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

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 unied model (for understanding the structures of gold cores), a new Au 42 (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 conrmation.


Introduction
The chemical and structural properties of thiolate-protected gold nanoclusters that entail strong goldsulfur (Au-S) covalent bond have received considerable attention over the past fteen years. 1 Since the report of the rst total crystalline structure of thiolate-protected gold nanocluster Au 102 (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][4][5][6][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 coreshell 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 uni ed model (GUM), [14][15][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, Au 25 (SR) 18 -, 18-20 whose six SR[Au(SR)] 2 protection motifs and the icosahedral Au 13 core are closely linked through Borromean rings. However, it is di cult to generalize the Borromean ring model to other thiolate-protected gold nanoclusters. In the TST model, a ne energy balance between the core cohesive energy and the shell-to-core binding energy was identi ed. 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 Au 42 (SR) 26 isomer is predicted to have lower energy than two crystallized isomers previously synthesized in the laboratory.

Results
Ring  Table 1. Note that in our previously developed GUM, the gold core of ligandprotected gold nanocluster can be viewed as several elementary blocks (triangular Au 3 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   Table 1). In addition, the structures of [Au 4 (μ 3 -S) 2 Table 1). Note that the interlocked structures containing [Au 5 (SR) n ] rings have not been found in the crystallized thiolate-protected gold nanoclusters. Although a theoretical structure Au 24 (SR) 20 was proposed to contain the interlocked [Au 5 (SR) 4 ] and [Au 7 (SR) 6 ] rings ( Figure S2), 29 it has not been con rmed by experiment yet. Moreover, the [Au 5 (SR) 5 ] ring has not been found in any thiolate-protected gold nanoclusters yet, however, the Au 10 (SR) 10 complex with two [Au 5 (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 3. [Au 6 (SR) n ] (0 ≤ n ≤ 6) rings.
In Figure  In Figure 5, three larger rings, i.e. the [Au 8 (SR) 8 ] ring in Au 20 (SR) 16 cluster, 25 16 and Au(I)-S complex Au 12 (SR) 12 ( Figure S8). 25,30 As listed in Table 1 As shown in Figure 8, the Au 24 (SR) 20 cluster is decomposed into two Au 12 (SR) 10 , fused together by sharing two gold atoms. Here, some Au-Au bonds of the Au 8 core are broken intentionally for clarity. Next, the Au 12 (SR) 10 can be further decomposed into two interlocked [Au 6 (SR) 5 ] rings. Thus, the structure of Au 24 (SR) 20 can be viewed as four [Au 6 (SR) 5 ] rings, fused or interlocked together. The larger Au 40 (SR) 24 cluster can be decomposed into two interlocked structures Au 24 (SR) 12 and Au 16 (SR) 12 (Figure 9a). Next, the Au 24 (SR) 12 can be viewed as one [Au 6 ] ring and six [Au 6 (SR) 5 ] rings fused together by sharing three gold atoms (Figure 9b), while the Au 16 (SR) 12 can be viewed as three [Au 6 (SR) 4 ] rings fused together by sharing a gold atom (Figure 9c). So, the structure of Au 40 (SR) 24  2. Understanding the structural stabilities of thiolateprotected gold nanoclusters.
In Table 2, the average distance (d 1 ) between the gold atoms in the atomic structures at the center of ring and the gold atoms in the ring, and the average distance (d 2 ) between two adjacent gold atoms in each ring are given. The measured values of d 1 and d 2 for the Au 4 (SR) 4 , Au 10 (SR) 10 , and Au 12 (SR) 12 complexes are also given in Table 2   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 rst. Based on the GUM, 14 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.

Conclusion
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 con rmation by experiments.

Con icts of interest
The authors declare no con icts of interest.