*3.4. Structural and Topological Complexity*

Calculation was performed in several stages and the main results are summarized in Table 3 and Figures 5 and 6. First, the topological complexity (**Tl**), according to the maximal rod (for chains) or layer symmetry group, was calculated, since these are the basic structural units. Second, the structural complexity (**Sl**) of the units was analyzed taking into account its real symmetry. The next contribution to information comes from the stacking (**LS**) of chained and layered complexes (if more than one layer or chain is in the unit cell). The fourth contribution to the total structural complexity is given by the interstitial structure (**IS**). The last portion of information comes from the interstitial H bonding system (**H**). It should be noted that the H atoms related to the U-bearing chains and layers were considered as a part of those complexes but not within the contribution of the H-bonding system. Complexity parameters for the whole structures were calculated using *ToposPro* package [87].



#### *Crystals* **2019** , *9*, 639


**Table 3.** *Cont.*

*Crystals* **2019** , *9*, 639


**Table 3.** *Cont.*

**Figure 5.** Ladder diagrams showing contributions of various factors to structural complexity in terms of bits per unit cell for the structures based on chains (**a**), layers with edge-linkage of polyhedra (**b**), layers with corner-linkage of polyhedra (**c**) and organically templated compounds (**d**). Legend: TI = topological information; CI = cluster information (valid for Prw and Nsb: See text for details); SI = structural information; LS = layer stacking; IS = interstitial structure; HB = hydrogen bonding. See Table 3 and text for details.

**Figure 6.** Ladder diagrams showing normalized contributions (in %) of various factors to structural complexity for the structures based on chains (**a**), layers with edge-linkage of polyhedra (**b**), layers with corner-linkage of polyhedra (**c**) and organically templated compounds (**d**). Legend: see Figure 5. See Table 3 and text for details.

#### **4. Discussion**

Structural features of natural uranyl selenites make one think about the conditions of their formation in nature. Analogies with synthetic compounds, which have a similar structure, allow some of the most probable pathways to be suggested. The formation of structural units with edge-sharing polyhedra in most cases indicates their hydrothermal origin, and the synthetic uranyl selenites **28** and **29**, whose structures are built upon the layers with a phosphuranylite topology (Figure 3g), are no exception. Both compounds were obtained from the aqueous medium at temperatures above 220 ◦C. In the case of compounds with structures based upon 1D units, the situation is somewhat more complicated. Topological type *cc*1–1:2–1, which is one of the most common among the U(VI)-bearing oxysalts, was repeatedly observed in the structures of compounds obtained at room temperature. However, synthetic uranyl selenite **9** was grown at slightly higher temperatures of 80 ◦C. Moreover, the presence of rather specific uranyl tetragonal bipyramids in the structure of derriksite refers to a family of isotypic uranyl phosphate [88], molybdate [89], and tellurite [90] compounds, which were obtained during hydrothermal (above 180 ◦C) or high temperature solid state (above 650 ◦C) syntheses. Analogously, the crystal structures of synthetic uranyl chromates [67,68] and molybdates [69], which are isotypic to that one of demesmaekerite, were obtained at hydrothermal conditions (above 120 ◦C) or solid state reactions (at 300 ◦C). Nevertheless, based on laboratory [91,92] and field observations, namely of the mineral association from Zálesí (Czech Republic) [8], it is clear that demesmaekerite and piretite (and several other unnamed or poorly identified U-Se phases) formed as a result of supergene alteration processes, which exclude hydrothermal activity. These observations are supported by the radioanalytical dating of demesmaekerite.

The crystal structure of derriksite is built on the 1D uranyl selenite complexes, whose symmetry is described by the þ *cm*11 rod symmetry group. However, its highest (topological) symmetry is described by the centrosymmetric þ *<sup>a</sup>*2/*m*11 rod group (Figure 7a). Stacking of chains doubles the complexity contribution of the uranyl selenite block (68.107 bits/cell) into the whole structure, but is still less than the contribution of the Cu-O interstitial block (96.370 bits/cell) and nearly equal to the contribution of the interstitial H-bonding system (64.287 bits/cell; Figure 5 and 6). Alteration of uranyl tetragonal bipyramids by pentagonal ones with the additional H2O molecule in the equatorial plane of *Ur* preserves the topology, but it doubles the size of the reduced segment of a chain and changes its maximal symmetry to the þ *<sup>a</sup>*2/*m*11 rod group (Figure 7b). The absence of the interstitial substructure makes the topological complexity parameters be equal to those for the whole structure of **8** and **9**.

**Figure 7.** 1D uranyl selenite units and their highest rod symmetry groups for derriksite (**a**), [(UO2)(HSeO3)2(H2O)] (**b**) and demesmaekerite (**c**). Legend: see Figure 1.

The topological symmetry of the uranyl selenite chain in the structure of demesmaekerite is monoclinic þ *<sup>a</sup>*21/*m*11 and is higher than its real triclinic <sup>þ</sup>-1 symmetry (Figure 7c). In this case, the uranyl selenite substructure (117.207 bits/cell) makes the largest contribution to the complexity of the whole structure. The interstitial complex contributes a slightly lower amount of information (85.926 bits/cell), and even less is accounted for in the H-bonding system (60.842 bits/cell; Figure 5 and 6).

The crystal structures of 17 uranyl selenites and selenite-selenates are built upon the layers of *cc*1–1:2–4 topological type and those are distributed almost equally between pure inorganic and organically templated compounds having various monovalent inorganic ions and protonated amine molecules of different shapes and sizes as an interstitial block. Moreover, this topology preserves changes in the chemical composition of uranyl-bearing layers, which involves the occurrence of uranyl selenites, selenite-hydrogen selenites, and hydrogen selenite-selenates. It is of interest that all isomers within this family of compounds, including chemical substitutions and two geometrical isomers (see Chapter 3.3.), have the highest symmetry of the layer described by the *p*21/*b* layer group (Figure 8). Furthermore, the topological symmetry is preserved in the structures of almost all compounds, except for two of them (Table 3). All three aforementioned cases point to the fact that the current topological type is unusually resistant and one of the most preferable in the systems with the U:*T* ratio = 1:2. As for the complexity calculations, certainly, those will primarily depend on the number of orbits (atoms). Thus, the H-free uranyl selenite layer has the lowest amount of information (152.196 bits/cell), next in a row would be the uranyl selenite-hydrogen selenite complex (172.080 bits/cell), and finally those containing selenate oxyanions (192.423 bits/cell). Analogously, complexity parameters for the whole structure majorly depend on the size of the aliphatic part of organic molecules.

**Figure 8.** (**a**–**d**) Uranyl selenite layers, symmetry elements, and the respective layer symmetry groups for various isomers of the *cc*1–1:2–4 topological type (**a**–**d**: see text for details). Legend: see Figures 1 and 2.

The crystal structures of three uranyl selenite minerals and two synthetic compounds are based on dense layers with a phosphuranylite anion topology. It is of interest that natural and synthetic compounds are described by the different orientation matrices (Figure 4). The (**ud**)(**du**) orientation of the lone electron pairs in the structures of synthetic uranyl selenites **28** and **29** resulted in the formation of layers with the *c*2/*m* topological symmetry (58.711 bits/cell), whereas the highest symmetry of those in natural compounds is described by the (**ud**)(**ud**) matrix and orthorhombic *pmmn* layer symmetry group (121.421 bits/cell). It should be noted that only Sr-bearing synthetic compound **28** has the real symmetry of the layer equal to the topological one. In the cases of marthozite, guilleminite, larisaite, and Li-bearing synthetic compound, topological symmetry is significantly reduced by the interstitial cations and H2O molecules (Table 3, Figures 4 and 5). The contribution of each of the components makes the marthozite the most complex inorganic uranyl selenite (960.860 bits/cell; Figures 5 and 6). It is of interest that the formation of a particular isomer causes the specific arrangement of the layers, and it appears that the (**ud**)(**ud**) isomer of the posphuranylite topology, which results in the formation of zig-zag layers, is more stable and most likely thermodynamically preferable among the others, since it has only been observed in the structures of natural layered uranyl selenites.
