Nanoscale uranium-based cage clusters inspired by uranium mineralogy

The ability to design and synthesize clusters of actinides with well defined structures has the potential to impact areas as diverse as recycling of used fuel in an advanced nuclear energy system, the creation of novel precursors for fabrication of fuels and waste forms (with nano-scale control of composition), and use of actinides in catalysis (Burns et al., 2005; Forbes et al., 2008a; Sigmon et al., 2009a,b,c; Unruh et al., 2010). Restricting discussion to uranium and the uranyl ion, there is no doubt that its solution chemistry is rich and complex. In inorganic aqueous solutions under acidic conditions the uranyl ion itself is an important species, but under alkaline conditions the uranyl ion is usually present as more complex clusters resulting from hydrolysis, and complexation with species in solution (such as carbonate). However, this complexity is potentially dwarfed by what can occur in solution when dozens of complex nano-scale clusters built from the uranyl ion are considered. Although the 26 clusters we have synthesized and reported to date are chemically similar, their range of sizes, charges, and charge/radius ratios suggest that their solubilities and stabilities in solution will differ significantly. Synthesis of nanoscale clusters of uranyl polyhedra adds considerable flexibility to the control of uranyl ions in solution, and there is evidence that this approach can be extended into the transuranium elements also.

Of the ~220 uranium minerals that have been described, more than 200 contain the oxidized hexavalent U cation (Finch and Murakami, 1999). However, the bulk of U in Earth's crust is tetravalent and the most important ore mineral is uraninite, UO_2+x. The diversity of U minerals arises from the complex crystal chemistry of U⁶⁺, which is present in mineral structures as part of the linear (UO₂)²⁺ uranyl ion (Burns et al., 1996, 1997; Burns, 2005). In this, the U⁶⁺ cation is strongly linked to two atoms of O by covalent bonds that are designated as triple or double bonds. The bonds are sufficiently strong so as to meet most of the bonding requirements of the O atoms (Burns et al., 1997). Hence, these O atoms seldom form strong bonds with additional cations, although they can form bonds with alkali and alkaline earth elements, and sometimes accept H bonds.

The uranyl ion has a formal valence of +2, and it occurs in mineral structures coordinated by four, five or six ligands that are arranged at the equatorial vertices of square, pentagonal, or hexagonal bipyramids (Fig. 1). These ligands correspond to O, OH, H₂O, and a variety of oxyanions such as silicate, sulphate, phosphate, and carbonate. Uranyl polyhedra are usually linked into structural units in minerals through the equatorial ligands only; as such, these structures are dominated by infinite sheets, although there are notable uranyl minerals with structural units consisting of clusters (e.g. liebigite, swartzite), chains (e.g. uranopilite, parsonsite) and frame-works (e.g. soddyite, weeksite).

Our interest in studtite, [(UO₂)(O₂)(H₂O)₂ (H₂O)₂], one of only two peroxide minerals (the other being its lower hydrate, metastudtite), began when it was found on used nuclear fuel that was in contact with deionized water (McNamara, 2002). In acidic to circum-neutral aqueous solutions, studtite is insoluble and precipitates rapidly. Although it was known for decades as a synthetic material prior to being described as a mineral (Walenta, 1973), crystals suitable for structure analysis have not been synthesized. Crystal-structure analysis using data collected from a micro crystal from Krunkelbach, Meszenschwand, Germany, revealed a structure with an unusual type of polyhedral connectivity (Burns and Kubatko, 2003). The connectivity became central to our efforts towards developing nano-scale cage clusters constructed from uranyl polyhedra.

The structure of studtite is elegantly simple (Fig. 2a,b). It contains only one uranium structural site occupied by a uranyl ion. The uranyl ions are coordinated by two H₂O groups and two peroxide units. Peroxide groups define two trans-equatorial edges of each hexagonal bipyramid, with the H₂O groups completing the equatorial coordination about the uranyl ion, where they are also in a trans configuration. The peroxide O–O bond length is ~1.45 Å, thus equatorial edges of bipyramids occupied by peroxide are shorter than normal (~2.8 Å).

The uranyl hexagonal bipyramids in the structure of studtite share their equatorial edges defined by peroxide, resulting in chains that are one polyhedron wide. These infinite chains are linked into the extended structure through hydrogen bonding only. Studtite, using peroxide created by the radiolytic breakdown of water that builds up over time (Hughes Kubatko et al., 2003), directed us to a chemical linkage that would prove essential for the ongoing development of nano-scale control of actinide chemistry.

Although the bonds within the uranyl ion are very strong and directional, those between the uranyl ion and the equatorial ligands of their bipyramidal coordination environments are much weaker, and typically ionic. As such, the linkages between uranyl ions that occur through equatorial ligands are generally pliable. Flat or somewhat corrugated sheets of uranyl polyhedra are the typical result. Disruption of the sheet-forming tendency of uranyl bipyramids may be accomplished by imposing curvature, and the peroxide bridge between uranyl ions does just that (Sigmon et al., 2009a).

In contrast to the trend of largely ionic linkages between the uranyl ion and coordinating ligands, the uranyl–peroxide interaction has covalent character (Vlaisavljevich et al., 2010). Evidence for a covalent bond between uranyl and coordinating peroxide comes in part from the structures of known uranyl peroxide compounds and clusters. Sigmon et al. (2009a) examined the details of structures that contain U–O₂–U bridges, several of which are cage clusters that we reported earlier. The U–O₂–U dihedral angle (the angle between planes defined by one or the other U⁶⁺ cation and the two O atoms of the peroxide group) in these structures tends to be in the range 130–155°. This led Sigmon et al. (2009a) to argue that the U–O₂–U bridge is inherently bent. Simulations using density function theory (DFT) reproduced the bent U–O₂–U interactions in several model clusters, as described later in this review, and also showed the presence of electron density along the uranyl–peroxide bonds, indicative of a covalent interaction (Vlaisavljevich et al., 2010).

Figure 2 illustrates conceptually the difference between a mineral structure that contains uranyl polyhedra (Fig. 2c), and nano-scale cage clusters built from uranyl peroxide polyhedra (Fig. 2d). The sheet is a fragment of the structure of the Pb uranyl oxide hydrate mineral wölsendorfite (Burns, 1999b). This mineral contains complex sheets of uranyl pentagonal and square bipyramids, with the longest primitive repeat distance in the sheet being 56.0 Å. Incorporation of peroxide along the equatorial edges of uranyl bipyramids imposes curvature, giving cage clusters such as those shown below the wölsendorfite sheet in Fig. 2d.

The purpose of this review article is to examine the structural topologies and features of nanoscale cage clusters constructed using the U–O₂–U curvature-imposing bridges. Here I compare these cage topologies with the structures of various groups of uranyl minerals, and I start by describing several structures of uranyl minerals.

All U⁶⁺ mineral structures contain the (UO₂)²⁺ uranyl ion, and their structures are built from uranyl square, pentagonal, and/or hexagonal bipyramids (Burns, 2005). In many cases, oxyanions such as silicate, phosphate, carbonate, arsenate and molybdate play essential roles in their structural units. Here I present a brief overview of uranyl mineral structures, as a prelude to extending structure topologies into cage clusters built from uranyl polyhedra.

Burns (2005) provided a hierarchical arrangement of 368 structures of inorganic uranyl compounds that included 89 minerals. Structures were grouped according to the connectivity of their structural units: clusters (7 minerals), chains (10 minerals), sheets (69 minerals) and frame-works (3 minerals). Graphical notations were adopted for cluster and chain structural units, as well as for sheets of polyhedra that are dominated by sharing of vertices, specifically those with autunite-type uranyl phosphate sheets. Other sheets were placed in the hierarchy according to the details of the topological arrangement of anions within the sheets. The utility of this approach is that rather distinct sheets of polyhedra often are based upon a single underlying sheet anion topology.

The structural units of seven uranyl carbonate minerals consist of a uranyl hexagonal bipyramid that shares three of its equatorial edges with carbonate groups (Fig. 3a). This cluster typically dominates the solution speciation of the uranyl ion under alkaline conditions in the presence of carbonate. In minerals, individual clusters tend to be linked through alkali or alkaline earth elements, and H bonding associated with H₂O groups is essential in the structures of all of these minerals except cejkaite, Na₄[(UO₂)(CO₃)₃]. No uranyl minerals other than carbonates have structural units that are isolated clusters.

Considerable topological diversity presents itself in the ten uranyl minerals with chain structural units. One of the most complex of these is the basis of the structure of uranopilite, [(UO₂)₆(SO₄)O₂(OH)₆(H₂O)₆] (Fig. 3c) (Burns, 2001). This chain contains clusters consisting of six uranyl pentagonal bipyramids that are connected through shared equatorial edges, and adjacent clusters are linked into a chain through a single sulphate tetrahedron. Individual chains are connected into the extended structure through H bonding only. Parsonsite, Pb₂[(UO₂)(PO₄)₂], also contains a topologically complex chain, in this case consisting of uranyl pentagonal bipyramids and phosphate tetrahedra (Fig. 3b) (Burns, 2000). Dimers of edge-sharing pentagonal bipyramids are linked into a chain by sharing equatorial edges and vertices with the phosphate tetrahedra.

The considerable complexity inherent in crystal structures of uranyl minerals becomes most apparent when those with sheet structural units are considered. The sheets in 16 uranyl oxide hydrate minerals consist only of uranyl bipyramidal polyhedra. Their relatively straightforward chemical compositions are in contrast to the extraordinary structural units some of these minerals present. Certainly the most complex are the sheet of uranyl pentagonal bipyramids in vandendriesscheite, Pb_1.57[(UO₂)₁₀O₆(OH)₁₁](H₂O)₁₁, (Fig. 3d) (Burns, 1997), and the sheet of uranyl square and pentagonal bipyramids in wölsendorfite, Pb_6.16Ba_0.36[(UO₂)₁₄O₁₉(OH)₄](H₂O)₁₂, (Fig. 3e) (Burns, 1999b). The primitive repeat distances in these sheets are 41.4 and 56.0 Å, respectively, despite their being built from only one or two types of polyhedra.

The sheets of uranyl polyhedra in both vandendriesscheite and wölsendorfite are unusually complex, and the underlying reasons behind this complexity, relative to other uranyl oxyhydrate minerals that contain simpler sheets, is unclear. Using a sheet anion-topology approach, it has been shown that the sheets of uranyl polyhedra in uranyl oxyhydrate minerals can be broken down into a few chain types (Miller et al., 1996). These chains can be arranged in sequences, side by side, that produce the various observed topologies (as well as hypothetical topologies). Using this approach, it is apparent that the complex topologies that underlie the sheets in vandendriesscheite and wölsendorfite are modular, meaning they can be regarded as combinations of slabs of much simpler topologies (Burns, 1999a).

In addition to the sheets that contain only uranyl polyhedra that are highlighted here, uranyl minerals and synthetic inorganic compounds provide a plethora of sheets that are built from uranyl polyhedra and a variety of oxyanions such as silicate, phosphate, arsenate, carbonate, etc. It is very rare for more than one of these types of oxyanions to occur in a structural sheet in uranyl compounds. Instead, where geochemical conditions warrant, different uranyl minerals with distinct sheet compositions and topologies coexist.

Only three uranyl minerals have framework structures. This structural class is much more populated when synthetic inorganic compounds are considered, and there were 56 structures in the structural hierarchy in 2005 (Burns, 2005). An interesting example is weeksite, K_1.26Ba_0.25Ca_0.12 [(UO₂)₂(Si₅O₁₃)]H₂O, (Fig. 3f) (Jackson and Burns, 2001). It contains sheets that consist of chains of edge-sharing uranyl pentagonal bipyramids that are cross-linked through bands of crank-shaft-like vertex sharing silicate tetrahedra. The apical (non-sheet) O atoms of the silicate tetrahedra are shared between adjacent sheets, resulting in a framework. Low-valence cations are located in interstitial positions, where they provide additional linkages between the sheet-like fragments of the structure.

Although they have never been found in a uranyl mineral, synthetic inorganic uranyl compounds may contain cation-cation interactions, and all of these have framework structures (Kubatko and Burns, 2006a; Alekseev et al., 2007). A cation–cation interaction in actinide chemistry refers to the situation where an O atom of one actinyl ion coordinates another actinyl ion. This O atom is strongly bonded to the actinide cation within the actinyl unit, but also forms a second bond as an equatorial ligand of a second actinyl ion. This type of interaction is rare in uranyl compounds (containing U⁶⁺) because the bonding requirements of the O atom of the uranyl ion are largely met by the bond to the uranyl-ion U⁶⁺ cation alone. Such cation–cation interactions are much more common when the actinyl ion contains a pentavalent cation, such as U⁵⁺ or Np⁵⁺ (Krot and Grigoriev, 2004; Forbes et al., 2006; Forbes and Burns, 2007; Forbes et al., 2007, 2008b). The lack of uranyl cation–cation interactions in minerals suggests that such a configuration is not very stable, at least under geochemical conditions in which uranyl minerals form.

Since we synthesized the first of the 26 nanoscale clusters that contain the uranyl ion, we have tried to understand three basic questions. Our search for the answers to these required an extensive combinatorial synthesis approach (about 20,000 synthesis experiments) and computational simulations of uranyl–peroxide interactions (Vlaisavljevich et al., 2010). I pose these questions here, and return to them after discussing the details of the 26 clusters that are the focus of this review article.

1. What factors(s) cause the polyhedra to assemble into nanostructures rather than into conventional extended structures?

2. Why is there such a wide range of cluster size (from 20 to 60 uranyl polyhedra)?

3. For a given number of vertices, what determines which topological isomer is selected?

An example of a large cluster, U₆₀, which is built only from uranyl peroxide polyhedra, is shown in Fig. 4 (Sigmon et al., 2009b). Traditional ball-and-stick representations of clusters as large and complex as U₆₀ are cumbersome and too detailed to give a clear picture of cluster topology (Fig. 4a). Instead, drawing the individual cation-centred polyhedra within a cluster provides a clear view of the overall topology and symmetry of the cluster (Fig. 4b). Further simplification is achieved by reducing the cluster to its graphical representation in which each vertex represents a U⁶⁺ cation and connectors indicate shared edges between the polyhedra associated with the corresponding two U⁶⁺ cations (Fig. 4c). This graphical representation facilitates examination of the polyhedral connectivity in three dimensions, as well as an analysis of the maximum symmetry of the cluster.

The uranyl ions in U₆₀ are oriented approximately perpendicular to the cluster walls (Fig. 4). Such an arrangement is standard in the various clusters we have synthesized that are based upon uranyl peroxide polyhedra. The uranyl ion O atoms extend into and away from the cluster. This is significant because these ligands are typically unreactive. The uranyl ion bond lengths in these clusters are ~1.8 Å, which is normal for the range of inorganic and organic structures that contain this largely inflexible unit (Burns et al., 1997). All of the uranyl ions in the clusters we have reported occur in hexagonal bipyramidal coordination. These polyhedra contain two or three peroxide groups that are arranged along equatorial edges of the bipyramids. Bond lengths between the U cation and the equatorial ligands are in the range of ~2.3 to 2.5 Å, and these interactions are much weaker than those within the uranyl ion. The sharing of equatorial edges corresponding to peroxide between uranyl polyhedra is a universal feature of all of the clusters we have synthesized.

We have reported synthesis of 26 clusters built from uranyl peroxide polyhedra (Burns et al., 2005; Forbes et al., 2008a; Sigmon, 2009a,b,c; Ling et al., 2010a,b; Unruh et al., 2010). Sixteen contain solely uranyl polyhedra, eight also contain pyrophosphate, and two are inorganic-organic uranyl-oxalate hybrid materials. Twenty-three are cage (closed) clusters whereas two are open rings (crowns) and one has a bowl-like shape. The following text describes the three open clusters, followed by the 23 cage clusters. The cage clusters are grouped according to the shapes of the polygons in their corresponding graphical representations. Those having squares in some combination with pentagons and/or hexagons are considered as a group, followed by those that contain exactly 12 pentagons and an even number of hexagons (the fullerenes).

In this article, clusters are designated with the notation U_xyV_z where x gives the number of uranyl ions within the cluster, y corresponds to a character string that includes “R” if an open ring structure is present and an alphabetic descriptor (starting with “a”) to distinguish clusters containing the same number of uranyl ions that would otherwise be confused. The V is an alphabetic string that signifies components other than uranyl polyhedra (here either pyrophosphate or oxalate), and z is an integer that provides the number of V units in the cluster.

Before embarking on descriptions of these complex clusters, I shall first comment on the typical coordination environments of the uranyl ion in cage clusters. There are two principal types of uranyl hexagonal bipyramids that have been used to form cage clusters (Fig. 5): those that contain two peroxide edges (designated diperoxide hexagonal bipyramids), and those with three peroxide edges (designated triperoxide hexagonal bipyramids). Where two peroxide groups are present in a hexagonal bipyramid in these clusters, they are always in a cis configuration. Note that it is not possible for a uranyl hexagonal bipyramid to contain more than three peroxide groups assuming bidentate coordination of the peroxide, and no uranyl hexagonal bipyramids in which only one edge is peroxide have been found to date in clusters. Where two of the equatorial edges of a hexagonal bipyramid are occupied by bidentate peroxide groups, it is common for a third edge to be defined by two hydroxyl groups. This situation gives a polyhedron of composition (UO₂)(O₂)₂(OH)₂.

In cage clusters, peroxide groups are bidentate to uranyl ions, and define equatorial edges of hexagonal bipyramids. In all examples found to date, such peroxide groups are shared between two uranyl polyhedra (Fig. 5a,b). In other words, a common bridge between two uranyl ions is the peroxide group, and the bridge is designated as U–O₂–U. The formal valence of peroxide is −2, and where it bridges between two uranyl ions there will be four U–O bonds extending to the peroxide group. Assuming equal bond lengths, each bond will correspond to 0.5 valence units (v.u.). This is an excellent match with the typical strength of a bond between the U⁶⁺ cation of a uranyl ion and an equatorial ligand. As a result, the peroxide bridge between uranyl ions is very stable and persists for years in aqueous solution. This may be contrasted to the fate of free peroxide in aqueous solution, where it rapidly breaks down.

In cage clusters built from uranyl hexagonal bipyramids, the edges that are shared between individual uranyl ions are either peroxide or defined by two hydroxyl groups (Fig. 5a–d). In other words, we have not found a cluster in which two uranyl ions share an edge defined by one peroxide O atom and one hydroxyl group. Neither have we found any examples of uranyl hexagonal bipyramids in clusters containing two peroxide edges that are in a trans arrangement, which would be consistent with the presence of two hydroxyl groups that are also in a trans configuration. However, the structure of studtite does present an example of uranyl hexagonal bipyramids that are linked through peroxide edges in a trans arrangement, with the remaining two equatorial vertices corresponding to H₂O groups.

All clusters discussed here were synthesized by combining an aqueous uranyl nitrate solution with peroxide, as well as with additional nutrients. Clusters self-assemble spontaneously under ambient conditions, and small-angle X-ray scattering (SAXS) data have shown that clusters can persist in water for several months (Burns et al., 2005). Evaporation of the solution, and in some cases simply aging the solution, causes clusters to precipitate into crystals that are suitable for X-ray diffraction (XRD) studies. Most of what we know about the structures of these clusters is derived from single-crystal studies. There is little doubt that crystals that form from solution give an incomplete and biased view of what species were present in solution at the time of crystallization, and we are currently using a combination of SAXS and electrospray ionization mass spectroscopy (ESI-MS) to study cluster evolution in solution.

The uranyl polyhedral portions of the clusters have an overall negative charge, and this charge can be quite high for the larger clusters. Alkali and alkaline earth cations are present as counterions both inside and outside the cluster walls. Where crystallized, counterions completely balance the charge of the cluster. In solution, counterions will be associated with the cluster, but the exact charge in any particular case is uncertain.

Cluster U₁₆ is the smallest extended cluster we have synthesized (Sigmon et al., 2009c). It has a distinct bowl-shape and its graph contains a topological square as well as four hexagons (Fig. 6a,b). The square is at the bottom of the bowl, and sides are defined by the hexagons. This topology can be extracted from that of the U₂₄ cage cluster. In synthesizing U₁₆, we used Cs as a counterion, and this large cation seems to have propped the cluster open, preventing it from continuing to grow into a closed sphere.

Clusters U_20R and U_24R are crown-shaped rings (Fig. 6c–f) (Sigmon et al., 2009c). Aside from their crown topologies, which are unique, these clusters are unusual in that their graphical representations each contain only one type of polygon. The graph for U_20R has only pentagons (Fig. 6d), whereas that corresponding to U_24R is built solely from hexagons (Fig. 6f). The U_20R graph can be extracted from that of U₂₈, but in the latter case the cage is built from uranyl hexagonal bipyramids that each contain three peroxide edges. Two different types of hexagonal bipyramids occur in both U_20R and U_24R: diperoxide and triperoxide bipyramids.

Open clusters such as U₁₆, U_20R and U_24R are less commonly encountered in our synthesis experiments than closed cages. This may indicate that they are less stable in solution than closed clusters, as might be expected, given that truncation of a crown or bowl-shape requires that the bonding requirements of some of the equatorial ligands within the bipyramid must be satisfied by linkages to counter ions. Open clusters, and especially cyclic structures such as U_20R and U_24R, hold some promise for use as linkers in as-yet-unrealized porous three-dimensional structures that take advantage of the unique topologies, cavity sizes, and pore sizes of uranyl-based cage clusters.

Seven cage clusters of uranyl polyhedra have been synthesized that contain topological squares (Fig. 7). These squares correspond to four-membered rings of peroxide-edge-sharing uranyl hexagonal bipyramids. In all cases, the four shared edges of the ring correspond to peroxide. A third edge of each bipyramid corresponds to two hydroxyl groups, and this is the third edge of the diperoxide bipyramid that is invariably shared with other uranyl polyhedra in cage clusters.

The smallest cage cluster we have synthesized that contains topological squares is U₂₄, with 24 uranyl diperoxide polyhedra and a diameter of 18.9 Å, as measured from the edges of bounding O atoms (Fig. 7a,b) (Burns et al., 2005). This cluster is built only from topological squares and hexagons. It has maximum T_d symmetry, and readers familiar with zeolite nomenclature are likely to recognize that it is topologically identical to the sodalite cage. The inner free diameter of this cluster, as measured from the edges of the bounding O atoms, is 6.3 Å. Pores are bounded by the four- and six-membered rings of uranyl hexagonal bipyramids.

The U_28a cluster is egg-shaped and lacks a centre of symmetry (Fig. 7c,d) (Unruh et al., 2010). There are 28 uranyl hexagonal bipyramids in the cluster, 24 being diperoxide polyhedra and four containing three peroxide edges. The graphical representation contains three squares, six pentagons, and seven hexagons. The top half contains pentagons only, and the bottom contains only hexagons and squares. The maximum symmetry of the topology is C_3v.

The graph representing the topology of U_28a has a hexagon at the base that is linked to three squares and three hexagons that alternate around the base, forming the lower walls of the cluster. Additional hexagons share edges with each of these three squares. The top of the cluster contains six pentagons that are arranged such that three of them are joined at the apex of the cluster.

Cluster U₃₀ is built from 14 uranyl diperoxide hexagonal bipyramids and 16 uranyl triperoxide bipyramids (Fig. 7e,f) (Unruh et al., 2010). Its graphical representation consists of squares, pentagons and hexagons. The base is a single hexagon that shares edges with six pentagons that form the lower walls of the cluster. The top is built from two squares and two hexagons, and the upper and lower portions of the cluster are joined through four hexagons and two pentagons. The cluster does not contain a centre of symmetry and has maximum symmetry C_2v.

Cluster U₃₂ contains 32 uranyl diperoxide bipyramids and has maximum symmetry C_4v (Burns et al., 2005). The graph of the U₃₂ cluster contains only two topological squares (Fig. 7g,h). These share all four of their edges with hexagons, in a similar configuration to that of the smaller U₂₄ cluster and identical to the topology of the U₁₆ cluster. Two topologically identical fragments are connected by a ring of edge-sharing pentagons. The graph of U₃₂ thus consists of two squares, eight pentagons, and eight hexagons.

Cluster U_36a is built entirely from uranyl diperoxide polyhedra and it has maximum point-group symmetry D_2d (Fig. 7i,j) (Unruh et al., 2010). Its graph contains four squares, four pentagons, and 12 hexagons. The top half is identical to the top half of the U₃₀ cluster, and consists of two squares, two pentagons, and six hexagons. The bottom half of U_36a is the mirror image of the top, rotated 90° to provide linkages between the pentagons and hexagons, consistent with the spontaneously −4 symmetry axis.

Cluster U₄₀ is built from 40 uranyl diperoxide polyhedra and has maximum symmetry D_4v (Fig. 7k,l) (Forbes et al., 2008a). Its graph contains two squares, eight pentagons, and 12 hexagons. Like U₃₂, the two ends of the graph correspond to the graph for the U₁₆ bowl-shaped cluster. In the U₄₀ graph, these two ends are separated by the 12 hexagons, and pentagons occur in the graph as pairs with a shared edge. The long dimension of these pairs extends in the elongation direction of the overall cluster. Four such pairs of pentagons are separated and connected through four hexagons, forming the equatorial region of the graph.

The largest cluster that we have synthesized that has a graph containing squares is U_44a, which is built from 44 uranyl diperoxide hexagonal bipyramids and has maximum symmetry D_2v (Fig. 7m,n) (Unruh et al., 2010). The cluster, which is dumbbell-shaped, is 31.3 Å long, as measured from the edges of the bounding O atoms. At its narrowest point, the cluster is only 12.1 Å wide.

The graph that corresponds to U_44a contains eight squares, 14 hexagons, and two octagons. The ends of the graph consist of four squares and six hexagons each, and are derivatives of the U₂₄ cluster topology. The two ends of the cluster are joined through two highly distorted hexagons, and two octagons.

Buckminsterfullerene, C₆₀, is a fullerene material and its nickname ‘buckyball’ is ingrained in the scientific and popular literature. Arthur C. Clark's novel 3001: The Final Odyssey uses buckyballs to build the station-ring that encircles Earth, and they are essential components of time machines in Simon Hawke's Reluctant Sorcerer series. In reality, C₆₀ is the most stable of a series of C clusters with fullerene topologies. Such topologies always contain 12 pentagons, and the smallest has 20 vertices and only has pentagons (Kroto et al., 1985; Fowler and Manolopoulos, 2006). As the number of vertices increases, fullerenes also contain hexagons. In the case of C₆₀, there are 20 hexagons in addition to the 12 pentagons, with 60 total vertices, each of which corresponds to a C atom.

Graphical isomer selection is an important aspect of the structures of C-based fullerenes (Fowler and Manolopoulos, 2006). For example, there are 1812 possible fullerene topologies that contain 60 vertices. Buckminsterfullerene adopts the one that has no adjacent pentagons, as well as the one with the highest symmetry. Adjacent pentagons in the topologies of C-fullerenes reduce their stability, as they create bond strain due to increased curvature. C₆₀ is the most stable C-fullerene because it is the smallest fullerene (smallest number of vertices) that has no adjacent pentagons. The other 1811 fullerene topologies with 60 vertices, as well as all fullerenes with fewer than 60 vertices, contain adjacent pentagons.

The smallest C-fullerene, the so called ‘baby buckyball’, stabilized by attachment of 10 Cl atoms, contains 50 C atoms (Xie et al., 2004). Of the 271 fullerene topologies that are possible for 50 vertices, the one with the smallest number of pentagonal adjacencies is selected.

Adjacent pentagons in C-fullerene topologies reduce stability because they increase local curvature, with a reduction in bonding orbital overlap (Kroto et al., 1985). The situation is very different in the case of cage clusters with fullerene topologies that are built from uranyl polyhedra. Specifically, linkages between the uranyl bipyramids are through the equatorial edges of the hexagonal bipyramids. In clusters that contain only uranyl bipyramids, these edges correspond to either peroxide groups or two hydroxyl groups. As discussed below, the U–O₂–U linkage is typically bent, and there is only a small energetic penalty for bending the U–(OH)₂–U bridge.

Unlike in C-based fullerenes, increases in local curvature have much less of an energetic penalty where the fullerene topologies are built from uranyl polyhedra. In contrast to C-fullerenes, it is possible to synthesize a range of cage clusters built from uranyl polyhedra that have fewer than 60 vertices, and that have an abundance of adjacent pentagons. We have reported the synthesis of six cage clusters built solely from uranyl peroxide polyhedra that have fullerene topologies, and describe each briefly in the following paragraphs.

The smallest closed cluster of uranyl polyhedra we have synthesized to date, U₂₀, consists of 20 uranyl triperoxide polyhedra and has maximum symmetry C_5v (Fig. 8a,b) (Sigmon et al., 2009a). The cluster has a diameter of 18.0 Å, as measured from the edges of bounding O atoms. Its graph is the simplest possible fullerene topology and contains only 12 pentagons. U₂₀ demonstrates unequivocally that adjacent topological pentagons present little or no energetic penalty in cage clusters built from uranyl polyhedra, as this cluster has more pentagonal adjacencies than exist in any other fullerene topology.

Cluster U₂₈ contains only uranyl triperoxide polyhedra (Fig. 8c,d) (Burns et al., 2005). Its graphical representation contains 12 pentagons and only two hexagons. This cluster has maximum symmetry T_d, and U₂₈ adopts the isomer with 28 vertices with minimal pentagonal adjacencies and the highest symmetry.

Cluster U₃₆ contains 12 uranyl triperoxide polyhedra and 24 uranyl diperoxide polyhedra (Fig. 8e,f) (Sigmon et al., 2009b). The corresponding graphical representation of the cluster contains the mandatory 12 pentagons and eight hexagons. The maximal symmetry of the cluster is D_6h. Of the 15 possible fullerene isomers with 36 vertices, U₃₆ selects the one with the least pentagonal adjacencies and the highest symmetry.

The U₄₄ cluster is built from uranyl triperoxide polyhedra (Fig. 8g,h) (Sigmon et al., 2009b). The cluster, which is distinctly peanut-shaped, has a graphical representation that consists of 12 pentagons and 12 hexagons. The maximum symmetry of this cluster is D_3d. Of the 89 possible fullerene topologies that contain 44 vertices, there are several that have fewer pentagonal adjacencies than that adopted by U₄₄. However, with the exception of highly non-spherical topologies, U₄₄ adopts the fullerene topology with 44 vertices that has the highest symmetry. This observation supports the argument that symmetry is more important than pentagonal adjacencies in the selection of fullerene isomers for cage clusters built from uranyl polyhedra. In many cases, the highest-symmetry fullerene isomer also has the fewest pentagonal adjacencies, as an even distribution of pentagons in the topology is consistent with higher symmetry. The observation that symmetry trumps pentagonal adjacencies was included in a ‘Research Highlights’ in Nature, which stated “Fullerenes usually have as few adjacent pentagons as possible, but the peanut bucks this trend. This is because the peanut shape has higher symmetry, which the uranyl clusters prefer over minimizing pentagonal neighbors”.

Cluster U₅₀ is built solely from uranyl diperoxide polyhedra (Fig. 8i,j) (Forbes et al., 2008a). It has maximum symmetry D_5h and a fullerene topology consisting of 12 pentagons and 15 hexagons. Of the 271 possible fullerene topologies that contain 50 vertices, U₅₀ selects the one with the fewest pentagonal adjacencies and the highest symmetry. This cluster is topologically identical to the C₅₀Cl₁₀ fullerene.

Cluster U₆₀ (Fig. 8k,l), which is built from uranyl diperoxide polyhedra and has maximum symmetry O_h, is the largest cage cluster we have synthesized using only uranyl polyhedra, with a diameter of 27.6 Å, measured from the edges of bounding O atoms (Sigmon et al., 2009b). The cage cluster encloses a cavity, for which the diameter is 11.9 Å, as measured from the edges of the bounding O atoms. U₆₀ is perhaps the most fascinating of the clusters we have synthesized using only uranyl peroxide polyhedra, in part because it is the largest, but more so because it is the uranyl analogue of the famous C₆₀ buckminsterfullerene. The graphical representation of U₆₀ has 12 pentagons and 20 hexagons, and is exactly the same as the topology of C₆₀. It has maximum symmetry O_h and is the smallest possible fullerene topology that has no adjacent pentagons.

The reader will have noticed that all clusters built from uranyl hexagonal bipyramids only involve shared edges between the bipyramids, and these are exclusively either equatorial edges defined by peroxide groups or by two hydroxyl groups. The U–O₂–U bridge is essential for creating the curvature that causes cage clusters to form, rather than the extended sheets that are typical of uranyl compounds. However, the bridges that correspond to two hydroxyl groups are not essential to the cluster formation. Replacement of these edges with other chemical entities that can bridge between uranyl ions could add chemical complexity and potentially tunability to properties of the cage clusters.

The search for chemical species that can bridge between uranyl ions, replacing the role of bipyramid edges defined by two hydroxyl groups, is simplified by an understanding of the characteristics needed. There are two basic requirements. First, the bridging species must be compatible with the geometrical constraints of the uranyl hexagonal bipyramid. The species needs to present two anions for bonding along the edge of a hexagonal bipyramid, with a separation on the order of ~2.8 Å. The second requirement is that the bond-valence deficiency of the anions must be an approximate match for the requirements of an equatorial ligand–uranium bond in a hexagonal bipyramid. In the bond-valence formalism, this corresponds to ~0.5 v.u.

Excellent candidate species for incorporation into the walls of cage clusters built from uranyl hexagonal bipyramids are pyrophosphate and oxalate units. Each of these is shown in Fig. 5, where it is apparent that the aforementioned geometrical and bond-strength requirements are essentially met. Extensive combinatorial synthesis experiments, coupled with single-crystal XRD studies of resulting crystals, has shown that both of these species can be incorporated into complex cage clusters that are based upon uranyl hexagonal bipyramids. As was the case in simpler clusters consisting of only uranyl hexagonal bipyramids, it is the U–O₂–U bridge that is the driver for the curvature of these clusters, and thus nanoscale clusters instead of extended two or three-dimensional structures.

There are several possible ways in which pyrophosphate or oxalate can coordinate a uranyl ion. The specific types of arrangements that have been used to create nanoscale clusters are shown in Fig. 5. Uranyl ions are coordinated by bidentate oxalate with a side-on arrangement (Fig. 5i,j). Pyrophosphate coordinates a uranyl ion by forming an equatorial edge of a hexagonal bipyramid by sharing two of its O atoms with the uranyl ion, one from each of the phosphate tetrahedra (Fig. 5e,f). Pyrophosphate also occurs where it links to three uranyl hexagonal bipyramids by sharing one vertex with each (Fig. 5g,h).

Cluster U₁₈Py₂PCP₆ contains 18 uranyl hexagonal bipyramids, two pyrophosphate groups, and six methylenediphosphonate groups (Fig. 9a–d) (Ling et al., 2010a). Two uranyl-polyhedral-based fragments are linked through the six methylenediphosphonate groups to form the cluster. One of these contains eight hexagonal bipyramids that are linked into two five-membered rings, with two polyhedra shared between the five-membered rings (Fig. 9c). U₁₈Py₂PCP₆ is unusual in the context of uranyl pyrophosphate clusters because one shared equatorial edge between two bipyramids is defined by hydroxyl, whereas most contain no hydroxyl at all. The remainder of the shared edges between these hexagonal bipyramids are peroxide. The other half of the cluster consists of 10 uranyl hexagonal bipyramids that are linked into an open ring through shared peroxide equatorial edges (Fig. 9d). Two pyrophosphate groups are located on the inside of this ring, where they each bridge between three different bipyramids.

Three uranyl pyrophosphate clusters contain 20 uranyl hexagonal bipyramids (Fig. 9e–o) (Ling et al., 2010a). These are U₂₀Py_6a, U₂₀Py_6b, and U₂₀Py₁₀, the first two being polymorphs of the same composition. Consider first the cluster U₂₀Py_6b (Fig. 9e–h). There are two distinct portions that are built from uranyl hexagonal bipyramids, and these are linked through six pyrophosphate units. One of these portions consists of eight uranyl hexagonal diperoxide polyhedra that are linked through shared peroxide equatorial edges to give two five-membered rings that have two bipyramids in common (Fig. 9g). This fragment is analogous to that found in U₁₈Py₂PCP₆ except that no hydroxyl groups are present in the case of U₂₀Py_6b. The other portion contains 12 hexagonal bipyramids, six triperoxide polyhedra and six diperoxide polyhedra (Fig. 9h). Each of the triperoxide bipyramids shares all three of their equatorial edges, which are defined by peroxide, with adjacent bipyramids. The uranyl diperoxide bipyramids share their two cis peroxide equatorial edges with other uranyl bipyramids, and a third edge is defined by O atoms of the pyrophosphate groups which link the two uranyl-polyhedral fragments together.

Cluster U₂₀Py_6a (Fig. 9i–k) is closely related to U₂₀Py_6b, the difference occurring in the two fragments formed by the linked uranyl hexagonal bipyramids. In U₂₀Py_6a, there are two identical fragments, each of which contains four triperoxide bipyramids and six diperoxide bipyramids (Fig. 9k). The triperoxide bipyramids each share all three peroxide edges with other bipyramids, and the diperoxide bipyramids share both of their cis peroxide units with other bipyramids. The result is three five-membered rings of polyhedra which have a common central bipyramid.

Cluster U₂₀Py₁₀ is very different from the other clusters containing 20 uranyl hexagonal bipyramids (Fig. 9l–o). It is elongated, with two ends defined by five-membered rings of edge-sharing uranyl diperoxide polyhedra (Fig. 9n). The equatorial region consists of a unique 10-membered ring of diperoxide bipyramids (Fig. 9o). The diperoxide bipyramids share their peroxide edges, in a cis configuration, around the ring geometry. Each bipyramid is linked to a single pyrophosphate group on alternating sides of the ring. These pyrophosphate groups bridge to the five-membered rings that terminate the cluster at either end.

Graphical representations of the uranyl pyrophosphate clusters that contain 20 uranyl hexagonal bipyramids are shown in Figure 9f,j,m. Vertices represent U⁶⁺ cations, blue lines represent shared polyhedron edges between uranyl bipyramids, and yellow lines correspond to bridges through pyrophosphate groups. Although they are variously distorted, the three graphs each consist of 12 pentagons only. These graphs are topologically identical to that of U₂₀ described above, and are fullerene topologies. Each of the uranyl pyrophosphate clusters containing 20 bipyramids are topological derivatives of the U₂₀ cluster in which selected shared peroxide edges are replaced by pyrophosphate bridges. Incorporation of these bridges increases the size of the cluster, changes the overall maximum symmetry, and results in different pore sizes as compared to the U₂₀ cluster.

Clusters U₂₄Py₁₂ and U₃₂Py₁₆ are both based on four-membered rings of peroxide-edge-sharing uranyl hexagonal bipyramids (Fig. 10a–c, 10l–n) (Ling et al., 2010a). There are six of these four-membered rings in U₂₄Py₁₂, and eight in U₃₂Py₁₆. Each hexagonal bipyramid is coordinated by a bidentate pyrophosphate group that defines an equatorial edge of the bipyramid. Pyrophosphate groups bridge between bipyramids of different four-membered rings. In the case of U₂₄Py₁₂, this results in a spherical cluster, whereas U₃₂Py₁₆ is rather flattened.

The graphical representation of cluster U₂₄Py₁₂ is shown in Fig. 10b. Here, each vertex represents a U atom, blue lines designate connections between uranyl polyhedra through shared equatorial edges, and yellow lines correspond to connections between U cations that are through pyrophosphate bridges. The graph contains only topological squares and distorted hexagons, and is topologically identical to that of U₂₄. U₂₄Py₁₂ is derived from U₂₄ by replacing each bridge between uranyl polyhedra that corresponds to two OH groups by a single pyrophosphate group.

The graph of cluster U₃₂Py₁₆, derived as for U₂₄Py₁₂, contains squares, hexagons, and two octagons (Fig. 10m). There is no topological analogue amongst known clusters that are built only from uranyl polyhedra. U₃₂Py₁₆ has dimensions of 28.2 and 18.0 Å, as measured from the edges of bounding O atoms. The cluster walls contain pores, the largest of which correspond to the topological octagons in the graphical representation. The free space of this pore is 6.3 Å, as measured from the edges of bounding O atoms. Smaller pores in the cluster, that correspond to distorted hexagons in the graphical representation, have a free diameter of ~4.1 Å.

Two clusters have been isolated that contain 26 uranyl hexagonal bipyramids and either 11 or 6 pyrophosphate groups: U₂₆Py₁₁ and U₂₆Py₆ (Ling et al., 2010a). These rather complex clusters differ significantly, despite having the same number of uranyl polyhedra (Fig. 10d–k).

Cluster U₂₆Py₁₁ contains two fragments that are built from uranyl hexagonal bipyramids, and these fragments are connected through eight bridging pyrophosphate groups (Fig. 10d–g). The top fragment consists of 16 uranyl hexagonal bipyramids, four of which are triperoxide polyhedra and 12 of which are diperoxide (Fig. 10f). In all cases, the peroxide groups correspond to edges that are shared between uranyl bipyramids. There are two five-membered rings of edge-sharing bipyramids that are connected through six additional bipyramids to create an open ring. Two pyrophosphate groups are located towards the centre of this ring, where each bridges between three bipyramids in an analogous fashion to the connectivity found in cluster U₁₆Py₂PCP₆. The lower half of the cluster consists of 10 uranyl diperoxide bipyramids that are linked, by sharing peroxide edges, into two five-membered rings (Fig. 10g). These rings are connected through a single pyrophosphate unit.

Cluster U₂₆Py₆ has 14 triperoxide and 12 diperoxide uranyl bipyramids (Fig. 10h–k). All of the peroxide groups are shared between uranyl ions, such that the cluster contains eight distinct five-membered rings of polyhedra. These are joined by common polyhedra into a ribbon that bends back toward itself. Connections between different polyhedra in this ribbon, that result in a cage cluster, are through six pyrophosphate groups.

Analysis of the graphical representations of clusters U₂₆Py₁₁ and U₂₆Py₆ shows that they are not topological derivatives of any known clusters that are built only from uranyl polyhedra.

Cluster U₃₆Ox₆ contains 36 uranyl hexagonal bipyramids and six oxalate groups (Fig. 11a,b) (Ling et al., 2010b). There are two types of uranyl polyhedra in the cluster, 24 uranyl triperoxide polyhedra and 12 diperoxide polyhedra that complete their coordination spheres with bidentate oxalate groups. The cluster is elongated with two distinct halves, built from uranyl polyhedra, that are linked through the oxalate groups in the equatorial region of the cluster.

The graphical representation of U₃₆Ox₆ is shown in Fig. 11b, in which each U⁶⁺ cation is a vertex, shared edges between uranyl bipyramids are shown as blue lines, and bridges through oxalate groups are shown as yellow lines. Note that the topology contains 12 pentagons and eight distorted hexagons. It is a fullerene topology, and corresponds to the graphical isomer adopted by U₃₆ that contains uranyl hexagonal bipyramids only.

Cluster U₆₀Ox₃₀ (Fig. 11c–d) is the largest cluster we have synthesized and reported in the literature, and also contains the most U atoms (together with U₆₀) (Ling et al., 2010b). It is delightfully simple, with all of the 60 uranyl diperoxide hexagonal bipyramids linked into five-membered rings that are independent of each other. Within these five-membered rings, the shared edges all correspond to peroxide groups. Each of the uranyl hexagonal bipyramids is coordinated by oxalate in a bidentate edge-on configuration, and each oxalate group bridges between two bipyramids from different five-membered rings.

The graphical representation of U₆₀Ox₃₀, produced as for U₃₆Ox₆ above, consists of 12 pentagons that correspond to the rings of bipyramids, and 20 distorted hexagons (Fig. 11d). Thus, this is a fullerene topology and U₆₀Ox₃₀ adopts the only 60-vertex fullerene isomer that has isolated pentagons only. This is the same isomer adopted by U₆₀ that has uranyl hexagonal bipyramids only, and C₆₀ buckminsterfullerene.

U₆₀Ox₃₀ is spherical and measures 31.0 Å from the edges of outer bounding O atoms, which can be compared with 27.0 Å for U₆₀. Note that U₆₀Ox₃₀ can be derived from U₆₀ simply by replacing shared edges of hexagonal bipyramids that are defined by two OH groups by a single oxalate group. This results in larger topological hexagons, and larger pore sizes in the corresponding clusters. Note that insertion of different bridges between the uranyl peroxide hexagonal bipyramids allows tuning of the sizes of these pore spaces. It also increases the inside diameter, which is 16.9 Å for U₆₀Ox₃₀, measured from the edges of bounding (interior) O atoms.

The graphical representations of the topologies of the 26 clusters of uranyl polyhedra that we synthesized and reported in the literature are summarized in Fig. 12. Here, the topologies are arranged based upon the shapes of their constituent polygons. From this summary, it is apparent that six clusters are built from combinations of pentagons and hexagons (the fullerenes), four consist of squares and hexagons, one is built from hexagons only, five consist of pentagons only, and five clusters contain squares, pentagons and hexagons. The graphs of four clusters, shown at the bottom of Fig. 12, contain polygons in addition to squares, pentagons and/or hexagons. Each of these contains pyrophosphate bridges. Note that no clusters have been synthesized that have graphs built solely from squares, nor do any of the clusters have graphs that can be constructed using squares and pentagons only. Examination of the graphs of the various topologies also shows that squares do not have adjacent pentagons. Put another way, where squares occur in a topology, they always share edges with hexagons, and never with pentagons. Pentagons regularly share edges with other pentagons or hexagons in these topologies, and hexagons also share edges with other hexagons. There are no examples of adjacent squares in a topology.

Small-angle X-ray scattering (SAXS) data provide information concerning the size, shape and dispersivity of objects in the range of 1 to 100 nm. The technique works well for clusters dissolved or suspended in solution, and has been applied to examine various uranyl peroxide cage clusters in solution (Burns et al., 2005; Ling et al., 2010a,b; Unruh et al., 2010).

We harvested crystals containing the U₂₆Py₆, U₃₂Py₁₆ and U₆₀Ox₃₀ clusters and dissolved each of them in different aliquots of ultra-pure water (Ling et al., 2010a,b). The SAXS data collected for the resulting solutions provided scattering curves consistent with the size and shapes of the clusters determined from the crystallographic studies. In other words, shape and size models fitted to the SAXS data have geometric parameters that are consistent with those determined for clusters crystallized and examined using single-crystal diffraction. Furthermore, SAXS data for solutions collected several days after crystals containing clusters were dissolved also are consistent with the presence of the nanoclusters in solution. This result is somewhat surprising, as the environment in which the clusters are dissolved is substantially different from that used for the synthesis of the clusters (i.e. different pH, different ionic strengths).

The SAXS data were collected for the mother solutions in contact with crystals known to contain U₂₄ after 2, 28 and 180 days from mixing (Burns et al., 2005). The SAXS data showed marked change in the scattering behaviour of the solution relative to the solution age. The data collected for the oldest solution could be modelled using a spherical shell with dimensions consistent with those for U₂₄ derived from the crystal-structure analysis. However, solutions examined after only 2 and 28 days of aging seem to be polydisperse. Note that crystals of U₂₄ can be harvested within a few days of preparing the mother solution, which indicates that mono-dispersivity of the clusters in solution is not a condition for crystal growth.

The SAXS data collected for mother solutions that had been in contact with crystals combining U₂₀Py₁₀, U₂₄Py₁₂, U₂₀Py_6a, U₂₀Py_6b, U₂₆Py₆ and U₃₂Py₁₆ all produced scattering profiles consistent with clusters of appropriate sizes in solution, although in most cases it was not possible to model the scattering using only a single cluster size and shape (Ling et al., 2010a). This is consistent with polydispersivity of the clusters in solution, even after clusters had crystallized.

Density functional theory (DFT) is a quantum mechanical theory that provides a computational approach to modelling bonding in structures. In this approach, many-electron systems are examined using functionals of the electron density. DFT has been applied to many actinide-bearing systems, with good success overall (Vlaisavljevich et al., 2010).

The computational cost of a quantum mechanical calculation increases very rapidly with the number of electrons in the system under study, and rigorous calculations that include all the components of a cage cluster containing tens of uranium atoms would be extremely expensive. However, considerable insight into such cage clusters can be attained by focusing high-level calculations on carefully chosen fragments of the clusters.

Vlaisavljevich et al. (2010) used high-level DFT calculations to study the formation of uranyl peroxide cage clusters. Many of the simulations examined the details of a cluster that consists of only two uranyl hexagonal bipyramids that are linked through a single shared equatorial edge. The details of the shared edge are of pivotal importance in this study, as it can either be a peroxide group or two hydroxyl groups. Calculations, which included full geometry optimizations, were done for cases where the uranyl ions are each coordinated by two additional peroxide or oxalate groups in a bidentate configuration (side-on in the case of oxalate). In order to neutralize the charge of the cluster, various counter ions were also included in the calculations. The positions of the counter ions were included in the geometry optimization.

The simulations provided geometrically reasonable clusters. Of considerable interest is the dihedral angle of the linkage between the two bipyramids. Where the shared edge is two hydroxyl groups, the optimized dihedral angles are ~180°. In contrast, where the shared edge is peroxide, the simulations give a cluster that has a bent dihedral angle (~150°).

Vlaisavljevich et al. (2010) examined the details of the electron density of simulated clusters containing two uranyl hexagonal bipyramids that share an edge defined by peroxide or two hydroxyl groups. In the case of the peroxide bridge, projections of molecular orbitals revealed a bonding molecular orbitals extending along the U–O_peroxo join that is a linear combination of the U 6p and the peroxo p orbitals. The U 5f and 6d orbitals are strongly involved in the bond to the uranyl ion O atoms. Calculations for the cluster containing an OH–OH bridge showed that no such bond exists along the U–OH.

Calculations were also done for clusters containing two uranyl hexagonal bipyramids with a shared peroxide edge in the presence of different counter ions. The optimized geometries showed a correlation between the U–O₂–U dihedral angle and the size of the counter ion. Larger counter ions give larger dihedral angles (i.e. closer to 180°).

The largest clusters that Vlaisavljevich et al. (2010) studied were five-membered rings of uranyl hexagonal bipyramids, with the shared equatorial edges all corresponding to peroxide groups. Each uranyl ion in the cluster was also coordinated by an oxalate group in a bidentate, side-on configuration. Simulations again provided reasonable geometries and showed that the U–O₂–U dihedral angles are strongly bent in the most stable configurations. Again, the dihedral angles varied with the choice of counter ions, with larger cations giving angles closer to 180°.

Earlier in this review, I asked three questions concerning the formation of cage clusters built from uranyl polyhedra. Here, each of these questions is addressed.

1. What factors(s) cause the polyhedra to assemble into nanostructures rather than into conventional extended structures? The covalent interaction that occurs between the U⁶⁺ of the uranyl ion and the peroxide O atoms favours a bent U–O₂–U dihedral angle (Vlaisavljevich et al., 2010). In inorganic structures in general, the interactions between the U atom of the uranyl ion and ligands located at the equatorial vertices of the bipyramid are ionic. In other words, there is no bonding orbital along these interactions, and as such they tend to be either flat, with a dihedral angle between shared uranyl ions of about 180°, or there is only a small energetic penalty for a bent configuration. Where peroxide is shared between two uranyl ions, in contrast, a bent configuration is significantly more stable.

   Dozens of minerals and compounds contain sheets that are built from uranyl bipyramds only (e.g. Fig. 3d,e). The sharing of equatorial edges between uranyl bipyramids occurs in most of these structures. However, the shared edges are defined by O²⁻ anions or OH⁻ groups, and there is probably no covalent interaction between these ligands and the U atom of the uranyl ion. Thus, the dihedral angles tend towards 180° and are somewhat flexible.

   Incorporation of peroxide edges that are shared between uranyl bipyramids favours a strongly bent dihedral angle. This is inconsistent with forming the wealth of sheet topologies found in uranyl oxyhydrate minerals and compounds, and instead is the driving force towards cage clusters.

   Despite a very extensive combinatorial synthesis approach, we have only found a single sheet that contains uranyl peroxide polyhedra (Kubatko and Burns, 2006b). This sheet contains only uranyl diperoxide hexagonal bipyramids. These occur as dimers where the shared equatorial edge between the bipyramids is defined by two OH groups and the U–(OH)₂–U dihedral angle is 180°. These dimers are linked to compositionally identical dimers through shared peroxide edges. In this case, however, the U–O₂–U dihedral angle is 134.8°. This strongly bent interaction is accommodated by a highly unusual sheet topology that contains large void spaces.

2. Why is there such a range of cluster sizes (from 20 to 60 uranyl polyhedra)? DFT simulations have shown that where peroxide is shared between two uranyl bipyramids, the U–O₂–U dihedral angle is larger (closer to 180°) if the counter ions are large, and the smallest dihedral angles occur where Li or Na are the counterions (Vlaisavljevich et al., 2010). In practice, these results from simulations indicate that the identity of the counter ions in the vicinity of uranyl hexagonal bipyramids that are bridged by peroxide groups to some extent influences the dihedral angle. The specifics of the dihedral angle relate to the degree of curvature within the wall of a cage cluster built from uranyl peroxide polyhedra. The computational results indicate that, in general, larger counterions will result in cages with less curvature, a finding that is compatible with most of the clusters found through our synthesis experiments. However, the situation is somewhat more complex in synthesized clusters, as several contain more than one type of counterion, and the role of H bonds that extend from OH groups at equatorial vertices of uranyl bipyramids is likely to be important as well.

3. For a given number of vertices, what determines which topological isomer is selected? Consider a cluster containing 60 linked uranyl hexagonal bipyramids. In the restricted case of the fullerene topologies, there will be 12 pentagons and 1812 ways in which the 60 vertices can be arranged. Extending the range of polygons permitted to include squares balloons, the total possible combinations with 60 vertices increases to 35,070 as calculated using CaGe, http://caagt.ugent.be/CaGe (Brinkman et al., 2010)

   In the case of C-based fullerenes, topologies that avoid adjacent pentagons are favoured. We find no such preference in cage clusters built from uranyl bipyramids, and have even synthesized the fullerene topology with 20 vertices and nothing but pentagonal adjacencies. Analysis of the symmetry of the clusters we have synthesized, as well as those that are topologically possible (i.e. that have plausible connectivity in terms of bond lengths and angles), indicates that, for a given number of vertices, there is a strong tendency for selection of the isomer with the highest symmetry.

   When fullerene topologies are considered, it is common for the highest symmetry isomer also to have the smallest number of pentagonal adjacencies. This occurs because spacing pentagons evenly over the cage graph is consistent with higher symmetry. Thus, in all but one case, the cage clusters of uranyl peroxide bipyramids with fullerene topologies adopt the isomer with the minimum pentagonal adjacencies. The lone exception, U₄₄, occurs where the highest-symmetry topologies do not correspond to the fewest pentagonal adjacencies.

Compositionally, cage clusters of uranyl peroxide polyhedra are most closely related to the sheets of uranyl polyhedra that occur in uranyl oxyhdrate minerals and synthetic compounds. Other than the obvious presence of curvature in the cage clusters, there are several other important topological differences between the cages and sheets. Note that the cage clusters are all built from uranyl hexagonal bipyramids, whereas most of the sheets of uranyl polyhedra in minerals contain uranyl pentagonal bipyramids. In the cage clusters, each uranyl hexagonal bipyramid is linked to exactly three others by the sharing of equatorial edges. In sheets of uranyl polyhedra, uranyl pentagonal bipyramids most commonly share four of their equatorial edges with adjacent bipyramids, and thus equatorial vertices of the central bipyramid are often shared by more than one of the four surrounding bipyramids.

Given that uranyl hexagonal bipyramids are used to form cage clusters, and that none have been found to link to more than three others through the sharing of their equatorial edges, ~50% of the surface of the walls of these clusters will correspond to areas within the bipyramids. In contrast, the packing of the uranyl pentagonal bipyramids within sheets that occur in minerals is considerably more dense, where the area that corresponds to bipyramids exceeds ~80%.

No uranyl minerals contain either pyrophosphate or oxalate. Uranyl phosphate minerals are well represented in nature, with the largest groups being the autunite and phosphuranylite groups. Autunite-group structures all contain sheets of uranyl square bipyramids and phosphate tetrahedra. These polyhedra are linked through shared vertices only, such that each of the equatorial O atoms of the uranyl square bipyramids are shared with phosphate tetrahedra. Each tetrahedron shares all four of its vertices with different uranyl bipyramids. In the phosphuranylite group of minerals, the structural units are sheets of uranyl pentagonal and hexagonal bipyramids, as well as phosphate tetrahedra. The bipyramids share some of their equatorial edges, giving chains that are two polyhedra wide. These chains are linked through phosphate tetrahedra, and each tetrahedron shares one of its edges with a bipyramid in a chain on one side, and a single vertex with a bipyramid on the other side. Topologically, uranyl phosphate sheets have very little in common with cage clusters built from uranyl hexagonal bipyramids and pyrophosphate groups.

Here, I have described the structures and topologies of 26 unique nanoscale clusters built from uranyl hexagonal bipyramids, as well as pyrophosphate or oxalate groups in some cases. These clusters spontaneously self-assemble in aqueous solution over a wide ranges of pH under ambient conditions. Crystallization facilitates determination of the details of their structures. Three of these clusters are open and are either bowl- or crown-shaped. The other 23 are closed cage clusters.

The 26 clusters reviewed all contain uranyl-peroxide-uranyl bridges, and these are inherently bent due to a covalent interaction between the U 6p and peroxide orbitals. The bent U–O₂–U interaction directs the formation of curved structures, rather than extended sheets that are common in uranyl compounds in the absence of peroxide.

Clusters built from uranyl hexagonal bipyramids display an extensive range of topologies. Most of these consist of some combination of squares, pentagons or hexagons. Six clusters built from uranyl polyhedra only, as well as several that also contain pyrophosphate or oxalate, adopt fullerene topologies. Topological isomers are selected so as to maximize the symmetry of the cluster, thereby spreading strain as evenly over the cluster as possible.

Cluster sizes span a considerable range (~1.5–3 nm), and contain 20–60 uranyl polyhedra. The specifics of the U–O₂–U dihedral angle depend upon the size and location of counter ions, with larger counter ions favouring a dihedral angle that is closer to 180°. This dihedral angle influences the curvature of cage clusters built from uranyl polyhedra, and thus also the size of closed clusters.

We continue to expand our research efforts concerning the nano-scale control of actinides in aqueous solution. We have synthesized and structurally characterized more than 20 additional clusters built from uranyl polyhedra and a variety of other bridging groups. These clusters will be the subjects of future communications, and will reveal an unprecedented level of cluster complexity. Whereas nanoscale actinide materials science is in its infancy, clusters based upon uranyl polyhedra are poised to overtake polyoxometalates and even keplerates in terms of diversity and complexity.

We are studying intensively the assembly and fate of uranyl-based cage clusters in solution using a combination of SAXS and ESI-MS, techniques which are providing insights into the competitions between different cluster topologies. Working with collaborators, we are measuring the solubilities, dissociation reactions, and heats of formation of uranyl-based cage clusters, and are complementing this work with computational studies. This range of approaches will be essential to developing a sophisticated understanding of structure-property relations in nanoscale uranyl-based cage clusters. Such an understanding will be integral to future attempts to design clusters for specific purposes, such as applications in advanced fuel cycles.

Finally, I reiterate that the impetus to create nanoscale uranyl-based clusters grew directly from our interest in the mineralogy of uranium, and studtite showed us the way, presenting a key example of a uranyl compound in which peroxide bridged between uranyl hexagonal bipyramids.

During preparation of this review, PCB was supported by the ‘Materials Science of Actinides Center’, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0001089.

Our research concerning nanoscale cage clusters of uranyl polyhedra was initiated under funding from the National Science Foundation Environmental Molecular Science Institute at the University of Notre Dame (EAR02-21966), and was later funded by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy, Grant No. DE-FG02-07ER15880. Since 1^st August 2009, our research concerning these cage clusters has been funded by the Energy Frontier Research Center.

The work summarized here is the result of the efforts of undergraduate students, graduate students, and post-doctoral researchers at the University of Notre Dame. These are T.Z. Forbes, J.G. McAlpin, R. Murphy, G.E. Sigmon, D.K. Unruh, J. Ling, B. Weaver, M. Ward, L. Pressprich, A. Burtner, J. Qiu, C.M. Wallace, and K.A. Kubatko.