External-field regulated superatoms

ABSTRACT

As a special class of stable atomic clusters, the superatom has become an exciting research topic in recent decades. They can mimic the chemistry and physics of individual atoms in the periodic table and find potential applications in a variety of fields. Traditional strategies for superatom design, however, have their own limitations. Herein, we review recent progress in the discovery of novel methodologies for superatom design, namely external-field regulated strategies (EFRS). We begin with a description of the basic concept of the superatom and the conventional electron-counting rules for superatom design, followed by a discussion of recent exploration about external-field regulated superatoms, where the oriented external electric field (OEEF), the ligand field, and the solvent field are presented. In the concluding section, we discuss the benefits and challenges of the EFRS together with some future research topics.

KEYWORDS:

• Superatoms
• external-field regulated strategies (EFRS)
• atomic clusters
• superhalogen
• superalkali

1. Introduction to superatoms

The past 40 years have witnessed the rapid development of cluster science in both the gas-phase and condensed-phase research about the atomically precise syntheses and potential applications [1–22]. As a bridge between atoms and bulk materials, atomic clusters are special species consisting of several to hundreds of atoms, whose diverse properties and functionalities are found to be related with their adjustable composition, shape, size, and quantum confinement effect [23–34]. This unique discovery has paved the way for the development of novel building blocks for the cluster assembly nanomaterials with tailored properties.

In this realm, a new era began when it was realized that some specific clusters featuring definite composition and size can mimic the physicochemical properties of individual elements in the periodic table. These clusters are termed as ‘superatoms’, which have potential in broadening the traditional two-dimensional (2D) periodic table to the three-dimensional (3D), replacing noble metals or significantly increasing the dimensionality of building blocks in the material design. In principle, the possibilities for designing superatoms are boundless, thereby rendering the 3D periodic table potentially infinite [22]. Following the suggestion of the theoretical superatom concept by Khanna and Jena [35] and the experimental discoveries by Castleman et al. [36], different kinds of superatoms, including superhalogens, superalkalis, rare earth superatoms, magnetic superatoms, non-noble metal superatoms etc., have been successively proposed and identified. Al₁₃ featuring the 1S²1P⁶1D¹⁰2S²1F¹⁴2P⁵ Jellium shell is a typical and famous superatom. The electron affinity (EA) of Al₁₃ (3.62 eV) [37] is similar to that of the Cl atom, which can be considered as a superhalogen. Particularly, in the superatomic framework, superhalogen and superalkali are the two most explored categories owing to their clear and simple criteria. Superalkalis are clusters featuring lower adiabatic ionization potentials (AIPs) than alkali atoms (3.89–5.39 eV) [38], while superhalogens represent a class of clusters whose adiabatic electron affinities (AEAs) are higher than those of halogen elements (3.06–3.62 eV) [39] in the periodic table. These two kinds of superatoms have been the subject of extensive research over the past several decades, and the family of them has also been remarkably expanded due to their fundamental significance and potential applications as super-oxidizers and super-deoxidizers.

This concise review highlights recent advancements in the construction of superhalogens and superalkalis, with a specific focus on novel strategies known as external-field regulated strategies (EFRS). Initially, traditional methods for designing various superatoms are presented. Subsequently, we delved into the discussion of several external-field methodologies, including the oriented external electric field (OEEF), ligand field, and solvent field, which serve as innovative approaches. Finally, a brief summary is presented with perspectives on the advantages of these EFRS and future research interests.

2. Traditional and novel regulated strategies in designing superatoms

2.1 Traditional strategies in superatom design

Back in 1981, Gutsev and Boldyrev suggested a MX_k + 1 formulation for constructing superhalogens, in which M is the metal atom, X is the halogen atom, and k is the highest valence of the metal atom [40]. In this case, LiF₂ serves as an exemplary illustration of a halogen atom. Building upon this, the same authors proposed that a cluster featuring one more electron than the shell closure configuration, e.g., Li₃O, Na₃O etc., exhibit characteristics akin to alkali atoms [39]. Consequently, superhalogens and superalkalis can be regarded as superatoms, as they imitate the chemical behavior of halogen and alkali atoms, respectively. The explicit concept of superatoms was first proposed by Khanna and Jena in 1992 [35], and since then, a significant body of research has been conducted to elucidate the fundamental science behind such a concept [1,36,41–57]. Various traditional electron-counting rules (ECRs) have been attempted to design superatoms, including the Jellium rule, Wade-Mingos rule, octet shell closure rule, 18-electron rule and so on. Here, we will first briefly discuss these traditional rules in the superatom design.

2.1.1 The Jellium rule

In the Jellium rule, a metal cluster can be conceptualized as two interconnected subsystems: the valence electrons and a positively charged ionic core. In the ordinary Jellium model framework, the ionic structure of the cluster is substituted with a uniform and spherically symmetrical distribution of positive charge. The electronic states of metal clusters correspond to delocalized orbitals 1S²1P⁶1D¹⁰2S²1F¹⁴ … , and the clusters demonstrate enhanced stability when the number of the valence electrons corresponds to a filled electronic shell [22]. The first metal cluster system that adheres to the Jellium rule is the Na clusters. In the Knight and co-workers’ experiments [58], the clusters with 8, 20, 40, 58, … Na atoms exhibit stronger abundance in the mass spectrum, which are termed as ‘magic’ clusters. The enhanced stability of these magic numbers was attributed to the electronic shell closure in the spherical Jellium model. Another classical example, which conforms to the Jellium model, is the Al₁₃¯ cluster featuring the 1S²1P⁶1D¹⁰2S²1F¹⁴2P⁶ electronic shell. The increased stability of this star cluster was originally observed by Castleman et al. [59]. Correspondingly, the neutral Al₁₃ cluster with 39 valence electrons needs one more electron to fill its 2P subshell, just like a halogen atom needs one more electron to close its np⁵ atomic shell. Hence, Al₁₃, whose EA was measured to be about 3.62 eV [37], behaves as a halogen atom, and can be considered as a typical superhalogen. Moreover, the superatomic characteristics of other clusters, like Au₂₀ [60], ligated clusters [54,57,61], Ti@Si₁₆ [62,63] and so on, can also be attributed to the Jellium rule.

2.1.2 The Wade-Mingos rule

The Wade-Mingos rule is another effective strategy in designing superatoms, which is originally proposed by Wade and Mingos, and works well in the polyhedral borane clusters (B_nH_m) [64–66]. In this rule, the valence electrons are separated into skeletal and external electrons, where the former form the cage bonding while the latter are responsible for covalent bonds with external ligands. Herein, 2n + 2, 2n + 4, and 2n + 6 electrons are needed to form closo, nido, and arachno boranes, in which n is the number of vertices in the borane polyhedron. B₁₂H₁₂^2- is a prime illustration of a closo-borane cluster, exhibiting a perfect icosahedral structure and ranking among the most stable dianions. Another example is the CB₁₁H₁₂ cluster. This cluster should mimic the chemistry of a halogen because it requires one more electron to satisfy the Wade-Mingos rule. Further theoretical study demonstrates its superhalogen characteristics because the EA of CB₁₁H₁₂ was calculated to be about 5.39 eV [67]. Similar phenomena also exist in the MB₁₂H₁₂ (M = Li, Na, K, Rb, and Cs) clusters, which are all superhalogens [67]. In addition, other clusters, such as Al₄H₆, Sn₁₂^2-, and Pb₁₂^2-, are also found to obey the Wade-Mingos rule [68–70].

2.1.3 The octet shell closure rule

The octet rule is a simple electron-counting rule, which describes the chemistry of elements with a low atomic number (<20) [71,72]. Noble gas atoms exhibit chemical inertness as a result of their complete outer s² and p⁶ electron shells. Conversely, halogen and alkali atoms are chemically reactive due to their deviation from the octet rule, with halogens having one electron less and alkalis having one electron more than required to satisfy this rule. The formula proposed by Gutsev and Boldyrev for designing superhalogens and superalkalis made use of such an octet electron-counting rule [39,40]. An example of the superhalogen is the LiF₂ cluster with an EA value of 5.45 eV [73], which is much larger than that of the F atom (3.40 eV). Multiple halogen atoms can also be attached to the metal atom to form superhalogens. As for AuF₆, its EA is as high as 8.6 eV [74]. In addition to metal clusters, the usage of the octet rule in constructing superhalogens can be extended to non-metallic clusters too. BH₄ and CN are typical superhalogens with VDEs of 4.42 and 3.86 eV, respectively [75,76]. Similarly, a cluster, which has one extra electron than needed to meet the octet rule, should behave as an alkali atom. The Li₃O cluster is just this case, and possesses an IP of 3.54 eV, which is lower than that of the Li atom (5.39 eV) [77]. More intriguingly, a kind of cluster featuring higher EA values than the superhalogen can be formed by decorating a metal atom of valence k with (k +1) superhalogens, which is named as hyperhalogens [78].

2.1.4 The 18-electron rule

The 18-electron rule is usually employed to design stable ‘magic’ superatoms involving the transition-metal (TM) atoms. Analogous to noble gas atoms, the 18-electron TM complexes are considered to achieve the electronic shell closure [79]. Some examples are Cr(C₆H₆)₂, Mo(CO)₆, [Fe(CN)₆]^4- and so on. This rule also works in the charged clusters, like TaAu₁₂¯ [80]. This cluster is very stable, and its EA is 3.76 eV, which is an all metal superhalogen.

Note that, due to the word limitation, we have not included other rules, such as the aromatic rule, isovalent rule, and multiple electron-counting rule etc., in this concise review. However, despite their successful application in constructing superatoms over the past few decades, these conventional strategies have clear limitations, as discussed above. That is, these traditional methodologies focus on changing the compositions or the number of valence electrons of parent clusters, representing methods of altering the clusters’ intrinsic properties in the superatom design. Therefore, they are relatively complicated and inconvenient to manipulate, especially in experiments. Given this fact, it would be a significant advancement if one could conveniently regulate the electronic properties of clusters without changing their intrinsic properties. This has promoted researchers, including our own group, to examine the potential of various external fields in modulating the electronic properties for the purpose of designing novel superatoms, which may also boost the potential applications of superatoms.

2.2 EFRS in superatom design

2.2.1 The OEEF in the superhalogen design

Lately, OEEF has captured more spotlight as a potential candidate for future green and smart reagents in synthetic chemistry and chemical biology [81]. Theoretically, the Shaik group has made great contributions in exhibiting the strong power of the OEEF in breaking chemical bonds, controlling reaction activity and so on [82,83]. Recent advanced STM technique employed by Aragonés et al. demonstrated the theoretically predicted catalytic capability of the OEEF in the Diels-Alder reaction, in which the OEEF strength generated by STM is relatively strong ranging from 0.3–1.0 V/ų [84]. Moreover, OEEF was also introduced into the field of cluster science very recently to regulate the electronic and optical properties of metal clusters [85,86]. It was observed that the first hyperpolarizability of some cluster compounds, i.e., (NLi₄)(BF₄) and (BLi₆)X (X = BeF₃ and BF₄), can be significantly increased by applying the OEEF with the intensity from 0 to 121 × 10⁻⁴ au [85]. Additionally, Li et al. found that some all-metal electrides can act as infrared (IR) nonlinear optical (NLO) switches upon the introduction of the OEEF that can drive a long-range excess electron transfer, in which the switching mechanism is a distinct nonbonding evolution named electronic structure isomerization [86].

The capability of the OEEF in regulating the electronic structures of metal clusters and designing superatoms was first attempted by our group theoretically [87]. The naked Au₁₉ and Au₂₀ (Figures 1(a–d)) clusters were taken as model systems, and density functional theory (DFT) was employed to examine the effect of OEEF on their electronic structures and properties. The EA values of these two model clusters were observed to continuously increase with the increment of OEEF (Figures 1(c,d)). As for Au₂₀, its EA value lifts to 3.75 eV at F_+z = 0.018 au, enabling it to behave as a superhalogen (Figure 1d). Moreover, the average Au-Au distances (Figure 1b) and the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO gap) in Au₁₉ are almost invariant under different OEEF intensities, indicating that the geometrical and energetic stabilities can be well maintained during the application of OEEF. These findings demonstrate that the OEEF can indeed regulate the electronic properties of metal clusters while maintaining their stability, providing a new way to design novel superhalogens.

Figure 1. Geometrical and electronic properties of model Au clusters under OEEF [87]. (a) Optimized geometry of Au₁₉ without OEEF, (b) variation of different Au-Au distances (a, b, c, and d in Å) in Au₁₉ under OEEF, and (c) and (d) theoretical EA values (in eV) of Au₁₉ and Au₂₀ as a function of different OEEF intensities (in au). Adapted with permission from ref 87. Copyright 2002 American Chemical Society.

Apart from the regulation effect on the clusters’ electronic properties, the OEEF can also lead to the oriented charge transfer along the electric field direction (Figure 2a), which further influences the reaction activity. It was observed that the OEEF works like a hand pushing electrons from the bottom of Au₁₉ to the top, which makes the top Au₃ moiety experience the largest electron-withdrawing process (Figure 2a). Such an electron aggregation process on Au₃ can further accelerate the CO oxidation reaction on it since it was found that the activation energy of the rate-determining step (E_a1, the OCOO moiety formation process) in the LH mechanism of the CO oxidation reaction significantly decreases following the monotonic enhancement of the OEEF intensities (Figures 2(b,c)). The 0.36 eV activation barrier without the OEEF drops to 0.10 eV upon the introduction of a 0.008 au OEEF, making it possible to oxidize CO at a low temperature. Interestingly, there exists an excellent linear relationship between OEEF intensities and E_a (Figure 2d), implying that the applied OEEF can precisely alter the reaction barrier at will.

Figure 2. The effect of the OEEF on charge transfer and CO oxidation reaction [87]. (a) NBO charge analysis for different regions under OEEF in Au₁₉, the reaction pathway of CO oxidation in the LH mechanism on Au₁₉ (b) without OEEF and (c) in different OEEF intensities, and (d) the reaction energy barriers under different OEEF intensities (in au). Adapted with permission from ref 87. Copyright 2002 American Chemical Society.

Similar situations also exist in the Ag₁₉ cluster [88]. That is, the non-superhalogen Ag₁₉ cluster can behave as a superhalogen upon the application of the OEEF because the original 3.00 eV EA value of Ag₁₉ in the absence of OEEF can go up to 3.88 eV at a 0.024 au F_+z (Figure 3a). It is known that one extra electron occupies the LUMO of the neutral cluster to form the corresponding anion. Therefore, the LUMO level of the neutral cluster governs the capability of attracting electrons of the cluster, relating with the cluster’s EA value. Thus, based on the calculations about the one-electron energy levels of the neutral cluster under different OEEF intensities (Figure 3b), it is suggested that the enhancement of the EA values of Ag₁₉ stems from the downward shift of the electronic spectrum caused by the introduction of the OEEF. Also, the calculated correlation between the EA values and the LUMO energy levels in Ag₁₉ under different OEEF intensities, which has a perfect linear relationship (Figure 3c), provides further evidence about the nature of the observed increment of the EA values of Ag₁₉ under OEEF. More importantly, for both the Au₁₉ and Ag₁₉ clusters, theoretical results show that a well-fitted polynomial formula could be obtained by fitting the calculated EA values with the OEEF intensities (Figures 1c and 3a), which means that one can obtain any desired EAs on the fitted curve by adjusting suitable OEEF intensities. This finding intriguingly exhibits the precise and continuous nature of the OEEF on the regulation effect of the electronic properties of metal clusters.

Figure 3. The effect of OEEF on the electronic properties of Ag₁₉ [88]. (a) Calculated EA values, (b) one-electron energy levels (in eV), and (c) correlation between the EA values and the LUMO energy levels of the neutral Ag₁₉ cluster under different OEEF intensities (in au). Adapted with permission from ref 88. Copyright 1993 Elsevier.

Additionally, the regulation effect of the OEEF in the superhalogen construction also works in other cluster systems including the tungsten carbide cluster (W₄C₄) [89], the zirconium oxide cluster (Zr₃O₃) [90], the niobium nitride cluster (Nb₂N₂) [38], and the manganese boride cluster (MnB₆) [91], which demonstrates the universality of this external field in the superatom design.

2.2.2 The ligand field in the superalkali and superhalogen design

The liquid-phase atomically precise cluster synthesis has experienced a rapid development during the past decade. Various metal clusters have been synthesized experimentally, including gold clusters, silver clusters, and other transition metal clusters etc [22]. However, due to their high surface Gibbs free energy, naked metal clusters are always highly reactive, which are easy to agglomerate forming bigger nanoparticles. Thus, the ligation strategy is a universal approach in the chemical synthesis of metal clusters, which can stabilize the naked clusters. Except for the stabilization effect, various ligands are utilized to regulate the electronic properties of metal clusters recently, and even employed to construct novel superhalogens and superalkalis.

The electron-donating ligands PH₃ and PEt₃ were attached to an experimentally synthesized Ni₉Te₆ cluster, in which eight PH₃ and PEt₃ ligands connected to the Ni sites (Figure 4a) [92]. The bare Ni₉Te₆ cluster has a high AIP value of 5.87 eV. However, it was observed that the attachment of eight PH₃ and PEt₃ ligands significantly decrease its AIP to 4.64 and 3.36 eV, respectively, both featuring the superalkali characteristics. The electronic energy spectrum (Figure 4b) reveals that, upon the ligation, the entire spectrum of Ni₉Te₆ goes to higher energies, where the electrons in the HOMOs of these ligated clusters are easier to be ionized. Moreover, in the ligation process, it was demonstrated that, in addition to the covalent bonding, the ligands can be thought of creating a crystal field due to the excess negative charge. Also, the shift of the HOMO and peaks (Figure 4c) indicates that the presence of ligands induces an internal electrostatic coulomb potential well by charging the Ni₉Te₆ that lifts its quantum states. Apart from the regulation of the electronic properties, the ligation process can also affect the magnetic properties of the cluster (Figure 4d).

Figure 4. The (a) optimized structures of Ni₉Te₆ and Ni₉Te₆(PEt₃)₈, (b) calculated one-electron energy levels in the Ni₉Te₆, Ni₉Te₆(PH₃)₈, and Ni₉Te₆(PEt₃)₈ clusters, (c) PDOS of the 3d Ni and p Te states of the bare Ni₉Te₆ and Ni₉Te₆ in the presence of six fictitious point charges together with the PDOS between the 3d-Ni, p-Te, and p-P states for Ni₉Te₆(PH₃)₈, and (d) energy landscape for the magnetization direction as a function of ϕ and θ. Adapted with permission from ref 92. Copyright 2002 American Chemical Society.

As mentioned above, modulation of the shell filling is a traditional strategy in designing superatoms. The species with one more or one less electron than the shell closure configuration usually behave as a superalkali or superhalogen. Interestingly, by employing the DFT calculations, Khanna et al. showed that the ionization energy of metal clusters featuring both filled and unfilled electronic shells can be significantly lowered by attaching suitable ligands [93]. The N-ethyl-2-pyrrolidone (EP = C₆H₁₁NO) ligand was attached to several typical Al or doped Al clusters, which are 39 e (Al₁₃ and BAl₁₂), 40 e (Al₁₃¯, CAl₁₂, and SiAl₁₂), and 41 e (PAl₁₂) clusters (Figure 5a). It was observed that the ligation process can continuously decrease the adiabatic ionization energies (AIE) of these clusters with distinct valence electrons, leading to the formation of superalkalis (Figure 5b). More importantly, different from traditional methodologies, such a AIE reduction process does not alter the superatomic states of these clusters (Figure 5c). Additionally, the AIE lowering was attributed to the upward shift of the electronic spectrum of the ligand induced charge transfer complexes via crystal field like effect. Similar phenomena also exist in other ligated clusters, which demonstrate that such a ligand field is indeed a novel strategy in remarkably altering the electronic properties of metal clusters while maintaining their geometrical and electronic structures [94].

Figure 5. Lowering the ionization energy of metallic clusters by organic ligands without changing shell filling [93]. (a) The optimized geometries of Al₁₃^0/-1 and MAl₁₂ (M = B, C, Si, and P) clusters, (b) the adiabatic ionization energies of the bare Al₁₃(EP)_n and MAl₁₂(EP)_n (M = B, C, Si, and P; n = 0–3) clusters, and (c) molecular orbital iso-surfaces of CAl₁₂(EP) cluster marked with the angular characters. Adapted with permission from ref 93. Copyright 2000 Nature Publishing Group.

Different from the OEEF that only works well in constructing superhalogens, it has been demonstrated that the ligand field can regulate the electronic properties of metal clusters in producing both the superalkalis and superhalogens. In one of our recent reports [95], ligands with different electron characteristics, i.e. the electron-donating PH₃ and electron-withdrawing CO ligands, were connected to the cubic W₄C₄ cluster to form the W₄C₄L_n (L = CO, PH₃; n = 1–6) complexes (Figure 6a). The AEAs of the clusters increase monotonically with the continuous addition of the CO ligand, while the PH₃ ligation process reduces the AIP of W₄C₄ (Figure 6b). And obviously, upon the ligation of six CO ligands, W₄C₄(CO)₆ turns to behave as a superhalogen since it has an AEA value of 3.23 eV (Figure 6b), which is higher than that of the I atom (3.06 eV). The superatomic properties of these ligated clusters were further verified by exploring the behavior of the salt generated via the superatoms. In this salt, a significant charge transfer (−0.95 |e|) takes place between W₄C₄(CO)₆ and the Na atom, resulting in an obvious ionic bond pattern (Figure 6c). These findings clearly demonstrate that appropriate ligands can manipulate the electronic properties of clusters for the construction of the superhalogen and superalkali species. Meanwhile, the potential of assembling the cubic W₄C₄ cluster into a cluster solid nanomaterial was also examined (Figure 6d), which exhibits a good stability and the metallic property [95].

Figure 6. The ligand field strategy in the superatom design [95]. The (a) optimized ground states of the neutral W₄C₄(CO)_n and W₄C₄(PH₃)_n (n = 1–6) clusters, (b) theoretical AEAs and AIPs of the ligated W₄C₄L_n (L = CO, PH₃; n = 1–6) clusters, (c) optimized ground-state structures of NaW₄C₄(CO)₆, NaW₄C₄ and the cut-plane LOL of the NaW₄C₄(CO)₆ cluster, and (d) the model of the W₄C₄ cluster solid. Adapted with permission from ref 95. Copyright 2001 the Royal Society of Chemistry.

In addition to the theoretical design, this kind of ligated cluster can also be produced in experiments [96,97]. By using Co₆S₈(PEt₃)₆ as a parent compound, Liu et al. synthesized the CO substituted Co₆S₈(PEt₃)_6-x(CO)_x clusters, which were then brought into the gas phase to form the corresponding anions by employing an infrared desorption/photoelectron-emission/supersonic helium expansion source [96]. Mass spectrometry (Figure 7a) confirms the successful production of these clusters with x up to 3, which are Co₆S₈(PEt₃)₅(CO)¯, Co₆S₈(PEt₃)₄(CO)₂¯, and Co₆S₈(PEt₃)₃(CO)₃¯, and corresponding photoelectron spectra of these ligated clusters were also obtained (Figure 7b). According to the experimental spectra and optimized ligated clusters (Figure 7c), it was observed that the clusters’ EA and VDE increase with the number of the CO ligands (Figure 7d), which demonstrates the tunability of the electronic spectra of these ligated clusters.

Figure 7. Turning the electronic properties via ligand substitution [96]. The (a) structure of Co₆S₈(PEt₃)_6-x and mass spectrum of Co₆S₈(PEt₃)_6-x(CO)_x¯ produced utilizing IR/PE anion source, (b) negative ion photoelectron spectra of Co₆S₈(PEt₃)_6-x(CO)_x¯ (x = 0–3), (c) theoretical lowest-energy structures of the Co₆S₈(PEt₃)_6-x(CO)_x¯ (x = 0–3) clusters, and (d) incremental differences in the experimental AEA values, the theoretical AEA values, and the LUMO values of Co₆S₈(PEt₃)_6-x(CO)_x, each with respect to Co₆S₈(PEt₃)₆. Adapted with permission from ref 96. Copyright 2001 the Royal Society of Chemistry.

Other examples of the ligand field induced superatom formation have also been discovered, demonstrating the feasibility and universality of the ligand field in designing novel superatoms [38,98–102].

2.2.3 The solvent field in the superhalogen construction

Apart from the aforementioned OEEF and ligand field, another external field that has recently garnered our interest is the solvent field [103]. Typical pure and doped gold cluster anions (Au_n^¯ (n = 2, 4, and 8) and MAu₈^¯ (M = Ge, Sn)) featuring various geometries, including the linear, planar, and 3D structures, were taken as model systems (Figure 8a). Compared with the gas phase, it was observed that polar solvents can obviously increase the VDEs of these model clusters giving rise to the superhalogen anions, and the VDE values increase following the enhancement of the static dielectric constants of the solvents (Figure 8b). The one-electron energy level calculations also demonstrate that the downward shift of the electronic spectrum accounts for the changes from non-superhalogen to superhaogen in different solvents (Figure 8c). These findings provide solid evidence that the solvent field can be considered as an effective external field in the superhalogen modulation, in which it can significantly increase the ability of the electron-withdrawing of gold cluster anions while maintaining their geometrical and electronic structures (Figure 8d).

Figure 8. Geometrical and electronic structures of anions under solvent [103]. The (a) theoretical lowest-energy geometries of the Au_n^¯ (n = 2, 4, and 8) and MAu₈^¯ (M = Ge, Sn) clusters, (b) calculated VDE values and (c) one-electron energy levels of the Au₄¯ cluster as well as (d) the average Au-Au bond lengths (in Å) of Au_n¯ (n = 2, 4, and 8) and MAu₈^¯ (M = Ge, Sn) in the gas phase and different solvents. Adapted with permission from ref 103. Copyright 1993 Elsevier.

In addition to model systems, a stable and experimentally identified gold nanocluster was also adopted to explore the regulation effect of the solvent. It was found that the cluster’s VDE increases from the original 2.36 eV to 3.22 eV by simply introducing the H₂O solvent, reaching the superhalogen zone (Figure 9a). This shows that the solvent field is effective in the superhalogen formation for both the simplified model naked clusters and practical ligand-protected nanoclusters. Moreover, by utilizing the DFT calculations with the explicit solvation model and the QM/MM simulations, it has been demonstrated that the solvent field can indeed enhance the electron-binding ability of the nanocluster anion rather than the ability of the solvent, H₂O here, itself (Figure 9b).

Figure 9. The (a) optimized structure of the Au₁₈(SCH₃)₁₄¯ cluster in water and VDE values together with HOMO levels of Au₁₈(SCH₃)₁₄^¯ in the gas phase and water, (b) optimized geometries of Au₁₈_nc@82H₂O^¯ and Au₁₈_nc@43H₂O@500H₂O^¯ used in the explicit solvent model and QM/MM MD simulation, and (c) schematic figure of the solvent field regulated superhalogen [103]. Adapted with permission from ref 103. Copyright 1993 Elsevier.

2.2.4 Dual external field (DEF) strategy in superatom design

Considering the fact that different external fields, e.g., the OEEF, the ligand field, and the solvent field, have the capability in regulating the electronic properties of metal clusters in constructing novel superatoms, it spurs our further interests in examining the modulation effect of the combination of multiple external fields. To this end, a dual external field (DEF) strategy was proposed by our group to combine the ligand field and OEEF to design hyperhalogen (Figure 10a) [104]. The design idea is to attach suitable ligands to metal clusters to obtain the superhalogen first, followed by the introduction of the OEEF to realize the formation of the hyperhalogen (Figure 10a). Different numbers of electron-withdrawing BO₂ ligands were linked to the model Au₈ cluster to form the ligated clusters (Figure 10b). Au₈(BO₂)₂ was estimated to have the highest EA value (3.60 eV), which exhibits the superhalogen characteristic (Figure 10c). Strikingly, the EA value of the Au₈(BO₂)₂ cluster dramatically soars to 6.73 eV upon the application of a 0.018 au OEEF, a second external field, giving rise to the hyperhalogen (Figure 10d). Therefore, it is obvious that the proposed DEF strategy, i.e., the ligation and the OEEF synergistic strategy, indeed can efficiently manipulate the electronic properties of clusters resulting in the formation of hyperhalogen, which represents a novel methodology in the hyperhalogen design. Furthermore, to further testify the applicability and universality of the proposed DEF strategy in more practical systems, an experimentally synthesized Ag₁₇ nanocluster was adopted (Figure 10e), and it is apparent that the proposed DEF strategy also works in more practical systems. Thus, the proposed DEF strategy provides a potential methodology for constructing hyperhalogens in the chemical synthesis of atomically precise clusters. That is, applying suitable ligands to first synthesize stable ligand-protected clusters followed by imposing the OEEF via the mechanically controllable break junction (MCBJ) technique.

Figure 10. Dual external field-engineered hyperhalogen [104]. The (a) schematic description of the concept of the proposed DEF regulation strategy for constructing the hyperhalogen, (b) optimized ground states of the neutral and anionic Au₈(BO₂)_n (n = 1−4) clusters, (c) calculated EA values of the Au₈(BO₂)_n (n = 1−4) clusters, (d) EA values of the Au₈(BO₂)₂ and Au₈ clusters under different OEEF intensities, and (e) geometry of the neutral Ag₁₇_nc as well as the EA values of Ag₁₇_nc under different OEEF intensities. Adapted with permission from ref 104. Copyright 2002 American Chemical Society.

3. Conclusions and outlooks

In this concise review, we first present the basic concept of the superatoms, and discuss traditional electron-counting rules (ECR), including the Jellium shell closure rule, the Wade-Mingos rule, the octet shell closure rule, and the 18-electron rule, for the superatom design. The focus of the present review is the recently advanced external-field regulated strategies (EFRS) in the theoretical design of superatoms. Combining the research work conducted by our group and other peers, various external-field methodologies, including the OEEF, the ligand field, and the solvent field, are described and discussed. Admittedly, due to the limitations of space, we do not provide an exhaustive review of all outstanding work related to cluster science and superatoms.

As discussed above, conventional ECRs need to change the clusters’ intrinsic properties, e.g., the compositions and the number of valence electrons of parent clusters, which is relatively complicated and inconvenient to regulate in both the gas-phase and liquid-phase experiments. In comparison to existing ECRs, the EFRS offers distinct advantages as a novel and noninvasive methodology. It not only enables the regulation of electronic properties in metal clusters, forming superatoms, but also ensures the preservation of their geometrical and energetic stability. From the point of view of the atomically precise cluster synthesis experiments, ligands, which can stabilize the naked cluster core, and solvents are indispensable and conveniently available. Thus, the discovery of the regulation effect of the ligand field and solvent field in dramatically altering the electronic properties of clusters without destroying their geometrical and energetic stability is of great significance. However, a drawback of these two external field strategies is the challenge of precisely adjusting the electronic properties of clusters. Because the number of the ligands that we can attach to the naked cluster cores is integral and different polar solvents have fixed static dielectric constants, the electronic properties, e.g., the EA and IP values, that these external fields can modulate are discontinuous. For instance, the theoretical EA values of Co₆Te₈(PEt₃)_n (n = 1–6) are six fixed values because one can just attach integral ligands to the naked core in the cluster synthesis. Such a drawback could be overcome by the OEEF methodology, which can realize the precise and continuous regulation of the electronic properties of clusters because the OEEF intensity is continuously adjustable. The capability of the precise and continuous regulation of the OEEF represents a significant advantage over conventional ECR strategies. However, unlike the ligand field and solvent field that are easy to achieve in the liquid-phase synthesis, the manipulation of the OEEF on precisely controlling the conformation of clusters in the liquid-phase experiments is still a challenge. From this point of view, in experiments, one needs to fix the cluster materials between gold STM tips or on the substrates, and the directions of the OEEF could be adjusted based on the actual alignment of the clusters. Recently advanced scanning tunneling microscope break junction (STM-BJ) and mechanically controllable break junction (MCBJ) methods may help in this case [84,105,106].

The EFRS opens a new avenue in the superatom design without disturbing the clusters’ intrinsic properties. However, as a new concept, further development is required to establish its theoretical framework. Some fundamental research topics, including understanding the inherent nature of the regulation effect of EFRS, exploring other valid external fields, and effectively coupling multiple external fields, are deserved to be comprehensively examined in the future.

Funding

This work is supported by the National Natural Science Foundation of China (NSFC) (Nos. 92161101, 21603119), the Taishan Scholars Project of Shandong Province (ts201712011), the Innovation Project of Jinan Science and Technology Bureau (2021GXRC032), the Instrument Improvement Funds of Shandong University Public Technology Platform (No. ts20220201), the Key Research & Developmental Program of Shandong Province (2021CXGC011202), the Natural Science Foundation of Shandong Province (ZR2020ZD35), the Young Scholars Program of Shandong University (YSPSDU, 2018WLJH48), the Qilu Youth Scholar Funding of Shandong University. The HPC Cloud Platform of Shandong University is also acknowledged for the support of theoretical calculations in some research references in this review.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [Nos. 92161101, 21603119]; Natural Science Foundation of Shandong Province [ZR2020ZD35]; Innovation Project of Jinan Science and Technology Bureau [2021GXRC032]; Taishan Scholars Project of Shandong Province [ts201712011]; Instrument Improvement Funds of Shandong University Public Technology Platform [ts20220201]; Key Research & Developmental Program of Shandong Province [2021CXGC011202]; Young Scholars Program of Shandong University [2018WLJH48], the Qilu Youth Scholar Funding of Shandong University. The HPC Cloud Platform of Shandong University is also acknowledged for the support of theoretical calculations in some research references in this review.