† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. U1804121 and 11304167).
Cluster science as a bridge linking atomic molecular physics and condensed matter inspired the nanomaterials development in the past decades, ranging from the single-atom catalysis to ligand-protected noble metal clusters. The corresponding studies not only have been restricted to the search for the geometrical structures of clusters, but also have promoted the development of cluster-assembled materials as the building blocks. The CALYPSO cluster prediction method combined with other computational techniques have significantly stimulated the development of the cluster-based nanomaterials. In this review, we will summarize some good cases of cluster structure by CALYPSO method, which have also been successfully identified by the photoelectron spectra experiments. Beginning with the alkali-metal clusters, which serve as benchmarks, a series of studies are performed on the size-dependent elemental clusters which possess relatively high stability and interesting chemical physical properties. Special attentions are paid to the boron-based clusters because of their promising applications. The NbSi12 and BeB16 clusters, for example, are two classic representatives of the silicon- and boron-based clusters, which can be viewed as building blocks of nanotubes and borophene. This review offers a detailed description of the structural evolutions and electronic properties of medium-sized pure and doped clusters, which will advance fundamental knowledge of cluster-based nanomaterials and provide valuable information for further theoretical and experimental studies.
A cluster is defined as an ensemble of chemically bonded atoms or molecules, and is an intermediate between isolated atoms or molecules and bulk solids or polymers. Since the properties of the clusters depend on the cluster size, their studies led to significant amount of work in different research areas such as catalysis, biomedicine, optoelectronics, etc. Earlier experimental studies were focused at alkali metal clusters,[1] ionic clusters,[2] and interactions of small gas species with positively charged clusters.[3] Based on the mass-spectrometry data, Knight et al.[1] developed the spherical jellium model, which became classic and significantly contributed[4] to cluster science.
A number of functional clusters are produced experimentally, which can serve as building blocks for nanomaterial applications.[5–9] For example, the novel, efficient, green catalysts based on the single atom cluster, which can be synthesis by different strategies.[10–14] The size-dependent monodisperse samples of Au11 cluster[15] have been reported by mass-selected soft-landing method.[10] A class of novel catalysts consists of Pt single atoms and cluster deposit on the surface of graphene nano-sheets have been synthesized by Atomic Layer Deposition (ALD) method, which are manifested much higher reactivity for methanol oxidation and superior CO tolerance compared with traditional Pt/C catalyst.[11] Meanwhile, the single-atom Pt/FeOx catalysts[12] are synthesized by using co-precipitation method, which have a great potential to riches the noble-metal catalysts in chemical industry based on single atom or cluster. Wu et al.[16] have synthesized a novel bimetal nanocluster Pt@Ag24 with a different electronic gap, which offer novel insights for rational design of metal nanoclusters and provide a guidance for follow-up works.[17,18]
Up to now, many theoretical models have been proposed for studying the geometric structures and electronic properties of clusters, such as shell model,[19] superatom,[20–24] and superlattice.[25,26] The ground state structures of clusters are the prerequisite to understand the corresponding electronic properties and tune their practical applications in next stage. Despite the enormous progress that has been made, the true lowest-energy structures in medium-sized cluster are, however, still a challenging problem. On one hand, the global minima are subtle sensitivity for the selected density functional theory, and the conventional method used for small clusters is not practical for larger clusters. On the other hand, the lowest-energy structures in the whole potential energy surface are exponentially increased with the number of atoms in the cluster increasing.[27,28] Here, we focus on the cluster structure predication through Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO)[29–31] method. Its effectiveness and validity have been demonstrated in many cluster systems.[27,32–37]
CALYPSO method has its own performances for predication cluster structures, which includes five main steps.[31] The efficiency of Particle Swarm Optimization (PSO) algorithm used in CALYPSO method for cluster structure predication is relied on the ‘self-improving’ strategy, which can overcome large barriers in the global potential energy landscapes.[38–40] About 48 point groups are randomly adopted to restrict the generation cluster structures. Meanwhile, the bond characterization matrix (BCM) technique based on the distances of all bond in the cluster structure is utilized to estimate the similar structures. As for each generation, the metropolis criterion[41] has been applied during the local optimizations, and the optimized structures can be accepted when the energy are lower than their parent structures. Generally, in our cluster structure searches, we have generated 30 generation structures. Each generation contains 50 structures, 70% of which are generated from the previous generation structure using PSO, other 30% are produce randomly to ensure continuous diversity. For each cluster size, about 1500 low energy isomers are obtained, and the top 50 low energy structures with energy differences less than 3 eV are collected as candidates for further re-optimization, in which the high-level ab initio calculations with a large basis set or precise pseudopotentials are adopted at each cluster size. More detailed process of CALYPSO structure predications can be found in our recent publication.[42]
The alkali metal Li cluster is a classic benchmark to understand various electronic properties of simple metal clusters since Li atom possesses only one valence electron.[43–46] Geometric structures of medium or large sized Lin (n = 20, 40, 58) magic clusters have been identified by CALYPSO method.[31] The Li20 cluster with Cs symmetry is the lowest energy structure and in good agreement with previous work.[47] The perfect 45-atom polyicosahedron along with five missing vertex atoms and mackay icosahedron motif are characterized to be the lowest-energy structures for Li40 and Li58 clusters, respectively.[23] Na is another free-electron-like metal.[48–51] The geometric and electronic properties of medium sized (range from 10 to 25 atoms) Na clusters have been studied by CALYPSO method and DFT calculations.[32] Our results have confirmed most geometric structures of previous studies,[50] and also identified a novel honeycomb-like structure of Na20 cluster. The honeycomb-like Na20 cluster is chemically stable with a large energy gap, which is in good agreement with Na mass spectra experiment.[1]
The alkaline earth metals always involve chemical bonding as typical interaction by their ns and np valence orbitals.[52,53] A detailed chemical bonding analysis of Mg cluster indicates that Mg17 cluster is the first locally
Boron, with electron configurations of 1s22s22p1,[62] shows predominantly bonding capacity. It is neighbor of carbon element that can easily form fullerene-like structures with sp2 and sp3 bond.[46] The sized-selected B cluster has attracted much interest due to the intriguing geometrical structures and unique electronic properties. The global minima planar or quasi-planar structures in both neutral and anionic clusters have investigated up to 38 atoms.[63–65] The 38-atom B cluster is uncovered by CALYPSO method. It is highly chemical stability with a large energy gap and a high double aromaticity.[66] We have also accomplished some works in this research field. Unlike previous works, we mainly focused on the guest elements doped into the host B clusters by using CALYPSO method. Our new geometrical structures are shown in Figs.
![]() | Fig. 3. Geometries of low-energy configurations of transition metal atom (Zr, Mo, Ru, Ta) doped medium-sized B clusters. |
![]() | Fig. 4. Simulated photoelectron spectrum of ![]() |
In Fig.
![]() | Fig. 5. Chemical bonding pattern of ![]() |
![]() | Fig. 6. Simulated photoelectron spectrum of the ground state of ![]() |
![]() | Fig. 7. Chemical bonding pattern of ![]() |
Silicon is the most important semiconducting material in the microelectronics industry. If current miniaturization trends continue, minimum device features will soon approach the size of atomic clusters. Thus, understand the size-depend structure evolution and electronic properties of Si clusters is of certain technological interest.[81,82] We have explored the growth behaviors of medium sized neutral, anionic and cationic Si clusters.[27] The results indicated that the geometrical structures of Si cluster transfer form prolate structure to spherical-like geometries at n = 26 for neutral cluster, n = 27 for anions, and n = 25 for cations. The calculated results accord well with previous experimental data and theoretical findings.[81,82] Nb is a typical positive element, which can dope into Si clusters to tune their electronic properties. Based on CALPSO method, we have obtained an anionic NbSi12 cluster,[34] as shown in Fig.
Binary alloy clusters have been subjected to intensive studies due to their unexpected stabilities and unique electronic properties. We have adopted CALYPSO method to investigate the Mg–Al binary alloy clusters,[90] as shown in Fig.
Size-selected clusters with dozens of or hundreds atoms possess catalytic and adsorption properties. For example, nano-sized Au particles, which exhibit abnormal strong catalytic capabilities in a great deal of chemical reactions, have been the subject of intense research. Among these studies, the CO oxidation catalyzed by nanometer Au particles has been extensively investigated not only for the mitigation of toxic pollutant CO but also for some other practical applications, such as developing CO sensors and improving the efficiency of CO2 lasers. Previous studies have suggested that CO reacts with molecularly adsorbed oxygen on catalytic Au particles to form carbonate species, which are then converted to CO2. It is therefore important to deeply understand the interaction mechanizations of Au clusters with CO. However, in contrast to the enormous progress that has been made in studies of anionic Au clusters, the physical pictures of neutral clusters are much less clear, due to the shortage of direct experimental probes for the uncharged species. Therefore, more detailed studies are needed to further understanding whether and how these neutral clusters interact with CO, CO2, O2, and other molecules.
CALYPSO, an efficient structure prediction method, has made significant contribution to uncover numerous intriguing clusters.[95–107] A large number of high symmetry geometric structures with goodish stability and novel bonding patterns are discovered, which are the perfect embryos for nanotubular, borophene and other building blocks. For example, 1D metalloboronanotube
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