*3.3. Topological Analysis*

The vast majority of the uranyl selenite crystal structures are based on the layered complexes of various topologies (Tables 1 and 2), and only nine compounds have chain-based crystal structures. However, among those nine compounds, two are uranyl selenite minerals.

Crystal structures of derriksite and another two synthetic compounds (Tables 1 and 2, Figure 1a–c), which are actually the same but were refined in different space groups, are based on the 1D units of the *cc*1–1:2–1 topological type (graph is an infinite chain of four-membered vertex-sharing rings). The graph corresponds to the type of chains, which were observed in the kröhnkite [63]. This topology is one of the most common and simplest chain topologies among U(VI)-bearing compounds with the [*T*Om] <sup>n</sup><sup>−</sup> groups (m = 3,4; *T* = S, Se, P, As). It was observed in the structures of uranyl-sulfate minerals as svornostite, K2Mg[(UO2)(SO4)2]2(H2O)8 [64], rietveldite, Fe(UO2)(SO4)2(H2O)5 [65], and their Mg-bearing synthetic analogues Mg[(UO2)(*T*O4)2(H2O)](H2O)4 (*T* = S, Se) [66]. Although the topology of chains is the same, their structures are remarkably different, representing two different isomers. In the case of derriksite (Figure 1c), U6<sup>+</sup> atoms present in the tetragonal bipyramidal coordination, where all four equatorial O atoms are shared with the [SeO3] <sup>2</sup><sup>−</sup> groups, and each selenite group in turn has only two O atoms shared with two neighbors' *Ur*. Uranyl selenite chains in the structure of derriksite are directed along [001] and the equatorial planes of uranyl bipyramids are arranged parallel to the (101). In between the chains, Cu-centered tri-octahedral layers are observed as being arranged parallel to (010), in which each Cu atom has four OH− groups shared with the neighbor Cu atoms and two more vertices in the *trans-*orientation are the third vertices of selenite pyramids, non-shared with U-centered bipyramids. Selenite groups are arranged in such a way that lone electron pairs from one side of the U-Se chain are directed in one way, and from the other side, in the opposite direction (*up* or *down*), relative to the equatorial planes of uranyl bipyramids. Thus, the sequence of orientation symbols could be written as (**u**)(**d**). The latter has been termed an *orientation matrix*. In the structures of synthetic [(UO2)(HSeO3)2(H2O)] [35,36] compounds, U6<sup>+</sup> atoms are arranged in the center of pentagonal bipyramids, in which four equatorial O atoms are shared with the [HSeO3] − groups and the fifth vertex is occupied by the H2O molecule. Hydrogen selenite groups also have two O atoms shared with two neighboring *Ur* and the third vertex is attributed to the OH− group. The linkage of chains into the 3D structure is carried out by the means of H-bonding between the neighbor chains only. The arrangement of lone electron pairs relative to the equatorial planes of uranyl bipyramids is staggered on both sides of the chain, so the orientation matrix for the current geometrical isomer is (**ud**)(**du**).

**Figure 1.** (**a**–**k**) 1D complexes in the crystal structures of natural and synthetic uranyl selenites (**a**–**k**: see text for details). Legend: U-bearing coordination polyhedra = yellow; Se atoms = orange; O atoms = red; H atoms = white; N atoms = light blue; black nodes = U atoms, white nodes = Se atoms. SeIVO3 trigonal pyramids and NO3 groups are shown in a ball-and-stick mode.

The crystal structure of demesmaekerite is based on the chains of the *cc*1–1:3–2 topology (Figure 1d,e), which is very similar to the previous type. The graph is a vertex-sharing infinite chain of

four-membered rings with additional one-connected selenite group to each *Ur*. This topology is quite rare and has been observed in the structures of two synthetic uranyl chromates Na4[(UO2)(CrO4)3] [67] and K5[(UO2)(CrO4)3](NO3)(H2O)3 [68], two uranyl molybdates Na3Tl5[(UO2)(MoO4)3]2(H2O)3 and Na13Tl3[(UO2)(MoO4)3]4(H2O)5 [69], and one uranyl selenate (C2H8N)3[(UO2)(SeO4)2(HSeO4)] [52]. U6<sup>+</sup> atoms are arranged in the centers of pentagonal bipyramids, so that four equatorial vertices of which are shared with two-connected selenite groups (as in previous type), and the fifth vertex that was occupied by H2O molecule, now is replaced by another one-connected [SeO3] <sup>2</sup><sup>−</sup> pyramid. Uranyl selenite chains are passing along the (101), and stacked one above the other, forming blocks parallel to (010). These blocks are separated by the sheets of edge-shared Cu- and Pb-centered coordination polyhedra. There are three types of Cu2+-centered octahedra in the structure of demesmaekerite, [CuO4(OH)2] <sup>8</sup><sup>−</sup>, [CuO3(OH)3] <sup>7</sup>−, and [CuO2(OH)3(H2O)]6<sup>−</sup>, and the single type of ninefold [Pb2<sup>+</sup>O6(OH)3] <sup>13</sup><sup>−</sup> complexes. Lone electron pairs of one- and two-connected selenite groups from one side of the U-Se chain are oriented in the same direction, while on the other side the direction is the opposite, thus the orientation matrix could be written as (**u**)(**d**).

The crystal structure of the organically templated compound **33** [48] is based on the uranyl selenite nitrate 1D complexes that belong to the *cc*1–1:2–12 topological type (Figure 1f,g). This topology has been observed in the structures of several uranyl and neptunyl sulfates and selenates, for example, see [70–73], and represents an infinite chain of edge-shared four-memebered cycles, in which each uranyl polyhedron has three equatorial vertices shared with three selenite groups while the left pair of O atoms is edge-shared with the [NO3] <sup>−</sup> group. Being three-connected to the neighbor *Ur*, [SeO3] 2− pyramids have a lone electron pair oriented either *up* or *down* relative to the equatorial planes of uranyl bipyramids in the (**ud**)<sup>∞</sup> sequence.

The crystal structures of Ca- [37] and Sr-bearing [38] isotypic uranyl selenites are based on 1D complexes of the *cc*1–1:2–14 topological type (Figure 1h,i), which are built by the dimers of edge-sharing uranyl pentagonal bipyramids that are interlinked by the pair of edge- and vertex-sharing selenite groups with another one-connected selenite group decorating the fifth non-shared equatorial vertices of U polyhedra from both sides of such a double-wide chain. It should be noted that [SeO3] <sup>2</sup><sup>−</sup> pyramids, which are involved in the linkage of U dimers, have lone electron pairs oriented *up* from one side of the chain, and *down* from the other side, thus illustrating the (**ud**)<sup>∞</sup> sequence. This type of chains occurs in the structures of two uranyl minerals: Parsonite, Pb2[(UO2)(PO4)2, [74] and hallmondite, Pb2[(UO2)(AsO4)2](H2O)*n*, [75].

The crystal structures of two more Sr- [37] and Na-hydronium-bearing [39] compounds are based on the uranyl selenite chains with an edge-sharing motif, similar to the previous one. Chains belong to the *cc*1–1:2–15 topological type (Figure 1j,k), and are built by the dimers of edge-sharing uranyl pentagonal bipyramids, which, in contrary to the aforementioned topology, are interlinked by a pair of only vertex-sharing selenite groups, while edge-sharing selenite pyramids in this case decorate both sides of the chain. Both compounds represent two different geometrical isomers, assuming the orientation of lone electron pairs. Thus, Sr uranyl selenite possesses the same (**ud**)<sup>∞</sup> sequence, as in a previous case, while the Na-bearing compound has a (**u**)<sup>∞</sup> sequence. This type of topology has been observed in several synthetic uranyl chromates, phosphates, and arsenates, as well as in lakebogaite, CaNa(Fe3<sup>+</sup>)2[(H(UO2)2(PO4)4(OH)2](H2O)8 [76].

The crystal structures of 17 synthetic uranyl selenites are based on the layers, which belong to the *cc*2–1:2–4 topological type (Figure 2a,b), the most common among the uranyl selenite compounds and among the layered uranyl compounds, generally. The topology consists of dense four-membered cycles and large hollow eight-membered rings. It is worth noting, that almost all sheets of this topology contain protonated [HSeO3] − groups with the H-bonds arranged inside the eight-membered cycles. Although the topology of the sheets remains the same, their real architecture is quite diverse, which occurs due to various blocks involved in the structure formation. Thus, the structures of these compounds are formed via combination of the [UO7] <sup>8</sup>−, [HSeO3] <sup>−</sup>, [SeO3] <sup>2</sup>−, and [SeO4] 2− coordination polyhedra through common oxygen atoms. Uranyl pentagonal bipyramids share all

of five equatorial O atoms with the selenite or selenate groups, while Se-bearing oxyanions act as two- or three-connected units. Such a diversity of building blocks opens up the possibility of a large number of geometric isomers' existence. Within the uranyl selenite and selenite-selenate compounds of *cc*2–1:2–4 topology, three isomers are distinguished: Layers, containing only selenite groups; those, having selenite and hydrogen selenite groups; and those with hydrogen selenite groups and selenate tetrahedra. However, what is the most interesting, is that all three isomers have a similar orientation of lone electron pairs and fourth non-shared vertices (for tetrahedra), which is described by the very simple (**ud**) matrix. Only except for the compound **36**, which has the (**ud**)(**du**) matrix.

**Figure 2.** (**a**–**j**) 2D complexes based on corner-sharing linkage in the crystal structures of synthetic uranyl selenites and selenite-selenates (**a**–**j**: see text for details). Legend: see Figure 1; SeVIO4 groups = orange tetrahedra.

The crystal structures of Ag-bearing uranyl selenite [41] is based on the layered complex of *cc*2–1:2–5 topological type (Figure 2c,d). This type of topology has been observed in the structures of several synthetic uranyl and neptunyl molybdates as Na2(UO2)(MoO4)2 [77] and K3NpO2(MoO4)2 [78]. Topological types *cc*2–1:2–4 and *cc*2–1:2–5 have nearly identical chemical composition and looks quite similar. Those graphs are built from the similar four- and eight-membered rings, and even have the same connectivity of black and white vertices (U and Se polyhedra, respectively), but the topologies are different due to differences in coordination sequence [18]. Such chemically identical, but topologically different structural units are called topological or structural isomers. It should be noted that the *cc*2–1:2–4 topology is much more representative among the inorganic oxysalt compounds than

*cc*2–1:2–5. If the lone electron pair of the selenite pyramid would be equated to the fourth non-shared vertex of the selenate tetrahedron, the current isomer can be described by the (**uddu**)(**dduu**) matrix.

The crystal structure of **41** [55] is based on the 2D complexes, possessing unprecedented topology for both the structural chemistry of uranium and the chemistry of inorganic oxysalts in general, of the *cc*2–1:2–14 type (Figure 2e,f). U atoms are arranged in the centers of pentagonal bipyramids. Each [SeO4] <sup>2</sup><sup>−</sup> group is three-connected, coordinating three uranyl ions, whereas protonated selenite groups coordinate one uranyl ion each. The topology is remarkable due to the presence of one-connected branches inside eight-membered cycles, which are actually selenous acid groups.

The crystal structure of **25** [41] is based on the layered complexes of *cc*2–1:2–19 topological type (Figure 3a,b), which is a derivative of the autunite topology [18], where each uranyl pentagonal bipyramid has only one edge shared with the selenite group. The graph of the layer consists of eight-membered rings only. The current isomer can be described by the (**uudd**)(**uddu**)(**dduu**)(**duud**) matrix.

**Figure 3.** (**a**–**n**) 2D complexes based on edge-sharing linkage in the crystal structures of natural and synthetic uranyl selenites and selenite-selenates (**a**–**n**: see text for details). Legend: see Figures 1 and 2.

Compound **26** [37] is the only known uranyl selenite, which crystal structure is based on the layered complexes of *cc*2–1:2–21 topological type (Figure 3c,d). The graph of the U-bearing sheet consists of dense 4-membered and large 12-membered rings. Double links between the black and white vertices in a graph indicate sharing of an edge between uranyl coordination polyhedra and the selenite pyramid. Despite the fact that [SeO3] <sup>2</sup><sup>−</sup> groups are two-connected, edge-sharing coordination generates a possibility for an orientational isomerism of the lone electron pair arrangement. Current isomer can be described by the (**ud**) matrix. It is of interest that interlayer Ba2<sup>+</sup> cations are actually arranged within the layer, inside the 12-membered rings.

Next compound, **42** [56], got into the review with a large tolerance. There are three nonequivalent positions of Se in the structure, only one of which was occupied by both Se(VI) and Se(IV), and the amount of the latter is very small (~0.07 per formula unit). The current topology of the *cc*2–2:3–4 type (Figure 2g,h) is one of the most common among synthetic uranyl sulfates, chromates, and selenates (>30 structures are known), but it has not been observed for any compound with a higher content of selenite ions than here.

The crystal structures of three organically templated compounds, **43** [57], **44**, and **45** [56], are based upon the layers with U:Se = 3:5 formed as a result of condensation of the [UO2] 2+, [UO2(H2O)]<sup>2</sup>+, [SeVIO4] <sup>2</sup>−, and [HSeIVO3] − coordination polyhedra by sharing common oxygen atoms. The corresponding graph of *cc*2–3:5–3 topology is built by four- and six-membered rings (Figure 2i,j). This topology of inorganic complexes is typical for uranyl selenite-selenates but has also been observed in some pure uranyl selenates, for instance, Rb4[(UO2)3(SeO4)5(H2O)] [79]. The presence of two-connected selenite trigonal pyramids and three-connected selenate tetrahedra gives rise to geometric isomerism. Thus, the orientation matrices can be written as (**ududud**)(**uddu**-) for the first and second, and (**duuudd**)(**uddu**-) for the third compound, respectively.

The simplest uranyl selenite, at least from the chemical point of view, [(UO2)(SeO3)] [33], has a layered structure (Figure 3e,f). According to Lussier et al. [80], the anionic topology of the layer of this compound belongs to the topology consisting of triangles and hexagons. The topology of the layer in this compound is the same as in mineral rutherfordine, [(UO2)(CO3)] [81,82], which is why it is called a rutherfordine anion topology. This topology consists of parallel chains of edge-sharing hexagons divided by dimers of edge-sharing triangles. Each of the hexagons is occupied by *Ur*, and one triangle per dimer is occupied by the [SeO3] <sup>2</sup><sup>−</sup> group. The other half of the triangles is vacant. Electroneutral sheets are linked together by van der Waals interactions only. It should be noted that recently, an isotypic neptunyl compound has been reported [34].

One of the most remarkable topological types within the uranyl selenite family of compounds is the phosphuranylite topology (Figure 3g,h): The crystal structures of marthozite, guilleminite, and larisaite are based on such layers, while haynesite and piretite (although their structures are still unknown) are supposed to have topologically the same architecture due to the similarity of their unit-cell parameters. Except for minerals, two more Li- and Sr-bearing synthetic uranyl selenites have structures based on the 2D units belonging to the phosphuranilite anion topology. The phosphuranilite topology contains two types of alternating infinite chains: Edge-sharing dimers of pentagons that are further linked by edge-sharing hexagons, and zig-zag chains of edge-sharing triangles and squares [80,83]. The topology can be described by the 61524232 ring symbol with pentagons and hexagons occupied by *Ur*, triangles are occupied by selenite anions, while squares stay vacant. In the crystal structures of natural and synthetic compounds, additional mono-, divalent cations, and H2O molecules are arranged in between the layers forming covalent and H-bonding systems to build the 3D structure. In the structure of marthozite, there are Cu2<sup>+</sup> cations arranged in between the layers and octahedrally coordinated by two O atoms of uranyl ions from the above and underlying layers and four O atoms of H2O molecules from the interlayer space. There are also four 'zeolite'-like H2O molecules arranged in the interlayer space, which are not covalently bonded to cations and held in the structure by H-bonds only. Na<sup>+</sup> and K<sup>+</sup> sites in the structure of larisaite are characterized by partial occupancies, as well as H2O molecules and hydronium cations, which are statistically distributed over six sites within the interlayer space. Thus, there are also two types of H2O molecules, those which coordinate alkali cations and 'zeolite'-like, as in the structure of marthozite. Na<sup>+</sup> and K<sup>+</sup> cations in the crystal structure of larisaite

alternately occupy neighbor cavities in the interlayer space, while in the structure of guilleminite, those cavities are equivalent and occupied only by Ba2<sup>+</sup> cations. It is of interest that according to previous works [1,27], only two sites of H2O molecules coordinating Ba<sup>2</sup><sup>+</sup> cations have been determined in the structure of guilleminite, leaving rather a large cavity to be vacant. Our single crystal XRD studies at low temperatures allowed us to determine the third site arranged within the void and occupied by the H2O molecule, which suggests a change to the formula of guilleminite to Ba[(UO2)3(SeO3)2O2](H2O)4. Such ambiguity allows reference to the variable character of H2O molecules' amount within these structures, which could depend on the chemical composition and conditions, and the temperature and humidity storage of samples. Another interesting feature is that the structures of natural and synthetic compounds belong to different geometrical isomers. The (**ud**)(**du**) isomer was determined in the structures of Li- and Sr-bearing synthetic uranyl selenites, while (**ud**)(**ud**) isomer was observed in the crystal structures of all three minerals. It should be noted that implementation of the (**ud**)(**du**) isomer results in formation of stepped layers, in which each subsequent chain of edge-sharing uranyl polyhedra is located above the level of the previous chain, whereas the (**ud**)(**ud**) isomer results in the formation of zig-zag uranyl selenite layers, in which the chains of edge-sharing uranyl polyhedra are alternately located above or below the mean plane of the layer (Figure 4).

**Figure 4.** (**a**–**d**) The crystal structure projections along the layers, uranyl selenite layers, symmetry elements, and the respective layer symmetry groups for guilleminite (**a**,**b**) and Sr[(UO2)3(SeO3)2O2](H2O)4 (**c**,**d**). Legend: see Figure 1.

Another topology that consists of hexagons, pentagons, squares, and triangles can be described by the 61534635 ring symbol (Figure 3i,j), and is quite rare. There are only three compounds known, whose structures are based on the layers of this type. Two of them are Cs-bearing [46] and organically templated [58] uranyl selenites, and the third one is a very exotic Cs2[(UO2)4(Co(H2O)2)2(HPO4)(PO4)] uranyl phosphate compound [84]. Layers are formed by the specific heptamers, and the uranyl hexagonal bipyramid is in the center, sharing each even equatorial edge with three uranyl pentagonal bipyramids, while the odd edges are shared with [SeO3] <sup>2</sup><sup>−</sup> groups. The linkage of these heptamers occurs via the third non-shared vertex of the selenite group and by the two additional selenite groups of each pentagonal bipyramid, which share all three O atoms with three neighbor heptamers. Thus, all pentagons and hexagons in the anion topology are occupied by the uranyl ions, triangles, and by the selenite groups while squares are vacant. It should be noted, that the arrangement of the lone electron pair in the structures of both uranyl selenites is different. In the structure of Cs-bearing uranyl

selenite, the orientation of the lone electron pairs around the core of uranyl bipyramids is uneven and can be described by the (**uuudduuuuudd**) matrix, while that in the structure of organically templated uranyl selenite is uniform (**uududuuddudd**), but it does not result in any visible differences in the distortion or undulations between the layers.

The crystal structure of the Cs-bearing uranyl selenite-selenate **31** [46] phase is based on the layers of a highly remarkable anion topology with the 61564636 ring symbol (Figure 3k,l), which could be assumed as the modular structure, composed of blocks from both the phosphuranylite and zippeite anion topologies. The latter, for instance, is one of the most common topologies among the natural uranyl sulfates [25]. The zippeite fragment of the topology includes selenate tetrahedra, and the phosphuranylite fragment contains selenite groups.

The crystal structure of the only uranyl diselenite compound [47] is based on the sheets of miscellaneous anion topology of the 815238 type (Figure 3m,n), consisting of octagons, pentagons, and triangles. The layered complex is built by the dimers of edge-sharing uranyl pentagonal bipyramids, which are arranged similarly as in the structures of such minerals as deliensite, Fe[(UO2)2(SO4)2(OH)2](H2O)7 [85] or plášilite, Na(UO2)(SO4)(OH)(H2O)2 [86], but the linkage character is remarkably different. Instead of isolated groups, uranyl dimers are interlinked lengthand side-ways through the vertex-sharing diselenite groups; besides, lone electron pairs within the [Se2O5] <sup>2</sup><sup>−</sup> oxyanions are co-directed. In those diselenite groups, which are arranged along the extension of the uranyl dimers, lone electron pairs are oriented towards one side relative to the plane of the sheet, and in those groups, arranged side-ways, the direction of the lone electron pair is the opposite. The crystal structure of **32** is anhydrous and free of additional ions, thus electroneutral layered complexes are linked into the 3D structure by the means of electrostatic interactions involving lone electron pairs only.
