)20+2n (n = 0–8) nanoclusters for odd n compared to that of the core with an even number of tetrahedral Au4 blocks in the Au28+4n(SR)20+2n (n = 0–8) nanoclusters for even n.


image file: d0nr05439a-f6.tif
Fig. 6 Computed second-difference energies of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with 1D and 2D growth modes via E = [E(n+2)E(n+1)] − [E(n+1)E(n)], in which E(n) denotes the energy of Au28+4n(SR)20+2n (n = 0–8) nanoclusters.
Table 1 Computed relative energies, HOMO–LUMO gaps, and the lowest vibrational frequencies of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes, where * denotes the experimentally crystallized structure. The R groups are simplified by H atoms
Gold nanoclusters Isomers Relative energy/eV HOMO–LUMO gaps/eV Lowest vibrational frequency/cm−1
Au28(SR)20 Au28-1D-Iso1* 0.00 1.77 8.87
Au28-2D-Iso2 0.22 1.69 9.06
Au32(SR)22 Au32-1D-Iso1 0.00 1.74 6.59
Au32-2D-Iso2 0.39 1.58 6.63
Au36(SR)24 Au36-1D-Iso1* 0.00 1.88 8.58
Au36-2D-Iso2* 0.15 1.44 9.86
Au36-2D-Iso3 0.18 1.77 9.45
Au40(SR)26 Au40-1D-Iso1 0.00 1.69 8.15
Au40-2D-Iso2 0.46 1.58 6.58
Au44(SR)28 Au44-1D-Iso1* 0.00 1.63 6.57
Au44-2D-Iso2 0.49 1.66 11.12
Au48(SR)30 Au48-1D-Iso1 0.00 1.55 8.39
Au48-2D-Iso2 0.31 1.47 9.59
Au52(SR)32 Au52-1D-Iso1* 0.00 1.47 7.58
Au52-2D-Iso2* 0.08 1.47 6.74
Au52-2D-Iso3 0.00 1.50 9.11
Au56(SR)34 Au56-1D-Iso1* 0.00 1.36 7.41
Au56-2D-Iso2 0.16 1.41 7.66
Au56-2D-Iso3 0.19 1.39 5.97
Au60(SR)36 Au60-1D-Iso1 0.00 1.33 7.17
Au60-2D-Iso2 0.69 1.28 6.09
Au60-2D-Iso3 0.09 1.36 8.46


Besides the GUM,14,15 the previously developed superatom network model using the adaptive natural density partitioning (AdNDP) analysis can also be used to describe the Au14+3n(6+n)+ of Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes, as shown in Fig. 7 and S6.[thin space (1/6-em)]21,22 Taking Au3513+ of Au56-2D-Iso2 as an example, it is observed that the 22e valence electrons of Au56-2D-Iso2 are equally distributed on eleven tetrahedral Au4 units. Thus, the Au35 core of Au56-2D-Iso2 can be viewed as a network of eleven 4c-2e (4c denotes 4 centres). Similar behaviour can also be seen in other gold nanoclusters (Fig. 7 and S6).


image file: d0nr05439a-f7.tif
Fig. 7 Visualization of the valence electron distributions in the Au14+3n(6+n)+ of Au28+4n(SR)20+2n (n = 6–8) nanoclusters. Au atoms are presented in yellow. * denotes the experimentally crystallized structure.

In Fig. 8 and S7, the computed optical absorption spectra of all Au28+4n(SR)20+2n (n = 0–8) nanoclusters with both 1D and 2D growth modes are presented. It can be seen that the prominent absorption peaks of 799 nm for Au52-1D-Iso1, 605 and 785 nm for Au52-2D-Iso2, and 856 nm for Au56-1D-Iso1 can well reproduce the experimental peaks at 800, 563, 762, and 845 nm, respectively, indicating the reliability of the theoretical methods employed in this study.5,7,10 Furthermore, the profiles of the absorption spectra and the locations of the prominent absorption peaks for Au28+4n(SR)20+2n (n = 0–8) isomers are distinctly different, suggesting that they are all distinct isomers. In addition, the two prominent absorption peaks (664 and 826 nm) of Au52-2D-Iso3, two prominent absorption peaks (682 and 849 nm) of Au56-2D-Iso2, two prominent absorption peaks (662 and 831 nm) of Au56-2D-Iso3, two prominent absorption peaks (656 and 856 nm) of Au60-2D-Iso2, and two prominent absorption peaks (694 and 896 nm) of Au60-2D-Iso3 await future experimental confirmation.


image file: d0nr05439a-f8.tif
Fig. 8 Computed absorption spectra of Au28+4n(SR)20+2n (n = 6–8) isomers. The prominent absorption peaks for three clusters are highlighted in red. The R groups are simplified by H atoms. * denotes the experimentally crystallized structure.

Conclusions

In summary, in light of GUM and structural evolution, six new atomic structures of thiolate-protected gold nanoclusters, i.e. Au32-2D-Iso2, Au40-2D-Iso2, Au48-2D-Iso2, Au56-2D-Iso2, Au56-2D-Iso3, and Au60-2D-Iso2, are predicted to completely present a two-dimensional (2D) growth mode of Au28+4n(SR)20+2n (n = 0–8) nanoclusters. In Au28+4n(SR)20+2n (n = 0–8) nanoclusters with 1D and 2D growth modes, the same number of gold-core atoms with different morphologies can be seen. The isomeric mechanism of the gold cores can be understood as the same number of elementary blocks with different packing modes. In addition, DFT calculations show that these newly predicted nanoclusters exhibit high chemical stabilities.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgements

The authors are supported by the Natural Science Foundation of China (Grant No. 11974195) and the Natural Science Foundation of Ningbo (Grant No. 2019A610182). The authors acknowledge computational support from the National Supercomputing Center in Guangzhou (NSCC-GZ).

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Footnote

Electronic supplementary information (ESI) available: The gold cores of previously crystallized and predicted gold nanoclusters, structural prediction of Au48-2D-Iso2, Au56-2D-Iso2, Au56-2D-Iso3, and Au60-2D-Iso2, the visualization of the valence electron distributions in the Au14+3n(6+n)+ of Au28+4n(SR)20+2n (n = 0–5) nanoclusters, the simulated optical absorption spectra of Au28+4n(SR)20+2n (n = 0–5) isomers, and cartesian coordinates of predicted thiolate-protected gold nanoclusters. See DOI: 10.1039/d0nr05439a

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