Rethinking the Structure of Gold Nanoclusters with fcc-Based Kernel through GUM

AuNCs can show different packing types such as fee and hep.

Since the discovery of Au36(SR)24, dozens of fee type nanoclusters have been crystallized [81]. Zeng et al. synthesized two fcc-based Au40(o-MBT)24 and AuS2(TBBT)32 in 2015 and found that their Au kernels can be segregated into two helixes consisting of several fused tetrahedral Au4 which is exactly one ofthe elementary blocks of GUM [92]. Later in 2016, the researchers in the same group produced another four fcc-based Au28(TBBT)20, Au36(TBBT)24, Au44(TBBT)28, and Au52(TBBT}32 nanoclusters; helix-like units were also found in these four AuNCs [93]. This is also the case for Au34(S-c-C6Hia)22 and Au42(S-c-C6Hai)26 [94]. All these studies share one point of view that helix-like Au kernels could be obtained based on the inhomogeneous distribution of Au-Au bond lengths. However, for some other fcc-based AuNCs, the decompositions of the Au kernels are not so obvious. For example, the Au cores of both Au30S(S-t-Bu)18 and Au30(S-t-Bt)18 were recognized as interpenetrating bicubocta- hedral geometry [95, 96]. In the structure determination study of [Au23(SC6H n)16]~ and Au24(SAdm)16, the authors saw the Au13 kernel as cuboctohedral [28, 97]. In addition, the Au10 core of Au21(S- Adm]is was treated as two octahedrons sharing one edge and the average Au-Au bond length for whole AuNC was calculated [42]. The average bond length was found to be roughly equal to that of bulk gold in this work [42]. Although structure evolution for AuNCs containing fcc-based kernels was reported very recently for further understanding of structural evolvement [81], the above studies suggest that the current knowledge about the structural information of Au kernel still needs to be enriched to check if the inhomogeneous distribution of Au-Au bond lengths also exists in non-helix-like AuNC cores. This point motivates this work partly. Through investigating the inhomogeneous distribution of Au-Au distances, examinations can also be done to see if the inhomogeneous distribution is in accordance with the distribution of the elementary blocks of GUM. To achieve these goals, the Au-Au distances within the Au cores and some other calculations were counted and analyzed.

Thiolate-protected gold clusters involved in this work were optimized using DFT. TPSS exchange-correlation functional was used in the optimization. This functional has been proven to be capable of obtaining the reasonable structures [98-100]. Initial geometry inputs were obtained from the experimental crystal structures. During the calculations, the ligands of AuNC were replaced by -SH to reduce the computational cost. Effective core basis set LANL2DZ was used for Au atoms and a larger SDD basis set was used as well for the purpose of comparisons and validations. Other atoms, including S, C, and H, were described by using 6-31G* basis set. Self-consistent calculations were considered as convergence when a criterion of 10"6 Hartree was reached. MP2 has been already proven to be able to reproduce aurophilic interaction [2, 101, 102]. Thus, MP2 calculations were also done in order to describe electron correlation accurately. All the calculations were done using Gaussian 09 package [103].

Segregation of Sample AuNCs Based on GUM

According to GUM, each Au atom and SR group possess +le and -le valence electrons, respectively. In the first step, all the thiol ligands were detached from the Au kernel accompanied with the electron transfer of 0.5e from each Au kernel atom to the corresponding S atom, that is, step a of Fig. 5.1. This step also presents that [Au23SR16]~ kernel is composed of three units, that is, Au3, Au7, and Au3. Distances between two Au atoms from the same or two different units were measured to check if there was any underlying principle. Step b of Fig. 5.1 also shows that these three units can further be decomposed into two Au4 blocks and two Au3 blocks, where the le valence electron of the Au atom in magenta was separated into two 0.5 e of each Au4.

The structural segregation of [AuSR]. All the -R groups are omitted for clarity. Color

Figure 5.1 The structural segregation of [Au23SR16]_. All the -R groups are omitted for clarity. Color: Au - magenta and dark yellow, S - dark green. Based on GUM, Au atoms are shown in different colors to represent different numbers of valence electrons in each Au atom, that is, magenta Au: le valence electron and dark yellow Au: 0.5e valence electron.

Validation of Calculations

We first show the results of validation of calculations before presenting further results. Since structural information is focused particularly in this work, the average bond length differences between the corresponding experimental and computational results were obtained for the purpose of comparison. Two types of representative bond lengths, that is, intra-unit Au-Au bond length and inter-unit Au-Au bond length, were counted. Inter-unit Au-Au bond length refers to the distance between two Au atoms in two different units, while intra-unit Au-Au bond length represents the Au-Au distance within a unit. Only the reasonably short inter-unit Au-Au bond was considered here. Eight relatively small AuNCs were selected as samples to get intra-unit and inter-unit Au-Au bond lengths. The results are shown in Fig. 5.2.

Two pseudopotential basis sets, that is, LANL2DZ and SDD, were tested. Figure 5.2 illustrates the differences between calculated average bond length and the corresponding experimental results. We can find that the bond length differences calculated using LANL2DZ were closer to those obtained from crystal structures in the majority cases. Thus, LANL2DZ was used exclusively in the calculations discussed in the following section.

Differences of average intra-unit and inter-unit Au-Au bond lengths using LANL2DZ basis set and SDD basis set over the experimental average bond length

Figure 5.2 Differences of average intra-unit and inter-unit Au-Au bond lengths using LANL2DZ basis set and SDD basis set over the experimental average bond length. -SR groups were replaced by -SH during calculations to lower the computation price.

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