The superatomic state beyond conventional magic numbers: Ligated metal chalcogenide superatoms

Throughout history, one of the prime objectives in physical sciences has been to identify periodic patterns in the chemical and physical behavior of matter and to seek the physical principles underlying such similarities.^1–3 The Periodic Table is the leading example in which the observed periodic behavior in the physical and chemical properties of atoms led to the periodic classification of the elements.¹ The subsequent developments of the atomic model allowed for a microscopic understanding of such behaviors and furthered our knowledge on how such behaviors could be modified. A similar challenge is now faced by the developments in the field of clusters and nanostructures. In particular, the field of cluster science continues on a rapidly expanding trajectory due to two considerations in large measure. First, developments over the past three dozen or so years have shown that novel behaviors emerge as the cluster size is reduced to the sub-nanometer scale. The electronic, chemical, and optical properties are all found to change with size, where even the addition or removal of a single atom leads to significant changes in a cluster’s properties.^4–6 This includes clusters of nonmagnetic solids being found to become magnetic,⁷ reactive metals becoming inert,^8–10 and noble metals becoming catalytically active.¹¹ The second consideration is the connection to the field of nanoscale science, where clusters offer the exciting prospect of serving as building blocks for new materials whose desired properties may be tailored through the selection of size and composition.^12–16 Due to the incredibly complex chemical space and diverse properties found in clusters, there is a critical need for identifying a central paradigm that could unify or integrate the enormous and diverse body of knowledge. Can one develop a Mendeleev-like classification¹ that could open the pathway to a grand unification of a large body of empirical data? In this Perspective, we examine how the conceptual basis of superatoms provides a unifying framework for identifying and classifying a wide range of atomic clusters. As the origin of the periodic behaviors of the elements lies in periodic shell closing, periodic electronic and geometric shell closures in metal clusters have been used to classify clusters as superatoms with a well-defined valence.^13,17,18 The parallel periodicities in atoms and metal clusters have proven to be a powerful organizing principle in understanding the properties of metal clusters and ligand-protected metal clusters.^13,19–21 However, for the superatomic concept to serve as a central paradigm, it must be extended beyond simple metal clusters. For this reason, there is a particular focus on extending the superatomic model to ligated metal-chalcogenide clusters.^16,21

In this Perspective, we start by outlining the initial ideas that led to the conceptual basis for defining superatomic states for clusters of simple metals where a confined, nearly free electron gas picture provides a reasonable description.¹³ This model led to the identification of halogen, inert, multiple valence, and magnetic superatoms in a grand collective effort between theory and experiment.^9,22–25 Unlike many other areas, many of the developments were led by theoretical predictions.¹³ This model also served to provide a fundamental understanding of cluster assemblies based on ligated gold and other metals.^20,26–29 However, recent tantalizing experimental developments have led to the stabilization of solids combining ligated metal-chalcogenide clusters with counterions.^16,30–35 These developments are based on wet chemical methods, enabling the synthesis of molecular building blocks composed of a central core of transition metals and chalcogens ligated with various ligands. These building blocks are highly stable, can be independently prepared in solutions, have charge donor/acceptor characteristics, and can form either unary or binary solids with complementary units maintaining the identity of their internal atomic structure.^36,37 These classes of stable ligated clusters cannot be described within a confined nearly electron gas and merit a new framework for their description. This Perspective is directed toward these developments and how the previous superatomic model can be extended by identifying periodic properties in their electronic structure and by analyzing concepts that control the properties of these new classes of superatoms. Figure 1 shows a pictorial depiction of the electronic shell structures in metallic clusters and metal–chalcogen clusters, highlighting the periodic electronic shell closures found in these two types of superatomic clusters. We show how such an understanding can enable ways of transforming their properties by changing the ligands. We demonstrate how the new motifs can be used as chemical dopants on two-dimensional semiconductors and that superatomic molecules that are fused together may be formed into nano-p–n junctions by controlling the ligands. The rest of this Perspective is dedicated to these and other applications of these superatoms.

Clusters offer a nearly endless number of possible combinations of size, compositions, and charged states, and any of these changes may result in a dramatic change in properties.¹³ The fundamental challenge is can we identify a central dogma or an organizing principle that could provide a consolidated framework for classifying the diverse range of clusters and observed behaviors. It was almost three dozen years ago that developments in experimental techniques allowed for studies on size-selected clusters in an interaction-free environment.⁴ Knight and co-workers observed variations in abundance in size-selected clusters of alkali atoms in molecular beams. They found that certain sizes were more abundant than others, and these highly abundant sizes were labeled as magic numbers in analogy with nuclear physics, where certain nuclei have higher binding energy.^4,38 In addition, the magic sizes showed higher ionization energy and low polarizability, patterns consistent with filled electronic shells.⁵ These observations led to the thinking that these periodic features emerged from the quantum confinement. A model for metal clusters was developed where nearly free electrons were confined to a sphere with a uniform positive background of the size of the cluster. The quantum states in such a confined nearly free electron gas are grouped into shells that order as 1S, 1P, 1D, 2S, 1F, 2P, …. The model accounted for the observed magic numbers in Na_n clusters at sizes 2, 8, 18, 20, 34, 40, …, along with higher ionization energies and lower polarizabilities associated with the clusters with filled shells.^5,39 The origin of the electronic shell structure comes from the orthogonality requirements for the nearly free electron gas, so if the cluster is spherical, the orthogonality constraint leads radial and angular nodes, just like in the atom. Note that, for the classic magic numbers to be effective, the valence electrons must behave as a free electron gas, and the cluster must be spherical. More direct evidence that the electronic shells control chemistry came from experiments on the reactivity of aluminum cluster anions with oxygen.^8–10 Bulk aluminum is highly reactive with oxygen, but experiments on Al_n^- showed that clusters, including Al₁₃^-, Al₂₃^-, …, were resistant to reacting with oxygen. This could be accounted for by the fact that these sizes correspond to filled electronic shells of 40 and 70 electrons, respectively, thus providing a direct chemical link to the electronic shell picture. In this model, Al had an electronic configuration of 1S², 1P⁶, 1D¹⁰, 1F¹⁴, and 2P⁶. This electronic configuration resembled that of a halogen anion and raised the possibility that Al₁₃ could behave like a halogen atom; by adding a single electron, the cluster has an effective valence of zero and becomes highly stable. This connects the idea that a cluster with an effective zero valent superatomic state was not merely electronically stable but also chemically stable. Theoretical studies, indeed, predicted an electron affinity of 3.34 eV that was later confirmed by experiments.^13,40 Joint experimental and theoretical studies also confirmed that Al₁₄ with 42 valence electrons behaved like an alkaline earth element.⁹ These studies led to a flurry of work identifying clusters mimicking multiple valence and magnetic elements.^{23,24,41–43} Furthermore, ligand protected gold clusters also fit the taxonomy of the superatom concept, with them containing a closed electronic shell.^20,28 The fact that many such clusters whose properties could be predicted based on their proximity to a highly stable zero valent state demonstrates that the superatom concept was applicable to a large number of metallic clusters.

While the above studies focused on the electronic properties, studies on larger clusters led to the importance of geometrical structures on stability and chemical behaviors. For example, abundance spectra in larger alkali and alkaline earth systems showed enhanced stability of clusters with complete geometrical shells.^44,45 The geometrical structures are also found to affect chemical behaviors. For example, in studies on the reactivity with polar reactants, such as water (H₂O) or methanol (CH₃OH), certain aluminum cluster anions that have closed electronic shells were found to be highly reactive.^46–49 Clusters with open geometric shells have defect-like structures that result in an uneven charge distribution over the surface of the cluster, which results in active sites and enhances reactivity. When the cluster forms a more compact and symmetric structure, the charge distribution becomes more even, quenching the active sites and making all sites on the cluster equally reactive. The importance of closed geometric shells is especially important in ligand protected metal clusters. The addition of unbalanced ligands may result in induced active sites, and ligands may activate adatoms, causing the etching of ligand protected clusters that do not possess closed geometric shells.^50,51 The second organizing principle for understanding the reactivity and stability of clusters is that clusters with closed geometric shells have significantly reduced reactivity, while clusters with geometries that are akin to defects enhance the reactivity.

The above discussion shows that both electronic and geometric shells are important for understanding the stability, redox properties, reactivity, and other properties of clusters. Symmetric compact clusters have electronic states grouped into electronic shells, and the occupancy of electronic shells determines the chemical behavior of clusters. Like atoms, clusters with filled shells are more stable, while clusters with unfilled shells tend to exhibit chemical valence as atoms. Hence, superatoms are clusters whose chemical and electronic properties are dominated by their proximity to a zero valent state, just like the valence of atoms in the Periodic Table. These features that were originally realized for the confined nearly free electron gas are not specific to metal clusters. Therefore, while the nature of electronic interactions leading to filled electronic shells may vary depending on the cluster type, numerous stable clusters do exhibit well-defined valence. Hence, these clusters can be regarded as superatoms, forming the third dimension of the Periodic Table. Previous studies by Khanna and co-workers had proposed superatoms resembling alkali, alkaline earth, and multiple valence atoms.^9,22,23,52 In a later development, Khanna and co-workers extended these concepts to magnetic superatoms, a development that has attracted considerable attention.^24,41 The superatom analogy for a confined electron gas has also led Reber and Khanna to propose a periodic table of cluster orbitals, Fig. 2, much like the Periodic Table for atomic orbitals.¹⁸ 

While these initial developments focused on clusters of metallic elements, it is important to ask how the concept can be extended to other classes of clusters. We now show how these considerations can be extended to metal-chalcogenide clusters.

Ligated metal-chalcogenide clusters are an important class of clusters that have drawn tremendous attention in recent years due to the synthesis of many crystalline materials in which these clusters serve as the building blocks. Many metal-chalcogenide clusters have been synthesized, including Co₆Se₈(PEt₃)₆, Co₆Te₈(PR₃)₆, Cr₆Te₈(PEt₃)₆, Fe₆S₈(PEt₃), Ni₉Te₆(PEt₃)₈, Ni₆Se₅(PR₃)₈, Ni₉Te₆(CO)₈, Re₆Se₈(PEt₃)₄Cl₂, and Co₉Te₆(CO)₈.^{16,21,35,53–56} The ligated clusters consist of a central core of transition metals and chalcogens and are stabilized by ligands, such as phosphines, CO, or other ligands. These interesting classes of superatoms are found to be highly stable and can be prepared in solutions using synthetic chemical methods. Furthermore, the ligands offer an additional pathway to tuning the properties of a cluster, either through stabilizing a closed electronic shell, inducing active sites, or controlling the donor–acceptor characteristics.^57,58 Depending on the ligand, they can have charge donor/acceptor characteristics that allow them to form a variety of solids when combined with complementary ions, including C₆₀, maintaining the identity of the metal-chalcogenide core. In Fig. 3, we show a few representative solids that have been formed using these clusters. As these atom-precise clusters can be assembled into materials, a vast library of superatomic clusters with unique and tunable physical and chemical properties have been found, and understanding the electronic properties of these clusters may help in understanding the collective behaviors of these superatom assembled materials.

We want to analyze the electronic structure of metal–chalcogen clusters and identify if these clusters have periodic closed electronic shells that can lead to superatomic states with a well-defined valence. As stated previously, the key criterion for a cluster to be considered a superatom is that the cluster has a well-defined valence. For the valence to be identified, we need to find valence electron counts that correspond to enhanced stability. Bonding in metal-chalcogenide clusters is a mixture of covalent bonding between the metal and the chalcogen and bonding and charge transfer complexes between the metal and the ligand. For this reason, a confined nearly free electron gas picture is not applicable to determine the electronic counts that lead to stable species. The reason that the nearly free-electron gas models do not apply in metal–chalcogen clusters is that the orbitals are formed from multiple atomic d orbitals, which have two intrinsic nodes, so the construction of orbitals that follow the radial and angular node structure of simple metal clusters is not possible. In principle, these clusters can be stabilized via two paradigms: the oxidation state of the metal atoms within the cluster may form a closed electronic shell or a shell of degenerate or nearly degenerate delocalized orbitals over the entire symmetric cluster may lead to a large HOMO–LUMO gap, which also leads to the stability associated with a closed electronic shell.^59,60 Stabilization may also occur via mixed valence or Jahn–Teller distortion,^61,62 but this will result in a symmetry breaking, and the cluster will no longer be octahedral.^63,64 To do this, we have combined our studies of many octahedral metal-chalcogenide clusters of the form M₆X₈L₆. Se was used as the chalcogen for all these clusters, and we focused on the 4d and 5d transition metals (Y–Pd and La, Hf–Pt). The theoretical methods we use are described in our work on phosphine ligands, in which we use the PBE gradient corrected functional⁶⁵ and the TZ2P basis set with the ADF⁶⁶ set of codes.⁶⁷ The electron counts were done by counting all the s and d electrons of the transition metal, six valence electrons from the Se, and two electrons per CO and PH₃ ligand. Some discussions in the field do not count the s-electrons of the chalcogen, so their electron counts are 16 lower than the counts listed here.⁶⁸ Figure 4 shows our calculated HOMO–LUMO gaps for different ligands and for the 4d and 5d series. Note that there are periodic electron counts with large HOMO–LUMO gaps that correspond to 76, 96, 100, and 114 valence electrons, with secondary peaks at 78 and 88 valence electrons. Octahedral M₆X₈L₆ clusters with 76 valence electrons are stable due to the local oxidation state of the atoms being +3. For example, Y₆Se₈(PH₃)₆²⁺ has a HOMO–LUMO gap of 1.77 eV. The valence of Se is −2, and the valence of Y is +3, so the cluster stabilized with a charge state of +2. This corresponds to one mode of stability, local stabilization of the atomic electronic structure. The local oxidation state is confirmed by Hirshfeld analysis of the atoms as most metal atoms in metal–chalcogen clusters are roughly neutral, while the charge on the Y₆Se₈(PH₃)₆ cluster is +0.4e⁻, and the Mulliken⁶⁹ charge shows a very similar s and d occupation to a Y(PH₃)₃⁺³ complex. A second mode of stabilization is through the filling of closely packed states that have the same energy due to the high octahedral symmetry of the cluster or similar energies due to coincidental degeneracy. Examples of electron counts with such large HOMO–LUMO gaps include 96, 100, and 114 valence electrons. The peak at 88 valence electrons is due to a Jahn–Teller distortion^61,62 that breaks the symmetry and leads to the different metal atoms having different charge states. On the other hand, the electron counts of 76, 78, 96, 100, and 114 have O_h symmetry. This result demonstrates that there are electron counts in metal–chalcogen clusters that correspond to enhanced electronic stability.

To understand the origin of the electronic shells in octahedral metal–chalcogen clusters, we have analyzed the electronic structure of four highly stable clusters of this category, Sc₆Se₈(CO)₆ Mo₆Se₈(CO)₆, Re₆Se₈(CO)₆²⁺, and Co₆Se₈(CO)₆. We chose these clusters due to their large HOMO–LUMO gap and because the Mo, Re, and Co based clusters are among the most commonly studied metal–chalcogen clusters in experiments.^70,71 We will consider these clusters to have 76, 96, 100, and 114 valence electrons within the metal–chalcogen cage by counting all the s and d electrons of the transition metal, six valence electrons from the Se, and two electrons per CO ligand. The energy of the molecular orbitals is plotted in Fig. 5 and shows the HOMO–LUMO gap of the clusters. Due to the highly symmetric structure of the clusters, there is a large degree of degeneracy in the electronic states, so when a group of closely packed states has enough electrons to fill that grouping, the cluster has a large HOMO–LUMO gap. Sc₆Se₈(CO)₆²⁺ was the first cluster that we found to have a reasonably large HOMO–LUMO gap of 1.22 eV with 76 valence electrons. We can consider this to be the electronic core of the octahedral clusters, and the large gap is due to Sc being in the +3 oxidation state, while Se is in the −2 oxidation state. We note that the LUMO is an A_1g orbital, with a decent gap until the next T_2u orbital. We note here that in these metal-chalcogenide clusters, the valence electrons do not behave as a nearly free electron gas. The high degree of degeneracy is due to their octahedral symmetry, and this leads to a tight packing of orbitals with gaps in-between. For this reason, assigning n and l quantum numbers to the orbitals in the metal–chalcogen clusters is not physically accurate, so, instead, we assign the orbitals using the irreducible representation of the orbital. For this reason, adding two electrons results in a cluster with a reasonably large HOMO–LUMO gap and 78 valence electrons. The next highly stable cluster is Mo₆Se₈(CO)₆, which has 96 valence electrons, and the gap is due to the A_1g, T_2g, T_1u, and T_2u orbitals being filled. The Mo₆Se₈ cluster has been synthesized many times and is a common metal-chalcogenide cluster.^70,71 Next, we note that the LUMO is an E_g orbital, two degenerate unfilled orbitals that make up the LUMO, and a large gap above these two states is seen in Mo₆Se₈(CO)₆. Hence, if you add four electrons to the cluster to get 100 valence electrons, one would expect high stability. Indeed, the octahedral metal–chalcogen cluster with the largest HOMO–LUMO gap is Re₆Se₈(CO)₆²⁺, which has exactly four more valence electrons than Mo₆Se₈(CO)₆. Re₆Se₈(CO)₆²⁺ has a HOMO–LUMO gap of 1.71 eV and is known in the literature to have a strong drive toward the +2 oxidation state. In Re₆Se₈(CO)₆²⁺, there is a grouping of three orbitals, a small gap, and a dispersed grouping of orbitals. The addition of 14 electrons leads to Co₆Se₈(CO)₆ with 114 valence electrons and has a HOMO–LUMO gap of 1.58 eV and is a well-known highly stable metal-chalcogenide cluster. The stability comes from the filling of the A_2g, T_1g, and T_2u orbitals. If we add additional electrons, by going to Ni, the cluster no longer tends toward octahedral structures, so the trend in octahedral metal–chalcogen ends at this point. These results demonstrate that metal-chalcogenide clusters have enhanced electronic stability at certain electron counts, and for this reason, the properties of such clusters are strongly affected by the stabilization they gain when they reach this valence. Thus, metal-chalcogenide clusters may be considered to have a well-defined valence, allowing their designation as superatoms.

Surface ligands are usually employed to protect clusters against reacting with outside reagents; however, recent studies have revealed that the ligands can also be used to control their redox properties.^{57,58,67,72,73} This effect in clusters is analogous to the way that ligands on a surface can result in band bending that changes the work function of the surface.^74–76 Studies in our group have shown that even the weakly interacting ligands can dramatically change the redox character by transforming metallic, semiconducting, or metal-chalcogenide clusters into donors with ionization energies that can be substantially lower than even the ionization energies of alkali atoms.⁶⁷ Through these changes, the superatomic clusters can be transformed into donors that can donate even multiple electrons with low ionization energies. A critical analysis indicated that the decrease in ionization energies results from what could be classified as initial and final state effects, as shown in Fig. 6. The initial state effect derives from the surface dipole and the formation of bonding/antibonding orbitals that shifts the HOMO of the bare cluster, as shown in Figs. 6(a) and 6(b). The final state effect stems from the enhanced binding of the donor ligand to the charged cluster and the electronic relaxation, as shown in Fig. 6(c).

The effect of ligation on the redox properties of clusters was investigated using theoretical studies that examined a vast range of metallic, transition metal, and semiconductor clusters. The objective was to understand the role of ligands in stabilizing multiply-charged ionic particles and the microscopic mechanisms underlying the interaction with ligands. In particular, we wanted to understand how a charge transfer ligand, such as phosphine, affects the ionization energies of clusters or nanoparticles. We initially considered the trimethylphosphine, PMe₃, ligands, which are a strong σ-donor generally increasing the electron density in the cluster core through the lone pair of the phosphorus. The investigations focused on the adiabatic ionization energy of metallic clusters: Au₇,⁷⁷ Au₁₁, Au₁₃Cl₂,⁷⁸ Ag₁₁, and Al₇;²³ an Al₄O₆ cluster as an illustrative of an insulator;^79–81 Ga₁₂N₁₂⁸² and Zn₁₂O₁₂⁸³ as a representative of semiconductor clusters; Co₆, Pd₆, and Pd₇ as a representative of transition metal clusters; and Mo₆Te₈⁷⁰ corresponding to the typical metal-chalcogenide clusters.¹⁶ Figure 7 shows the ground state geometry and ionization energy (I.E.) of bare and fully ligated clusters considered in this study. It is interesting to note that the addition of ligands universally lowers the ionization energy of clusters irrespective of the nature of cluster. It was found that the initial state effect is larger in simple metal and noble metal clusters, while the final state effect played a dominant role in the transition metal and transition metal-chalcogenide clusters.

For the present Perspective, we are particularly interested in the effect of ligands on the electronic spectrum of metal-chalcogenide clusters. We illustrate our findings by considering a Co₆Te₈(PEt₃)₆ cluster that has a closed electronic shell with a high HOMO−LUMO gap (1.24 eV). The Co₆Te₈(PEt₃)₆ cluster has a low ionization energy and also a low electron affinity. Replacement of PEt₃ ligands by CO was found to monotonically increase the ionization energy of the cluster from 4.91 to 7.03 eV. The increase in the ionization energy is followed by a similar increment in the electronic affinity values from 1.19 eV for Co₆Te₈(PEt₃)₆ to 2.60 eV for Co₆Te₈(CO)₆. The unusual feature, in this case, is that irrespective of the combination of CO or PEt₃ ligands, the ligated clusters always have a closed shell electronic configuration with a high HOMO–LUMO gap ranging from 1.24 to 1.39 eV. Figure 8 shows the electronic levels for various combinations of PEt₃ and CO. Note that the main effect of adding CO is a downward shift in the electronic spectrum as PEt₃ ligands are successively replaced by CO. By changing the ligand, the polarity of the interaction between the 4s orbital of cobalt and the lone pair of the ligand change, but the effective valence electron count remains the same. Thus, the change in the electronic character is not associated with a change in the electron count but to an upward or downward shift in the electronic spectrum that can be rationalized as the attached ligands, forming a Coulomb well that surrounds the cluster and may alter the energy of the states depending on the donor–acceptor characteristics of the ligand. The donor–acceptor concept explains this by the donor ligands, such as phosphines, raising the electronic spectrum, and acceptor ligands, lowering the spectrum. This is a powerful concept that can be used to control the electronic spectrum and the binding characteristics of the cluster’s electronic and catalytic applications.^84–88 Before we go into this, we first discuss the experimental confirmation of the theoretical findings.

To put the redox effect of ligands into perspective, we also studied the effect of ligands on the multiple ionization of the clusters. Figure 9 plots the first, second, third, and fourth ionization potential of the Co₆Se₈(PEt₃)₆, Co₆Te₈(PEt₃)₆, and Co₆Se₈ clusters and the K, Ca, Al, and Si atoms. The ionization of the phosphine ligated clusters is significantly lower than that of the bare cluster in all cases, further confirming that the phosphine donor makes the ligated cluster a better donor. For comparison, we also show the ionization energy of several atoms, and we note that the fourth ionization energy of the ligated clusters is lower than the second ionization energy for the alkaline earth calcium. This shows the power of ligation and that it can create clusters that can readily donate multiple electrons.

We collaborated with the experimental groups of Professor Kit Bowen at Johns Hopkins University and Professor Xavier Roy at Columbia University to confirm the theoretical predictions about the lifting of the electronic spectrum upon addition of donor ligands (PEt₃) and lowering of the spectrum upon addition of acceptor ligands (CO).^89,90 To make the parent anions Co₆S₈(PEt₃)_6−x(CO)_x⁻ in the gas phase, a specialized infrared desorption/laser photoemission (IR/PE) supersonic helium expansion source was employed. Briefly, a Co₆S₈(PEt₃)_6−x(CO)_x sample was synthesized, and then IR laser vaporization was performed on a graphite bar that was coated with the Co₆S₈(PEt₃)_6−x(CO)_x sample. A second laser pulse struck a nearby photoemitter to generate electrons in order to make the neutral clusters anionic. This produced anionic Co₆S₈(PEt₃)_6−x(CO)_x clusters, and then, an anion photoelectron spectroscopy experiment was performed to measure the electron affinity (EA) and to probe the electronic structure of the ligated cobalt sulfide clusters. Mass spectrometry was also performed, and Co₆S₈(PEt₃)₅(CO)⁻, Co₆S₈(PEt₃)₄(CO)₂⁻, and Co₆S₈(PEt₃)₃(CO)₃⁻ were observed in the spectrum, confirming their stability. The electron affinity and vertical detachment energy increased monotonically with the increase in the number of CO ligands, which offers clear experimental evidence that CO acts as a superior acceptor and that phosphine acts as a superior donor. The anion photoelectron spectra are shown in Fig. 10 for Co₆S₈(PEt₃)_6−x(CO)_x⁻ (x = 0–3). To make contact with experiments, we modeled the electronic structure of the superatoms and then compared the calculated peaks positions with those of the anion photoelectron spectra. The photoelectron spectra offer a fingerprint of the ground state geometry and electronic states of both the neutral and anionic clusters, so this effectively tests our theoretical model. The adiabatic electron affinity (AEA) is ascertained by finding the onset of the lowest energy peak, and the vertical detachment energy (VDE) can also be ascertained from the spectra. The value of the AEA is calculated by taking the energy difference between the ground state of the anion and the ground state of the neutral cluster. The VDE is calculated by taking the energy difference between the ground state of the anion and the neutral cluster with the exactly the same structure as the anion. Both the AEA and VDE values of Co₆S₈(PEt₃)_6−x(CO)_x increase progressively as PEt₃ is replaced with CO, with the VDEs being observed to be 1.30, 1.51, 1.95, and 2.09 eV, respectively. The AEA of this superatom increasesconsistently from 1.1 to 1.8 eV as PEt₃ is replaced with CO, while the Co₆S₈ core remains the same. To test the agreement between experiment and theory, Table I shows the calculated and experimental values. Good agreement between experiments and theory is seen, which is also clear from the peak comparison in the anion photoelectron spectra shown in Fig. 10. The key result is that the AEA and both VDE values increase as PEt₃ ligands are successively replaced with CO; however, the HOMO–LUMO gap of the clusters is maintained across the cluster series [Fig. 11(a)]. The photoelectron study provides unambiguous and direct evidence that the donor/acceptor characteristics of this superatom may be tuned via ligand exchange.

The shift in the absolute values of the HOMO and LUMO and the associated shift in the electron affinities are due to PEt₃ being an electron donor, while CO is an acceptor. PEt₃ binds via a charge transfer complex mechanism and is a strong σ-donor, while CO is a π-acceptor. The donor causes an increase in charge density in the cluster core, raising the electronic spectrum, and CO is electron withdrawing, which lowers the electronic spectrum of the cluster. The raising of the electronic spectrum due to donor ligands lowers the AEA, and the addition of acceptor ligands causes a lowering of the electronic spectrum, which, in turn, leads to an increase in the AEA.

Further experimental collaborations with the research groups of Professor Kit Bowen and Professor Xavier Roy confirmed the theoretical predictions that the I.E. and electron affinity (AEA) are reduced as PEt₃ ligands are successively added to a bare cluster.⁹⁰ We again used anion photoelectron spectroscopy to probe the EA and peaks in photo-detachment spectra of a series of cobalt sulfide clusters whose ligand shells consist of differing numbers of PEt₃ ligands. In these experiments, the cluster Co₆S₈(PEt₃)₆ is synthesized and then laser vaporized on an inanimate carbon rod and then ionized with a photoemitter source, after which the cluster with different numbers of ligands are formed and can be systematically studied. Clusters of Co₆S₈(PEt₃)_x⁻ with x ranging from 0 to 6 were formed and identified via mass spectroscopy. The theoretical studies predict that the addition of charge donating PEt₃ ligands decreases the ionization energy (I.E.) and the electron affinity (E.A.) of clusters. The photoelectron spectroscopy provided measurements of the vertical detachment energy (VDE) and the adiabatic electron affinity (AEA) of anionic clusters. Figure 12 compares the experimental findings and the theoretical calculations. Remarkable agreement between theory and experiment validates the theoretical prediction that the addition of PEt₃ ligands, indeed, reduces the E.A. consistent with a lifting of the LUMO of the cluster. As the lifting of LUMO is accompanied by a lifting of HOMO, these findings also imply that it is possible to generate superdonors (clusters that can donate multiple electrons with low I.E.) or acceptors by adding charge transfer ligands to the clusters. The next step was to examine if these spectral changes could be used to create dopants or p–n junctions. We first discuss using such ligated clusters as chemical dopants in semiconductors to alter the electronic characteristics of semiconductors.

The electronic, optical, and transport properties of semiconductors can be exquisitely controlled via doping with impurities.^91–93 These impurities are implanted in intrinsic semiconductors, and the dopants can be either substitutional or interstitial. However, a limited number of dopants can be implanted in a semiconductor. Another strategy that may work around this constraint is charge transfer doping of two-dimensional semiconductors, in which molecular or cluster dopants bind to the surface and dope the thin film in which the carrier density may be controlled through the donation of carriers or through band bending effects.⁹⁴ 

Motivated by our findings that the addition of ligands can lead to clusters with tunable redox properties, we investigated if ligated chalcogenide clusters can be used as dopants to create novel semiconductors where the impurity level could be manipulated, and the clusters could donate multiple electrons. The experimental study of Yu et al. at Columbia University motivated the study of this particular system, who found that by binding Co₆Se₈(PEt₃)₆ clusters on p-type WSe₂ support, the two-dimensional WSe₂ semiconductor was converted from a p-type to an n-type semiconductor.⁹⁵ This reveals a strategy for doping two-dimensional semiconductors with superatoms clusters to control the nature of the semiconductor. Our studies were directed at understanding how a layer of WSe₂ could be doped by a superatom and how the Fermi level of the doped system could be controlled to change from p- to n-type.⁹⁶ While bulk WSe₂ is an indirect bandgap semiconductor, previous studies have shown that monolayer transition metal-chalcogenide is a direct bandgap semiconductor. We first examine the band structure of the direct bandgap monolayer of WSe₂. The generalized gradient approximation (GGA) using the gradient corrected functional proposed by Perdew et al. was used to study the electronic properties.⁶⁵ Additional calculations using the HSE06⁹⁷ hybrid functional were also performed due to the GGA functional generally finding bandgap energies that are lower than in the experiment. The PBE bandgap energy was 1.98 eV, and the hybrid HSE06 bandgap energy was 2.54 eV. For comparison, the experimental bandgap energy is measured to be 2.02 eV. As the GGA-PBE functional was found to be closer to the experimental value, the PBE functional was used for the remaining studies.

We examined the electronic structure of the metal chalcogenide superatoms bound to the WSe₂ surface to identify whether the cluster could act as a tunable charge transfer dopant. We found that Co₆Se₈(PEt₃)₆ preferred to bind as Co₆Se₈(PEt₃)₅ with the WSe₂ surface acting as the sixth ligand, as shown in Fig. 13. The Co₆Se₈(PEt₃)₅ cluster binds to the WSe₂ surface with an energy of 3.19 eV, which is much higher than the binding energy of the Co₆Se₈(PEt₃)₆ cluster. The PEt₃ ligand binds to Co₆Se₈(PEt₃)₆ with an energy of 2.45 eV, so the energetics favor the Co₆Se₈(PEt₃)₅ cluster binding to the surface where the WSe₂ surface acts as a sixth ligand. This occurs because the lone pair of Se atom in WSe₂ may act as a charge-transfer complex in effectively the same way as the lone pair of the phosphine ligands, so the support acts as a ligand. The binding of Co₆Se₈(PEt₃)₅ to the support has decreased the bandgap energy from 2.02 eV for the monolayer to a HOMO–LUMO gap of 0.52 eV for the superatom duped cluster, and after the cluster has bound, the filled donor states are located on the cluster and the unfilled acceptor states are also positioned on the superatoms. This means that electrons may be excited from the filled cluster orbitals to the empty superatomic orbitals, which will transform the surface into an n-type semiconductor. The metal-chalcogenide cluster has transferred 0.05e⁻ to the WSe₂ surface according to a Bader⁹⁸ analysis, which is due to the analysis assigning the electron lone pair of Se, rather than the Co atom on the cluster that is bound to the support. This transformation of the nature of the semiconductor to n-type simply requires the cluster linking to form a complex; no reconstruction of the semiconductor is required. Another unique property of this type of doping is that the impurity states are localized on the superatom, while in traditional semiconductors, the impurity states have a large radius due to the dielectric function of the host.

Another class of two-dimensional semiconductors that we have studied is phosphorene that has been experimentally isolated via mechanical exfoliation starting with black phosphorus.⁹⁹ It has a direct bandgap in the visible to the mid-infrared range and high hole mobility of 10⁵ cm²/(V s). Phosphorene is an interesting 2D semiconducting material because it has an ambipolar (n- or p-type semiconductor) character, and the bandgap can be optimized by the number of layers and functionalization. Our interest in phosphorene was fueled by the possibility of phosphorene nano-ribbons as they allow tunable properties by changing width, thickness, and passivation of edges. We are especially interested in nano-ribbons due to their exotic properties, including room temperature magnetism, spin density waves, and applications in photovoltaic water splitting, batteries, and interesting electronic properties, including the possibility of tuning the bandgap by varying the width of the ribbon. The possibility of individual ribbons offers the possibility of tuning the properties by selectively functionalizing the surface. Our objective is to develop nano-p–n junctions by doping nano-ribbons with selected superatoms. To demonstrate this intriguing aspect, we carried out a theoretical study to explore if the nature of a phosphorene can be controlled by supporting selected superatoms or clusters as charge transfer dopants. One strategy for this was to use ligand exchange in Re₆S₈R₅ (R = Cl, PH₃) to control the Fermi energy of the material. Chlorine is a strong electron acceptor, so exchanging the electron-donating phosphine with Cl on the cluster has a significant effect on the Fermi energy of the material. As shown in Fig. 14, for all phosphine and one Cl case, the cluster HOMO is inserted into the gap. This makes the material n-type, with the filled cluster levels approaching the conduction band of phosphorene. The addition of a second Cl results in a closed electronic shell, and we find that the HOMO of the cluster now lies below the valence band of the phosphorene sheet, while the LUMO of the cluster is above the conduction band of phosphorene. Therefore, we now have an undoped semiconductor material. The addition of third chlorine results in the LUMO of the cluster being pinned to the valence band of phosphorene, and because this cluster orbital is unoccupied, this is now a p-type material. Therefore, the ligand exchange when using Cl and phosphine ligands can result in the transformation of the material from n-type to p-type. Re₆S₈ has a strong propensity toward having two Cl and being in the +2 oxidation state, and it is possible to form other oxidation states that would lead to n-type or p-type semiconductors. Furthermore, it demonstrates that even in phosphorene with its relatively high Fermi energy, one may still transform the type of semiconductor that it is via charge transfer doping with superatoms.

The ability of ligands to control the location of the electronic spectrum of superatomic clusters can offer a strategy for inducing internal electric fields within materials.^100,101 In order to separate electron–hole pairs for photon harvesting or for directed electrical transport as in a diode to occur, a junction with an internal electric field is necessary.^102,103 At the interface between n- and p-type semiconductors, there is a difference in the chemical potential across the junction, which results in a flow of electrons across the junction, the formation of a depletion layer, and an internal electric field across the junction. Directed transport can result by changing the applied voltage, which, in turn, changes the thickness of the depletion layer. To create a cluster analog of a p–n junction, two superatomic clusters may be fused together, and then, their chemical potentials must be different. Typically, when two superatomic clusters bind together to form a fused cluster, the two clusters are the same, so there is no difference in the chemical potential and no significant dipole moment, and it will have no internal electric field. A chemical potential difference can occur when two different atom precise clusters are fused together, but this requires unrealistically precise control of chemistry. Fused dimers of ligated metal-chalcogenide clusters have been synthesized; however, how can we induce an internal electric field and control the energy levels across the fused cluster? As we have discussed, donor ligands, such as phosphine, can lower the electronic spectrum, and acceptors, such as CO ligands, can raise the electronic spectrum, suggesting that such internal electric field may be induced by unbalanced donor and acceptor ligands on opposite sides of the fused cluster.

We recently demonstrated^100,101 that large dipole moments in the fused molecular clusters could be generated by combining identical metal-chalcogenide clusters and breaking the symmetry by ligating opposite units of the fused cluster with donor or acceptor ligands. Re₈S₈L₆ was the most effective example of this phenomenon, and it has a large HOMO–LUMO gap when the cluster is in the +2 oxidation state. Therefore, we fused two Re₆S₈Cl₂ clusters as the addition of two Cl atoms leads to a +2 oxidation state and a large gap. The donor ligand PMe₃ (trimethylphosphine) was added to one side of the fused cluster to make that side of the junction a donor, and CO acceptor ligands were added to the other side of the junction, making that side an acceptor. Figure 15 shows the ground state atomic structure, HOMO–LUMO gap, electron affinity, and ionization energy of the clusters as the first four PMe₃ ligands are added to Re sites and as PEt₃ are replaced by CO. The electron affinity of Re₆S₈Cl₂(CO)₄ is 3.21 eV, which is close to the value of a halogen, so the CO ligated cluster is a strong electron acceptor, while Re₆S₈Cl₂(PMe₃)₄ has an ionization energy of 6.00 eV, making the phosphine ligated cluster a strong electron donor. Note that no matter what the combination of ligands, the cluster has a large HOMO–LUMO gap, and note that while the strength of the electron donor or acceptor characteristics changes drastically, the clusters are all closed-shell due to the effective electron count of the cluster being the same in all cases. Instead, the change in the donor/acceptor strength is due to the shifting of the electronic spectrum by the ligands. This can be clearly seen in Fig. 16, in which the absolute HOMO and LUMO of the ligated clusters are graphed.

Because the ligands may shift the chemical potential of the clusters switching the cluster from a donor to an acceptor, we fused two Re₆S₈Cl₂(L)₄ clusters and added unbalanced ligands with the donor PMe₃ on one side and the acceptor CO ligands on the other side. The interface between the two superatoms is linked via the sulfur atom of one cluster binding to the Re atom of the adjacent cluster and vice versa. Hence, one Re₆S₈Cl₂ cluster was bound with three CO acceptor, and the other side was bound with three donor PMe₃ ligands to form the Re₆S₈Cl₂(CO)₃:Re₆S₈Cl₂(PMe₃)₃ motifs. Figure 17(a) shows the structure of the used superatomic dimer with two Re₆S₈Cl₂(PMe₃)₃ motifs, Fig. 17(b) represents the mixed cluster, i.e., Re₆S₈Cl₂(PMe₃)₃:Re₆S₈Cl₂(CO)₃, and Fig. 17(c) represents the two Re₆S₈Cl₂(CO)₃ clusters. The calculated binding energies of the fused clusters are 1.67, 1.80, and 1.62 eV, respectively, which show that the fused clusters are reasonably stable. Note that the highest binding energy of the fused clusters is the case with mixed ligands, and the stability is enhanced due to the donor–acceptor pair enhanced binding. The HOMO–LUMO gaps of the clusters are 2.00, 1.11, and 1.48 eV, and they all have significant bandgap energies. To determine if the fused clusters have an internal electric field, we next examine the dipole moment of the clusters. The fused mixed cluster has a massive dipole moment of 11.2 D, while the dipole moment of the fused clusters with all PMe₃ is 0.31 D, and the fused cluster with all CO ligands is 0.30 D. The large dipole moment of the mixed ligand fused cluster is caused by the charge shift due to a strikingly strong internal electric field. To understand the dynamics of electron–hole pairs generated in the fused clusters, we calculated the optical spectra using Time Dependent Density Functional Theory¹⁰⁴ (TD-DFT). The HOMO–LUMO excitation was found to be optically weak, while the first strong absorption, which corresponds to the effective optical gas, is 1.52 eV [Fig. 17(d)]. This lowest energy strong optical absorption is caused by the eighth lowest electronic excitation because it is the lowest energy excitation with a non-negligible oscillator strength. The all CO ligated fused cluster has an optical gap of 1.50 eV, and the PMe₃ ligated fused cluster has an optical gap of 2.03 eV. The explanation for this is that in the fused cluster with unbalanced ligands, an excitation of the CO side of the cluster strongly absorbs light; however, all the lower energy excitations are optically weak. This is due to the electron and hole being separated by the internal electric field, and the resulting lack of overlap between the two states should inhibit electron–hole pair recombination.

The central question of this particular study is whether fused donor–acceptor units are analogous to a p–n junction and whether the fused clusters with unbalanced ligands are likely to be able to separate electron–hole pairs. There is a net charge transfer of 0.14e⁻ from the PMe₃ donor side to the CO acceptor side, which is again consistent with the donor–acceptor hypothesis. Next, we want to identify the location of the electron and hole in the fused clusters, so we examined the charge density of the anionic and cationic clusters. Figure 18(a) plots the isosurface of the excess charge of the negatively charged fused cluster and the excess charge is located on the CO side of the cluster at the acceptor site. Figure 18(b) plots the isosurface of the electron–hole of the cationic cluster, which is almost entirely located on the donor PMe₃ side of the cluster. This shows that the electron and hole are on the opposite sides of the fused cluster. Another canonical feature of the p–n junction is the band bending at the interface. To identify if there is such band bending between the donor and acceptor superatoms, we plotted the local density of states in the different regions of the fused cluster in Figs. 18(c) and 18(d). The acceptor side of the cluster has a negligible local charge density of states at the HOMO energy level, and the valence band energy is shifted down to be −0.49 eV on the acceptor side. The conduction band energy is 1.12 eV on the acceptor side, giving the CO side an effective bandgap energy of 1.61 eV. On the PMe₃ donor side of the fused cluster, the valence band is at the HOMO, 0.00 eV, and the conduction band is at 1.73 eV. This means that the band bending between the PMe₃ and CO side shifts up by 0.49 eV, and the conduction band shifts up by 0.61 eV on the PMe₃ side vs the CO side. Thus, the bandgap energy is maintained on both sides of the junction, but there is a significant band bending across the junction between the donor and acceptor sides of the fused cluster. This means that our cluster analog of a p–n junction has the equivalent of band bending across the interface.

To understand the electronic response and the magnitude of the band bending, an external electric field was applied to the unbalanced cluster, and the effect on the band energies was studied. Figure 19 shows the density of states as a function of the field. The effective voltage of the band bending can be found by finding the strength of the external field that cancels out the band bending in the superatomic molecule. The band bending is canceled out when the voltage across the terminal Re atoms is −1.55 V. This can be determined because the dipole moment reaches a minimum and the HOMO–LUMO gap reaches a maximum. The HOMO–LUMO gap reaches a maximum because the valence bands on both sides of the cluster are aligned at this field strength. When the applied electric field has the opposite polarity, positive toward the CO side and negative toward the PMe₃ side, the electronic spectrum on the acceptor CO side is shifted deeper in energy as compared to the PMe₃ side. This is also reduces the HOMO–LUMO gap, and the band bending from the PMe₃ valence band to the CO valence band increases to 1.19 eV, while remember it was 0.49 eV at zero field. This means that the fused superatoms could be used as a rectifier by having less resistance when the field is applied in one direction and more when the field is applied in the opposite direction. This is because the shifts in the valence and conduction bands will change the barrier and carriers will have to overcome when they cross the interface. What is notable is that this effect is due to the misalignment of states across the interface of the fused clusters and not due to the depletion layer.

To show that nanowires of fused clusters have similar electronic properties, we graph the local density of states of four Re₆S₈Cl₂L₄ clusters fused together in a wire in Fig. 20. The dipole moment is 17.6 D due to the unbalanced ligands. The band bending is even more pronounced than the dimer, with the band bending of the valence band being 1.00 eV. The majority of the band bending is at the junction, but there is some additional shift in the valence band across the outer and central ligated clusters. We also calculated the absorption spectrum of the tetramer, and it again shows that the oscillator strengths of the lower energy excitations are quite weak and that the optical gap is made up of excitations on the CO side of the tetramer. Therefore, the excited electron will be on the CO side of the molecule and the electron–hole is on the PMe₃ side of the cluster. The weak optical absorption is due to the separation of the electron and electron–hole. For this reason, electron–hole pair recombination will be inhibited. When we applied an external electric field across the tetramer, band alignment occurs when the voltage is 1.7 V. The importance of this result is that the cluster p–n junction concept may extended to longer nanowires and may even be used to form more complex junctions, such as p–n–p- or n–p–n-type junctions.

Band bending across the interface of fused superatoms also occurs for clusters with a Co₆S₈ core. Fused Co₆S₈(CO)₅: Co₆S₈(PMe₃)₅ clusters are shown in Fig. 21. The cluster is energetically stable, binding by 2.45 eV, and that the cluster has a dipole moment of 18.0 D, larger than that for the rhenium cluster. The dipole moment is substantially larger due to the cobalt clusters having six donor and acceptor ligands instead of four as seen in the rhenium cores because the cobalt cluster do not require chlorine to close its electronic shell. The HOMO–LUMO gap is much smaller than that of rhenium, 0.29 eV, and this is because the frontier orbitals are localized in the interface between the two clusters. The optical absorption is shown in Fig. 21(b), and there is a weak absorption corresponding to the excitation in the interface; however, the absorption of the individual CO and PMe₃ cluster’s HOMO–LUMO gap is stronger. The increase in absorption for the cobalt clusters vs the rhenium suggests that the chance of electron–hole pair recombination will be larger in cobalt. The band bending in the Co₆S₈(CO)₅: Co₆S₈(PMe₃)₅ fused cluster is shown in Fig. 21(c). The valence band in the CO side is found to be at −0.68 eV below the HOMO, while the valence band on the PMe₃ side is −0.21 eV below the HOMO [Fig. 21(c)]. Note that the HOMO is in the interface. This shows that unbalanced donor/acceptor ligands on opposite sides of the cluster will induce a large internal electric field in different clusters, and we have also studied a similar concept with aluminum clusters.¹⁰¹ While the cobalt cluster appears to be a poor choice for photon harvesting due to the presence of these defect states in the junction, the concept is general and may be applied to other fused clusters.

In this Perspective, we have highlighted how a combination of electronic and geometric features can enable selected compact clusters to have a well-defined valence, enabling their description as superatoms. For clusters of metallic elements, a confined nearly free electron model provides a convenient framework to identify the superatoms, and the valence electronic states in these clusters can be approximately labeled by the principal and angular momentum quantum numbers much in the same way as atoms. The conceptual framework of superatoms could be extended to ligated metal-chalcogenide classes of clusters due to their periodic electronic properties. We have shown that clusters marked by the octahedral core, ligated with donor or acceptor ligands show higher stability for valence electron counts of 96, 100, and 114, assuming that each ligand contributes two electrons to the electron count that includes valence electrons from the metal and chalcogens. This means that the redox properties of these clusters may be determined based on their zero valent state, making their designation as superatoms a powerful organizing principle.

The electronic spectrum of the clusters can be lifted or lowered by changing the type of ligands, providing an unprecedented ability to design clusters that can either donate or accept multiple electrons. In fact, the ionization energies of some of these clusters can be lower than those of any element, providing a unique ability to design donor or acceptor superatoms. Thus, the ligands not only protect the metal–chalcogen core but also affect their redox character. This ability contributes to the formation of the ionic solids as the clusters are combined with counterions and is critical to many crystalline structures formed from these superatomic building blocks.

The superdonors/acceptors provide an unprecedented ability to control the transport characteristics of two-dimensional semiconductors. Metal-chalcogenide clusters can be used as charge transfer dopants, thus avoiding the conventional doping that requires the replacement of host atoms by the donor/acceptor substitutes. The doping can be tuned via ligand exchange, and the doping can be accomplished without disturbing the underlying lattice. This offers a powerhouse example of how materials made from superatoms combine tunability in a range in between molecular solids and bulk materials. What is more remarkable is that the control over the electronic spectrum can be used to design nano-p–n junctions at the scale of a single nanometer. As shown, even a superatomic molecule made of identical clusters can exhibit a large internal electric field as one side is coated with the donor and the other side is coated with acceptor ligands. The superatomic molecule exhibits rectification characteristics but can also hold promise for light harvesting. The transport properties in these clusters and the transport in superatomic crystalline materials and the collective behaviors that emerge as the cluster assemblies are formed, offering a rich field of study at the interface between traditional semiconductors and nanoscale materials.

An area that we have not emphasized is the creation of magnetic building blocks that could not only be used to stabilize magnetic solids but also lead to spin-based transport either through chemical dopants or as p–n junctions. Metallic superatoms follow the same general principles as Hund’s rule,^41,105,106 but the Jahn–Teller distortions often quench the spin magnetic moment. However, the strong bonds within metal-chalcogenide clusters make these superatoms less fluxional, allowing for the stabilization of high spin magnetic moment superatoms. Some such magnetic superatoms have already been synthesized. For example, [Ni₉Te₆(PEt₃)₈][C₆₀] is magnetic. SQUID measurements indicated that the individual clusters behave as isolated localized magnets with a magnetic moment of around 5.4 µ_B per functional unit.³⁰ First-principles theoretical studies on [Ni₉Te₆(PEt₃)₈][C₆₀] provided a magnetic characterization of the system. The metallic core has a spin magnetic moment of 5.3 µ_B in agreement with the experiment. We also showed that the magnetic motifs separated by C₆₀ experience a weak superexchange that stabilizes a ferromagnetic ground state as observed around 2 K.¹⁰⁷ In addition, an interesting phenomenon may emerge in the magnetic properties of cluster dimers.^34,108 The stabilization of the magnetic state in metal-chalcogenide clusters offers an alternative form of superatom that stabilizes a high magnetic state. The nature of the exchange coupling in the cluster solids of magnetic superatoms is also likely to produce interesting results. Furthermore, the nature of electronic transport in magnetic cluster solids is expected to be different than in conventional magnetic solids since the transport may involve counterions.¹⁰⁹ 

In order for the field of cluster science to continue on a rapidly expanding trajectory, several challenges must be addressed. The challenge of identifying organizing principles that are robust for systems beyond simple metal and metal-chalcogenide clusters is needed. As the superatom concept requires clusters to have a well-defined valence, identifying such zero valence superatomic states in different systems is critical. Extending the superatomic concept to magnetic clusters in metal-chalcogenide is also a promising direction. Understanding collective behaviors in cluster assembled materials is also a major challenge in this field. The properties of clusters may drastically change as they are assembled, just as the properties of atoms drastically change when they are assembled into crystalline solids. Understanding the emergent behaviors in the nanocrystals, including the conduction, magnetic properties, and chemical properties, is necessary for the field to continue to thrive. Of course, while this Perspective has focused on conceptual developments in finding organizational principles in cluster science, the field will rise or fall depending on new methods for synthesizing a wide range of cluster assembled materials with new cluster building blocks and new architectures.

The authors acknowledge funding from the U.S. Department of Energy (DOE) under Award No. DE-SC0006420.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.