*3.3. Structural Complexity*

The information-based complexity parameters for **1**–**4** are given in Table 5. This approach, recently developed by S.V. Krivovichev [28–30] and successfully implemented in [22,31,32], allowed to compare the structures in terms of their information content and to analyze contributions of various substructural building blocks into the complexity of the whole structure. Structural complexity is a negative contribution to the configurational entropy of a crystalline compound and thus could help to understand and describe the processes of various structures formation in the laboratory and, what is of special interest, in nature.


**Table 5.** Structural and topological complexity parameters for the uranyl sulfate compounds.

The general trend in evolution of crystallization was recently summarized as follows [33–36]: complexities of structures formed on the latter stages of crystallization are higher than those for the phases growing on the primary stages, wherein very complex structures may form as transitional architectures prior or between phases with relatively small amounts of structural information.

The evaluation was performed in several steps (Figure 3). First, the topological complexity (**TI**), according to the maximal rod (for chains) or layer symmetry group, was calculated since these are the basic structural units. Second, the structural complexity (**SI**) of the units was analyzed, taking into account its real symmetry. The next contribution to information came 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 was given by the interstitial structure (**IS**). And the last portion of information came 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. For instance, contribution of **H** was equal to the difference between complexity parameters for the whole structure and those for the structural model with no H atoms; contribution of **IS** was equal to the difference between complexity parameters for the structural model with no H atoms and those for the structural model with no interstitial substructure at all; etc. Complexity parameters for the aforementioned contributions were calculated manually using the general formulae [28–30]. Complexity parameters for the whole structures were calculated using the *ToposPro* package [37]. Complexity calculations showed that the crystal structures of **1**, **2**, and **4** should be described as intermediate, possessing the values below 500 bits/cell, while compound **3** just slightly passed through this border (508.168 bits/cell) and should be described as complex.

**Figure 3.** Ladder diagrams showing contributions and normalized contributions (in %) of various factors to structural complexity in terms of bits per unit cell. Legend: TI = topological information; CI = cluster information; SI = structural information; LS = layer stacking; IS = interstitial structure; HB = hydrogen bonding. See Table 5 and text for details.
