Pengye
Liu
^{a},
Wenhua
Han
^{a},
Mengke
Zheng
^{a} and
Wen Wu
Xu
*^{ab}
^{a}Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo 315211, China. E-mail: xuwenwu@nbu.edu.cn
^{b}Laboratory of Clean Energy Storage and Conversion, Ningbo University, Ningbo 315211, China

Received
21st July 2020
, Accepted 16th September 2020

First published on 17th September 2020

In this paper, six new atomic structures of thiolate-protected gold nanoclusters, i.e. Au_{32}(SR)_{20}, Au_{40}(SR)_{26}, Au_{48}(SR)_{30}, two Au_{56}(SR)_{34}, and Au_{60}(SR)_{36}, are predicted. Considering these six newly predicted structures and six previously predicted or crystallized Au_{28}(SR)_{20}, Au_{36}(SR)_{24}, Au_{44}(SR)_{28}, Au_{52}(SR)_{32}, and Au_{60}(SR)_{36} altogether, the two-dimensional (2D) growth mode of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters is completely presented to compare with their one-dimensional (1D) growth mode. In Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with both 1D and 2D growth modes, the same number of gold-core atoms with different morphologies can be seen. Furthermore, the growth of the gold cores occurs via sequential fusion of one tetrahedral Au_{4} unit by sharing one gold atom. In addition, density functional theory calculations show that these six newly predicted gold nanoclusters following the 2D growth mode have relative energies very close to those of their isomeric structures following the 1D growth mode, large highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO–LUMO) gaps, and all-positive harmonic vibration frequencies, indicating their high stabilities. Therefore, the complete presentation of the 2D growth mode of Au_{28+4n}(SR)_{20+2n} (n = 0–8) is beneficial not only for a better understanding of the structural growth of gold nanoclusters, but also for a theoretical guidance on the prediction of new stable structures for experimental confirmation.

With the rapid increase in the number of isomeric structures of thiolate-protected gold nanoclusters, structural isomerism for thiolate-protected gold nanoclusters has become increasingly common.^{9} It is no exception for Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters. A new Au_{52}(SR)_{32} isomer has been shown to have the same number of gold-core atoms but different morphology compared with Au_{52}(SR)_{32} following the 1D growth mode.^{10} This behavior can also be seen in the predicted Au_{28}(SR)_{20} isomer.^{9} Inspired by the structures predicted for Au_{28}(SR)_{20} and the crystallized Au_{52}(SR)_{32} isomer, three new isomeric structures of Au_{36}(SR)_{24}, Au_{44}(SR)_{28}, and Au_{52}(SR)_{32} were predicted.^{11} Among them, the Au_{36}(SR)_{24} isomer was experimentally confirmed. In addition, another Au_{36}(SR)_{24} isomer was predicted to have the same core as the newly crystallized isomer.^{8} Considering these isomers altogether, a two-dimensional (2D) growth mode was identified among Au_{28+4n}(SR)_{20+2n} (n = 0, 2, 4, and 6) nanoclusters. Recently, an isomeric structure of Au_{60}(SR)_{36} obeying the 2D structural evolution was predicted by removing 6 four-coordinated μ_{4}-sulfido motifs in crystallized Au_{60}(μ_{4}-S)_{6}(SR)_{36}.^{12,13}

For convenience, Au_{28+4n}-1D-Iso1 and Au_{28+4n}-2D-Iso2/Iso3 (n = 0–8) are used to represent the Au_{28+4n}(SR)_{20+2n} (n = 0–8) isomers following 1D and 2D growth modes, respectively, as shown in Fig. 1 and S1.† When comparing the Au_{28+4n}-1D-Iso1 (n = 0–8) nanoclusters with Au_{28+4n}-2D-Iso2/Iso3 (n = 0, 2, 4, 6, and 8) nanoclusters, one can see that there are several “missing” gold nanoclusters (Fig. 1 and S1†), i.e. Au_{28+4n}-2D-Iso2/Iso3 (n = 1, 3, 5, and 7). Therefore, in order to completely present the 2D growth of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters, six new atomic structures of thiolate-protected gold nanoclusters, i.e. Au_{32}-2D-Iso2, Au_{40}-2D-Iso2, Au_{48}-2D-Iso2, Au_{56}-2D-Iso2, Au_{56}-2D-Iso3, and Au_{60}-2D-Iso2, are predicted to fill some vacant spaces. Density functional theory (DFT) calculations show that these six newly predicted gold nanoclusters with the 2D growth mode have relative energies very close to those of their isomeric structures with the 1D growth mode, large highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO–LUMO) gaps, and all-positive harmonic vibration frequencies, indicating their high stabilities.

Fig. 2 Structural prediction of Au_{32}-2D-Iso2. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity. |

Similarly, a new Au_{23} core can be obtained by fusing one tetrahedral Au_{4} on the Au_{20} core of Au_{36}-2D-Iso3 by sharing one gold atom or removing one tetrahedral Au_{4} from the Au_{26} core of Au_{44}-2D-Iso2 (Fig. 3).^{11} Then the protection motifs on the Au_{23} core can be obtained from Au_{28}-1D-Iso1 and Au_{44}-2D-Iso2, resulting in the structural prediction of Au_{40}-2D-Iso2. Following the same way presented in Fig. 2 and 3, other four new structures of Au_{48}-2D-Iso2 (Fig. S2†), Au_{56}-2D-Iso2 (Fig. S3†), Au_{56}-2D-Iso3 (Fig. S4†), and Au_{60}-2D-Iso2 (Fig. S5†) can also be obtained.

Fig. 3 Structural prediction of Au_{40}-2D-Iso2. Au atoms are presented in wine, blue, and dark green, respectively. S is presented in yellow. The R groups are omitted for clarity. |

Considering these six new structures and previously predicted or crystallized gold nanoclusters altogether, the 2D growth of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters can be completely presented, as shown in Fig. 4. In Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with both 1D and 2D growth modes, the same number of gold-core atoms with different morphologies can be seen. Furthermore, the growth of the gold cores occurs via sequential fusion of one tetrahedral Au_{4} unit (highlighted in blue color in Fig. 4) by sharing one gold atom. When the value of n reaches 5 (Au_{48}-2D-Iso2), the 2D evolutionary pathway breaks into two. In addition, based on the GUM,^{14,15} the gold cores of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with both 1D and 2D growth modes can be viewed as several tetrahedral Au_{4} elementary blocks fusing or packing together. The isomeric mechanism of the gold cores can be understood as the same number of elementary blocks with different packing modes.^{9}

It was also noted that the gold core in Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters can be described by the recently developed new polyhedral approach, in which the gold core is constituted of several tetrahedral Au_{4} and octahedral Au_{6} blocks.^{16,17} The average Au–Au distance in a tetrahedral Au_{4} block and the average Au–Au distance between two neighboring tetrahedral Au_{4} blocks in the gold cores of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with both 1D and 2D growth modes were calculated, as shown in Fig. 5. The calculated average Au–Au distance in a tetrahedral Au_{4} block is within the range of 2.80–2.90 Å, close to the Au–Au distance in bulk gold, that is, 2.88 Å. While the calculated average Au–Au distance between two neighboring tetrahedral Au_{4} blocks is within the range of 3.0–3.15 Å, the “holes” are closely related to octahedral units.^{16,17} Therefore, the gold cores of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with both 1D and 2D growth modes are composed of several compact tetrahedral Au_{4} blocks fusing together, with octahedral Au_{6} blocks among them.

With the obtained 6 structures, density functional theory (DFT) calculations using the Gaussian 09 program package were performed to obtain the electronic properties of these clusters.^{18} Specifically, the Perdew–Burke–Ernzerhof (PBE) functional, the all-electron basis set 6-31G* for H and S, and effective-core basis set LANL2DZ for Au were adopted.^{19} In order to avoid prolonged computational time, the R groups were substituted by H atoms in all calculations. However, it should be noted that the ligand effects are very important for the properties of thiolate-protected gold nanoclusters.^{20} As shown in Table 1, the computed relative energies and HOMO–LUMO gaps of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with both 1D and 2D growth modes are quite close, suggesting the likelihood of high chemical stabilities of the predicted structures. The computed harmonic vibrational frequencies of these 6 nanoclusters were all positive, indicating that the 6 structures are local minima on the potential energy surfaces. In addition, the second-difference energies of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with 1D and 2D growth modes are computed via E = [E_{(n+2)} − E_{(n+1)}] − [E_{(n+1)} − E_{(n)}], in which E_{(n)} denotes the energy of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters, as shown in Fig. 6. The zigzag curves of the second-difference energies show that the Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters for odd n are less stable than those with an even n. This behavior can be understood from the lower symmetry of the core with an odd number of tetrahedral Au_{4} blocks in the Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters for odd n compared to that of the core with an even number of tetrahedral Au_{4} blocks in the Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters for even n.

Gold nanoclusters | Isomers | Relative energy/eV | HOMO–LUMO gaps/eV | Lowest vibrational frequency/cm^{−1} |
---|---|---|---|---|

Au_{28}(SR)_{20} |
Au_{28}-1D-Iso1* |
0.00 | 1.77 | 8.87 |

Au_{28}-2D-Iso2 |
0.22 | 1.69 | 9.06 | |

Au_{32}(SR)_{22} |
Au_{32}-1D-Iso1 |
0.00 | 1.74 | 6.59 |

Au_{32}-2D-Iso2 |
0.39 | 1.58 | 6.63 | |

Au_{36}(SR)_{24} |
Au_{36}-1D-Iso1* |
0.00 | 1.88 | 8.58 |

Au_{36}-2D-Iso2* |
0.15 | 1.44 | 9.86 | |

Au_{36}-2D-Iso3 |
0.18 | 1.77 | 9.45 | |

Au_{40}(SR)_{26} |
Au_{40}-1D-Iso1 |
0.00 | 1.69 | 8.15 |

Au_{40}-2D-Iso2 |
0.46 | 1.58 | 6.58 | |

Au_{44}(SR)_{28} |
Au_{44}-1D-Iso1* |
0.00 | 1.63 | 6.57 |

Au_{44}-2D-Iso2 |
0.49 | 1.66 | 11.12 | |

Au_{48}(SR)_{30} |
Au_{48}-1D-Iso1 |
0.00 | 1.55 | 8.39 |

Au_{48}-2D-Iso2 |
0.31 | 1.47 | 9.59 | |

Au_{52}(SR)_{32} |
Au_{52}-1D-Iso1* |
0.00 | 1.47 | 7.58 |

Au_{52}-2D-Iso2* |
0.08 | 1.47 | 6.74 | |

Au_{52}-2D-Iso3 |
0.00 | 1.50 | 9.11 | |

Au_{56}(SR)_{34} |
Au_{56}-1D-Iso1* |
0.00 | 1.36 | 7.41 |

Au_{56}-2D-Iso2 |
0.16 | 1.41 | 7.66 | |

Au_{56}-2D-Iso3 |
0.19 | 1.39 | 5.97 | |

Au_{60}(SR)_{36} |
Au_{60}-1D-Iso1 |
0.00 | 1.33 | 7.17 |

Au_{60}-2D-Iso2 |
0.69 | 1.28 | 6.09 | |

Au_{60}-2D-Iso3 |
0.09 | 1.36 | 8.46 |

Besides the GUM,^{14,15} the previously developed superatom network model using the adaptive natural density partitioning (AdNDP) analysis can also be used to describe the Au_{14+3n}^{(6+n)+} of Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with both 1D and 2D growth modes, as shown in Fig. 7 and S6.†^{21,22} Taking Au_{35}^{13+} of Au_{56}-2D-Iso2 as an example, it is observed that the 22e valence electrons of Au_{56}-2D-Iso2 are equally distributed on eleven tetrahedral Au_{4} units. Thus, the Au_{35} core of Au_{56}-2D-Iso2 can be viewed as a network of eleven 4c-2e (4c denotes 4 centres). Similar behaviour can also be seen in other gold nanoclusters (Fig. 7 and S6†).

In Fig. 8 and S7,† the computed optical absorption spectra of all Au_{28+4n}(SR)_{20+2n} (n = 0–8) nanoclusters with both 1D and 2D growth modes are presented. It can be seen that the prominent absorption peaks of 799 nm for Au_{52}-1D-Iso1, 605 and 785 nm for Au_{52}-2D-Iso2, and 856 nm for Au_{56}-1D-Iso1 can well reproduce the experimental peaks at 800, 563, 762, and 845 nm, respectively, indicating the reliability of the theoretical methods employed in this study.^{5,7,10} Furthermore, the profiles of the absorption spectra and the locations of the prominent absorption peaks for Au_{28+4n}(SR)_{20+2n} (n = 0–8) isomers are distinctly different, suggesting that they are all distinct isomers. In addition, the two prominent absorption peaks (664 and 826 nm) of Au_{52}-2D-Iso3, two prominent absorption peaks (682 and 849 nm) of Au_{56}-2D-Iso2, two prominent absorption peaks (662 and 831 nm) of Au_{56}-2D-Iso3, two prominent absorption peaks (656 and 856 nm) of Au_{60}-2D-Iso2, and two prominent absorption peaks (694 and 896 nm) of Au_{60}-2D-Iso3 await future experimental confirmation.

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## Footnote |

† Electronic supplementary information (ESI) available: The gold cores of previously crystallized and predicted gold nanoclusters, structural prediction of Au_{48}-2D-Iso2, Au_{56}-2D-Iso2, Au_{56}-2D-Iso3, and Au_{60}-2D-Iso2, the visualization of the valence electron distributions in the Au_{14+3n}^{(6+n)+} of Au_{28+4n}(SR)_{20+2n} (n = 0–5) nanoclusters, the simulated optical absorption spectra of Au_{28+4n}(SR)_{20+2n} (n = 0–5) isomers, and cartesian coordinates of predicted thiolate-protected gold nanoclusters. See DOI: 10.1039/d0nr05439a |

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