Symmetric Growth of Dual-Packed Kernel: Exploration of the Evolution of Au40(SR)24 to Au49(SR)27 and Au58(SR)30 Clusters via the 2e --Reduction Cluster Growth Mechanism.

The symmetric and periodic growth of metal core and ligand shell has been found in a number of ligand-protected metal clusters. So far, the principle of symmetric growth has been widely used to understand and predict the cluster structure evolution. In this work, based on the experimentally resolved crystal structure of Au40(o-MBT)24 and Au49(2,4-DMBT)27 clusters and a newly proposed two-electron (2e -) reduction cluster growth mechanism, the evolution pathway from the quasi-face-centered-cubic (fcc)-structured Au40(SR)24 cluster to the dual fcc- and nonfcc-packed Au49(SR)27 and Au58(SR)30 clusters was studied. The current research has clarified two important issues of cluster structure evolution. First, the formation of the dual-packed fcc and nonfcc kernel structure has been rationalized based on a 2e -reduction-based seed-mediated cluster growth pathway. Second, it is found that the symmetrical growth does not necessarily lead to the formation of stable cluster structures. It was found that the formation of dual-packed kernels in the Au49(SR)27 cluster is favorable because of the stability of the intermediate cluster structures and the relatively high thermodynamic stability of the cluster itself. However, although the structure of Au58(SR)30 cluster conforms to the principle of symmetric growth, the tension between the ligand shell and the gold atom of the metal nucleus increases significantly during the cluster size evolution, and the stability of the intermediate clusters is poor, so the formation of the Au58(SR)30 cluster is unfavorable. This study also shows that the 2e --reduction cluster growth mechanism can be used to explore the structural evolution and stability of thiolate-protected gold clusters.

Introduction

Ligand-protected noble-metal clusters have become a research hotspot in the field of nanoscience because of their unique physicochemical properties.[1−6] In particular, because of the relatively excellent chemical stability of thiolate-protected gold nanoclusters (usually referred to as the Au(SR) cluster, hereinafter denoted as RS-AuNCs), tremendous efforts have been devoted to the study of the structure and properties of such clusters.[3,5,7−17] Pioneered by the breakthrough of successful crystallization of the Au102(SR)44 cluster in 2007,[18] a large amount of RS-AuNCs has been experimentally crystallized, and precise atomic structures were characterized.[3] On this basis, researchers can further explore the evolution of cluster structures and the structure–property relationship in order to understand more clearly the role of clusters as a mesoscopic substance in the process of connecting micro and macromatter and to develop its potential applications.[3,8,19−21]

X-ray single crystal diffraction analyses showed that the RS-AuNCs consisted of a symmetrical gold core and outer staple motifs.[7] Until 2012, it was found that almost all the determined atomic structures of thiolate and the mixed phosphine/halide/thiolate-protected gold nanoclusters contained multiple-twinned gold core structures, and the icosahedron or its derivate served as the basic structural units of gold core.[22−27] As more unprecedented stable cluster sizes and cluster structures were determined, it was discovered that these clusters showed different configurations of core structures, such as icosahedron, dodecahedron, face-centered cubic (fcc), hexagonal closet packing (hcp), and body-centered cubic (bcc) configurations.[3,17]

These resolved cluster crystal structures revealed some inherent structural evolution patterns, among which a typical evolution pattern is symmetry or periodicity.[11,28] For example, the core structures of Au21(SR)15[11,29] and Au23(SR)16–[30] clusters can be seen as one and two triangular Au3, growing symmetrically on both sides of the Au7 core of Au20(SR)16,[31] respectively. A similar case of symmetric growth occurs in the sequences of Au28(SR)20[32] → Au29(SR)19[33,34] → Au30(SR)18[35] and Au44(SR)28[36] → Au68(SR)36[37] → Au92(SR)44,[38] although the structure of Au68(SR)36 have not been experimentally confirmed. The gold quantum boxes, including the Au28, Au36, Au44, and Au52 magic series, reported by Jin et al., can also be regarded as a result of growing Au3 triangles symmetrically on both sides of the double Au7 core, starting from Au28(TBBT)20.[36] Based on the experimentally determined cluster structures, a structure evolution map of the fcc-structured RS-AuNCs has been further proposed recently, which revealed the basic evolution pattern of RS-AuNC cluster containing an fcc core.[11]

Although the symmetric growth has been found in a number of ligand-protected gold clusters and the principle has been used to understand and predict the structural evolution of ligand-protected gold clusters, the following question is raised: is the symmetric growth an eternal law in the evolution of RS-AuNCs? Recently, the new progress in the experimental studies indicated that the kernel atoms of RS-AuNCs can be packed into a dual-packed kernel configuration.[39−41] Such a dual-packed kernel cluster exhibited a subnanoscale heterojunction structure. Through the density functional theory (DFT) calculations, an interesting finding was obtained: the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of dual-packed kernel Au49(2,4-DMBT)27 cluster are distributed in the fcc and nonfcc components of gold kernels, respectively.[40] Further experimental studies revealed that kernel packing greatly influences the electrochemical gap (EG), and the fcc structure exhibits a larger EG than the investigated nonfcc structure. Because the EG is correlated to some fundamental physicochemical properties of the materials, such dual-packed kernel metal clusters were expected to possess novel electronic and optical properties compared with the regular icosahedral or fcc gold clusters. Another prototype of dual-packed kernel clusters was found in a low-temperature isomer of the Au38(SC2H4Ph)24 cluster.[41] In the isomeric Au38(SC2H4Ph)24 cluster, the metal core was composed of an icosahedral Au13 and a group of fcc-structured Au atoms. The newly discovered dual-packed kernel clusters implied a new evolution pathway of the RS-AuNCs, which raised interesting questions with regard to the cluster structure evolution and growth mechanism. The first question is as follows: is there a new cluster sequence with the core structure that adopts a hybrid dual-packed fcc and nonfcc configuration? The second question is as follows: What is the formation mechanism of the dual-packed kernel structures? The last but not least, is the principle of symmetric growth maintained in the evolution of clusters?

In this study, based on the crystal structure of the Au40(o-MBT)24[42] and Au49(DMBT)27[40] clusters, we explored the evolution pathway from the fcc-structured Au40(SR)24 to the dual-packed fcc and nonfcc clusters Au49(SR)27 and Au58(SR)30. The coordinate files of the clusters involved in the evolution path are presented in the Supporting Information. Very recently, we noted that Xu et al. predicted the atomic structure of Au58(SR)30 based on the symmetric growth of the nonfcc part of the Au49(SR)27 cluster.[43] Their predicted cluster structure is consistent with that of the Au58-iso2 in this study. Different from the previous report, this work reported a very comprehensive study on the formation mechanism of the nonfcc kernel structure on the Au49(SR)27 and Au58(SR)30 clusters based on a newly proposed 2e—reduction-assisted seed-mediated cluster evolution mechanism.[44] An evolution pathway from the Au40(SR)24 to the Au49(SR)27 and then to the Au58(SR)30 was mapped out first based on the 2e–-reduction cluster growth mechanism, which explained the formation of the nonfcc kernel structure on the Au49(SR)27 and the Au58(SR)30 clusters. More importantly, the mapped evolution pathway enabled us to assess the stability of the intermediate and the product clusters with the dual-packed kernel. In the present study, energy evaluation by the DFT calculations showed that the formation of dual-packed kernel intermediate clusters Au43(SR)25, Au46(SR)26, and Au49(SR)27 is energetically favorable. However, the latter cluster evolution pathway from Au49(SR)27 to Au58(SR)30 was unfavorable in terms of both poor thermodynamic stability of intermediate clusters (i.e., Au52(SR)28 and Au55(SR)29) in the size-growth process and the low stability of the dual-packed structure of Au58(SR)30. Therefore, although the Au58(SR)30 conformed to the principle of the symmetric growth of the cluster structure, its low thermodynamic stability may not be conducive to its formation. This study also suggested that in order to study the evolution of clusters, it is necessary to comprehensively study the structural stability of clusters and the thermodynamics of the formation process. The 2e— reduction-assisted cluster size growth mechanism is a good scenario to explore the structure evolution, stability, and formation process of RS-AuNCs.

Computational Method and Details

In this work, the cluster structural optimizations were performed by DFT, with the R groups simplified with CH3. The Perdew–Burke–Ernzerhof (PBE) functional[45] and the d-polarization basis set (DND) were used for the elements C, H, and S. The DFT semicore pseudopotential (DSPP) approximation with some degree of relativistic correction into the core was used for Au implemented in the Dmol[3] package.[46,47] The dispersion effect was considered in the structural optimization and calculations of the transition state (TS) using the Tkatchenko and Scheffler method.[48] In addition, in order to get closer to the experimental facts, the conductor-like screening model (COSMO) solvent model[49] was adopted to reflect the solvent effect with water as the solvent. The time-dependent DFT (TD-DFT), as implemented in the Amsterdam density functional (ADF) software package,[50] was utilized for calculating the ultraviolet–visible (UV–vis) spectra of the as-predicted cluster sequence. The triple-zeta polarized (TZP) basis set with the inclusion of the scalar relativistic effect via a zeroth-order regular approximation (ZORA) implemented in the ADF package was adopted. The TD-DFT calculations evaluated the lowest 500 singlet-to-singlet excitation energies. The structures of the clusters involved in the spectral calculations in this work are relatively large. Considering that the cluster structures do not change significantly after the ligands are replaced by the H atoms, we therefore use H atoms as substituents to simplify the ligands to save computational costs. Such spectral accuracy is sufficient for the qualitative analysis of the optical absorption characteristics of the gold clusters.

Results and Discussion

Evolution Pathway of Cluster Structures from 16e– Au40(SR)24 to 22e– Au49(SR)27

Figure a,b displays the structure anatomy of the Au40(SR)24 and Au49(SR)27 clusters. According to the “divide-and-protected” scheme,[51,52] the two clusters can be formulated as Au25[Au(SR)2]6[Au3(SR)4]3 and Au34(SR)3[Au(SR)2]3[Au2(SR)3]6, respectively. Considering that each bridge SR group or [Au(SR)] motif can bind one Au-6s electron, the total number of free valence electrons of the Au40(SR)24 and Au49(SR)27 clusters was 16 and 22, respectively, and the Au core in the two clusters can be viewed as Au259+ and Au3412+, respectively. For both clusters, they showed a good relationship between the total number of free valence electrons and the polyhedron building blocks in the metal core. Our recent studies suggested that the tetrahedron-Au4 and the triangle-Au3 unit in the RS-AuNCs can be viewed as the basic 2e– building block, that is, Au42+ or Au3+.[11] Based on this viewpoint, the 16e– and 22e– of Au40(SR)24 and Au49(SR)27 clusters correspond to their unique metal core stacking configurations. As shown in Figure a,b, the gold core in Au40(SR)24 was made of eight vertex-shared Au4 tetrahedra. Each Au4 tetrahedron can be considered as a 2e– unit (Au42+). As for the Au49(SR)27 cluster, the 22e– originates from 11 Au42+ units.

Figure 1

Comparative analysis of the gold core and the Au-SR ligand motifs of the Au40(SR)24 and Au49(SR)27 clusters. (a, b) Structural anatomy and (c) structural differences between Au40(SR)24 and Au49(SR)27.

In view of the structure of the gold core of Au40 and Au49 clusters, the gold core in Au40 has a fcc-geometry made of a central Au7 bi-tetrahedron and a Kekulé ringlike conjugated Au4 tetrahedron ring,[42] while the gold core in the Au49 cluster can be regarded as adding three new Au3 triangular units to the gold core of the Au40 cluster.[40] Based on the structures of the gold cores in the Au40 and Au49 clusters, a new cluster size growth mechanism may be implied. Quite evidently, there are some intermediate clusters in the size evolution from Au40 to Au49. Exploring the geometries and relative stabilities of these intermediate clusters will enable us to gain a deeper understanding of the evolutionary mechanism of the RS-AuNCs.

As shown in Figure b, the Au core of the Au49(SR)27 cluster can be evolved from the Au core of the Au40(SR)24 cluster by “growing” three triangular Au3 units on the vertex of three symmetric Au4 tetrahedra. At the same time, three trimeric staples on one side of the Au40 cluster lose three SR groups (the transparent red ball in Figure c), and the trimeric staple and its adjacent monomer staple each has an Au atom (turquoise balls) that contributes to the formation of a newly added Au3 unit. Because of the growth of three new triangle Au3 units and the rearrangement of the ligand motifs, the gold core of the Au49(SR)27 cluster forms a hybrid fcc and nonfcc dual-packed configuration.

Based on the analysis on the structure and valence electron number of the Au40(SR)24 and Au49(SR)27 clusters, a stepwise 2e– evolution pathway is suggested. It proposes that the Au49(SR)27 cluster can be evolved from the Au40(SR)24 cluster by the sequential growth of Au4 tetrahedra and ligand motifs, that is, Au40(SR)24 (16e–) + Au3(SR)1 → Au43(SR)25 (18e–) + Au3(SR)1 → Au46(SR)26 (20e–) + Au3(SR)1 → Au49(SR)27 (22e–). In the proposed cluster evolution pathway, Au43(SR)25 and Au46(SR)26 are two intermediate clusters, and their structures can be constructed based on Au40(SR)24 by adding one or two Au3(SR)1 units, as shown in Figure .

Figure 2

Constructed structures of intermediate clusters Au43(SR)25, Au46(SR)26, and Au49(SR)27-iso. Color labels: Turquoise, newly added Au atoms in the gold core during size evolution; Light orange, Au; pink, Au and sulfur in foreign fragments; red, sulfur. The R groups are omitted for clarity.

The mapped structural evolution pathway displayed in Figure implies a seed-mediated cluster growth mechanism. That is, Au40(SR)24 can be viewed as a seed cluster. Upon reacting with the thiolate–gold complexes (e.g., three [Au3(SR)3]) under the reductive environment, it may gradually grow into a larger-size Au49(SR)27 cluster through three 2e–-incrementation steps. The seed-mediated cluster growth process can be therefore formulated as eqs 23, where the 2e– in each cluster size growth step comes from the reduction reagent such as NaBH4 or CO.

The theoretical speculated seed-mediated cluster growth process is supported by the recent experimental observation of the seed-mediated growth of RS-AuNCs. Xie et al. found that in the reduction environment, the magic stable Au25(SR)18– (8e–) cluster can irreversibly grow into larger-size Au38(SR)24 (14e–) and Au44(SR)26 (18e–) clusters, and the size growth of clusters demonstrated clear stepwise 2e– increamentations.[53] Based on the above discussion, we have manually constructed the structure of intermediate clusters Au43(SR)25, Au46(SR)26, and Au49(SR)27, and the structures of these intermediate clusters are displayed in Figure . Note that following the proposed 2e–-evolution pathway, the resulted Au49(SR)27 cluster has slightly different Au-S skeleton structure compared with the experimentally resolved structure of Au49(2,4-DMBT)27.[40] The theoretically constructed isomer structure was then referred to as Au49(SR)27-iso in this work. Herein, we focused on the geometric structure and the relative stabilities of the intermediate Au43(SR)25, Au46(SR)26, and Au49(SR)27-iso clusters. Very recently, Wu et al. reported the synthesis and crystal structure of the Au43(CHT)25 cluster (CHTH = cyclohexanethiol).[54] In contrast to the Au43(SR)25 cluster found in this work, the Au43(CHT)25 cluster reported in their work contained a quasi-fcc gold kernel. DFT calculations were performed to investigate the relative stabilities of two isomeric structures of Au43(SR)25 clusters. The results showed that the experimentally resolved structure was slightly stable than the theoretically proposed Au43 cluster by 0.29 eV (SR = SCH3), which indicates that the newly constructed Au43 cluster structure model is energetically stable. On the other hand, we also compared the relative stability of Au49(SR)27-iso and the experimentally resolved structure of Au49(2,4-DMBT)27. It was found that the Au49(SR)27-iso in the evolution pathway is a higher-energy isomer compared with the experimental crystal structure, which is less stable by 0.47 eV (SR = SCH3).

Seed-Mediated Cluster Size Growth Mechanism from Au40(SR)24 to Au49(SR)27

Because the Au40 and Au49 clusters demonstrated a clear structural evolution pattern in both the Au core and ligand motifs, an intriguing question is raised: can we find an evolutionary mechanism from Au40 to Au49 clusters? Recent studies of real-time monitoring of the bottom-up growth and the seed-mediated growth of water-soluble RS-AuNCs by UV–vis absorption and electrospray ionization mass spectrometry (ESI-MS) have revealed several valuable details of the formation and seed-mediated size-evolution mechanism of RS-AuNCs at the molecular- or even atomic level.[53,55] Among them, the seed-mediated growth of Au44(MBA)26 from Au25(MBA)18 in the mild CO-reduction system reported by Yao et al. clarified several fundamental puzzles of the NC field at the molecular level, especially the uncovering of an interesting gold cluster growth principle—the 2e– hopping pathway.[53]

In the present study, the suggested stepwise 2e–-incrementation size-evolution pathway from Au40 to Au49 clusters agreed very well with the growth principle of water-soluble RS-AuNCs. Inspired by these experimental facts and combined with the 2e–-incrementation pathway displayed in Figure , here, we proposed a new mechanism to address the evolution process from the Au40(SR)24 cluster to the Au49(SR)27 cluster using CO as a model reduction agent. As mentioned in the reaction eqs 23, the size-evolution from the Au40(SR)24 cluster to Au49(SR)27 cluster can be divided into three 2e–-incrementation size-growth steps. In each cluster size-growth step, 2e– reduction is required to achieve the growth of a new tetrahedron Au4 unit in the core and the new ligand motifs. Here, using CO as a model reduction agent, Scheme illustrates the basic idea of the newly proposed CO reduction-assisted 2e– reduction-assisted gold cluster growth mechanism.[44]

Scheme 1

Explanation of the Proposed Carboxylation–Decarboxylation Reaction Mechanism Based on CO Reduction. Turquoise, Au Atoms in Staple Motifs; Pale Blue, Au Atoms in Gold Core; Yellow, Sulfur; Red, Oxygen; Gray, Carbon; White, Hydrogen. R Groups Are Omitted for Clarity

In the first reaction step, an Au(I)–thiolate complex such as a [Au(SR)] reacts with CO to form a [Au(SR)-CO] species, which can further react with OH– via a Hieber base reaction to generate a [Au(SR)-COOH]− species in the alkaline environment. This activation mechanism is essentially the same as that previously proposed by Xie et al.[53] However, different from Xie’s proposal, we, herein, suggested a new intermolecular association mechanism to account for the gold-core formation and 2e–-hopping process. As illustrated in Scheme , if the Au40(SR)24 cluster is considered as a seed cluster, we propose that the [Au(SR)-COOH]− species may attach onto the surface of Au40(SR)24 by the insertion of the terminal Au-COOH– group between an Au–S bond on the surface of the seed cluster. This intermolecular association leads to the formation of a new anionic complex formulated [Au40(SR)24][Au(SR)-COOH]−.

After the formation of the anionic complex, the COOH– group subjects a decarboxylation reaction with the OH– in the solution. The decarboxylation reaction results in 2e– injection, and the remaining [Au40(SR)24][Au(SR)] complex has a −2 valence state. The [Au40(SR)24][Au(SR)]2– complex may further relax into the neutral state by the removal of two SR– groups (Figure c). During this SR– removal process, the terminal Au atom of the newly added [Au3(SR)1]− fragment bonded with a S atom. The resulted intermediate was formulated as Au43(SR)25. Then, the metastable Au43(SR)25 transforms into the more stable structure by collapsing a motif Au atom into the metal core, which bonded two metal-core gold atoms to form a new tetrahedron Au4 unit, as shown in Figure d. The energy barrier of this Au atom migration process was only 0.32 eV. The whole process is described in Figure .

Figure 3

Illustration of the size evolution from Au40(SR)24 to Au43(SR)25 based on the carboxylation–decarboxylation mechanism using CO as the model reduction agent. (a) Framework of Au40(SR)24. (b) Carboxylated Au3(SR)3 fragment is inserted between an Au–S bond in the ligand of Au40. (c) Process of decarboxylation. In this process, two SR groups (marked by red circles) are eliminated, which come from the Au40 and Au3(SR)3 fragments, respectively. (d) TS structure in the process of evolution from Au40(SR)24 to Au43(SR)25 (This process involves the collapse of motif Au). (e) Skeleton structure of Au43(SR)25. Light orange/pink/turquoise, Au atoms; bright green/pink, sulfur. R groups are omitted for clarity.

The cluster size growth process from Au40(SR)24 to Au43(SR)25 can be summarized as given in eq , where the 2e– reduction and the growth of a new tetrahedron Au4 unit and a new piece of the [Au3(SR)4] motif fragment are achieved using carboxylation and decarboxylation processes. Once the Au43(SR)25 is formed, it can further grow into larger-size Au46(SR)26 and Au49(SR)27-iso clusters using two additional 2e–-reduction processes. Using CO as the reduction agent, the two cluster size growth reactions can be formulated as eqs and 6, respectively. Figure S1 displays the details of these two clusters size growth steps. The energy profiles, as shown in Figure , indicate that the two cluster size growth processes are both energetically favorable.

Figure 4

Energy curve of the dual-packed cluster sequence from Au40(SR)24 to Au49(SR)27-exp based on the carboxylation and decarboxylation mechanism. C1, C3, and C5 are cluster species formed by Au40(SR)24, Au43(SR)25, and Au46(SR)26 combined with one [Au3(SR)3COOH]− fragment, respectively. C2, C4, and C6 are the products of decarboxylation of [Au40(SR)24-Au3(SR)3COOH]−, [Au43(SR)25-Au3(SR)3COOH]−, and [Au46(SR)26-Au3(SR)3COOH]−, respectively. TS1, TS2, and TS3 represent the transition states of motif Au collapse and nucleation. TS4a and TS4b indicate two different ways of isomerization between the Au49 isomers: the former is the rearrangement of the staples, and the latter is the rotation of the core.

An isomerization process is required to form the experimentally resolved Au49(SR)27 cluster from Au49(SR)27-iso. Considering that the difference between the two clusters is mainly due to the arrangement of three ligand motifs on the surface (Figure a), we considered two isomerization pathways. As shown in Figure b, the first one, perhaps the most intuitive, is performed by the rearrangement of dimer motifs, which required breaking three Au–S bonds. DFT calculations show that the TS energy barrier of such a ligand-rearrangement process is 1.27 eV (TS4a in Figure ). However, considering that the average distance between the three Au atoms (Au1, Au2, and Au3 in Figure a) in the kernel of Au49-iso (2.941 Å) is close to the Au–Au bond length in the core tetrahedral units, we assumed that the rotation of these three core Au atoms drives the outer ligand for distortion to occur, leading to isomerization of the structure (Figure c). The energy barrier of the TS generated in such an isomerization manner is 0.66 eV (TS4b in Figure ). According to the Eyring equation,[56] it is estimated that such isomerization barriers can be crossed at room temperature. It is worth mentioning that Häkkinen et al. pointed out in their work that the chiral inversion of Au38 clusters does not need the break of the Au–S bonds (2.5 eV), but only the collective rotation (1–1.5 eV) of the core Au atoms can achieve the chiral inversion.[15] Therefore, we believe that the isomerization between the two Au49 is likely to be caused by the rotation of the Au3 unit.

Figure 5

Structural differences and isomerization mechanism of two Au49 isomers. (a) Surface ligands of the two Au49 are arranged differently. (b) and (c) Two possible isomerization mechanism of two Au49 isomers. Light orange/turquoise/pink/dark red/plum/indigo, Au atoms; red/pink, sulfur. R groups are omitted for clarity.

The relative stabilities of Au43(SR)25, Au46(SR)26, and Au49(SR)27-exp were further examined by cluster transformation reaction eqs 89, respectively. The reactant clusters in these equations were adopted from the crystal structures or theoretical models.[36,37,57,58] The formation energy of the clusters is defined as E(products) – E(reactants), where E is the electronic energy. Using SCH3 as the model SR group, the formation energies of Au43(SR)25, Au46(SR)26, and Au49(SR)27-exp are computed to be 0.42, 0.17, and 0.02 eV, respectively.

The favorable chemical and thermodynamic stabilities of the intermediate clusters were further demonstrated by DFT calculations. First, The HOMO–LUMO (H–L) gaps of clusters in this sequence are presented in Table S1. The value of H–L gaps gradually decreases from Au40 to Au49-exp and then increases. Note that the H–L gap of Au49-iso is relatively small, which can be attributed to its ligand motif arrangements. By isomerizing the ligand motifs, the Au49-exp cluster not only demonstrates higher thermodynamic stability but also larger H–L gaps. Such a tendency confirms that the Au49-iso tends to isomerize into the Au49-exp. Second, as shown in Table S1, there is no imaginary frequency in the calculations of the frequencies of these clusters, indicating that all clusters are thermodynamically stable. The Cartesian coordinates of the as-predicted optimal structures of these clusters (Au43(SR)25, Au46(SR)26, and Au49(SR)27-iso) are shown in the Supporting Information. The UV–vis spectra of the as-predicted dual-packed clusters were also calculated, as shown in Figure S2.

Symmetric Growth of Dual-Packed Kernels from the Au49(SR)27 to Au58(SR)30 Cluster

A prominent feature of the structural evolution of the RS-AuNCs is that the clusters exhibited symmetric growth of the polyhedron core and ligand motifs. For instance, the one-dimensional (1D) symmetrical growth of double-helix tetrahedron Au4 units was clearly identified according to the crystal structure of Au28(TBBT)20, Au36(TBBT)24, Au44(TBBT)28, and Au52(TBBT)32.[36] In addition, the centrosymmetric growth of triangular Au3 units and ligand motifs from Au28(SR)20 to Au30(SR)18 clusters,[33] as well as the two-dimensional (2D) crystal face growth from Au44(SR)28 to Au92(SR)44 clusters[37] were also discovered.

In view of the nearly D3 symmetry of the Au40 cluster, it is natural to consider whether or not the cluster size growth may happen on both sides of the cluster, which will lead to the formation of a larger-size cluster formulated Au58(SR)30, with symmetrical distribution of six newly added triangular Au3 units. This new cluster size evolution process can be formulated as Au49(SR)27 + Au1(SR)3 → Au52(SR)28 + Au1(SR)3 → Au55(SR)29 + Au1(SR)3 → Au58(SR)30. During this process, three triangular Au3 units are further formed on the Au49(SR)27. Based on this assumed evolution pathway, four new clusters, Au52(SR)28, Au55(SR)29, Au58(SR)30-iso1, and Au58(SR)30-iso2, are perspective. Note that the Au58(SR)30 (marked as Au58-iso1) obtained through this growth mechanism may transform into the Au58-iso2 via structural isomerization. The latter cluster was also predicted by Xu et al.[43] based on a similar symmetric evolution of the cluster structure. Herein, our DFT calculations showed that the Au58-iso2 was 0.78 eV more stable than the Au58-iso1, and the energy barrier of isomerization was determined to be 1.17 eV (Figure S3).

However, it is found that the optimized core structure of the product Au58-iso2 cluster is significantly different from those of Au40 and Au49-exp. As shown in Figure , the two conjugated tetrahedron Au4 units at the center of the Au58-iso2 core adopt a consistent orientation. In terms of the overall cluster structure, three trimeric staples are gradually shortened to monomer staples in the process of Au40 to Au49 and then to Au58. Correspondingly, the tension of the staples gradually increases. As a result, the core structure is distorted to a great extent. For instance, the two tetrahedron Au4 units in the core with lower staple tension adopt a misalignment arrangement of about 60° in the Au40 cluster. After the growth of three new triangular Au3 units and ligand motifs on one side, in the Au49-exp, the relatively large tension caused by the shortening of the staples induces a slight twist in the two Au4 units. Finally, to the Au58-iso2, the orientations of these two Au3 units overlaps, as shown in Figure .

Figure 6

Comparison of the ligand layer structure and core structures of Au40, Au49-exp, and Au58-iso2 clusters. R groups are omitted for clarify.

The gradual structural distortion of gold cores from the Au49 to Au58 cluster displayed in Figure prompts us to examine the stability of the cluster structures. It should be pointed out that it is difficult to quantitatively evaluate the intrinsic tension in the Au58-iso2. Here, the relative stabilities of intermediate Au52, Au55, Au58-iso2 clusters were evaluated by the reaction eqs 1112. It is found that unlike the favorable formation energy (0.17–0.49 eV) of Au43, Au46, and Au49-iso clusters in the size-growth pathway from the Au40(SR)24 to Au47(SR)29 cluster, the formation energies of intermediate clusters such as Au52, Au55, and Au58-iso2 in this new size-evolution pathway are as large as 1.68, 1.91, and 1.62 eV, respectively, using the experimentally resolved stable cluster species Au92(SR)44, Au12(SR)12, Au18(SR)14, and Au24(SR)16 as the references.[38,57−59] Such large positive formation energies showed that the intermediate cluster Au52(SR)28, the Au55(SR)29 cluster, and the product Au58(SR)30-iso2 cluster were energetically less stable.

In order to further explore the possibility of cluster size-growth from Au49 to Au58, we plotted the energy profile of this process. It is seen from Figure that such a growth process needs to cross relatively high energy barriers. In light of high energy barriers during this cluster size growth pathway and the relatively low stability of the intermediate clusters, the formation of Au58(SR)30 is not supported. Although the Au58(SR)30 cluster followed the principle of symmetric growth from Au40(SR)24 to Au49(SR)27-exp, the tension between the ligand shell and the gold atom in the metal core increases significantly during the cluster size evolution, and the stability of the intermediate clusters is poor, which indicates that the formation of the Au58(SR)30 cluster is not favorable.

Figure 7

Energy curve of the hypothetical reaction path from Au49-exp to Au58-iso2. C1, C3, and C5 are cluster species formed by Au49(SR)27-exp, Au52(SR)28, and Au55(SR)29 inserted by one [Au3(SR)3COOH]− fragment, respectively. C2, C4, and C6 are the products of decarboxylation of [Au49(SR)27-Au3(SR)3COOH]−, [Au52(SR)28-Au3(SR)3COOH]−, and [Au55(SR)29-Au3(SR)3COOH]−, respectively. TS1, TS2, and TS3 represent the TSs of motif Au collapse and nucleation. TS4 means the TS of the isomerization process from Au58-iso1 to Au58-iso2.

Conclusions

In conclusion, based on the 2e–-reduction cluster growth mechanism, the formation mechanism of the dual-packed kernel structure in the Au49(SR)27 and the Au58(SR)30 clusters was studied. The DFT energy calculation results showed that the favorable formation of dual-packed kernels in the Au49(SR)27 cluster is due to the stability of the intermediate cluster structures as well as the relatively high thermodynamic stability of the cluster itself. However, although the structure of Au58(SR)30 clusters conforms to the principle of symmetric growth, the tension between the ligand shell and the metal core gold atoms increases significantly during the cluster size evolution, and the stability of the intermediate clusters is poor, which hinders the formation of the Au58(SR)30 cluster. This study shows that it is necessary to consider the structural stability and thermodynamics of cluster formation when studying the evolution of clusters according to the symmetry growth principle. The 2e—reduction-assisted cluster size growth mechanism provides a good scheme for exploring the evolution path of cluster structures and evaluating the stability of clusters.