Unraveling the Atomic Structures of 10-Electron (10e) Thiolate-Protected Gold Nanoclusters: Three Au32(SR)22 Isomers, One Au28(SR)18, and One Au33(SR)23.

The atomic structures of 10-electron (10e) thiolate-protected gold nanoclusters have not received extensive attention both experimentally and theoretically. In this paper, five new atomic structures of 10e thiolate-protected gold nanoclusters, including three Au32(SR)22 isomers, one Au28(SR)18, and one Au33(SR)23, are theoretically predicted. Based on grand unified model (GUM), four Au17 cores with different morphologies can be obtained via three different packing modes of five tetrahedral Au4 units. Then, five complete structures of three Au32(SR)22 isomers, one Au28(SR)18, and one Au33(SR)23 isomers can be formed by adding the thiolate ligands to three Au17 cores based on the interfacial interaction between thiolate ligands and gold core in known gold nanoclusters. Density functional theory calculations show that the relative energies of three newly predicted Au32(SR)22 isomers are quite close to two previously reported isomers. In addition, five new 10e gold nanoclusters have large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps and all-positive harmonic vibration frequencies, indicating their high stabilities.

Introduction

Over the past years, the structures of thiolate-protected gold nanoclusters, expressed as Au(SR), have facilitated abundant experimental and theoretical research efforts.[1−4] A large number of thiolate-protected gold nanoclusters with different free valence electron numbers have been obtained via both experimental X-ray crystallography and theoretical predictions, as shown in Table S1, in which the gold nanoclusters with different free valence electron numbers covering 4e, 6e, 8e, 10e, 12e, 14e, 16e, 18e, 20e, etc. were summarized. Among medium-sized clusters with different free valence electron numbers, there are many structures of 8e gold nanoclusters, i.e., Au23(SR)16–, Au24(SR)16, Au25(SR)18–, Au28(SR)20, etc.[5−11] Taking Au28(SR)20 nanoclusters as an example, two crystallized isomers and four predicted isomers were reported.[8−11] However, it shows that 10e thiolate-protected gold nanoclusters have not received extensive attention. No crystallized structures of 10e gold nanoclusters were experimentally determined and only three predicted structures, i.e., Au29(SR)19 and two Au32(SR)22 isomers, were theoretically proposed,[11,12] which hinders the deep understanding and controllable design of the 10e thiolate-protected gold nanoclusters.

With the development of theoretical models, i.e., “divide and protect” rule,[13] superatom complex (SAC) model,[14] superatom network (SAN) model,[15] grand unified model (GUM),[16,17] and so on, the model-guided design of the theoretical structures of thiolate-protected gold nanoclusters have become increasingly feasible. Taking GUM as an example, the structures of the gold cores in Au(SR) can be viewed as several elementary blocks of triangular Au3 and tetrahedral Au4, obeying the dual rule packing or fusing together. As a consequence, based on GUM, the gold cores with different sizes and morphologies can be constructed via fusing or packing the elementary blocks. Then, the thiolate ligands can be added to the designed gold cores to form the complete structures of the thiolate-protected gold nanoclusters based on the interfacial interaction between thiolate ligands and gold core in known gold nanoclusters. Following this way, the full picture of one-dimensional (1D) and two-dimensional (2D) growth modes of Au28+4(SR)20+2 (n = 0–8) nanoclusters were presented based on GUM by predicting 15 theoretical structures of thiolate-protected gold nanoclusters.[10,11,18,19] Among them, the predicted Au36(SR)24 with 2D growth mode was confirmed by experimental X-ray crystallography.[19]

In this work, five new 10e thiolate-protected gold nanoclusters including three Au32(SR)22 isomers, one Au28(SR)18, and one Au33(SR)23 are theoretically predicted based on GUM. Density functional theory (DFT) calculations show that these structures have large highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps and all-positive vibrational frequencies, indicating their high stabilities.

Calculation Methods

All of the predicted structures (−R group is replaced by −H) in this work were optimized using the DFT method implemented in the Gaussian 09 program package.[20] The Perdew–Burke–Ernzerhof (PBE) and Becke’s three-parameter hybrid functional with the Lee–Yang–Parr correlation functional B3LYP,[21,22] all-electron basis set 6-31G* for H and S, and effective-core basis set LANL2DZ for Au were applied. Then, the time-dependent DFT was employed to calculate the absorption spectra of the thiolate-protected gold nanoclusters in this work.

Results and Discussion

Up to date, only three 10e thiolate-protected gold nanoclusters, i.e., Au29(SR)19 and two Au32(SR)22 isomers, were theoretically proposed. Au29(SR)19 was obtained from Au28(SR)20 and Au30(SR)18 nanoclusters via the “gold-atom insertion, thiolate-group elimination” mechanism.[12] A new atomic structure of Au32(SR)22 (referred to as Au32(SR)22-Iso1) was predicted as an intermediate structure of crystallized Au28(SR)20 and Au36(SR)24 via theoretical modulation of the double-helical cores of experimentally determined nanoclusters.[11] In addition, the structure of the Au32(SR)22 isomer (referred to as Au32(SR)22-Iso2) was obtained based on GUM.[18] It can be found that the above three 10e thiolate-protected gold nanoclusters have the same number (17) of gold core atoms (Figure ). The Au17 core of Au29(SR)19 can be viewed as four tetrahedral Au4 and one triangular Au3 elementary blocks packing or fusing together (Figure a). While both of the Au17 cores of two Au32(SR)22 isomers can be viewed as five tetrahedral Au4 elementary blocks packing or fusing together (Figure b,c), indicating that the different packing modes of the same number (5) of elementary blocks can result in Au17 cores with different morphology.[10]

Figure 1

Structural decompositions of Au29(SR)19 (a), Au32(SR)22-Iso1 (b), and Au32(SR)22-Iso2 (c). Au atoms with 1e valence electrons are presented in wine and green. Au atoms with 0.5e valence electrons are presented in gold. S is presented in yellow. The R groups were omitted for clarity.

Actually, according to GUM,[16,17] different packing modes of five tetrahedral Au4 elementary blocks can generate various cores. Here, four kinds of Au17 cores with different morphology, i.e., Au17-1, Au17-2, Au17-3, and Au17-4, are presented (Figure ). Among them, Au17-2 and Au17-4 are the cores of two Au32(SR)22 isomers (Au32(SR)22-Iso1 and Au32(SR)22-Iso2).[11,18] Therefore, new atomic structures of 10e thiolate-protected gold nanoclusters can be predicted by adding the thiolate ligands on the designed Au17 cores based on the interfacial interaction between thiolate ligands and gold core in known gold nanoclusters.

Figure 2

Different packing modes of five tetrahedral Au4 elementary blocks resulting in four kinds of Au17 cores with different morphologies, i.e., Au17-1, Au17-2, Au17-3, and Au17-4.

For the Au17-1 core, it can be viewed as removing three Au4 units from the Au26 core of Au44(SR)28 following 2D growth mode (Figure S1).[19] Since the Au17-1 core (highlighted by filling with wine color in Figure ) can be found in the Au26 core of Au44(SR)28, four [Au2(SR)3] and one [Au(SR)2] can be combined with the Au17-1 core come to form the Au17[Au2(SR)3]4[Au(SR)2] structure. Similarly, since the Au17-1 core has the same Au14 structure (highlighted by filling with wine color in Figure ) as two Au28(SR)20 isomers do,[11,18] the Au17[Au2(SR)3]4[Au(SR)2] structure can further bind with one [Au2(SR)3] and one [Au4(SR)5] to form the complete structure of Au32(SR)22 (referred as Au32(SR)22-Iso3). The result shows that the protection motifs of Au32(SR)22-Iso3 are able to from Au44(SR)28 and two Au28(SR)20 structures.

Figure 3

Structural prediction of Au32(SR)22-Iso3. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity.

For the Au17-2 core, it can be viewed as fusing one Au4 on the Au14 core of Au28(SR)20 by sharing one gold atom or removing one tetrahedral Au4 from the Au20 core of Au36(SR)24 (Figure S1).[11] Since the Au17-2 core (highlighted by filling with wine color in Figure ) can be found in the Au20 core of Au36(SR)24, two [Au2(SR)3] can be combined with the Au17-2 core to form the Au17[Au2(SR)3]2 structure, which can further bind with two [Au2(SR)3] and one [Au4(SR)5] to form the complete structure of Au32(SR)22 (referred as Au32(SR)22-Iso4) following the same way. The result shows that the protection motifs of Au32(SR)22-Iso4 can be obtained from Au36(SR)24 and two Au28(SR)20 structures. In addition, another new atomic structure of Au28(SR)18 can also be predicted by adding four [Au2(SR)3] and three [Au(SR)2] on the Au17-2 core, as shown in Figure S2. Therefore, it can be found that three predicted atomic structures, i.e., Au32(SR)22-Iso1, Au32(SR)22-Iso4, and Au28(SR)18, have the same Au17-2 core, suggesting that the structural predictions of these gold nanoclusters were achieved by redistributing the Au–S “staple” motifs on the same Au17-2 core.[23]

Figure 4

Structural prediction of Au32(SR)22-Iso4. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity.

For the Au17-3 core, it can be viewed as fusing one Au4 on the Au14 core of Au28(SR)20 by sharing one gold atom (Figure S1).[11] Similarly, the protection motifs on the Au17-3 core can be obtained from three Au28(SR)20 isomers, resulting in the structural prediction of Au32(SR)22 (referred to as Au32(SR)22-Iso5) following the same way (Figure ). In addition, another new atomic structure of Au33(SR)23 can also be predicted by adding two [Au(SR)2], two [Au2(SR)3], four [Au3(SR)4], and one [Au4(SR)5] on the Au17-3 core, as shown in Figure S3.

Figure 5

Structural prediction of Au32(SR)22-Iso5. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity.

With the newly obtained structures of five 10e thiolate-protected gold nanoclusters, i.e., Au32(SR)22-Iso3, Au32(SR)22-Iso4, Au32(SR)22-Iso5, Au28(SR)18, and Au33(SR)23, and the previously predicted two 10e gold nanoclusters Au32(SR)22-Iso1 and Au32(SR)22-Iso2, the electronic properties of these nanoclusters was obtained by density functional theory (DFT) calculations using the PBE functional. As shown in Table , the computed relative energies of three newly predicted Au32(SR)22 isomers, i.e., Au32(SR)22-Iso3, Au32(SR)22-Iso4, and Au32(SR)22-Iso5, are close to that of two previously predicted isomers, i.e., Au32(SR)22-Iso1 and Au32(SR)22-Iso2. In addition, these five Au32(SR)22 isomers have large HOMO–LUMO gaps and all-positive harmonic vibrational frequencies, suggesting the likelihood of high chemical stabilities of the three predicted Au32(SR)22 isomers. For another two newly predicted 10e gold nanoclusters, i.e., Au28(SR)18 and Au33(SR)23, DFT calculations also show that both of them have large HOMO–LUMO gaps and all-positive harmonic vibrational frequencies (Table S2). The B3LYP functional was also used to check the relative energies of five Au32(SR)22 isomers (Table S3), showing they have very close relative energies. In addition, the superatom network model using the adaptive natural density partitioning analysis was used to describe the 10e thiolate-protected gold nanoclusters,[15,24] as shown in Figures and S4. Taking the Au177+ cores of five Au32(SR)22 isomers as examples, we show that the 10e valence electrons of each Au32(SR)22 isomer are equally distributed on five tetrahedral Au4 units. Thus, the Au177+ cores of each Au32(SR)22 isomer can be viewed as a network of five 4c–2e (4c denotes 4 centers). Similar behavior can also be seen in the Au177+ cores of Au28(SR)18 and Au33(SR)23 (Figure S4).

Table 1

Computed Relative Energies, HOMO–LUMO Gaps, and the Lowest Vibrational Frequencies of Five Au32(SR)22 Isomers Using the PBE Functionala

	relative energy (eV)	HOMO–LUMO gaps (eV)	lowest vibrational frequency (cm–1)
Au32(SR)22-Iso1	0.00	1.74	6.59
Au32(SR)22-Iso2	0.39	1.58	6.63
Au32(SR)22-Iso3	0.51	1.55	10.51
Au32(SR)22-Iso4	0.55	1.74	5.06
Au32(SR)22-Iso5	0.55	1.90	6.75

The R groups are simplified by H atoms.

Figure 6

Structures of five Au32(SR)22 isomers as well as their Au177+ cores and the visualization of the valence electron distributions in the Au177+ cores. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow.

In Figures and S5, the computed optical absorption spectra of 10e thiolate-protected gold nanoclusters are presented. Figure shows that five Au32(SR)22 isomers have distinct absorption peaks. Au32(SR)22-Iso1 shows one step peak at 410 nm and two broad peaks at 532 and 602 nm, Au32(SR)22-Iso2 shows two broad peaks at 550 and 699 nm, Au32(SR)22-Iso3 shows three broad peaks at 474, 524 and 643 nm, Au32(SR)22-Iso4 shows three absorption peaks at 395, 474, and 642 nm, and Au32(SR)22-Iso5 shows two step peaks at 434 and 490 nm and two broad peaks at 537 and 629 nm. The distinct absorption peaks of five Au32(SR)22 isomers suggest they are all distinct isomers. In addition, the Kohn–Sham (KS) orbital energy levels of each 10e nanoclusters are also presented (Figures and S5). Taking Au32(SR)22-Iso3 as an example, the absorption peak at 524 nm mainly stems from the HOMO + 3 to LUMO + 1, LUMO + 2 and LUMO + 3 and HOMO + 4 to LUMO + 1, LUMO + 2 and LUMO + 3, and the absorption peak at 643 nm mainly stems from HOMO + 3, HOMO + 4, and HOMO + 5 to LUMO. In addition, the absorption peaks of all of the Au32(SR)22 isomers mainly involve the Au(sp) → Au(sp) transitions.

Figure 7

Computed absorption spectra and diagrams of the Kohn–Sham (KS) orbital energy levels of five Au32(SR)22 isomers. The prominent absorption peaks are highlighted in red. The R groups are simplified by H atoms.

In addition, due to the same Au17 core but different protection ligands between Au32(SR)22-Iso1 and Au32(SR)22-Iso4, the molecular orbitals from HOMO – 5 to LUMO + 5 as well as their contributions for both nanoclusters are presented in Figure and Table , respectively. Although they have the same Au17 cores, it can be seen in Figure that both Au32(SR)22-Iso1 and Au32(SR)22-Iso4 have different molecular orbitals, which can be attributed to the different protection ligands for both nanoclusters. This behavior is also reflected in their different orbital contributions in Table .

Figure 8

Molecular orbitals from HOMO – 5 to LUMO + 5 for Au32(SR)22-Iso1 (upper panel) and Au32(SR)22-Iso4 (lower panel).

Table 2

Orbital Contributions from HOMO – 5 to LUMO + 5

	Au(6sp)		Au(5d)		S(3p)
	Au32(SR)22-Iso1 (%)	Au32(SR)22-Iso4 (%)	Au32(SR)22-Iso1 (%)	Au32(SR)22-Iso4 (%)	Au32(SR)22-Iso1 (%)	Au32(SR)22-Iso4 (%)
LUMO + 5	84.69	93.49	6.38	2.97	8.17	3.21
LUMO + 4	78.23	81.62	9.33	8.29	11.87	9.60
LUMO + 3	75.89	80.91	10.48	8.34	13.08	10.41
LUMO + 2	85.04	88.68	6.37	4.95	8.26	6.04
LUMO + 1	79.81	84.15	9.58	7.40	10.32	8.18
LUMO	75.92	76.89	11.71	10.86	11.92	11.94
HOMO	42.76	42.19	41.45	41.19	15.61	16.50
HOMO – 1	36.79	57.78	42.57	30.22	20.47	11.85
HOMO – 2	44.10	38.99	38.88	41.18	16.89	19.69
HOMO – 3	45.15	41.22	37.90	41.80	16.76	16.83
HOMO – 4	44.04	55.61	36.46	32.33	19.38	11.99
HOMO – 5	52.44	61.98	33.41	25.53	14.01	12.37

Conclusions

In summary, based on GUM and the interfacial interaction between thiolate ligands and gold core in known gold nanoclusters, the atomic structures of five 10e thiolate-protected gold nanoclusters are theoretically predicted. DFT calculations suggest these predicted 10e nanoclusters exhibit high chemical stabilities. We expect that the predictions of these structures could stimulate future experimental and theoretical interests in 10e thiolate-protected gold nanoclusters.