A Ring Model for Understanding How Interfacial Interaction Dictates the Structures of Protection Motifs and Gold Cores in Thiolate-Protected Gold Nanoclusters

doi:10.21203/rs.3.rs-39976/v1

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A Ring Model for Understanding How Interfacial Interaction Dictates the Structures of Protection Motifs and Gold Cores in Thiolate-Protected Gold Nanoclusters

https://doi.org/10.21203/rs.3.rs-39976/v1

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Understanding the role of interfacial interactions between the protection motifs SR[Au(SR)]_x (x = 0, 1, 2, 3, ...) and gold cores on the stabilities of the thiolate-protected gold nanoclusters is still a challenging task. Although several theoretical models, including the superatom complex, super valence bond, and superatom network, have provided insights into the stabilities of either the overall structures or the gold cores, a model that can illuminate how the interfacial interaction dictates the unique structures of the protection motifs and gold cores is still lacking. Herein, we present a ring model, on the basis of comprehensive analyses of all 95 previous experimentally crystallized and theoretically predicted thiolate-protected gold nanoclusters, to offer a deeper insight into the structure-interaction relationship for this class of clusters. In the ring model, all the thiolate-protected gold nanoclusters can be generically viewed as fusion or interlocking of several [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) rings. The aurophilic interactions among these rings are expected to play a key role in the stabilization of the thiolate-protected gold nanoclusters. Guided by the ring model and the grand unified model (for understanding the structures of gold cores), a new Au₄₂(SR)₂₆ isomer is predicted, whose total energy is even lower than those of two previously crystallized isomers, thereby giving credence to the predictability of the ring model. The ring model provides not only a mechanistic understanding of the interactions between the protection ligands and gold cores in the thiolate-protected gold nanoclusters, but also a practical guidance on predicting new thiolate-protected gold nanoclusters for experimental synthesis and confirmation.

Computational Chemistry

Nanoscience

thiolate-protected gold nanoclusters

ring model

interfacial interaction

The chemical and structural properties of thiolate-protected gold nanoclusters that entail strong gold-sulfur (Au-S) covalent bond have received considerable attention over the past fifteen years.¹ Since the report of the first total crystalline structure of thiolate-protected gold nanocluster Au₁₀₂(p-MBA)₄₄ (p-MBA = p-mercaptobenzoic acid) in 2007,² the studies on the structures of thiolate-protected gold nanoclusters both through experimental crystallization and theoretical predictions have increased dramatically.^3-7 A common structural feature of the thiolate-protected gold nanoclusters is that each cluster is composed of a gold core and a number of oligomeric SR[Au(SR)]_x (x = 0, 1, 2, 3, ...) protection motifs, all exhibiting core-shell interfacial structure.^3,7,8 Several theoretical models, such as superatom complex (SAC) model,⁹ super valence bond (SVB) model,¹⁰ superatom network (SAN) model,^11,12 borromean ring model,¹³ grand unified model (GUM),^14-16 and thermodynamic stability theory (TST),¹⁷ have been proposed to elucidate various properties of these core-shell clusters. For example, SAC was developed to describe the electronic structures of the thiolate-protected gold nanoclusters. SVB, SAN, and GUM were to describe generic properties of the gold cores. Borromean ring model can illuminate the structure of the prototype cluster, Au₂₅(SR)₁₈^-,^18-20 whose six SR[Au(SR)]₂ protection motifs and the icosahedral Au₁₃ core are closely linked through Borromean rings. However, it is difficult to generalize the Borromean ring model to other thiolate-protected gold nanoclusters. In the TST model, a fine energy balance between the core cohesive energy and the shell-to-core binding energy was identified. Despite of major progresses in the development of various models to understand the stabilities of either the overall structures or the gold cores, a model that can elucidate how the interfacial interaction dictates the unique structures of the protection motifs and gold cores is still lacking, which hinders the tractable design of the thiolate-protected gold nanoclusters.

In this communication, we present development of a ring model, on the basis of comprehensive analyses of all previous experimentally crystallized and theoretically predicted thiolate-protected gold nanoclusters, to offer a deeper insight into the structure-interaction relationship for these nanoclusters. We show that the nanoclusters can be decomposed into several fused or interlocked rings, namely, [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m). These [Au_m(SR)_n] rings entail aurophilic interactions that play a key role to stabilize the thiolate-protected gold nanoclusters. Furthermore, guided by the ring model and the previously developed GUM, a new Au₄₂(SR)₂₆ isomer is predicted to have lower energy than two crystallized isomers previously synthesized in the laboratory.

Ring model: [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) rings.

Development of the ring model is based on detailed analysis of structures of all 95 thiolate-protected gold nanoclusters, and their atomistic structures were either determined from previous experiments (totally 41 crystallized structures) or predicted from density-functional theory (DFT) computation (totally 54 structures) over the past fifteen years. Several types of ring structures, i.e. [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m), have been identified, as shown in Figures 1-6. In addition, the number of gold atoms in the gold core (N_Au-core), the number of elementary blocks (N_eb) that the gold-core atoms belong to, the number of gold atoms in the protection motifs (N_Au), and the number of sulfur atoms in the protection motifs (N_S) are listed in Table 1. Note that in our previously developed GUM, the gold core of ligand-protected gold nanocluster can be viewed as several elementary blocks (triangular Au₃ and tetrahedral Au_4,both satisfying duet rule) fused or packing together.^14-16

Table 1 The number of gold core atoms (N_Au-core), the elementary blocks (N_eb) that the gold-core atoms belong to, the number of gold atoms in the protection motifs (N_Au), and the number of S atoms in the protection motifs (N_S) in [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) rings. For every ring class, two equations to describe the relationship among N_Au-core, N_eb, N_Au, and N_S are also presented. The superscripts, 1a and 1b, in the table denote the corresponding ring structures shown in Figure 1a and Figure 1b, respectively.

Ring Class	Specific Rings	N_Au-core	N_eb	N_Au	N_S	Protection Motifs	Equations
[Au₄(SR)_n] (1 < n ≤ 4)	[Au₄(μ₃-S)₂(SR)₂]^1a	0	0	4	4	[Au₄(μ₃-S)₂(SR)₂] ring	N_Au = 4 – N_Au-core N_S = 4 – N_eb
	[Au₄(SR)₃]^1b	2	1	2	3	SR[Au(SR)]₂
	[Au₄(SR)₂]^1c	3	2	1	2	SR[Au(SR)]
	[Au₄(SR)₂]^1d	4	2	0	2	2SR
[Au₅(SR)_n] (1 ≤ n < 5)	[Au₅(SR)₄]^2a	2	1	3	4	SR[Au(SR)]₃	N_Au = 5 – N_Au-core N_S = 5 – N_eb
	[Au₅(SR)₃]^2b,2c	4	2	1	3	SR + SR[Au(SR)]
	[Au₅(SR)₂]^2d	4	3	1	2	SR[Au(SR)]
	[Au₅(SR)]^2e	5	4	0	1	SR
[Au₆(SR)_n] (0 ≤ n ≤ 6)	[Au₆(SR)₆]^3a	0	0	6	6	[Au₆(SR)₆] ring	N_Au = 6 – N_Au-core N_S = 6 – N_eb
	[Au₆(SR)₅]^3b	2	1	4	5	SR[Au(SR)]₄
	[Au₆(SR)₄]^3c	3	2	3	4	SR[Au(SR)]₃
	[Au₆(SR)₄]^3d	4	2	2	4	2SR[Au(SR)]
	[Au₆(SR)₃]^3e	5	3	1	3	SR + SR[Au(SR)]
	[Au₆(SR)₃]^3f	4	3	2	3	SR[Au(SR)]₂
	[Au₆(SR)₃]^3g	6	3	0	3	3SR
	[Au₆(SR)₂]^3h	5	4	1	2	SR[Au(SR)]
	[Au₆(SR)₂]³ⁱ	6	4	0	2	2SR
	[Au₆(SR)]^3j	6	5	0	1	SR
	[Au₆]^3k	6	6	0	0	-
[Au₇(SR)_n] (n = 4 or 5)	[Au₇(SR)₅]^4a	4	2	3	5	SR[Au(SR)] + SR[Au(SR)]₂	N_Au = 7 – N_Au-core N_S = 7 – N_eb
	[Au₇(SR)₄]^4b	5	3	2	4	SR + SR[Au(SR)]₂
	[Au₇(SR)₄]^4c	5	3	2	4	2SR[Au(SR)]
[Au₈(SR)_n] (n = 4, 6, or 8)	[Au₈(SR)₈]^5a	0	0	8	8	[Au₈(SR)₈] ring	N_Au = 8 – N_Au-core N_S = 8 – N_eb
	[Au₈(μ₃-S)₂(SR)₄]^5b	4	2	4	6	SR + SR[Au(μ₃-S)Au(SR)]₂
	[Au₈(SR)₄]^5c	6	4	2	4	2SR[Au(SR)]
[Au₁₀(SR)_n] (n = 4)	[Au₁₀(SR)₄]^5d	8	6	2	4	2SR[Au(SR)]	N_Au = 10 – N_Au-core N_S = 10 – N_eb
[Au₁₂(SR)_n] (n = 4)	[Au₁₂(SR)₄]^5e	10	8	2	4	2SR[Au(SR)]	N_Au = 12 – N_Au-core N_S = 12 – N_eb

1. [Au₄(SR)_n] (1 < n ≤ 4) rings.

As shown in Figure 1, four types of [Au₄(SR)_n] (1 < n ≤ 4) rings are identified. Except two R ligands, the [Au₄(μ₃-S)₂(SR)₂] ring structure (Figure 1a) observed in the thiolate-protected gold nanocluster Au₃₈(μ₃-S)₂(SR)₂₀ is the same as [Au₄(SR)₄] ring,²¹ either detected experimentally as an isolated form or observed within the [Au₈(SR)₈] ring to form an Au₁₂(SR)₁₂ structure (Figure S1).^22,23 The [Au₄(SR)₃] ring seen in Au₂₁(SR)₁₅ (Figure 1b) can be formed by binding a SR[Au(SR)]₂ protection motif (N_Au = 2 and N_S = 3) with two gold atoms in a tetrahedron Au₄ elementary block (N_Au-core = 2 and N_eb = 1).²⁴ The [Au₄(SR)₂] ring seen in Au₂₀(SR)₁₆ (Figure 1c) is formed by binding a SR[Au(SR)] protection motif (N_Au = 1 and N_S = 2) with two gold atoms at the two ends of the bi-tetrahedron Au₇ structure.²⁵ So, three gold-core atoms belong to the two tetrahedral Au₄ elementary blocks (N_Au-core = 3 and N_eb = 2). While the [Au₄(SR)₂] ring seen in Au₃₈(μ₃-S)₂(SR)₂₀ (Figure 1d) can be viewed as binding two SR motifs (N_Au = 0 and N_S = 2) with four gold-core atoms in two triangular Au₃ elementary blocks (N_Au-core = 4 and N_eb = 2).²¹ So, the values of N_Au-core, N_eb, N_Au, and N_S in [Au₄(SR)_n] rings satisfy the two equations N_Au = 4 – N_Au-core and N_S = 4 – N_eb (see Table 1). In addition, the structures of [Au₄(μ₃-S)₂(SR)₂] (Figure 1a) and [Au₄(SR)₂] (Figure 1d) rings in the Au₃₈(μ₃-S)₂(SR)₂₀ cluster indicate a structural transformation from [Au₄(SR)₂] ring (Figure 1d) to [Au₄(μ₃-S)₂(SR)₂] ring (Figure 1a), which can be achieved by adding two three-coordinated μ₃-sulfido (μ₃-S) atoms onto the two triangular Au₃ elementary blocks that are bound with the [Au₄(SR)₂] ring (Figure 1d)

2. [Au₅(SR)_n] (1 ≤ n < 5) rings.

In Figure 2, the [Au₅(SR)₄], [Au₅(SR)₃], [Au₅(SR)₂], and [Au₅(SR)] rings are identified from the crystallized Au₁₆(SR)₁₂,²⁶ Au₃₀(SR)₁₈,²⁷ Au₄₃(SR)₂₅,²⁸ and Au₃₈(μ₃-S)₂(SR)₂₀ clusters.²¹ The [Au₅(SR)₄] ring in Figure 2a is formed by combing a SR[Au(SR)]₃ protection motif (N_Au = 3 and N_S = 4) with two gold-core atoms belonging to a triangular Au₃ elementary block (N_Au-core = 2 and N_eb = 1). The [Au₅(SR)₃] ring in Figure 2b can be generated by combining one SR[Au(SR)] and one SR (N_Au = 1 and N_S = 3) with four gold-core atoms belonging to two triangular Au₃ elementary blocks (N_Au-core = 4 and N_eb = 2). The [Au₅(SR)₂] ring in Figure 2c is formed by combining a SR[Au(SR)] protection motif (N_Au = 1 and N_S = 2) with four gold-core atoms belonging to three tetrahedral Au₄ elementary blocks (N_Au-core = 4 and N_eb = 3). While the [Au₅(SR)] ring in Figure 2d is formed by combining a SR protection motif (N_Au = 0 and N_S = 1) with five gold-core atoms belonging to four tetrahedral Au₄ elementary blocks (N_Au-core = 5 and N_eb = 4). Thus, the values of N_Au-core, N_eb, N_Au, and N_S in [Au₅(SR)_n] (1 ≤ n < 5) rings satisfy two equations N_Au = 5 – N_Au-core and N_S = 5 – N_eb (see Table 1). Note that the interlocked structures containing [Au₅(SR)_n] rings have not been found in the crystallized thiolate-protected gold nanoclusters. Although a theoretical structure Au₂₄(SR)₂₀ was proposed to contain the interlocked [Au₅(SR)₄] and [Au₇(SR)₆] rings (Figure S2),²⁹ it has not been confirmed by experiment yet. Moreover, the [Au₅(SR)₅] ring has not been found in any thiolate-protected gold nanoclusters yet, however, the Au₁₀(SR)₁₀ complex with two [Au₅(SR)₅] interlocked rings has been seen in both experiment and simulations (Figure S3).³⁰

Furthermore, in thiolate-protected gold nanoclusters with face-centered cubic (FCC) cores,^26-28 the [Au₅(SR)_n] ring is always located on the top of a tetrahedron Au₄ elementary block, in which a special gold atom (highlighted by a red circle in the tetrahedral Au₄ elementary block) near the [Au₅(SR)_n] ring does not bind with the SR motif, as shown in Figure 2a-2d. The average bond length between this special gold atom and the gold atoms in the [Au₅(SR)_n] rings is 2.84 Å, indicating strong interactions between them. Hence, the [Au₅(SR)_n] ring can be viewed as a protection motif, covering this special gold atom so that it does not need to bind with an extra SR motif. For Au₃₈(μ₃-S)₂(SR)₂₀ with a body-centered cubic (BCC) core,²¹ however, this special gold atom near the [Au₅(SR)] ring no longer exists (Figure 2e) due to the gold core with different symmetry.

3. [Au₆(SR)_n] (0 ≤ n ≤ 6) rings.

In Figure 3a-k, the [Au₆(SR)₆] ring in Au₂₂(SR)₁₈,³¹ [Au₆(SR)₅] ring in Au₂₁(SR)₁₅,³² [Au₆(SR)₄] ring in Au₂₈(SR)₂₀ and Au₂₃(SR)₁₆^- clusters,^33,34 [Au₆(SR)₃] ring in Au₃₀(SR)₁₈,Au₃₆(SR)₂₄,^27,35 and Au₆₈(SR)₃₆ clusters,³⁶ [Au₆(SR)₂] ring in Au₃₄(SR)₂₂ and Au₉₂(SR)₄₄ clusters,^37,38 [Au₆(SR)] ring in Au₉₂(SR)₄₄cluster,³⁸ and [Au₆] ring in Au₄₀(SR)₂₄ cluster are presented.³⁹ Among them, only the [Au₆(SR)₆] ring in Au₂₂(SR)₁₈ (Figure 3a) and the [Au₆(SR)₃] ring in Au₆₈(SR)₃₆ (Figure 3g) have not been observed in the crystallized nanoclusters. The compositions of [Au₆(SR)_n] (0 ≤ n ≤ 6) rings are also analyzed in Table 1, in which the values of N_Au-core, N_eb, N_Au, and N_S in the [Au₆(SR)_n] (0 ≤ n ≤ 6) rings also satisfy two equations N_Au = 6 – N_Au-core and N_S = 6 – N_eb. Moreover, the same number of gold and sulfur atoms but completely different compositions can be seen in the [Au₆(SR)₄] rings (Figure 3c and 3d), [Au₆(SR)₃] rings (Figure 3e, 3f, and 3g), and [Au₆(SR)₂] rings (Figure 3h and 3i). Unlike the [Au₄(SR)_n] (1 < n ≤ 4) and [Au₅(SR)_n] (1 ≤ n < 5) rings, the [Au₆(SR)_n] (0 ≤ n ≤ 6) rings tend to adopt the interlocked ring structures with one Au atom being located at the center of the ring (Figure S4), very similar with the Au₁₂(SR)₁₂ composed of two [Au₆(SR)₆] interlocked rings (Figure S5).³⁰

4. [Au₇(SR)_n] (2 < n < 5) ring.

In Figure 4a, the [Au₇(SR)₅] ring can be identified in Au₃₈(SR)₂₄ nanocluster by combining one SR[Au(SR)] and one SR[Au(SR)]₂ (N_Au = 3 and N_S = 5) with four gold-core atoms belonging to two tetrahedral Au₄ elementary blocks (N_Au-core = 4 and N_eb = 2).⁴⁰ In Figure 4b and 4c, two types of [Au₇(SR)₄] rings, both found in crystallized Au₄₃(SR)₂₅ nanocluster,²⁸ can be formed, respectively, by combining one SR[Au(SR)]₂ and one SR (N_Au = 2 and N_S = 4) with five gold-core atoms belonging to two tetrahedral Au₄ and one triangular Au₃ elementary blocks (N_Au-core = 5 and N_eb = 3), and by combining two SR[Au(SR)] (N_Au = 2 and N_S = 4) with five gold-core atoms belonging to three tetrahedral Au₄ elementary blocks (N_Au-core = 5 and N_eb = 3). Thus, the values of N_Au-core, N_eb, N_Au, and N_S in [Au₇(SR)_n] rings satisfy two equations N_Au = 7 – N_Au-core and N_S = 7 – N_eb. It should be noted that one half of the [Au₇(SR)₄] ring bypasses the middle of the bi-tetrahedron Au₇ structure and the other half bypasses an end of Au₇, while the whole [Au₆(SR)₃] ring tends to bypass the middle of the bi-tetrahedron Au₇ structure (Figure S6). This difference can be attributed to difference in the arrangement of one gold-core atom in the two rings. In addition, the [Au₇(SR)₄] ring tends to interlock with another two rings (Figure S7), different from the two interlocked [Au₆(SR)_n] rings.

5. Other larger rings including [Au₈(SR)_n] (n = 4 and 8), [Au₁₀(SR)₄], and [Au₁₂(SR)₄].

In Figure 5, three larger rings, i.e. the [Au₈(SR)₈] ring in Au₂₀(SR)₁₆ cluster,²⁵ [Au₈(μ₃-S)₂(SR)₄] ring in Au₃₈(μ₃-S)₂(SR)₂₀ cluster,²¹ [Au₈(SR)₄] ring in Au₂₈(SR)₂₀ cluster,⁴¹ [Au₁₀(SR)₄] ring in Au₇₂(SR)₄₀ cluster,⁴² and [Au₁₂(SR)₄] ring in Au₉₂(SR)₄₄ cluster,³⁸ are identified. Among them, the [Au₁₀(SR)₄] ring has not been confirmed by experiment yet. The [Au₈(SR)₈] ring can be seen in both thiolate-protected gold nanocluster Au₂₀(SR)₁₆ and Au(I)-S complex Au₁₂(SR)₁₂ (Figure S8).^25,30 As listed in Table 1, the compositions of each ring in Figure 5 also satisfy two equations. In addition, the [Au₈(SR)₄], [Au₁₀(SR)₄], and [Au₁₂(SR)₄] rings tend to interlock with another 2, 3, and 4 rings, respectively.

1. The stabilities of [Au_m(SR)_n] rings.

In most of [Au_m(SR)_n] rings, the number of sulfur atoms is less than the number of gold atoms. In isolated forms, these independent rings are unstable, contrary to the high stabilities of the elementary blocks in the gold cores (as described by GUM).^14-16 Although the structural decompositions of thiolate-protected gold nanoclusters into [Au_m(SR)_n] rings are not reflective of the electronic structure, the ring model can be still helpful to understand the interfacial interactions between SR[Au(SR)]_x (x = 0, 1, 2, 3, ...) protection motifs and gold cores. Notably, the insufficient number of sulfur atoms in [Au_m(SR)_n] rings can actually be offset by the growth of the μ₃-S onto the triangular Au₃ to form the Au₃(μ₃-S) units or by the growth of the four-coordinated μ₄-sulfido (μ₄-S) into the tetrahedral Au₄ to form the Au₄(μ₄-S) units. As shown in our recent work,⁴³ the structural transformation from thiolate-protected nanoclusters to more stable Au(I)-S complexes can be achieved by gradually adding the μ₃-S and/or μ₄-S motifs to the gold core. Among these predicted complexes, the number of sulfur atoms eventually becomes balanced, namely, there are the same number (6) of gold atoms as the sulfur atoms in each [Au₆S_q(SR)_6-q] ring (integer q is the number of μ₃-S and μ₄-S atoms). Therefore, with the increment of the number of μ₃-S and μ₄-S atoms, the transformation from the unstable [Au_m(SR)_n] rings associated with the thiolate-protected nanoclusters to the stable [Au_m(SR)_m] rings associated with the Au(I)-S complexes can be achieved.

2. The atomic structures at the center of rings.

With the increment of the radii of rings, the atomic structures at the center of rings become increasingly complex, as shown in Figure 6. No extra gold atoms at or near the center of the smallest [Au₄(SR)₃] ring can be seen (Figure 6a). For the [Au₅(SR)₃] ring with a larger radius, there is one gold atom below the center of the ring (Figure 6b), and the average bond length between the gold atom and the gold atoms in the [Au₅(SR)₃] rings is 2.84 Å. While for the [Au₆(SR)_n] ring, one gold atom (Figure 6c) or a triangular Au₃ (Figure 6d) located at the center of ring can be found. With further increase of the radii of the rings, there are one, two, three and, four tetrahedral Au₄ structures observed in the [Au₇(SR)₄], [Au₈(SR)₈], [Au₁₀(SR)₄], and [Au₁₂(SR)₄] rings, respectively (Figure 6e-h). The same trend can also be observed in other rings.

3. Non-ring structures associated with thiolate-protected gold nanoclusters.

Besides the [Au_m(SR)_n] rings associated with the thiolate-protected gold nanoclusters, there are protection motifs that do not exhibit the ring structures. For example, a SR[Au(SR)]₂ motif should bind with the Au(111) facet in Au₃₆(SR)₂₄ or with the Au(100) facet in Au₄₂(SR)₂₆,^35,44 as shown in Figure 7a and 7b. For the fused tetrahedron Au₆ core with an Au-Au edge in Au₄₂(SR)₂₆,⁴⁴ a SR[Au(SR)] motif is needed to bind with two surface gold atoms (Figure 7c). These bonding modes between the protection motifs and the gold core, as shown in Figure 7, are very common in the thiolate-protected gold nanoclusters, which can be classified as a supplemental information to understand the interfacial interactions between non-ring SR[Au(SR)]_x (x = 0, 1, 2, 3, ...) protection motifs and gold cores.

Applications of [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) ring model

1. Structural decompositions.

According to the ring model, the complete structures of 95 thiolate-protected gold clusters can be decomposed into several [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) rings that can be fused, or packed, or interlocked together. Most of the crystallized and predicted structures up to date belong to this family of nanoclusters. Two distinct structural decompositions of the crystallized Au₂₄(SR)₂₀ and Au₄₀(SR)₂₄ clusters are depicted in Figures 8 and 9 as examples,^39,45 while decompositions of other clusters are plotted in the Supporting Information.

As shown in Figure 8, the Au₂₄(SR)₂₀ cluster is decomposed into two Au₁₂(SR)₁₀, fused together by sharing two gold atoms. Here, some Au-Au bonds of the Au₈ core are broken intentionally for clarity. Next, the Au₁₂(SR)₁₀ can be further decomposed into two interlocked [Au₆(SR)₅] rings. Thus, the structure of Au₂₄(SR)₂₀ can be viewed as four [Au₆(SR)₅] rings, fused or interlocked together. The larger Au₄₀(SR)₂₄ cluster can be decomposed into two interlocked structures Au₂₄(SR)₁₂ and Au₁₆(SR)₁₂ (Figure 9a). Next, the Au₂₄(SR)₁₂ can be viewed as one [Au₆] ring and six [Au₆(SR)₅] rings fused together by sharing three gold atoms (Figure 9b), while the Au₁₆(SR)₁₂ can be viewed as three [Au₆(SR)₄] rings fused together by sharing a gold atom (Figure 9c). So, the structure of Au₄₀(SR)₂₄ can be viewed as three [Au₆(SR)₄], one [Au₆], and six [Au₄(SR)₂] rings fused or interlocked together. For other 93 thiolate-protected gold clusters, their structural decompositions based on the ring model are shown in Figures S9-S101.

2. Understanding the structural stabilities of thiolate-protected gold nanoclusters.

In Table 2, the average distance (d₁) between the gold atoms in the atomic structures at the center of ring and the gold atoms in the ring, and the average distance (d₂) between two adjacent gold atoms in each ring are given. The measured values of d₁ and d₂ for the Au₄(SR)₄, Au₁₀(SR)₁₀, and Au₁₂(SR)₁₂ complexes are also given in Table 2 for comparison. The very close d₁ and d₂ values of the rings and complexes suggest that the aurophilic interactions play an important role in stabilization of the thiolate-protected gold nanoclusters.^46,47 Specifically, the role of protection motifs SR[Au(SR)]_x (x = 0, 1, 2, 3, ...) is not only for binding the surface gold atoms of the gold core via strong Au-S covalent bond, but also for generating the [Au_m(SR)_n] rings with aurophilic interactions among the gold atoms within the rings. Considering the ring model and GUM altogether, the stabilities of thiolate-protected gold nanoclusters can be mainly attributed to the following four factors: (1) the high stabilities of the elementary blocks or secondary blocks for the formation of the gold cores, (2) the aurophilic interactions between two neighboring elementary blocks, (3) the strong Au-S covalent bonds, and (4) the aurophilic interactions among the protection motifs and gold cores.

Table 2. The average distance d₁ between the gold atoms in the atomic structures at the center of ring, and the average distance d₂ between two adjacent gold atoms in the ring of the thiolate-protected gold nanoclusters. The measured values of d₁ and d₂ for Au₄(SR)₄, Au₁₀(SR)₁₀, Au₁₂(SR)₁₂ complexes are also given for comparison.

Rings	d₁/Å	d₂/Å
[Au₄(SR)₄]	-	3.24
[Au₄(SR)_n] (1 < n < 4)	-	3.23
[Au₅(SR)₅]	-	3.60
[Au₅(SR)_n] (1 < n < 5)	-	3.47
[Au₆(SR)₆]	3.44	3.49
[Au₆(SR)_n] (0 ≤ n ≤ 6)	3.20	3.56
[Au₇(SR)₄] (n = 4 or 5)	3.07	3.57
[Au₈(SR)₈]	3.06	3.56
[Au₈(SR)_n] (n = 4, 6, or 8)	3.27	3.32
[Au₁₀(SR)₄]	3.05	3.21
[Au₁₂(SR)₄]	3.00	3.02

3. Structural prediction.

Importantly, the ring model can be also used to predict new structures of the thiolate-protected gold clusters. To this end, a gold core should be constructed first. Based on the GUM,^14-16 the gold core of ligand-protected gold nanoclusters can be viewed as several elementary blocks (either the triangular Au₃ or tetrahedral Au₄, both satisfying the duet rule) fused or packed together. As an example, here, a new Au₂₈ core composed of eight tetrahedral Au₄ units can be constructed (Figure 10). Next, based on the ring model, the protection motifs including four SR[Au(SR)]₂, six SR[Au(SR)], and two SR can be easily added to the Au₂₈ core to yield a new Au₄₂(SR)₂₆ isomer, consisting of six [Au₆(SR)₃] and one [Au₁₀(SR)₄] rings (Figure S46). DFT computation shows that this new isomer has lower energy than two crystallized isomers reported previously,^44,48 thereby giving credence to the effectiveness of the ring model for predicting new and highly stable clusters.

In conclusion, a ring model is proposed to describe the interfacial interactions between SR[Au(SR)]_x (x = 0, 1, 2, 3, ...) protection motifs and gold cores in thiolate-protected gold nanoclusters. A central concept of the ring model is that the gold nanoclusters can be decomposed into several [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) rings, fused or interlocked together. The aurophilic interactions among these rings play an important role in stabilizing the thiolate-protected gold nanoclusters. The ring model not only provides a deep chemical insight into the interfacial interactions between protection motifs and gold core in thiolate-protected gold nanoclusters, but also offers a simple way to construct and design new nanoclusters for future confirmation by experiments.

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgment

WWX is supported by Natural Science Foundation of China (Grant No. 11974195) and the Natural Science Foundation of Ningbo (Grant No. 2019A610182). WWX also acknowledges computational support from National Supercomputing Center in Guangzhou (NSCC-GZ).

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A Ring Model for Understanding How Interfacial Interaction Dictates the Structures of Protection Motifs and Gold Cores in Thiolate-Protected Gold Nanoclusters

Status:

Version 1

Abstract

Figures

Introduction

Results

Ring model: [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) rings.

1. [Au₄(SR)_n] (1 < n ≤ 4) rings.

2. [Au₅(SR)_n] (1 ≤ n < 5) rings.

3. [Au₆(SR)_n] (0 ≤ n ≤ 6) rings.

4. [Au₇(SR)_n] (2 < n < 5) ring.

5. Other larger rings including [Au₈(SR)_n] (n = 4 and 8), [Au₁₀(SR)₄], and [Au₁₂(SR)₄].

Discussion Of The Ring Model

1. The stabilities of [Au_m(SR)_n] rings.

2. The atomic structures at the center of rings.

3. Non-ring structures associated with thiolate-protected gold nanoclusters.

Applications of [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) ring model

1. Structural decompositions.

2. Understanding the structural stabilities of thiolate-protected gold nanoclusters.

3. Structural prediction.

Conclusion

Declarations

Conflicts of interest

Acknowledgment

References

Additional Declarations

Supplementary Files

Status:

Version 1

A Ring Model for Understanding How Interfacial Interaction Dictates the Structures of Protection Motifs and Gold Cores in Thiolate-Protected Gold Nanoclusters

Status:

Version 1

Abstract

Figures

Introduction

Results

Ring model: [Aum(SR)n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) rings.

1. [Au4(SR)n] (1 < n ≤ 4) rings.

2. [Au5(SR)n] (1 ≤ n < 5) rings.

3. [Au6(SR)n] (0 ≤ n ≤ 6) rings.

4. [Au7(SR)n] (2 < n < 5) ring.

5. Other larger rings including [Au8(SR)n] (n = 4 and 8), [Au10(SR)4], and [Au12(SR)4].

Discussion Of The Ring Model

1. The stabilities of [Aum(SR)n] rings.

2. The atomic structures at the center of rings.

3. Non-ring structures associated with thiolate-protected gold nanoclusters.

Applications of [Aum(SR)n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) ring model

1. Structural decompositions.

2. Understanding the structural stabilities of thiolate-protected gold nanoclusters.

3. Structural prediction.

Conclusion

Declarations

Conflicts of interest

Acknowledgment

References

Additional Declarations

Supplementary Files

Status:

Version 1

Ring model: [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) rings.

1. [Au₄(SR)_n] (1 < n ≤ 4) rings.

2. [Au₅(SR)_n] (1 ≤ n < 5) rings.

3. [Au₆(SR)_n] (0 ≤ n ≤ 6) rings.

4. [Au₇(SR)_n] (2 < n < 5) ring.

5. Other larger rings including [Au₈(SR)_n] (n = 4 and 8), [Au₁₀(SR)₄], and [Au₁₂(SR)₄].

1. The stabilities of [Au_m(SR)_n] rings.

Applications of [Au_m(SR)_n] (m = 4 - 8, 10, 12, and 0 ≤ n ≤ m) ring model