Structural predictions of three medium-sized thiolate-protected gold nanoclusters Au₄₄(SR)₃₀, Au₅₆(SR)₃₂, and Au₆₀(SR)₃₄

Abstract

The knowledge of structural evolution among thiolate-protected gold nanoclusters is not only helpful for understanding their structure–property relationship but also provides scientific evidence to rule-guided structure predictions of gold nanoclusters. In this paper, three new atomic structures of medium-sized thiolate-protected gold nanoclusters, i.e. Au₄₄(SR)₃₀, Au₅₆(SR)₃₂, and Au₆₀(SR)₃₄, are predicted based on the grand unified model and ring model. Two structural evolution rules, i.e., Au₄₄(SR)₂₈ + [Au₁₂(SR)₄] → Au₅₆(SR)₃₂ + [Au₁₂(SR)₄] → Au₆₈(SR)₃₆ and Au₄₄(SR)₃₀ + [Au₈(SR)₂] → Au₅₂(SR)₃₂ + [Au₈(SR)₂] → Au₆₀(SR)₃₄ + [Au₈(SR)₂] → Au₆₈(SR)₃₆, are explored. The generic growth patterns underlying both sequences of nanoclusters can be viewed as sequential addition of four and three highly stable tetrahedral Au₄ units on the cores, respectively. In addition, density functional theory calculations show that these three newly predicted gold nanoclusters have very close formation energies with their adjacent structures, large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) gaps, and all-positive harmonic vibration frequencies, indicating their high stabilities.

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Introduction

The knowledge of structural evolution among thiolate-protected gold nanoclusters is beneficial for better understanding their structure–property relationship.^1–4 Thanks to the structural determination of Au₂₈(TBBT)₂₀ (TBBT = 4-tert-butyl-benzenethiolate), Au₃₆(TBBT)₂₄, Au₄₄(TBBT)₂₈, and Au₅₂(TBBT)₃₂, a “magic series” Au_8n+4(TBBT)_4n+8 (n = 3–6) with a uniform anisotropic growth pattern was identified as a typical case to investigate their size-dependent properties.^5,6 For example, the size-dependent quantum confinement nature understood by the empirical scaling law and classical “particle in a box” model and the redshift of the onset of the optical absorption spectra with the increment of cluster size can be observed in this “magic series”. The femtonanosecond excited state dynamics of this “magic series” demonstrate that the relaxation of hot carriers and recombination of band-edge carriers will slow down as the size increases from Au₂₈(TBBT)₂₀ to Au₅₂(TBBT)₃₂. In addition, the evolution of the catalytic activity of the “magic series” Au_8n+4(TBBT)_4n+8 (n = 3–5) can potentially be attributed to the periodic evolution in the inner cores.

Another important application for the understanding of structural evolution among thiolate-protected gold nanoclusters is to provide scientific evidence to rule-guided structure predictions of gold nanoclusters.^7–9 To date, ten groups of “magic series” of thiolate-protected gold nanoclusters have been identified, as shown in Table 1, resulting in a large number of structural predictions of gold clusters.^5,6,10–14 Particularly, among these predicted structures, two atomic structures of Au₄₄(SR)₂₈ and Au₃₆(SR)₂₄ were experimentally confirmed by X-ray crystallography.^15,16 For each “magic series” of thiolate-protected gold nanoclusters, their structural evolution can be viewed as the addition of a common motif or addition of several highly stable triangular Au₃ or tetrahedral Au₄ units on the cores. Taking the “magic series” Au_28+n(SR)_20−n (n = 0–2) as an example, the structural evolution of Au₂₈(SR)₂₀, Au₂₉(SR)₁₉, and Au₃₀(SR)₁₈ can be viewed as sequential addition of a common motif [Au(SR)₋₁], namely Au₂₈(SR)₂₀ + [Au(SR)₋₁] → Au₂₉(SR)₁₉ + [Au(SR)₋₁] → Au₃₀(SR)₁₈, or sequential addition of one highly stable triangular Au₃ unit on the cores.

Table 1 Several groups of “magic series” of thiolate-protected gold nanoclusters as well as their common motifs and the number of units added on the core^a

“Magic series” of gold nanoclusters	Common motif	Number of units added to the core
		Triangular Au3	Tetrahedral Au4
a (*) denotes the newly identified “magic series” of thiolate-protected gold nanoclusters in this work.
Au28+4n(SR)20+2n (n = 0–6)	[Au4(SR)2]	0	1
Au28+n(SR)20−n (n = 0–2)	[Au(SR)−1]	1	0
Au44+24n(SR)28+8n (n = 0–2)	[Au24(SR)8]	0	8
Au22+6n(SR)18+2n (n = 0–3)	[Au6(SR)2]	0	2
Au40+9n(SR)24+3n (n = 0–3)	[Au9(SR)3]	0	3
Au28+26n(SR)20+14n (n = 0–4)	[Au26(SR)14]	0	6
Au36+36n(SR)24+16n (n = 0–4)	[Au36(SR)16]	0	10
Au44+42n(SR)28+18n (n = 0–4)	[Au42(SR)18]	0	12
Au52+52n(SR)32+20n (n = 0–4)	[Au52(SR)20]	0	16
Au52+24n(SR)32+10n (n = 0–4)	[Au24(SR)10]	0	7
Au44+12n(SR)28+4n (n = 0–2)*	[Au12(SR)4]	0	4
Au44+8n(SR)30+2n (n = 0–3)*	[Au8(SR)2]	0	3

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With the development of theoretical models, i.e., the grand unified model (GUM) and ring model,^17,18 structural insights into the better understanding of thiolate-protected gold nanoclusters can be obtained, thereby providing theoretical tools to identify “magic series” of thiolate-protected gold nanoclusters with different common motifs. In the GUM, the gold cores of ligand-protected gold nanoclusters can be viewed as several triangular Au₃(2e) or tetrahedral Au₄(2e) elementary blocks packing or fusing together.¹⁹ Meanwhile in the ring model, the interfacial interactions between SR [Au(SR)]_x (x = 0, 1, 2, 3,…) protection motifs and gold cores in thiolate-protected gold nanoclusters can be understood by several [Au_m(SR)_n] (m = 4–8, 10, 12, and 0 ≤ n ≤ m) rings. Based on the GUM and ring model, some thiolate-protected gold nanoclusters, such as Au₁₅(SR)₁₃, Au₂₂(SR)₁₆, and Au₃₀(SR)₂₀, were predicted to have high stability.^20–22 In this paper, based on the GUM and ring model, two new groups of “magic series” of thiolate-protected gold nanoclusters (Au_44+8n(SR)_30+2n (n = 0–3) and Au_44+16n(SR)_28+4n (n = 0–2)) were identified via structural predictions of three medium-sized nanoclusters (Au₄₄(SR)₃₀, Au₅₆(SR)₃₂, and Au₆₀(SR)₃₄).

Results and discussion

We focused on three thiolate-protected gold nanoclusters Au₄₄(SR)₂₈, Au₅₂(SR)₃₂, and Au₆₈(SR)₃₆, and found an interesting phenomenon: a top view of these structures reveals that they are hexagonal, while their gold cores are round (Fig. 1),^23–25 suggesting that Au₄₄(SR)₂₈, Au₅₂(SR)₃₂, and Au₆₈(SR)₃₆ have very similar morphology. In addition, these thiolate-protected gold nanoclusters follow the grand unified model (GUM) and their gold cores can be regarded as several tetrahedral Au₄ elementary blocks following the duet rule.^17,18 This interesting phenomenon led us to ponder the question: Are there other new intermediate structures with similar morphology between these thiolate-protected gold nanoclusters?

Fig. 1 Structures and their gold cores of Au₄₄(SR)₂₈ (a and b), Au₅₂(SR)₃₂ (c and d), and Au₆₈(SR)₃₆ (e and f) nanoclusters.

In Fig. 2, the Au₂₆ core of Au₄₄(SR)₂₈ is formed by the face-to-face combination of two Au₁₃ units, which can be regarded as four tetrahedral Au₄ fusing together by sharing three Au atoms. The Au₅₀ core of Au₆₈(SR)₃₆ nanoclusters is composed of two Au₂₅ units, which can be decomposed into eight tetrahedral Au₄ fusing together by sharing seven Au atoms. Thus, the Au₂₆ core fused with four tetrahedral Au₄ (blue atoms in Fig. 2a) or the Au₅₀ core removed four tetrahedral Au₄ (blue atoms in Fig. 2a) will form a new Au₃₈ core. In the same way, a new Au₄₁ and Au₂₃ core can be formed by removing three tetrahedral Au₄ (blue atoms in Fig. 2b) from the Au₅₀ core of Au₆₈(SR)₃₆ nanoclusters or the Au₃₂ core of Au₅₂(SR)₃₂ nanoclusters. It can be seen from the top view in Fig. 2 that these new cores are all round.

Fig. 2 The construction of new Au₃₈, Au₂₃, and Au₄₁ cores (a and b). Au: magenta and blue, respectively. The blue atoms are the added gold atoms.

Employing the newly constructed Au₃₈, Au₂₃, and Au₄₁ cores, new structures of thiolate-protected gold nanoclusters can be predicted by the GUM and ring model. In Fig. 3, the process for the Au₃₈ core involves several steps. Initially, three [Au₂(SR)₃] protection motifs are added around the Au₃₈ core, resulting in the formation of three [Au₆(SR)₃] rings and an Au₃₈[Au₂(SR)₃]₃ structure. Subsequently, three [Au₂(SR)₃] protection motifs are further added around the structure Au₃₈[Au₂(SR)₃]₃, forming three [Au₆(SR)₃] rings and an Au₃₈[Au₂(SR)₃]₆ structure. In the third step, [Au₂(SR)₃] protection motifs are incorporated behind the structure Au₃₈[Au₂(SR)₃]₆, resulting in the formation of a single [Au₆(SR)₃] ring and Au₃₈[Au₂(SR)₃]₇ structure. Then, in the fourth step, three [SR] molecules are added to the middle of the structure Au₃₈[Au₂(SR)₃]₇, forming another [Au₆(SR)₃] ring and Au₃₈(SR)₃[Au₂(SR)₃]₇ structure. Finally, the structure Au₃₈(SR)₃[Au₂(SR)₃]₇ undergoes the addition of four [Au(SR)₂] protection motifs, leading to the prediction of a new structure, Au₅₆(SR)₃₂. Since the structure is the intermediate structure between Au₄₄(SR)₂₈ and Au₆₈(SR)₃₆, a new evolutionary path Au_44+8n(SR)_30+2n (n = 0–3) was identified.

Fig. 3 The structural prediction of a new structure Au₅₆(SR)₃₂ based on the ring model and GUM. The rings are filled with green color, and Au (111) facets are filled with wine color. Au: wine and dark green; S: yellow. The R groups are omitted for clarity.

In Fig. 4, we illustrate the structure prediction of another gold nanocluster starting from an Au₄₁ core. Initially, six [Au₂(SR)₃] protective motifs were introduced, resulting in the formation of six [Au₆(SR)₃] rings and an Au₄₁[Au₂(SR)₃]₆ structure. Subsequently, three [SR] ligands were added, leading to the creation of a single [Au₆(SR)₃] ring and Au₄₁[Au₂(SR)₃]₆[SR]₃ structure. Next, two [Au(SR)₂] ligands were further added to Au₄₁[Au₂(SR)₃]₆[SR]₃ to form two [Au₆(SR)₂] rings and an Au₄₁[SR]₃[Au₂(SR)₃]₆[Au(SR)₂]₂ structure. Finally, one [Au₂(SR)₃] and three [Au(SR)₂] ligands were bonded to the Au₄₁[SR]₃[Au₂(SR)₃]₆[Au(SR)₂]₂ structure to achieve the full structure prediction of Au₆₀(SR)₃₄. Since the structure is the intermediate structure between Au₅₂(SR)₃₂ and Au₆₈(SR)₃₆, a new evolutionary path Au_44+8n(SR)_30+2n (n = 1–3) was identified. In addition, the structure prediction of Au₄₄(SR)₃₀ nanoclusters starting from the Au₂₃ core is presented in Fig. 5 following the same way as the structure prediction of Au₅₆(SR)₃₂ and Au₆₀(SR)₃₄. Interestedly, the structure of Au₄₄(SR)₃₀ nanoclusters can be brought into the evolutionary path of Au_44+8n(SR)_30+2n (n = 0–3).

Fig. 4 The structural prediction of a new Au₆₀(SR)₃₄ isomer based on the ring model and GUM. The rings are filled with green color and Au (111) facets are filled with wine color. Au: wine and dark green; S: yellow. The R groups are omitted for clarity.

Fig. 5 The structural prediction of a new structure Au₄₄(SR)₃₀ based on the ring model. The rings are filled with green color and Au (111) facets are filled with wine color. Au: wine and dark green; S: yellow. The R groups are omitted for clarity.

Employing Gaussian 09 software,²⁶ density general function theory (DFT) calculations for Au_44+8n(SR)_30+2n (n = 0–3) and Au_44+12n(SR)_28+4n (n = 0–2) were performed to obtain the electronic properties of Au₄₄(SR)₃₀, Au₅₆(SR)₃₂, and Au₆₀(SR)₃₄ structures. In all calculations, the Perdew–Burke–Ernzerhof (PBE) and the all-electron basis set 6-31G* for H and S, and effective-core basis set LANL2DZ pseudopotential groups for Au were adopted.^27,28 In addition, the R groups were simplified with H atoms in order to save computational costs. In Table 2, the computed harmonic vibrational frequencies of three new structures as well as other two reported structures are all positive, which indicates that these structures are located at the local minima of potential energy surfaces. The highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) gaps of the predicted nanoclusters are 1.71, 1.36, and 1.33 eV, respectively. The large HOMO–LUMO gaps and all-positive harmonic vibrational frequencies suggest that the predicted structures have high chemical stability. Furthermore, the formation energy E = E_(n−1) + E_(n+1) − E_(n) of these newly predicted structures in two magic series Au_44+8n(SR)_30+2n (n = 0–3) and Au_44+12n(SR)_28+4n (n = 0–2) was calculated. The results show that the formation energies of Au₄₄(SR)₃₀, Au₅₆(SR)₃₂, and Au₆₀(SR)₃₄ structures are 0.50, 0.26, and 0.04 eV, respectively, suggesting their very close stability to their adjacent nanoclusters.

Table 2 The calculated HOMO–LUMO gaps and the lowest vibrational and frequencies of two magic series Au_44+8n(SR)_30+2n (n = 0–3) and Au_44+12n(SR)_28+4n (n = 0–2)

Structures	HOMO–LUMO gaps/eV	Lowest vibrational frequency/cm^−1
Au44(SR)28	1.660	11.120
Au44(SR)30	1.714	7.491
Au52(SR)32	1.470	6.737
Au56(SR)32	1.361	10.680
Au60(SR)34	1.333	8.162
Au68(SR)36	1.170	—

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The superatom network model with natural density zoning (AdNDP) analysis was always employed to describe thiolate-protected gold nanoclusters.²⁹ Taking the Au₂₃⁹⁺ core of Au₄₄(SR)₃₀ in Fig. 6 as an example, the 14 valence electrons of Au₄₄(SR)₃₀ can be viewed to be equally distributed on seven Au₄ units. Therefore, the Au₂₃⁹⁺ core of Au₄₄(SR)₃₀ can be regarded as a network of seven 4c–2e (4c and 2e represent 4 centers and 2 electrons, respectively) units. A similar behaviour can also be seen in the Au_(23+9n)^(9+3n)+ core of Au_44+8n(SR)_30+2n (n = 0–3) and the Au_(26+12n)^(10+4n)+ core of Au_44+12n(SR)_28+4n (n = 0–2) nanoclusters (Fig. 6).

Fig. 6 Visualization of the valence electron distributions in the Au_(23+9n)^(9+3n)+ core of Au_44+8n(SR)_30+2n (n = 0–3) and the Au_(26+12n)^(10+4n)+ core of Au_44+12n(SR)_28+4n (n = 0–2) nanoclusters. Au atoms are presented in yellow.

In Fig. 7 and 8, the optical absorption spectra and corresponding Kohn–Sham (KS) orbital energy levels of six nanoclusters computed by the time-dependent DFT (TD-DFT) method at the PBE/LANL2DZ level are shown. In addition, 300 singlet states were included in all TD-DFT calculations. Taking Au₅₆(SR)₃₂ in Fig. 7 as an example, Au₅₆(SR)₃₂ shows two broad peaks at 672 and 875 nm. The absorption peak at 875 nm mainly stems from the HOMO to LUMO, LUMO+1, and LUMO+2, and the absorption peak at 672 nm mainly stems from HOMO to LUMO+7 and LUMO+8, HOMO−7 and HOMO−8 to LUMO+2, HOMO−10 to LUMO+1, and HOMO−9 and HOMO−10 to LUMO. In addition, the absorption peaks of all the nanoclusters in Fig. 7 and 8 mainly involve the Au(sp) → Au(sp) transitions, which may be attributed to their similar morphology.

Fig. 7 The calculated optical absorption spectra and energy leap spectra of structures in the magic series Au_44+12n(SR)_28+4n (n = 0–2). The lines in blue, green, red, and black represent the 6sp of Au, 5d of Au, 3p of S, and others, respectively.

Fig. 8 The calculated optical absorption spectra and energy leap spectra of structures in the magic series Au_44+8n(SR)_30+2n (n = 0–3). The lines in blue, green, red, and black represent the 6sp of Au, 5d of Au, 3p of S, and others, respectively.

Conclusions

In summary, we have predicted the theoretical structures of three medium-sized nanoclusters Au₄₄(SR)₃₀, Au₅₆(SR)₃₂, and Au₆₀(SR)₃₄ based on the GUM and ring model, resulting in two new magic series Au_44+8n(SR)_30+2n (n = 0–3) and Au_44+16n(SR)_28+4n (n = 0–2). DFT calculations show that the predicted structures have high chemical stability and are likely to be synthesized in the laboratory. Our work further proves the high reliability and practicality of the GUM and ring model in designing the structures of thiolate-protected gold nanoclusters.

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 Natural Science Foundation of Xinjiang Uygur Autonomous Region (Grant No. 2022D01B137).

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Footnotes

† Electronic supplementary information (ESI) available: The cartesian coordinates of the three predicted thiolate-protected gold nanoclusters. See DOI: https://doi.org/10.1039/d3na00372h

‡ W. Han and G. Wang contributed equally to this work.

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