English

• 1. INTRODUCTION

  Chemistry of actinide elements (An = Ac–Lr) is the key of radio- and nuclear chemistry^{[1, 2]}. The actinide elements-especially uranium and plutonium – lie at the heart of nuclear energy, and detailed understanding of the formation, stability and properties of actinide compounds is central to the safe storage of nuclear wastes, nuclear fuel cycles, and the environ-mental clean-up of actinide‑contaminated sites^{[3, 4]}. While acti-nide gas-phase molecules and solids are widely studied, experimental research work on actinide-containing clusters is relatively rare because of the difficulty in handling of heavy-element compounds with radioactivity and chemotoxicity^{[5, 6]}. Theoretical and computational investigations of actinide clusters are also less common due to the complicated electron correlations and significant relativistic effects of actinide elements^{[7, 8]}. The actinide elements are more or less com parable to early transition metals (the groups 3 to 5) because of their low electronegativity. For example, electronegativities of Th–Cm lie in the range of 1.1 to 1.5, while Bk–Lr all at 1.3. As a result, early actinide elements likely have the tendency to form stable clusters of actinide-oxides, nitrides and fluorides, as in the case of the early transition metals^[9]. Especially, existence and richness of stable heteropolyacid series of early transition metals point to the possibility of forming actinide polyoxometalate (POM) clusters^[10-12].

  Over the last two decades, a series of actinide oxide clusters were synthesized and characterized, including thorium-based [Th₆O₈] clusters^[13-15], protactinium clusters^[16], uranium (especially uranyl) clusters^[17], as well as those of Np and Pu elements^{[18, 19]}. There are also serval theoretical studies on polyactinide clusters, including uranyl peroxide cages such as the multi-uranyl clusters abbreviated as U₂, U₅ and U₂₀ clusters^{[20, 21]}, and M₆O₁₉ cluster^[22]. The present work is to provide a selective overview of the field rather than a comprehensive review of the rich literatures. We will briefly discuss the quantum chemical features of actinide elements and then introduce some of the actinide clusters. The summary of the theoretical studies will be followed by the conclusion and perspective remarks.

  2. ELECTRONIC STRUCTURE FEATURES OF ACTINIDES

  Before we present the summary of the actinide cluster research, a brief overview of the electronic structure features of actinides is helpful for later discussion. The early actinide elements such as Ac, Th, Pa and U are rather electropositive, thus bearing some resemblance to early transition metals, while Np and Pu are more on the bordering area between early and later actinide elements of Am, Cm, …, and Lr^[23]. The actinide elements feature 7s, 5f and 6d orbitals in the valence space, but these orbitals with different shell and angular momentum (l = 0, 1, 2, 3) have rather different radial distribution and orbital energies, which lead to unprecedented complicatedness in their geometries, electronic structures, and physiochemical properties. The 5f orbitals are not only more contracted than 7s and 6d orbitals but also fall inside the semi-core 6s6p manifold in terms of the radii of the maximum radial density distribution D(r) = r²R(r)², where r and R are the distances of electron from the nucleus and the radial wavefunction, respectively (Fig. 1). However, unlike 4f orbitals in lanthanide elements, where 4f orbitals are extremely contracted because of the quantum primogenic effect^[24-26] (i.e., the first-shell, nodeless atomic orbitals of each angular quantum number (i.e., 1s, 2p, 3d, 4f, 5g, …) and tend to be rather contracted in radial distribution due to the lack of Pauli repulsion from any inner orbitals with the same angular momentum), the 5f orbitals of actinides are less contracted, especially for the early actinides. For example, the radius at the maximum radial density distribution r_4f is ~0.35 Å for Nd while r_5f is ~0.57 Å for U based on numerical Dirac-Hartree-Fock calculations, although they both are f-elements that have six valence electrons^[27]. Therefore, early actinide 5f orbitals can more or less participate in covalent orbital overlap with other metals or ligands in molecules, clusters and solid-state compounds. The so-called actinide contraction and increased effective nuclear charge across the actinide series from Ac to Lr make the 5f orbitals gradually lower in energy and more contracted in radial distribution^[28].

  Figure 1

  

  Figure 1.  Radial density distribution (D(r) = r²R(r)²) of uranium atom

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  Another important aspect that is relevant for the stability of actinide clusters is the general trend of oxidation state (OS) change from early to later actinides^{[29, 30]}. The concept of formal OS has a long history of nearly two hundred years, which is one of the most useful classifications in chemistry^[31-33]. The highest OS of the actinide elements in the 7^th-row of the Periodic Table, Fr(+1), Ra(+2), Ac(+3), Th(+4) and Pa(+5) continues to U(+6) and Np(+7), then starts to decrease after Pu(+7), as shown in Fig. 2. The highest possible OS of Pu(+8) had been speculated to exist in gas phase PuO₄ molecule, but it has later been verified to be unlikely through advanced quantum chemistry studies^[34-36]. Plutonium stands at the border of OS alteration from going up to going down upon increasing the atomic number and valence electrons, and has been ex-plained with the concept of "plutonium turn^[37]". The most stable OS of actinides later than Am are mainly +3, which leads to the notorious difficulty in lanthanide-actinide separation of trivalent f-element ions^{[38, 39]}. The actinide ions in aqueous so-lution feature water coordination in the first solvation shell^{[40, 41]}. At different redox potentials, pH values, and concentration of An ions, the hydrolysis of actinide-water systems in solution can cause the formation of actinide-oxo or hydroxyl clusters. The strong Lewis acidity and the possibility for the 6d and 5f orbitals of early actinides in their ubiquitous +4 or +6 oxidation states to contribute to the bonding with oxygen atom make it feasible to form actinide-oxo and hydroxyl clusters. Here all the orbital radial distribution, orbital energies and the stability of different oxidation states play central roles in dictating the stabilities of actinide clusters.

  Figure 2

  

  Figure 2.  Identified formal oxidation states of actinides (An = Ac-Lr) elements. The most stable OSs are shown in filled blue circles

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  3. EXPERIMENTAL STUDIES OF ACTINIDE CLUSTERS (An = Th, Pa, U, Np & Pu)

  3.1 Thorium clusters

  While actinium with 6d¹7s² electron configuration mainly behaves as a transition metal, thorium (6d²7s²5f⁰) represents the beginning of actinide elements with 5f orbitals starting to play a non-negligible role. Most polynuclear thorium clusters are formed by the most stable tetravalent ions Th(Ⅳ) because of their propensity to undergo hydrolysis to form Th(OH)_n^4-n and Th(OH₂)_m⁴⁺ in solution^[42]. As the ion concentration increases, with appropriate temperature and pH values as well as other coexisting counterions, the condensation of these species via either olation (equation 1) or oxolation (equation 2) reactions starts to form polynuclear clusters, which comprise of Th-(OH)-Th or Th-O-Th linkages. Examples of the corresponding oligomers include the dimer of Th₂(OH)₂^6+[43], tetramer [Th₄(μ₄-O)(μ-Cl)₂]^12+[44], hexamer Th₆(O)₄(OH)₄^12+[45], octamer Th₈(O)₄(OH)₈^16+[46], decamer Th₁₀(O)₄(OH)₈²⁴⁺, etc^[47]. More comprehensive review of this kind of cluster species was published in 2013^[48].

  $\text { Th-OH + Th-OH } \mathrm{O}_2 \rightarrow \text { Th-(OH)-Th }+\mathrm{H}_2 \mathrm{O}$

  (1)

  $ \text { Th-OH }+\text { Th-OH } \rightarrow \text { Th-(O)-Th }+\mathrm{H}_2 \mathrm{O} $

  (2)

  One well-known example is the hexanuclear cluster with a novel [Th₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺ core, which is decorated by anionic ligand such as R-COO^- (R = H, CH₃, etc.) shells and results in the termination of oligomers to form neutral molecular clusters^[49]. In this highly charged cluster core cation, the four triply bridged μ₃-O^2- oxo groups and four μ₃-OH^- hydroxo groups are found to be separated as much as possible, forming the highest allowed symmetry with a pseudo-O_h geometry structure (Fig. 3(a)). This M₆X₈ type of cluster core is an important building block of actinide clusters and also exists for An = U, Np, Pu (see below). There is another series of hexanulcear actinide clusters An₆(H₂O)_m[C₆H₃(PO₃)-(PO₃H)]₆(NO₃)_n⁽⁶⁻ⁿ⁾ (An = Th, U, Np and Pu) reported by Diwu and her coworkers^[50], in which the actinide centers are nine-coordinated by five oxygen atoms from the 1, 2-pheny-lenediphosphonate ligand and four from either NO₃^- or H₂O. Periodic trend has been discussed and it is found that the cavity sizes of these clusters are tunable according to the ionic radii of the actinide ions.

  Figure 3

  

  Figure 3.  (a) Pseudo-O_h geometry of the hexanuclear cluster with a [Th₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺ core; (b) and its ligated neutral structure [Th₆(μ₃-O)₄(μ₃-OH)₄]L₁₂^[45]. Color codes for atoms: red sphere, O; gray, C; white, H; light blue, U; deep blue, N.

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  Organic or inorganic anion ligands can coordinate to terminate these core cluster cations into neutral clusters as shown in Fig. 3(b). Some of them are bridged by the linkage ligand and aggregate into solid-state materials with fascinating properties^[51]. For example, Zhao and his co-workers have reported the synthesis of the first transition-metal (TM)–Th MOF (Metal Organic Framework), which is radiation resistant and highly robust with a capacity for ReO₄^– uptake. Wang and his co-workers have reported a new MOF structure containing [Th₃(μ₃-O)(COO)₉]⁺ building blocks with unique properties of excellent anion-exchange capability for various anions such as large ones of MB²⁻ (methy blue) and PFOS (perfluorooctane sulfonate) that are hard to be mimicked by transition metals and lanthanide elements based MOFs. Thorium peroxide clusters are scarce, and one example is the trinuclear cluster of [Th₃(O₂)₃(terpy)₃]^{2+ [52]}.

  3.2 Protactinium clusters

  The experimental results of protactinium (Pa) clusters are extremely rare because of the high radioactivity, toxicity and scarcity of Pa. The distinctiveness of Pa lies in that its 5f and 6d atomic orbital levels are energetically close to each other and 5f orbitals start to become more important than in Th. In 2018, Wilson et al reported the synthesis of a tetranuclear Pa peroxide cluster of A₆[Pa₄(μ₄-O)(μ₂-O₂)₆F₁₂] (A = Rb, Cs, (CH₃)₄N)^[16]. The four pentavalent Pa⁵⁺ ions locate on the vertices of a tetrahedron with slight distortion with an average Pa–Pa distance of 3.77 Å, in the middle of which there is a μ₄-O^2- anion connecting with the surrounding four Pa⁵⁺ ions with a mean bond angle ∠Pa–O–Pa of 109.5° and an average Pa–O bond distance of 2.313 Å. The four Pa⁵⁺ ions on the vertices of the tetrahedron are bridged by six edge-sharing μ₂: η-O₂^2- peroxo ligands with a mean Pa–O₂ bond length of 2.36 Å. Each Pa⁵⁺ ion is further capped by three extra fluoride F^- ions and the total coordination number (CN) is therefore ten. The protactinium clusters tend to maintain the Pa(Ⅴ) oxidation state and few clusters with Pa in lower OS are known.

  Figure 4

  

  Figure 4.  Geometry of [Pa₄(μ₄-O)(μ₂-O₂)₆F₁₂]^6- with CN = 10 for Pa(Ⅴ). The metal site Pa is in black, oxygen atoms in magenta, and fluorine in turquoise. This figure is taken from references ^[16]

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  3.3 Uranium clusters

  Uranium has the richest chemistry in actinide clusters, which have been comprehensively reviewed and discussed previously^[17]. Herein we select some typical uranium oxo clusters composed of U(Ⅳ), U(Ⅴ) and U(Ⅵ) ions, respectively. The rich and intriguing U(Ⅵ) series of uranyl peroxo clusters will also be discussed.

  3.3.1   Polynuclear uranium-oxo clusters

  U(Ⅳ) oxo clusters include a series of polynuclear actinide clusters. The trinuclear core cluster of [U₃(μ₃-O)]¹⁰⁺ is decorated by L¹ (H₄L¹ = N, N^'-bis(3-hydroxysalicylidene)-2-methyl-1, 2-propanediamine) and Cl^-[9] or sulfate groups^[53]. Here the three U(Ⅳ) ions are held by a central μ₃-O^2- anion and form a nearly equilateral triangle. A tetranuclear complex of [U₄(μ₄-O)(L²)₂(H₂L²)₂(py)₂]²⁺ (H₄L² = N, N^'-bis(3-hydroxysalicylidene)-2, 2-dimethyl-1, 3-propanediamine) has four U(Ⅳ) ions located on the vertices of a tetrahedron and is held by a central μ₄-O^2- anion^[9]. A hexanuclear core cluster of [U₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺, with a similar topology as the aforementioned [Th₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺ cluster, is coor-dinated by several types of ligands and counterions^[54]. An octanuclear compound of U₈Cl₂₄O₄(cp*py)₂, cp*py = tetra-methyl-5-(2-pyridyl)cyclopentadiene, features an octaura-nium(Ⅳ) [U₈Cl₂₄O₄] cluster core^[55].

  As mentioned earlier, the M₆X₈ type of building block is common in actinide clusters. The decanuclear cluster [U₁₀(μ₃-O)₆(μ₄-O)₂(μ₃-OH)₆]¹⁸⁺ could be viewed as the fu-sion of two U₆O₈ cages by sharing two U and two O atoms with a topology of two near octahedral structures (Fig. 5(a))^[10], in which there are twelve μ₃-O bridges and six of them are μ₃-OH ones. The rest two O^2- ions are μ₄-O^2- bridging the two U₆O₈ cages.

  Figure 5

  

  Figure 5.  Topology of the uranium oxide clusters of (a) U₁₀O₁₄ core, (b) U₁₃O₁₆ core, (c) U₁₆O₂₃ core, (d) U₂₄O₃₂ core and (e) U₃₈O₅₆ cores. These figures are taken from references ^{[10, 56]}

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  Actinide clusters with higher nuclearity also exist. For example, [U₁₃(μ₃-O)₈(μ₄-O)₄(μ₃-OH)₄]²⁴⁺ is another type of structure that could be described as merging from two U₆O₈ cages by sharing with one U(Ⅳ) ion as the summit (Fig. 5(b)), in which two additional U(Ⅳ) ion are connected by the oxo groups from the two neighboring cages. Besides, larger clusters of [U₁₆(O)₁₅(μ₃-OH)₈]²⁶⁺ and [U₂₄(μ₃-O)₁₄(μ₄-O)₁₆ (μ₃-OH)₂]³⁴⁺ can be viewed as the merge of four or six U₆O₈ cages by sharing faces and edges (Fig. 5(c) & 5(d)). Thirteen fused U₆O₈ octahedron cages lead to the cluster of [U₃₈(O)₅₆]⁴⁰⁺, in which each cage shares five edges with five neighboring ones (Fig. 5(e)). The [An₃₈O₅₆]⁴⁰⁺ (An = U, Np and Pu) clusters consisting of 38 An(Ⅳ) metals connected by 56 O^2- linkages are a series of very interesting actinide clusters that connect the clusters and bulk actinide oxide crystals. They are the largest An(Ⅳ) polynuclear oxide clusters reported thus far and are stable in solution in a colloidal form. Of particular interest is the Pu₃₈ cluster, which is the first one synthesized in 2008 and the Np₃₈ cluster was the last one found in 2018^{[19, 57]}. More details of these [An₃₈O₅₆]⁴⁰⁺ (An = U, Np and Pu) clusters will be discussed in sections of 3.4 and 3.5, respectively.

  3.3.2   Polynuclear uranyl-peroxo clusters

  The aforementioned uranium-oxo clusters all feature U(Ⅳ). In fact the non-uranyl clusters usually tend to have lower OS of uranium. The linear dioxo U(Ⅵ) moiety UO₂²⁺ (uranyl) is ubiquitous in underground water, seawater, and the environmental chemistry of uranium. Especially noteworthy is the uranyl peroxide compounds and nanoparticles, which feature the peroxo ligand as connecting bridges between UO₂²⁺ units (Fig. 6a). The uranyl peroxide clusters are very stable species that are of relevance to the migration of actinides in the natural environment. For example, leakage from nuclear waste storage tanks or accidents such as at Fukushima-Daiichi might provide conditions where these nanoparticles are likely to form, and may be implicated in the enhanced corrosion of nuclear fuel in seawater.

  Figure 6

  

  Figure 6.  (a) Polyhedral and ball-and-stick representations of U₂ ([(UO₂)₂(O₂)₅]^6-); (b) polyhedral and graphical representations of U₆₀ ([(UO₂)(O₂)(OH)]₆₀^60-). Each vertex in the graph of (b) represents a uranyl polyhedron. The red balls are oxygen atoms and yellow balls are the uranium atoms (a); Yellow polyhedra represent uranyl peroxide hexagonal bipyramids in (a) & (b). These figures are taken from references^{[17, 67]}

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  The enthralling family of uranyl-peroxo nanoparticles recently synthesized by Burns et al. provides a rich source of information on these systems; more than 40 uranyl-peroxo clusters have been isolated and structurally characterized. The nanoparticles (and the smaller cluster) are labeled according to the number of uranyl polyhedra they possess; So far, U₂₀, U₂₄, U₂₈, U₃₂, and up to U₆₀ species (Fig. 6b) are all known, where the ligands are omitted and only the number of uranyl polyhedra is counted in the clusters^[58-60]. For example, Li₂₄[UO₂(O₂)(OH)]₂₄·aLiCl·bLiNO₃ is a U₂₄ species, where the charges are balanced by additional alkali-metal cations^[58].

  In contrast to the geometric structures and some spectroscopic properties, very little is known about the electronic structures, bonding types, redox properties, and chemical reaction mechanisms, except for a few species with the smallest known building block that includes two uranyl and a bridging bidentate peroxo (O₂^2-) ligand; these clusters include dimer up to the hexamer [UO₂(O₂)(H₂O)]_n (n = 2, 3, 4, 5, and 6)^{[61, 62]}. In addition, U₂₀ and U₂₈ macrocyclic clusters have been investigated by using density functional theory (DFT) and wavefunction theory (WFT) at the CASSCF/CASPT2 level with small active-space^[63-65]. The inherent bent structure of a U-O₂-U model dimer is suggested to be the driving force for the self-assembly of uranyl peroxide units into nanoclusters with different nuclearity^[66]. Alkali metal cations were sug-gested in computational studies as templates and to stabilize tetragonal-, pentagonal- and hexagonal building blocks, which then condense to form nanoclusters such as capsules with a central cavity^{[10, 64]}. While U₂₄, U₂₈ and U₆₀ are the three structurally well-characterized uranyl-peroxide clusters, theoretical investigations are lacking, holding back the understanding of their bonding, electronic structures, and self-assembly mechanisms^[58].

  Of particular interest is the U₆₀ cluster as shown in Fig. 6(b) above that has a fullerene topology, which is one typical example among the inorganic fullerene-like complexes such as the Ti₄₂ cluster synthesized by Zhang and coworkers^[68]. The U₆₀ cage composition formula is [UO₂(O₂)(OH)]₆₀^60-, and it has been experimentally investigated by ESI-MS and Raman spectroscopy^[58]. A correlation between uranyl-peroxo-uranyl dihedral bond angles and the position of the symmetric stretching Raman mode of the peroxo ligand has been found. A number of other interesting cage clusters of uranyl are found already and reviewed previously^{[17, 69]}.

  3.4 Neptunium clusters

  Similar to their analogues of Th and U, neptunium oxide clusters also have the hexanuclear [Np₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺ cluster, which aggregates into the first example of Np(Ⅳ) based transuranium-based MOFs via 4, 4-biphenyldicarboxylate linkers^[70]. The largest disclosed molecules of Np are the Np₃₈ cluster complexes consisting of 38 Np⁴⁺ cations bridged by 56 O^2- anions in the [Np₃₈O₅₆]⁴⁰⁺ core^[19].

  Concerning actinyl (AnO₂²⁺) peroxide clusters of other actinides, the Np₂₄ species is the only neptunyl peroxide cluster reported to date^[71]. It is topologically similar to U₂₄ and its composition is [NpO₂(O₂)(OH)]₂₄^24-. According to the experimental structure analysis, most of the Np atoms are in hexavalent Np⁶⁺(5f ¹) state, but some Np–O bond lengths suggest that Np⁵⁺(5f ²) is also present. This complicated cluster requires further theoretical investigations for a clear understanding of the number of f-electrons, oxidation state of each center, and the possible local and total spin. Since U₂₄ and Np₂₄ clusters have the same topology, hybrid U_mNp_n (m + n = 24) peroxide clusters seem not impossible, and the computationally aided design of more robust multi-center magnetic clusters with Np centers would be of great interest.

  3.5 Plutonium clusters

  Among the various plutonium oxide nanoclusters, two well-defined nanoclusters with lower oxidation state Pu(Ⅳ) are of M₆X₈ and An₃₈O₅₆ types, namely [Pu₆(μ₃-OH)₄(μ₃-O)₄(H₂O)₆-(HGly)₁₂Cl₁₈]^6- and [Pu₃₈O₅₆Cl₅₄(H₂O)₈]^14- clusters^{[18, 72, 73]}. Similar to Th(Ⅳ), U(Ⅳ) and Np(Ⅳ), the Pu₆ cluster has a hexanuclear [Pu₆O₄(OH)₄]¹²⁺ core formed in an acidic aqueous solution. The Pu₆ cluster with the same core [Pu₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺ stabilized by 1, 4, 7, 10-tetraazacyclododecane-1, 4, 7, 10 -tetra-acetic acid (DOTA) ligands was also synthesized and it has a high solubility over a large pH range. This cluster is the first water-soluble Pu(Ⅳ) cluster, and is thus important for plutonium environmental migration^[74]. For the [Pu₃₈O₅₆]⁴⁰⁺ core cluster, 54 chloride ions and 8 water molecules decorate its surface and there are three groups of Pu⁴⁺ centers: six Pu⁴⁺ cations compositing the center of the cluster, eight Pu⁴⁺ near the corners of the pseudo-cubic cluster and the remaining 24 Pu⁴⁺ cations siting along the faces of the pseudo-cube (Fig. 7). Each Pu⁴⁺ ion has four quasi-localized 5f electrons, offering the potential to design multi-center magnetic actinide materials via these clusters.

  Figure 7

  

  Figure 7.  Geometry of [Pu₃₈O₅₆Cl₅₄(H₂O)₈]^14- cluster with structural linkages between Pu(Ⅳ) (green), O^2- (red), O_water (blue) and Cl^- (yellow)^[57]

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  4. THEORETICAL AND COMPUTATIONAL STUDIES OF ACTINIDE CLUSTERS

  Relativistic quantum chemistry investigations have been performed to explore the geometry structures, electronic structures and unique properties of the actinide clusters. Gagliardi, Vlaisavljevich and their coworkers have conducted systematic computational studies of the curvature mechanism for the uranyl-peroxide-uranyl interaction in the uranyl peroxide clusters, as mentioned earlier. They have investigated the [(UO₂)₂(O₂)₅]^6- in Na₂Rb₄[(UO₂)₂(O₂)₅], [(UO₂)₂(O₂)-(C₂O₄)₄]^6- in K₆[(UO₂)₂(O₂)(C₂O₄)₄] and [(UO₂)₂(O₂)₄(OH)₂]^6- in K₆[(UO₂)₂(O₂)₄(OH)₂] with two uranyl hexagonal bi-pyramids sharing one peroxide edge or two hydroxyl groups^[69]. The U–O₂–U dihedral angles are calculated to be 153.1°, 152.9° for the former two, and 180.0° for the latter one, respectively. They have also studied larger clusters such as [(UO₂)₅(O₂)₅(C₂O₄)₅]^10- in K₁₀[(UO₂)₅(O₂)₅(C₂O₄)₅] consisting of a five-membered ring of bipyramids connected by five peroxide edges and the five U-O₂-U dihedral angles are within the range of 137.5°~144.5°^[69]. Furthermore, the five alkali counterions Li⁺, Na⁺, K⁺, Rb⁺ and Cs⁺ have also been considered for their effect on the dihedral angles^[20]. They have investigated the uranyl persulfide clusters based on both DFT and multiconfigurational WFT and show that the U-S₂-U dihedral angles of the model clusters are bent according to the partial covalent interaction to encourage curvature^[75].

  Hu and Kaltsoyannis have computationally investigated a series of E@M₁₂@An₂₀ Matryoshka ("Rusian Doll") clusters (E = S^2-, Se^2-, Te^2-, and Po^2-; M = K⁺, Rb⁺, Cs⁺, Ag⁺, Mg²⁺, Fe²⁺, Mn²⁺; An = U, Np and Pu) inspired by the experimentally synthesized U₂₀ uranyl cage cluster by Burns group^[76]. The S@Mn₁₂@Pu₂₀ is predicted to have the highest ground state spin with spin values of S = 100/2 for a molecular cluster^[21]. As discussed earlier, they also studied the [Th₆O₄(OH)₄]¹²⁺ cluster through computational modeling^[45]. Kaltsoyannis and his coworkers have computationally investigated a mixed valence neptunyl(Ⅵ/Ⅴ) cluster of [(Np^ⅥO₂Cl₂)(Np^ⅤO₂Cl(thf)₃)₂] with Np^ⅤO₂⁺-Np^ⅤO₂⁺ cation-cation interaction (CCI)^[77], which has been shown to play an important role among clusters of actinyl cations^[65].

  Li and his coworkers have performed systematic theoretical investigations on the hexanuclear polyoxometalate [M₆L₁₉]^2- clusters with six-valence-electron metal elements M = Cr, Mo, W, Sg, Nd and U^[22]. They show that the [U₆L₁₉]^2- cluster prefers the rare T_h symmetry with U=O−U bonding of cross-linked U₄O₄ rings both in vacuum and in solution environments due to the pseudo-Jahn-Teller distortion from O_h symmetry, while the three clusters [M₆L₁₉]^2- with heavy transition metals (M = Mo, W and Sg) prefer the O_h Lindqvist structure and feature significant (d-p)π aromaticity. Similar to the [M₆L₁₉]^8- (M = V, Nb, Ta) series, the reduced [U₆L₁₉]^8- cluster with U(Ⅴ) has also been studied. It is found to prefer T_h symmetry in vacuum and O_h one in a dielectric environment. While early actinides tend to form polyacid like clusters, there are clear differences from those of transition metals. Further experimental work is still needed to explore this field.

  It is worth noting that while we discuss the actinide clusters with oxo, hydroxyl, halide ligands, other actinide clusters are known as well. For example, a joint experimental and computational study reveals a diuranium carbide cluster with U=C=U unit in the I_h(7)-C₈₀ fullerene cage^[78]. This endohedral fullerene UCU@I_h(7)-C₈₀ reveals a cage-stabilized bent U=C=U cluster with carbide bridge and short U=C bond distances (2.03 Å). Theoretical calculations indicate that it has two U(f ¹)=C double bonds and the formal oxidation state of U is +5. Moreover, Lu, Infante and coworkers have com-putationally investigated the U₂ compound placed inside the C₆₀, C₇₀ and C₈₄ clusters^[79]. It shows that whereas the small size of C₆₀ cavity is able to constrain U₂ in its center with U-U bonding character, U₂ prefers to connect to the cage walls without U-U bond for larger clusters such as C₇₀ and C₈₄. These theoretical studies show that actinide clusters hold promises for a variety of interesting properties and need to be studied with further theoretical efforts.

  5. CONCLUSIONS AND PERSPECTIVES

  In this article, we have summarized recent research progresses on some selected actinide clusters. It is interesting to note that this area is undergoing rapid progress in recent years. Due to the complexity of actinide elements, the understanding of their compounds and clusters are rather limited. The early 5f actinide elements with an abundance of oxidation states can behave like d-transition metal elements with high-lying 6d orbitals and relatively less contracted 5f orbitals that are able to participate in covalent bonding. Thus, these actinide valence orbitals play interesting roles in forming stable clusters. For example, based on the summary above, An(Ⅳ) (An = Th, U, Np and Pu) prefers to form highly symmetric An₆^ⅣO₈ core clusters, similar to the well-known early transition metal TM₆^ⅣO₈ clusters (TM = Ti, Zr and Hf) that are the promising building blocks for robust MOF materials^[80-82]. Furthermore, An₆^ⅣO₈ core clusters are able to merge into larger clusters up to An₃₈O₅₆ clusters (An = U, Np and Pu) with the same topology. The missing of analog Th₃₈O₅₆ as well as TM₃₈O₅₆ (TM = Ti, Zr and Hf) clusters so far is another intriguing research topic to explore.

  The richness and variance of oxidation states of the early actinides can lead to different rules in forming clusters, which requires more researches to figure out the electronic mechanism behind. For example, different from An(Ⅳ), actinides with higher oxidation states such as U(Ⅵ) and Np(Ⅴ/Ⅵ) prefer to form peroxide cage clusters instead of polynuclear oxide clusters. Clearly different oxidation states of actinides prefer different cluster topologies, which makes this field of actinide clusters full of new surprises. Computational modeling based on global minimum structural search can help to predict stable clusters of different actinide oxidation states.

  When the actinide elements become heavier, their 6d orbital energies remain largely the same while their 5f orbital energy goes lower quickly^{[28, 37]}. Together with the actinide contraction, the later actinide elements with more contracted 5f orbitals and lower orbital energies behave more like the 4f lanthanide elements with fewer types of oxidation states and have much fewer examples of stable clusters. The current paper is to provide a brief synopsis for the development of this exciting area and to inspire more experimental exploration of possible actinide clusters with oxo, peroxo, hydroxyl, fluoro and other hard Lewis base ligands. Research progresses in the field have shown that computational modeling based on DFT approach with scalar relativistic corrections is useful for the prediction of geometric structure and bonding analysis. However, high level WFT methods based on relativistic quantum chemistry are necessary to reveal the excited states, magnetic and spec-troscopic properties. Clearly comprehensive theoretical and computational investigations can provide critical insights on the stability and electronic structures, which can be used to guide the design and synthesis of actinide cluster complexes with unique geometric structures, interesting bonding mechanism, and magnetic properties. Future investigations on actinide clusters are needed to explore the clustering and reaction mechanism, redox properties, and their solvation and deposition in light and dense solutions. Research efforts in these directions will help the innovative research and development in nuclear waste treatment, underground water cleanup, uranium extraction from seawater, and nuclear fuel cycles in radio- and nuclear chemistry.

  
  
• 1. [1]

     Bursten, B. E. P., E. J.; Sonnenberg, J. L. Recent advances in actinide chemistry; May, I., Alvares, R., Bryan, N., Eds.; Springer: Berlin 2006.

  2. [2]

     Morss, L. R. E., N. M.; Fuger, J.; Katz, J. J., Eds. The chemistry of the actinide and transactinide elements, 3rd ed.; Springer: Dordrecht. 2006.

  3. [3]

     Li, J.; Dai, X.; Zhu, L.; Xu, C.; Zhang, D.; Silver, M. A.; Li, P.; Chen, L.; Li, Y.; Zuo, D.; Zhang, H.; Xiao, C.; Chen, J.; Diwu, J.; Farha, O. K.; Albrecht-Schmitt, T. E.; Chai, Z.; Wang, S. ⁹⁹TcO₄^- remediation by a cationic polymeric network. Nat. Commun. 2018, 9, 3007. doi: 10.1038/s41467-018-05380-5

  4. [4]

     Wang, Y.; Liu, Z.; Li, Y.; Bai, Z.; Liu, W.; Wang, Y.; Xu, X.; Xiao, C.; Sheng, D.; Diwu, J.; Su, J.; Chai, Z.; Albrecht-Schmitt, T. E.; Wang, S. Umbellate distortions of the uranyl coordination environment result in a stable and porous polycatenated framework that can effectively remove cesium from aqueous solutions. J. Am. Chem. Soc. 2015, 137, 6144‒6147. doi: 10.1021/jacs.5b02480

  5. [5]

     Walther, C.; Denecke, M. A. Actinide colloids and particles of environmental concern. Chem. Rev. 2013, 113, 995‒1015. doi: 10.1021/cr300343c

  6. [6]

     Shi, W. Q.; Yuan, L. Y.; Wang, C. Z.; Wang, L.; Mei, L.; Xiao, C. L.; Zhang, L.; Li, Z. J.; Zhao, Y. L.; Chai, Z. F. Exploring actinide materials throughsynchrotron radiation techniques. Adv. Mater. 2014, 26, 7807‒7848. doi: 10.1002/adma.201304323

  7. [7]

     Wang, D.; van Gunsteren, W. F.; Chai, Z. Recent advances in computational actinoid chemistry. Chem. Soc. Rev. 2012, 41, 5836‒5865. doi: 10.1039/c2cs15354h

  8. [8]

     Kaltsoyannis, N. Recent developments in computational actinide chemistry. Chem. Soc. Rev. 2003, 32, 9‒16. doi: 10.1039/b204253n

  9. [9]

     Salmon, L.; Thuery, P.; Ephritikhine, M. Polynuclear uranium(Ⅳ) compounds with (μ₃-oxo)U₃ or (μ₄-oxo)U₄ cores and compartmental Schiff base ligands. Polyhedron 2006, 25, 1537‒1542. doi: 10.1016/j.poly.2005.10.015

  10. [10]

      Biswas, B.; Mougel, V.; Pecaut, J.; Mazzanti, M. Base-driven assembly of large uranium oxo/hydroxo clusters. Angew. Chem. Int. Ed. Engl. 2011, 50, 5745‒5748. doi: 10.1002/anie.201101327

  11. [11]

      Long, D. L.; Tsunashima, R.; Cronin, L. Polyoxometalates: building blocks for functional nanoscale systems. Angew. Chem. Int. Ed. Engl. 2010, 49, 1736‒1758. doi: 10.1002/anie.200902483

  12. [12]

      Nocton, G.; Burdet, F.; Pecaut, J.; Mazzanti, M. Self-assembly of polyoxo clusters and extended frameworks by controlled hydrolysis of low-valent uranium. Angew. Chem. Int. Ed. Engl. 2007, 46, 7574‒7578. doi: 10.1002/anie.200702374

  13. [13]

      Boyen, H. G.; Kastle, G.; Weigl, F.; Koslowski, B.; Dietrich, C.; Ziemann, P.; Spatz, J. P.; Riethmuller, S.; Hartmann, C.; Moller, M.; Schmid, G.; Garnier, M. G.; Oelhafen, P. Oxidation-resistant gold-55 clusters. Science 2002, 297, 1533‒1536. doi: 10.1126/science.1076248

  14. [14]

      Turner, M.; Golovko, V. B.; Vaughan, O. P. H.; Abdulkin, P.; Berenguer-Murcia, A.; Tikhov, M. S.; Johnson, B. F. G.; Lambert, R. M. Selective oxidation with dioxygen by gold nanoparticle catalysts derived from 55-atom clusters. Nature 2008, 454, 981‒983. doi: 10.1038/nature07194

  15. [15]

      Chang, C. M.; Cheng, C.; Wei, C. M. CO oxidation on unsupported Au₅₅, Ag₅₅, and Au₂₅Ag₃₀ nanoclusters. J. Chem. Phys. 2008, 128, 124710. doi: 10.1063/1.2841364

  16. [16]

      Wilson, R. E.; De Sio, S.; Vallet, V. Protactinium and the intersection of actinide and transition metal chemistry. Nat. Commun. 2018, 9, 622. doi: 10.1038/s41467-018-02972-z

  17. [17]

      Qiu, J.; Burns, P. C. Clusters of actinides with oxide, peroxide, or hydroxide bridges. Chem. Rev. 2013, 113, 1097‒1120. doi: 10.1021/cr300159x

  18. [18]

      Knope, K. E.; Soderholm, L. Plutonium(Ⅳ) cluster with a hexanuclear [Pu₆(OH)₄O₄]¹²⁺ core. Inorg. Chem. 2013, 52, 6770‒6772. doi: 10.1021/ic4007185

  19. [19]

      Martin, N. P.; Volkringer, C.; Roussel, P.; Marz, J.; Hennig, C.; Loiseau, T.; Ikeda-Ohno, A. {Np₃₈} clusters: the missing link in the largest poly-oxo cluster series of tetravalent actinides. Chem. Commun. 2018, 54, 10060‒10063. doi: 10.1039/C8CC03744B

  20. [20]

      Qiu, J.; Vlaisavljevich, B.; Jouffret, L.; Nguyen, K.; Szymanowski, J. E.; Gagliardi, L.; Burns, P. C. Cation templating and electronic structure effects in uranyl cage clusters probed by the isolation of peroxide-bridged uranyl dimers. Inorg. Chem. 2015, 54, 4445‒4455. doi: 10.1021/acs.inorgchem.5b00248

  21. [21]

      Hu, H. S.; Kaltsoyannis, N. High spin ground states in matryoshka actinide nanoclusters: a computational study. Chemistry 2018, 24, 347‒350. doi: 10.1002/chem.201705196

  22. [22]

      Jiang, N.; Schwarz, W. H.; Li, J. Theoretical studies on hexanuclear oxometalates [M₆L₁₉]^q- (M = Cr, Mo, W, Sg, Nd, U). Electronic structures, oxidation states, aromaticity, and stability. Inorg. Chem. 2015, 54, 7171‒7180. doi: 10.1021/acs.inorgchem.5b00372

  23. [23]

      Kelley, M. P.; Su, J.; Urban, M.; Luckey, M.; Batista, E. R.; Yang, P.; Shafer, J. C. On the origin of covalent bonding in heavy actinides. J. Am. Chem. Soc. 2017, 139, 9901‒9908. doi: 10.1021/jacs.7b03251

  24. [24]

      Pyykkö, P. Dirac-fock one-centre calculations part 8. The ¹Σ states of ScH, YH, LaH, AcH, TmH, LuH and LrH. Physica scripta 1979, 20, 647‒651. doi: 10.1088/0031-8949/20/5-6/016

  25. [25]

      Kaupp, M. The role of radial nodes of atomic orbitals for chemical bonding and the periodic table. J. Comput. Chem. 2007, 28, 320‒325. doi: 10.1002/jcc.20522

  26. [26]

      Tang, Y.; Zhao, S.; Long, B.; Liu, J. C.; Li, J. On the nature of support effects of metal dioxides MO₂ (M = Ti, Zr, Hf, Ce, Th) in single-atom gold catalysts: importance of quantum primogenic effect. J. Phys. Chem. C 2016, 120, 17514‒17526. doi: 10.1021/acs.jpcc.6b05338

  27. [27]

      Descalaux, J. P. Relativistic dirac-fock expectation values for atoms with Z = 1 to Z = 120. At. Data Nucl. Data Tables. 1973, 12, 311‒406. doi: 10.1016/0092-640X(73)90020-X

  28. [28]

      Li, J.; Bruce, E. B. Electronic structure of cycloheptatrienyl sandwich compounds of actinides: An(η₇-C₇H₇)₂ (An = Th, Pa, U, Np, Pu, Am) J. Am. Chem. Soc. 1997, 119, 9021‒9032. doi: 10.1021/ja971149m

  29. [29]

      Su, J.; Windorff, C. J.; Batista, E. R.; Evans, W. J.; Gaunt, A. J.; Janicke, M. T.; Kozimor, S. A.; Scott, B. L.; Woen, D. H.; Yang, P. Identification of the formal +2 oxidation state of neptunium: synthesis and structural characterization of {Np(Ⅱ)[C₅H₃(SiMe₃)₂]₃}. J. Am. Chem. Soc. 2018, 140, 7425‒7428. doi: 10.1021/jacs.8b03907

  30. [30]

      Kelley, M. P.; Deblonde, G. J.; Su, J.; Booth, C. H.; Abergel, R. J.; Batista, E. R.; Yang, P. Bond covalency and oxidation state of actinide ions complexed with therapeutic chelating agent 3, 4, 3-LI(1, 2-HOPO). Inorg. Chem. 2018, 57, 5352‒5363. doi: 10.1021/acs.inorgchem.8b00345

  31. [31]

      Hu, S. X.; Li, W. L.; Lu, J. B.; Bao, J. L.; Yu, H. S.; Truhlar, D. G.; Gibson, J. K.; Marcalo, J.; Zhou, M.; Riedel, S.; Schwarz, W. H. E.; Li, J. On the upper limits of oxidation states in chemistry. Angew. Chem. Int. Ed. Engl. 2018, 57, 3242‒3245. doi: 10.1002/anie.201711450

  32. [32]

      Wang, G.; Zhou, M.; Goettel, J. T.; Schrobilgen, G. J.; Su, J.; Li, J.; Schloder, T.; Riedel, S. Identification of an iridium-containing compound with a formal oxidation state of Ⅸ. Nature 2014, 514, 475‒477. doi: 10.1038/nature13795

  33. [33]

      Riedel, S.; Kaupp, M. The highest oxidation states of the transition metal elements. Coordin. Chem. Rev. 2009, 253, 606‒624. doi: 10.1016/j.ccr.2008.07.014

  34. [34]

      Huang, W.; Xu, W. H.; Schwarz, W. H.; Li, J. On the highest oxidation states of metal elements in MO₄ molecules (M = Fe, Ru, Os, Hs, Sm, and Pu). Inorg. Chem. 2016, 55, 4616‒4625. doi: 10.1021/acs.inorgchem.6b00442

  35. [35]

      Huang, W.; Pyykko, P.; Li, J. Is octavalent Pu(Ⅷ) possible? Mapping the plutonium oxyfluoride series PuO_nF_8-2n (n = 0-4). Inorg. Chem. 2015, 54, 8825‒8831. doi: 10.1021/acs.inorgchem.5b01540

  36. [36]

      Huang, W.; Xu, W. H.; Su, J.; Schwarz, W. H.; Li, J. Oxidation states, geometries, and electronic structures of plutonium tetroxide PuO₄ isomers: is octavalent Pu viable? Inorg. Chem. 2013, 52, 14237‒14245. doi: 10.1021/ic402170q

  37. [37]

      Liu, J. B.; Chen, G. P.; Huang, W.; Clark, D. L.; Schwarz, W. H.; Li, J. Bonding trends across the series of tricarbonato-actinyl anions [(AnO₂)(CO₃)₃]^4- (An = U-Cm): the plutonium turn. Dalton Trans 2017, 46, 2542‒2550. doi: 10.1039/C6DT03953G

  38. [38]

      Panak, P. J.; Geist, A. Complexation and extraction of trivalent actinides and lanthanides by triazinylpyridine N-donor ligands. Chem. Rev. 2013, 113, 1199‒1236. doi: 10.1021/cr3003399

  39. [39]

      Wang, Z.; Pu, N.; Tian, Y.; Xu, C.; Wang, F.; Liu, Y.; Zhang, L.; Chen, J.; Ding, S. Highly selective separation of actinides from lanthanides by dithiophosphinic acids: an in-depth investigation on extraction, complexation, and DFT calculations. Inorg. Chem. 2019, 58, 5457‒5467. doi: 10.1021/acs.inorgchem.8b01635

  40. [40]

      Dau, P. D.; Su, J.; Liu, H. T.; Liu, J. B.; Huang, D. L.; Li, J.; Wang, L. S. Observation and investigation of the uranyl tetrafluoride dianion (UO₂F₄²⁻) and its solvation complexes with water and acetonitrile. Chem. Sci. 2012, 3, 1137‒1146. doi: 10.1039/c2sc01052f

  41. [41]

      Yang, X.; Chai, Z.; Wang, D. Theoretical investigation on the mechanism and dynamics of oxo exchange of neptunyl(Ⅵ) hydroxide in aqueous solution. Phys. Chem. Chem. Phys. 2015, 17, 7537‒7547. doi: 10.1039/C4CP04586F

  42. [42]

      Fanghänel, T.; Neck, V. Aquatic chemistry and solubility phenomena of actinide oxides/hydroxides. Pure Appl. Chem. 2002, 74, 13.

  43. [43]

      Wilson, R. E.; Skanthakumar, S.; Sigmon, G.; Burns, P. C.; Soderholm, L. Structures of dimeric hydrolysis products of thorium. Inorg. Chem. 2007, 46, 2368‒2372. doi: 10.1021/ic0617691

  44. [44]

      Travia, N. E.; Scott, B. L.; Kiplinger, J. L. A rare tetranuclear thorium(Ⅳ) μ₄-oxo cluster and dinuclear thorium(Ⅳ) complex assembled by carbon-oxygen bond activation of 1, 2-dimethoxyethane (DME). Chemistry 2014, 20, 16846‒16852. doi: 10.1002/chem.201404551

  45. [45]

      Xu, H.; Cao, C. S.; Hu, H. S.; Wang, S. B.; Liu, J. C.; Cheng, P.; Kaltsoyannis, N.; Li, J.; Zhao, B. High uptake of ReO₄^- and CO₂ conversion by a radiation-resistant thorium-nickle [Th₄₈Ni₆] nanocage-based metal-organic framework. Angew. Chem. Int. Ed. Engl. 2019, 58, 6022‒6027. doi: 10.1002/anie.201901786

  46. [46]

      Knope, K. E.; Vasiliu, M.; Dixon, D. A.; Soderholm, L. Thorium(Ⅳ)-selenate clusters containing an octanuclear Th(Ⅳ) hydroxide/oxide core. Inorg. Chem. 2012, 51, 4239‒4249. s doi: 10.1021/ic202706s

  47. [47]

      Falaise, C.; Kozma, K.; Nyman, M. Thorium oxo-clusters as building blocks for open frameworks. Chemistry 2018, 24, 14226‒14232. doi: 10.1002/chem.201802671

  48. [48]

      Knope, K. E.; Soderholm, L. Solution and solid-state structural chemistry of actinide hydrates and their hydrolysis and condensation products. Chem. Rev. 2013, 113, 944‒994. doi: 10.1021/cr300212f

  49. [49]

      Knope, K. E.; Wilson, R. E.; Vasiliu, M.; Dixon, D. A.; Soderholm, L. Thorium(Ⅳ) molecular clusters with a hexanuclear Th core. Inorg. Chem. 2011, 50, 9696‒9704. doi: 10.1021/ic2014946

  50. [50]

      Diwu, J.; Wang, S.; Albrecht-Schmitt, T. E. Periodic trends in hexanuclear actinide clusters. Inorg. Chem. 2012, 51, 4088‒4093. doi: 10.1021/ic2023242

  51. [51]

      Li, Y.; Yang, Z.; Wang, Y.; Bai, Z.; Zheng, T.; Dai, X.; Liu, S.; Gui, D.; Liu, W.; Chen, M.; Chen, L.; Diwu, J.; Zhu, L.; Zhou, R.; Chai, Z.; Albrecht-Schmitt, T. E.; Wang, S. A mesoporous cationic thorium-organic framework that rapidly traps anionic persistent organic pollutants. Nat. Commun. 2017, 8, 1354. doi: 10.1038/s41467-017-01208-w

  52. [52]

      Galley, S. S.; Van Alstine, C. E.; Maron, L.; Albrecht-Schmitt, T. E. Understanding the scarcity of thorium peroxide clusters. Inorg. Chem. 2017, 56, 12692‒12694. doi: 10.1021/acs.inorgchem.7b02216

  53. [53]

      Lin, J.; Yue, Z.; Silver, M. A.; Qie, M.; Wang, X.; Liu, W.; Lin, X.; Bao, H. L.; Zhang, L. J.; Wang, S.; Wang, J. Q. In situ reduction from uranyl ion into a tetravalent uranium trimer and hexamer featuring ion-exchange properties and the alexandrite effect. Inorg. Chem. 2018, 57, 6753‒6761. doi: 10.1021/acs.inorgchem.8b01098

  54. [54]

      Falaise, C.; Volkringer, C.; Vigier, J. F.; Henry, N.; Beaurain, A.; Loiseau, T. Three-dimensional MOF-type architectures with tetravalent uranium hexanuclear motifs (U₆O₈). Chemistry 2013, 19, 5324‒5331. doi: 10.1002/chem.201203914

  55. [55]

      Moisan, L.; Le Borgne, T.; Thuery, P.; Ephritikhine, M. An ion pair formed by protonated Fe(cp*py)₂ and the octanuclear cluster U₈Cl₂₄O₄(cp*py)_2, cp*py is tetramethyl-5-(2-pyridyl)cyclopentadiene. Acta Crystallog. C 2002, 58, m98‒m101. doi: 10.1107/S0108270101020029

  56. [56]

      Chatelain, L.; Faizova, R.; Fadaei-Tirani, F.; Pecaut, J.; Mazzanti, M. Structural snapshots of cluster growth from {U₆} to {U₃₈} during the hydrolysis of UCl₄. Angew. Chem. Int. Ed. Engl. 2019, 58, 3021‒3026. doi: 10.1002/anie.201812509

  57. [57]

      Soderholm, L.; Almond, P. M.; Skanthakumar, S.; Wilson, R. E.; Burns, P. C. The structure of the plutonium oxide nanocluster Pu₃₈O₅₆Cl₅₄(H₂O)₈^14-. Angew. Chem. Int. Ed. 2008, 47, 298‒302. doi: 10.1002/anie.200704420

  58. [58]

      McGrail, B. T.; Sigmon, G. E.; Jouffret, L. J.; Andrews, C. R.; Burns, P. C. Raman spectroscopic and ESI-MS characterization of uranyl peroxide cage clusters. Inorg. Chem. 2014, 53, 1562‒1569. doi: 10.1021/ic402570b

  59. [59]

      magQiu, J.; Burns, P. C. Clusters of actinides with oxide, peroxide, or hydroxide bridges. Chem. Rev. 2013, 113, 1097‒120. doi: 10.1021/cr300159x

  60. [60]

      Unruh, D. K.; Ling, J.; Qiu, J.; Pressprich, L.; Baranay, M.; Ward, M.; Burns, P. C. Complex nanoscale cage clusters built from uranyl polyhedra and phosphate tetrahedra. Inorg. Chem. 2011, 50, 5509‒5516. doi: 10.1021/ic200065y

  61. [61]

      Miro, P.; Ling, J.; Qiu, J.; Burns, P. C.; Gagliardi, L.; Cramer, C. J. Experimental and computational study of a new wheel-shaped {[W₅O₂₁]₃[(U(Ⅵ)O))₂(μ-O₂)]₃}^30- polyoxometalate. Inorg. Chem. 2012, 51, 8784‒8790. doi: 10.1021/ic3005536

  62. [62]

      Pere, M.; Simon, P.; Mickael, G.; Adria, G.; Carles, B. On the origin of the cation templated self-assembly of uranyl-peroxide nanoclusters. J. Am. Chem. Soc. 2010, 132, 17787‒17794. doi: 10.1021/ja1053175

  63. [63]

      Miro, P.; Bo, C. Uranyl-peroxide nanocapsules: electronic structure and cation complexation in [(UO₂)₂₀(μ-O₂)₃₀]^20-. Inorg. Chem. 2012, 51, 3840‒3845. doi: 10.1021/ic300029d

  64. [64]

      Gil, A.; Karhanek, D.; Miro, P.; Antonio, M. R.; Nyman, M.; Bo, C. A journey inside the U₂₈ nanocapsule. Chemistry 2012, 18, 8340‒8346. doi: 10.1002/chem.201200801

  65. [65]

      Vlaisavljevich, B.; Miro, P.; Ma, D.; Sigmon, G. E.; Burns, P. C.; Cramer, C. J.; Gagliardi, L. Synthesis and characterization of the first 2D neptunyl structure stabilized by side-on cation-cation interactions. Chemistry 2013, 19, 2937‒2941. doi: 10.1002/chem.201204149

  66. [66]

      Albrecht-Schmitt, T. E. Actinide materials adopt curvature: nanotubules and nanospheres. Angew. Chem. Int. Ed. 2005, 44, 4836‒4838. doi: 10.1002/anie.200500936

  67. [67]

      Sigmon, G. E.; Ling, J.; Unruh, D. K.; Moore-Shay, L.; Ward, M.; Weaver, B.; Burns, P. C. Uranyl-peroxide interactions favor nanocluster self-assembly. J. Am. Chem. Soc. 2009, 131, 16648‒16649. doi: 10.1021/ja907837u

  68. [68]

      Gao, M. Y.; Wang, F.; Gu, Z. G.; Zhang, D. X.; Zhang, L.; Zhang, J. Fullerene-like polyoxotitanium cage with high solution stability. J. Am. Chem. Soc. 2016, 138, 2556‒2559. doi: 10.1021/jacs.6b00613

  69. [69]

      Vlaisavljevich, B.; Gagliardi, L.; Burns, P. C. Understanding the structure and formation of uranyl peroxide nanoclusters by quantum chemical calculations. J. Am. Chem. Soc. 2010, 132, 14503‒14508. doi: 10.1021/ja104964x

  70. [70]

      Martin, N. P.; Marz, J.; Feuchter, H.; Duval, S.; Roussel, P.; Henry, N.; Ikeda-Ohno, A.; Loiseau, T.; Volkringer, C. Synthesis and structural characterization of the first neptunium based metal-organic frameworks incorporating {Np₆O₈} hexanuclear clusters. Chem. Commun. 2018, 54, 6979‒6982. doi: 10.1039/C8CC03121E

  71. [71]

      Burns, P. C.; Kubatko, K. A.; Sigmon, G.; Fryer, B. J.; Gagnon, J. E.; Antonio, M. R.; Soderholm, L. Actinyl peroxide nanospheres. Angew. Chem. Int. Ed. 2005, 44, 2135‒2139. doi: 10.1002/anie.200462445

  72. [72]

      Soderholm, L.; Almond, P. M.; Skanthakumar, S.; Wilson, R. E.; Burns, P. C. The structure of the plutonium oxide nanocluster [Pu₃₈O₅₆Cl₅₄(H₂O)₈]¹⁴⁻. Angew. Chem. Int. Ed. 2008, 120, 304‒308. doi: 10.1002/ange.200704420

  73. [73]

      Wilson, R. E.; Skanthakumar, S.; Soderholm, L. Separation of plutonium oxide nanoparticles and colloids. Angew. Chem. Int. Ed. 2011, 123, 11430‒11433. doi: 10.1002/ange.201105624

  74. [74]

      Tamain, C.; Dumas, T.; Guillaumont, D.; Hennig, C.; Guilbaud, P. First evidence of a water-soluble plutonium(Ⅳ) hexanuclear cluster. Eur. J. Inorg. Chem. 2016, 2016, 3536‒3540.

  75. [75]

      Grant, D. J.; Weng, Z.; Jouffret, L. J.; Burns, P. C.; Gagliardi, L. Synthesis of a uranyl persulfide complex and quantum chemical studies of formation and topologies of hypothetical uranyl persulfide cage clusters. Inorg. Chem. 2012, 51, 7801‒7809. doi: 10.1021/ic3008574

  76. [76]

      Sigmon, G. E.; Ling, J.; Unruh, D. K.; Moore-Shay, L.; Ward, M.; Weaver, B.; Burns, P. C. Uranyl peroxide interactions favor nanocluster self-assembly. Figshare 2009.

  77. [77]

      Cornet, S. M.; Haller, L. J.; Sarsfield, M. J.; Collison, D.; Helliwell, M.; May, I.; Kaltsoyannis, N. Neptunium(ⅵ) chain and neptunium(ⅵ/ⅴ) mixed valence cluster complexes. Chem. Commun. 2009, 917‒919.

  78. [78]

      Zhang, X.; Li, W.; Feng, L.; Chen, X.; Hansen, A.; Grimme, S.; Fortier, S.; Sergentu, D. C.; Duignan, T. J.; Autschbach, J.; Wang, S.; Wang, Y.; Velkos, G.; Popov, A. A.; Aghdassi, N.; Duhm, S.; Li, X.; Li, J. A diuranium carbide cluster stabilized inside a C₈₀ fullerene cage. Nat. Commun. 2018, 9, 2753. doi: 10.1038/s41467-018-05210-8

  79. [79]

      (a) Infante, I.; Gagliardi, L.; Scuseria, G. E. Is fullerene C₆₀ large enough to host a multiply bonded dimetal? J. Am. Chem. Soc. 2008, 130, 7459‒7465.
      (b) Wu, X.; Lu, X. Dimetalloendofullerene U₂@C₆₀ has a U-U multiple bond consisting of sixfold one-electron-two-center bonds. J. Am. Chem. Soc. 2017, 129, 2171‒2177.

  80. [80]

      Wu, R. H.; Guo, M.; Yu, M. X.; Zhu, L. G. Two titanium(ⅳ)-oxo-clusters: synthesis, structures, characterization and recycling catalytic activity in the oxygenation of sulfides. Dalton Trans 2017, 46, 14348‒14355. doi: 10.1039/C7DT02516E

  81. [81]

      Yuan, S.; Qin, J. S.; Lollar, C. T.; Zhou, H. C. Stable metal-organic frameworks with group 4 metals: current status and trends. ACS Cent. Sci. 2018, 4, 440‒450. doi: 10.1021/acscentsci.8b00073

  82. [82]

      Yuan, S.; Qin, J. S.; Xu, H. Q.; Su, J.; Rossi, D.; Chen, Y.; Zhang, L.; Lollar, C.; Wang, Q.; Jiang, H. L.; Son, D. H.; Xu, H.; Huang, Z.; Zou, X.; Zhou, H. C. [Ti₈Zr₂O₁₂(COO)₁₆] cluster: An ideal inorganic building unit for photoactive metal-organic frameworks. ACS. Cent. Sci. 2018, 4, 105‒111. doi: 10.1021/acscentsci.7b00497

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  Figure 1  Radial density distribution (D(r) = r²R(r)²) of uranium atom

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  Figure 2  Identified formal oxidation states of actinides (An = Ac-Lr) elements. The most stable OSs are shown in filled blue circles

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  Figure 3  (a) Pseudo-O_h geometry of the hexanuclear cluster with a [Th₆(μ₃-O)₄(μ₃-OH)₄]¹²⁺ core; (b) and its ligated neutral structure [Th₆(μ₃-O)₄(μ₃-OH)₄]L₁₂^[45]. Color codes for atoms: red sphere, O; gray, C; white, H; light blue, U; deep blue, N.

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  Figure 4  Geometry of [Pa₄(μ₄-O)(μ₂-O₂)₆F₁₂]^6- with CN = 10 for Pa(Ⅴ). The metal site Pa is in black, oxygen atoms in magenta, and fluorine in turquoise. This figure is taken from references ^[16]

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  Figure 5  Topology of the uranium oxide clusters of (a) U₁₀O₁₄ core, (b) U₁₃O₁₆ core, (c) U₁₆O₂₃ core, (d) U₂₄O₃₂ core and (e) U₃₈O₅₆ cores. These figures are taken from references ^{[10, 56]}

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  Figure 6  (a) Polyhedral and ball-and-stick representations of U₂ ([(UO₂)₂(O₂)₅]^6-); (b) polyhedral and graphical representations of U₆₀ ([(UO₂)(O₂)(OH)]₆₀^60-). Each vertex in the graph of (b) represents a uranyl polyhedron. The red balls are oxygen atoms and yellow balls are the uranium atoms (a); Yellow polyhedra represent uranyl peroxide hexagonal bipyramids in (a) & (b). These figures are taken from references^{[17, 67]}

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  Figure 7  Geometry of [Pu₃₈O₅₆Cl₅₄(H₂O)₈]^14- cluster with structural linkages between Pu(Ⅳ) (green), O^2- (red), O_water (blue) and Cl^- (yellow)^[57]

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