Unraveling a generic growth pattern in structure evolution of thiolate-protected gold nanoclusters†

Precise control of the growth of thiolate-protected gold nanoclusters is a prerequisite for their applications in catalysis and bioengineering. Here, we bring to bear a new series of thiolateprotected nanoclusters with a unique growth pattern, i.e., Au20(SR)16, Au28(SR)20, Au36(SR)24, Au44(SR)28, and Au52(SR)32. These nanoclusters can be viewed as resulting from the stepwise addition of a common structural motif [Au8(SR)4]. The highly negative values of the nucleus-independent chemical shift (NICS) in the center of the tetrahedral Au4 units suggest that the overall stabilities of these clusters stem from the local stability of each tetrahedral Au4 unit. Generalization of this growth-pattern rule to large-sized nanoclusters allows us to identify the structures of three new thiolateprotected nanoclusters, namely, Au60(SR)36, Au68(SR)40, and Au76(SR)44. Remarkably, all three large-sized nanoclusters possess relatively large HOMO–LUMO gaps and negative NICS values, suggesting their high chemical stability. Further extension of the growth-pattern rule to the infinitely long nanowire limit results in a one-dimensional (1D) thiolate-protected gold nanowire (RS-AuNW) with a band gap of 0.78 eV. Such a unique growth-pattern rule offers a guide for precise synthesis of a new class of large-sized thiolate-protected gold nanoclusters or even RS-AuNW which, to our knowledge, has not been reported in the literature.


Introduction
Since the first successful crystallization of the thiolateprotected gold nanocluster Au 102 (SR) 44 in 2007, 1 research into the structural evolution and structure-property relationship of thiolate-protected gold nanoclusters has attracted considerable attention due to high potential of these nanoclusters for applications in electronics, catalysis and bioengineering. [2][3][4][5][6][7] Significant advancement in structure determination has been made on the basis of X-ray crystallography, 1,8-20 single-particle transmission electron microscopy (SP-TEM), 21 as well as densityfunctional theory (DFT) computation [22][23][24][25][26][27][28][29][30] in conjunction with the "divide and protect" formulation. 4,31 Although the latter formulation can be very useful in seeking optimal ligand patterns for given gold-core structures, generic growth patterns of the gold nanoclusters are still largely unknown, which hinders the development of large-sized ligand-protected gold nanoclusters for optical and electronic applications.
In this communication, we report a growth-pattern rule that has been revealed based on previously known (via X-ray crystallography) and/or theoretically predicted structures of a series of ligand-protected gold nanoclusters, i.e., Au 20 (SR) 16 , 25,32 Au 28 (SR) 20 , 13,40 Au 36 (SR) 24 , 15 Au 44 (SR) 28 , 28,33 and Au 52 (SR) 32 . 12 These clusters can be viewed as structural evolutions from the starting cluster Au 20 (SR) 16 32 . Fig. 1 illustrates the structural evolution of the face-centered-cubic (FCC) type of Au kernels in these clusters via sequential addition of the "boat-like" Au 8 motif.

Computational methods
All clusters were optimized using the DFT method implemented in the Dmol 3 7.0 code. 34,35 To this end, the generalized gradient approximation in the Perdew-Burke-Ernzerhof (PBE) 36 form was employed together with the double numeric polarized (DNP) basis set and the semi-core pseudopotential. In all our computations, the R group in the ligands is simplified as a methyl group or hydrogen atom. All the optmized structures of the nanoclusters are presented in ESI Fig. S1 gen atom), nucleus-independent chemical shift (NICS) analysis was performed to examine the aromaticity of the clusters using the B3LYP functional 37,38 with LANL2DZ and 6-31G* basis set implemented in the Gaussian 09 package. 39

Results and discussion
As shown in Table 1, the atomic structures of Au 28 (SR) 20 , 13 Au 36 (SR) 24 , 15 and Au 52 (SR) 32 20 nanoclusters have been determined via X-ray crystallography. Note that Au 20 (SR) 16 may have two isomeric structures. The theoretically predicted structure 25 (see Fig. 1(a)) can well reproduce the optical absorption spectrum of Au 20 (PET) 16 (PET = SCH 2 CH 2 Ph), 33 and it has a distinct Au kernel of the crystallized Au 20 (TBBT) 16 (TBBT = SPh-t-Bu) cluster. 8 However, considering the close total energy of these two structures (their energy difference is 0.3 eV with capped methyl groups for simplicity), one of the two isomers is likely the same as the theoretically predicted structure. A similar situation was reported in the cases of Au 40 (o-MBT) 24 43 (o-MBT = ortho-methylbenzenethiol) and Au 40 (PET) 24 . 44 The structure prediction of Au 44 (SR) 28 28,33 was based on the structural rules derived from the crystallization of Au 28 (SR) 20 and Au 36 (SR) 24 , i.e., Au 28 (SR) 20 + [Au 8 (SR) 4 ] → Au 36 (SR) 24 ( Fig. 1 4 ] → Au 44 (SR) 28 ( Fig. 1(c)). The excellent agreement between experimental and computed optical absorption spectra of Au 44 (SR) 28 validates the predicted structure of Au 44 (SR) 28 , which is solely based on the growthpattern rule derived from Au 28 (SR) 20 and Au 36 (SR) 24 . Additional evidence comes from the crystallization of the Au 52 (SR) 32 nanocluster, 20 whose structure can be viewed as adding the [Au 8 (SR) 4 ] motif to the predicted structure of Au 44 (SR) 28 ( Fig. 1(d)). It should be noted that the recently reported Au 28 (S-c-C 6 H 11 ) 20 (where -c-C 6 H 11 = cyclohexyl) 40 cluster exhibits a similar Au 20 kernel structure to crystallized Au 28 (TBBT) 20 (ESI Fig. S2 †). Therefore, the two crystallized structures of Au 28 (SR) 20 can be evolved from Au 20 (SR) 16 ( Fig. 1(a)). Besides the different surface-protecting ligands, the two isomeric structures have different staple motifs. According to the "divide and protect" formulation, 45 Au 20 (SR) 16 , Au 28 (SR) 20 , Au 36 (SR) 24 , Au 44 (SR) 28 , and Au 52 (SR) 32 can be divided into Au 8 Fig. 2. It is known that NICS values have been commonly used as an index to measure the local aromaticity of fullerene cages 46 or small metal clusters. 47 In addition, NICS analyses have been applied successfully to evaluate the stabilities of gold fullerene structures, such as Au 32 48 and Au 42 . 49 Recently, NICS analyses of the Au 20 (SR) 16 cluster were performed to support the concept of a superatom-network (SAN); 50 a theory to explain the stability of thiolate-protected gold nanoclusters. Thus, it is sensible to examine the stabilities of Au 20 (SR) 16 , Au 28 (SR) 20 , Au 36 (SR) 24 , Au 44 (SR) 28 , and Au 52 (SR) 32 based on the computed NICS values corresponding to the center of the tetrahedral Au 4 units of these clusters. It can be seen that the absolute NICS values (see Table 2) at the centers of the tetra-   36 ?
This work Au 76 (SR) 44 \ (ref. 43) This work hedral Au 4 units are large; larger than those at the centers of the total structures. The NICS results suggest notable aromaticity in the tetrahedral Au 4 units. As such, the overall stabilities of Au 20 (SR) 16 , Au 28 (SR) 20 , Au 36 (SR) 24 , Au 44 (SR) 28 , and Au 52 (SR) 32 likely stem from the local stability of each tetrahedral Au 4 unit. The unique growth-pattern rule derived among the series of clusters, Au 20 (SR) 16 , Au 28 (SR) 20 , Au 36 (SR) 24 , Au 44 (SR) 28 and Au 52 (SR) 32 , suggests the possible existence of larger-sized clusters through continuously adding the motif [Au 8 (SR) 4 ], e.g., Au 52 (SR) 32 44 , where the newly created Au 60 (SR) 36 , Au 68 (SR) 40 , and Au 76 (SR) 44 all possess the FCC-type Au-kernels (Fig. 3). Fig. 4 presents the computed HOMO-LUMO gaps of the optimized nanoclusters from the small-sized Au 20 (SR) 16 to large-sized Au 76 (SR) 44 , as well as the experimentally measured optical gaps of Au 20 (SR) 16 , Au 28 (SR) 20 , Au 36 (SR) 24 , and Au 44 (SR) 28 . The computed gaps reproduce the experimental gaps quite well except for Au 28 (SR) 20 . Nevertheless, the computed gap of Au 28 (SR) 20 is consistent with a previous theoretical study. 14 The HOMO-LUMO gaps of Au 60 (SR) 36 , Au 68 (SR) 40 , and Au 76 (SR) 44 are all greater than 1.0 eV, comparable to those of Au 64 (SC 6 H 11 ) 32 51 and Au 67 (PET) 35 . 52 Doublehelix structures made of tetrahedral Au 4 units can be seen in the three new structures (ESI Fig. S4 †), and are also present in Au 20 (SR) 16 , Au 28 (SR) 20 , Au 36 (SR) 24 , Au 44 (SR) 28 and Au 52 (SR) 32 clusters. Furthermore, the NICS analyses (ESI Table S1 and Fig. S6 †) also show that the overall stabilities of Au 60 (SR) 36 , Au 68 (SR) 40 , and Au 76 (SR) 44 are likely due to the local stability of each tetrahedral Au 4 unit. The large HOMO-LUMO gaps and the negative NICS values suggest high stability of the newly predicted structures. It should be noted that the Au 76 (4-MEBA) 44 (4-MEBA = 4-(2mercaptoethyl)benzoic acid) nanocluster has been synthesized recently by Takano et al. 53 Although Au 76 (4-MEBA) 44 has the same number of Au atoms and ligands as Au 76 (SR) 44 , a comparison of the computed and experimental X-ray diffraction (XRD) and optical absorption spectra suggests that the two clusters may have different structures in their Au-kernels (ESI Fig. S5 †). It is known that surface-protecting thiolates can have significant effects on the structures of gold nanoclusters even with the same number of Au and S atoms. For example, the marked differences in their absorption spectra indicate that Fig. 2 The structures of Au 8 in Au 20 (SR) 16 , Au 14 in Au 28 (SR) 20 , Au 20 in Au 36 (SR) 24 , Au 26 in Au 44 (SR) 28 , and Au 32 in Au 52 (SR) 32 . Au atoms are both olive and wine. Table 2 Computed nucleus-independent chemical shift (NICS) values of Au 20 (SR) 16 , Au 28 (SR) 20 , Au 36 (SR) 24 , Au 44 (SR) 28 , and Au 52 (SR) 32 . "0" denotes the NICS values at the centers of the total structures. "1-10" denote the NICS values at the centers of tetrahedral Au 4 units of these clusters (ESI Fig. S3 Fig. 3 The optimized structures of Au 60 (SR) 36 , Au 68 (SR) 40 , and Au 76 (SR) 44 , where the methyl groups are omitted for clarity. Au and S atoms are in gold and red, respectively.

as well as
Au 28 (TBBT) 20 13 and Au 28 (S-c-C 6 H 11 ) 20 . 40 Moreover, even with the same ligands, different Au 38 (PET) 24 isomers have been detected. 15,54 Lastly, if the growth-pattern rule is extended to the infinitely-long nanowire limit by repeatedly adding [Au 8 (SR) 4 ] units in one direction, the thiolate-protected gold nanowire (RS-AuNW) can be obtained, as shown in Fig. 5(a) and (b). The present RS-AuNW also exhibits a double-helix structure made of tetrahedral Au 4 units, which is very different from that of previously proposed vertex-and face-sharing icosahedral thiolated Au nanowires 55  narrow-gap semiconductor. It is also found that the valence band of the present RS-AuNW is mainly contributed to by the Au(5d), S(3p) Au(6s), and Au(6p) atomic orbitals, while the conduction band is mainly due to the Au(6sp) atomic orbitals.

Conclusions
In conclusion, a generic growth-pattern rule is identified based on the series of nanoclusters Au 20 (SR) 16 , Au 28 (SR) 20 , Au 36 (SR) 24 , Au 44 (SR) 28 , and Au 52 (SR) 32 , which can be viewed as the sequential addition of [Au 8 (SR) 4 ] units. The large negative nucleus-independent chemical shift (NICS) values in the centers of the tetrahedral Au 4 units indicate that the integral stabilities of these clusters are determined by the local stability of each tetrahedral Au 4 unit. Extension of the rule to largersized nanoclusters than the state-of-the-art gives rise to new structures of nanoclusters such as Au 60 (SR) 36 , Au 68 (SR) 40 , and Au 76 (SR) 44 . All three large-sized nanoclusters exhibit relatively large HOMO-LUMO gaps and negative NICS values, suggesting their high chemical stability. It is also found that the computed XRD and optical absorption spectra of Au 76 (SR) 44 are not the same as those of Au 76 (4-MEBA) 44 from experiments, suggesting the two nanoclusters may have different Au-kernel structures. Finally, extension of the growth-pattern rule to the infinitely long nanowire limit results in a 1D RS-AuNW with a band gap of 0.78 eV. The unique growth-pattern rule offers a guide for future synthesis of a new class of large-sized thiolateprotected gold nanoclusters or even RS-AuNW that has not been reported in the literature.   4 The computed HOMO-LUMO gaps of the optimized nanoclusters from small-sized Au 20 (SR) 16 to large-sized Au 76 (SR) 44 , and the measured optical gaps.
11574340), "Hundred People Project" from Chinese Academy of Sciences, "Pu-jiang Rencai Project" from Science and Technology Commission of Shanghai Municipality (13PJ1410400), and CAS-Shanghai Science Research Center (CAS-SSRC-YJ-2015-01). The computational resources utilized in this research were provided by Shanghai Supercomputer Center, National Supercomputer Centers in Tianjin and Shenzhen, and special program for applied research on super-computation of the NSFC-Guangdong joint fund (the second phase). X.C.Z. is supported by the USTC Qian-ren B (1000-Talents Program B) fund for summer research.