New Perspectives on the Electronic and Geometric Structure of Au70S20(PPh3)12 Cluster: Superatomic-Network Core Protected by Novel Au12(µ3-S)10 Staple Motifs

In order to increase the understanding of the recently synthesized Au70S20(PPh3)12 cluster, we used the divide and protect concept and superatom network model (SAN) to study the electronic and geometric of the cluster. According to the experimental coordinates of the cluster, the study of Au70S20(PPh3)12 cluster was carried out using density functional theory calculations. Based on the superatom complex (SAC) model, the number of the valence electrons of the cluster is 30. It is not the number of valence electrons satisfied for a magic cluster. According to the concept of divide and protect, Au70S20(PPh3)12 cluster can be viewed as Au-core protected by various staple motifs. On the basis of SAN model, the Au-core is composed of a union of 2e-superatoms, and 2e-superatoms can be Au3, Au4, Au5, or Au6. Au70S20(PPh3)12 cluster should contain fifteen 2e-superatoms on the basis of SAN model. On analyzing the chemical bonding features of Au70S20(PPh3)12, we showed that the electronic structure of it has a network of fifteen 2e-superatoms, abbreviated as 15 × 2e SAN. On the basis of the divide and protect concept, Au70S20(PPh3)12 cluster can be viewed as Au4616+[Au12(µ3-S)108−]2[PPh3]12. The Au4616+ core is composed of one Au2212+ innermost core and ten surrounding 2e-Au4 superatoms. The Au2212+ innermost core can either be viewed as a network of five 2e-Au6 superatoms, or be considered as a 10e-superatomic molecule. This new segmentation method can properly explain the structure and stability of Au70S20(PPh3)12 cluster. A novel extended staple motif [Au12(µ3-S)10]8− was discovered, which is a half-cage with ten µ3-S units and six teeth. The six teeth staple motif enriches the family of staple motifs in ligand-protected Au clusters. Au70S20(PPh3)12 cluster derives its stability from SAN model and aurophilic interactions. Inspired by the half-cage motif, we design three core-in-cage clusters with cage staple motifs, Cu6@Au12(μ3-S)8, Ag6@Au12(μ3-S)8 and Au6@Au12(μ3-S)8, which exhibit high thermostability and may be synthesized in future.

q, in which m, n and p are the numbers of Au, S and SR, respectively, whereas q is the charge of the cluster. The super shells for spherical Au clusters is |1S 2 |1P 6 |1D 10 |2S 2 1F 14 |2P 6 1G 18 | . . .  . . present special stability and they are magic number clusters. The theoretically predicted Au 12 (SR) 9 + and Au 8 (SR) 6 are 2e magic clusters.
Cheng et al. introduced the superatom-network (SAN) model, which has been used to explore the stability of Au 18 (SR) 14 , Au 20 (SR) 16 , Au 24 (SR) 20 , Au 44 (SR) 28 and Au 22 (SR) 18 clusters [8,36,37]. Based on the concept of SAN model, the Au-core of Au-L cluster can be viewed as a network of 2e Au n (n = 3, 4, 5 or 6) superatoms. The interactions between the superatoms are main non-bond interactions.
Here, we investigate the electronic and geometric structure of Au 70 S 20 (PPh 3 ) 12 to obtain deep understanding of it. Based on the superatom complex (SAC) model, this cluster is a 30e compound [35]. The number of valence electrons for Au 70 S 20 (PCH 3 ) 12 cluster does not satisfy the magic number electrons of SAC model. Kenzler et al. reported that the Au core of Au 70 S 20 (PPh 3 ) 12 cluster is Au 22 , and the protecting tetrahedral shell is composed of four Au 4 S 4 units, four S atoms and 32 gold atoms, and no staple motif presents [21]. We are interested in the synthesized Au 70 S 20 (PPh 3 ) 12 cluster, which has 20 µ 3 -S atoms. Now that the number of the valence electrons does not satisfy the SAC model, why it is stable? How do the 20 µ 3 -S atoms protect the Au-core? What are the protecting motifs of the cluster? With these questions in mind, we tried to analyze the electronic and geometric structure of the cluster using existing theories and models. This work attempts to explain the structure and properties from a new perspective.

Materials and Methods
We start from the experimental structure of Au 70 S 20 (PPh 3 ) 12 determined as reported by Kenzler et al [21] and the total charge is set to zero. Considering the calculation amount, we used CH 3 instead of all the Ph ligands, and the structure was then relaxed using the Gaussian 09 software (Revision B 01; Gaussian, Inc., Wallingford, CT, USA) [38]. Density-functional theory (DFT) calculations were employed to optimize the geometric structure using Perdew-Burke-Ernzerhof (PBE0) functional [39]. The basis set of Au element is Lanl2dz, while 6-31G * is used for S, P, C, H elements. The molecular orbital (MO) and natural bond orbital (NBO) calculations of Au cores were also carried out at the same level, whereas the basis set of Au element was Lanl2mb. The adaptive natural density partitioning (AdNDP) method was used to analyze the chemical bonding patterns [40]. MOLEKEL software (version 5. 4.0.8, Swiss National Supercomputing Centre, Manno, Switzerland) [41] was used to view the chemical bonding patterns. The superatom-network (SAN) model was taken to analyze the chemical bonds in Au 70 S 20 (PPh 3 ) 12 cluster [36].

Geometric Structure
The structure of the relaxed Au 70 S 20 (PCH 3 ) 12 cluster is given in Figure 1b, which is in D 2 symmetry. The structural parameters computed here reproduce well with the experimental results. Based on the divide-and-protect concept [22], different building blocks were tried to find the proper segmentation mode. The cluster can be viewed as Au-core and protecting motifs. Through analysis on the structure, the protecting motifs include twelve separate PCH 3 and (Au-S) n motifs. According to the segmentation analysis in Supplementary Materials, Au 70 S 20 (PCH 3 ) 12 cluster is divided into three parts as Figures 2 and 3   The Au 3 (µ 3 -S) unit has been proposed as an elementary block and used to design a group of quasi-fullerence hollow-cage [Au 3n (µ 3 -S) 2n ] n− clusters with high stability [46]. [Au 12 (µ 3 -S) 10 Figure S1 gives Au-Au contacts in the optimized structure of Au 70 S 20 (PCH 3 ) 12 cluster: (a) Au 22 innermost core is 5 × 2e SAN, (b) Au 22 innermost core is a 10e-superatomic molecule. Also given are the aurophilic contacts between motifs and superatoms and the aurophilic contacts between superatoms. Noticeable gold-gold interactions (baby blue and black lines in Figure S1a,b, Supporting Materials) between the Au atoms in [Au 12 (µ 3 -S) 10 ] 8− and neighboring gold cores are present. The Au-Au aurophilic distances range from 2.82-3.01 Å, with the average Au-Au distance being 2.91 Å smaller than the Au-Au van der Waals radii (3.32 Å) [48,49]. The blue lines in Figure S1a label the aurophilic interactions between Au 6 and Au 4 cores, and the interactions between Au 4 cores. The green lines in Figure S1b label the aurophilic interactions between Au 22 and neighboring Au 4 cores. The Au-Au distances range from 2.86-3.01 Å, and the average Au-Au distance is 2.93 Å. The short bond distance between Au and Au indicates strong aurophilic interactions. Thus, the interaction mode between six-tooth staple motifs and Au cores includes clamping and aurophilic interactions, which stabilize the Au 70 S 20 (PCH 3 ) 12 cluster. Here, the staple motif can extend to six-tooth mode. The staple motif only includes Au and S elements, which is obviously different from previous staple motifs. From above analysis, we can see that both the position of the six-tooth staple motifs and Au-Au contacts in the cluster dedicate to the stability of Au 70 S 20 (PCH 3 ) 12 cluster.

Chemical Bonding Analysis
In order to verify the electronic structure of Au 70 S 20 (PCH 3 ) 12 cluster, we carried out chemical bonding analysis. The electronic structure of the cluster followed the SAN model, that is, it had a network of fifteen 2e-superatoms, abbreviated as 15 × 2e SAN, which contained five 2e-Au 6 and ten 2e-Au 4 superatoms. We took the Au 46 16+ core out of the cluster separately while keeping the structure identical to that in Au 70 S 20 (PCH 3 ) 12 cluster to analyze the chemical bonds. As expected, AdNDP analysis in Figure 4 indicated that there are 10 four-center-two-electron (4c-2e) bonds with occupancy numbers (ON) = 1.54−1.56 |e|, five 6c−2e bonds with ONs = 1.63−1.68 |e|. Vertex-sharing Au 4 superatoms were present in the experimentally determined Au 20 (SR) 16 and Au 36 (SR) 24 clusters [33,34]. For purposes of confirming the segmentation scheme, the difference of Au-Au distances inside the Au 46 core and those between Au 46 core and two six-tooth staple motifs were recorded. Figure S2 (Supporting Materials) displays all the Au-Au distances, which include the distances between Au 46 core and two six-tooth staple motifs (black dots), the Au-Au distances in Au 22 core (red dots), in two Au 4 superatoms on top and bottom of the cluster (blue dots), in the four pairs of vertex-sharing Au 4 superatoms (purple dots). The average Au-Au distances of the above four groups were 2.90, 2.91, 2.82, and 2.86 Å, respectively. From the figure, we can see that, the Au-Au distances between Au 46 core and two six-tooth staple motifs and distances in the Au 22 core were relatively bigger than other two groups. The Au 22 core was consistent with the former report [21]. The reason for the Au-Au distances in Au 22 core being relatively bigger are probably that the repulsive interactions of Au atoms can be reduced in this way. Lower repulsion is helpful to form a Au 22 core. The Au-Au distances in the ten Au 4 superatoms were shorter than those between the Au-core and staple motifs, which follow the concept of SAN model. The shorter Au-Au distances were helpful to the formation of Au 4 superatoms. In short, the existence of ten Au 4 superatoms were reasonable, which has been supported from the viewpoint of Au-Au distances.
Further analysis of the innermost Au 22 12+ core was performed and the structure of Au 22 12+ core stayed the same as that in Au 46 16+ core. The results are given in Figure 5. From Figure 5a, we can see

Aromatic Analysis
NICS-scan method is proposed by Stanger, which is similar to the screen method of aromatic center and has been used to predict the aromatic properties of molecules and clusters [52][53][54]. Here, we use NICS-scan method to further verify the existence of Au 4 superatoms and we have demonstrated the existence of Au 4 superatoms in Au 20 (SR) 16 , Au 28 (SR) 20 and Au 30 S 2 (SR) 18 clusters in our former work [19,36]. Figure 6 8 , Ag 6 @Au 12 (µ 3 -S) 8 , and Au 6 @Au 12 (µ 3 -S) 8 Clusters
Jiang et al. have predicted several core-in-cage gold sulfide Au x S y − clusters observed in MALDI fragmentation of Au 25 (SR) 18 − cluster theoretically [42]. They stated that the Au core in the core-in-cage cluster may catalyze reactions. Inspired by the half-cage [Au 12 (µ 3 -S) 10 ] 8− staple motif, the cubic [Au 12 (µ 3 -S) 8 ] 4− cluster can be regarded as a cage staple motif. Thus, we designed three core-in-cage clusters, Cu 6 @Au 12 (µ 3 -S) 8 , Ag 6 @Au 12 (µ 3 -S) 8 , and Au 6 @Au 12 (µ 3 -S) 8 . The structures, models and AdNDP analysis of the three designed clusters are collected in Figure 7. The core-in-cage clusters can keep O h symmetry after relaxation. The harmonic vibrational frequencies of the three clusters are all positive, indicating they are real local minima on potential energy surfaces. The infrared spectrograms (IR) of them are given in Figure S3. The HOMO-LUMO gaps of Cu 6 @Au 12 (µ 3 -S) 8 , Ag 6 @Au 12 (µ 3 -S) 8 , and Au 6 @Au 12 (µ 3 -S) 8   In order to study the thermodynamic stability of the Cu 6 @Au 12 (µ 3 -S) 8 , Ag 6 @Au 12 (µ 3 -S) 8 and Au 6 @Au 12 (µ 3 -S) 8 clusters, Cu 6 @Au 12 (µ 3 -S) 8 cluster is taken as a test case. The thermodynamic stabilities of Cu 6 @Au 12 (µ 3 -S) 8 cluster is further confirmed by ab initio molecular dynamics (AIMD) simulations. The AIMD studies of the cluster is carried out using Vienna ab initio simulation package (VASP) with PBE0 method [39,56]. Four different temperatures at 300, 500, 700, and 1000 K with a simulation time of 8ps have been performed. The AIMD simulations of Cu 6 @Au 12 (µ 3 -S) 8 cluster are plotted in Figure S4. From the figure, it is obvious that the structure of Cu 6 @Au 12 (µ 3 -S) 8 cluster can keep after simulation in the temperature range of 300-1000 K, indicating its high thermostability.

Conclusions
In conclusion, we have explored the electronic and geometric structure of the recently determined Au 70 S 20 (PPh 3 ) 12  innermost core is viewed as a network of five 2e-Au 6 superatoms, the Au 46 16+ core can be described as a 15 × 2e SAN consisting of 10 × 2e Au 4 and 5 × 2e Au 6 superatoms. The vertex-sharing Au 7 core exists in the experimentally determined Au 20 (SR) 16 and Au 36 (SR) 24 clusters. A new branching staple motif, six-tooth staple motif, [Au 12 (µ 3 -S) 10 ] 8− , is discovered in Au-L clusters for the first time.
The six-tooth staple motif is obviously different from common staple motifs, which have six S legs.
Here the newly discovered staple motif enriches the staple motif family. The NICS-san method has been used to confirm the presence of Au 4 superatoms. The new segmentation method here can properly explain the structure and stability of Au 70 S 20 (PPh 3 ) 12 cluster. The reason for the stability and the nature of bonds have been given. Concretely, the six-tooth staple motifs, the superatom network, the aromatic of the superatoms and Au-Au interactions contribute to the stability of the cluster. We have designed three core-in-cage Cu 6 @Au 12 (µ 3 -S) 8 , Ag 6 @Au 12 (µ 3 -S) 8 , and Au 6 @Au 12 (µ 3 -S) 8 clusters based on [Au 12 (µ 3 -S) 8 ] 4− . The three clusters are stable in O h symmetry. Each of them has one 6c-2e bond in the core. Aromatic analysis reveals that they are aromatic molecules. The [Au 12 (µ 3 -S) 8 ] 4− cluster has been experimentally synthesized, and the three constructed clusters are stable based on our computation, thus the three designed clusters may be synthesized in future. Our work will provide some new perspectives to the electronic structure and stability of Au 70 S 20 (PPh 3 ) 12 cluster. The concept of half-cage and cage staple motif could offer some reference to future synthesis of Au-L clusters.