Next Article in Journal
Certain Inclusion Properties for the Class of q-Analogue of Fuzzy α-Convex Functions
Next Article in Special Issue
Temperature-Dependent Phase Variations in Van Der Waals CdPS3 Revealed by Raman Spectroscopy
Previous Article in Journal
Investigations of Symmetrical Incomplete Information Spreading in the Evidential Reasoning Algorithm and the Evidential Reasoning Rule via Partial Derivative Analysis
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Symmetry
Volume 15
Issue 2
10.3390/sym15020508
symmetry-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

2d, or Not 2d: An Almost Perfect Mock of Symmetry

by
Vladislav Komarov
1,2,*,
Ruslan Galiev
1 and
Sofya Artemkina
1,*
1
Nikolaev Institute of Inorganic Chemistry SB RAS, 3, Akad. Lavrentiev Ave., 630090 Novosibirsk, Russia
2
Inorganic Chemistry, Department of Natural Sciences, Novosibirsk State University, 1, Pirogova Str., 630090 Novosibirsk, Russia
*
Authors to whom correspondence should be addressed.
Symmetry 2023, 15(2), 508; https://doi.org/10.3390/sym15020508
Submission received: 29 December 2022 / Revised: 30 January 2023 / Accepted: 4 February 2023 / Published: 14 February 2023
(This article belongs to the Special Issue Symmetry/Asymmetry in 2D Materials)
Browse Figures
Versions Notes

Abstract

:
The paper is related to an interesting case of revision of X-ray crystal structure with a lack of experimental data. Complexes V4OSe8I6·X (X = I2 or 3,5-dimethylpyrazole) with O-centered complex molecules [V4O(μ-Se2)4I4(μ-I)2] were synthesized in our group. In the further search for new relative compounds in the V-Se-I-O system, we obtained several crystals with different structures, including “V4OSe6I3”, with incredibly complicated connectivity of {V4O(Se2)4I6} units bridged via both diselenide and iodide ligands. Due to the absence of phase-pure products and the possible instability of some of the phases under ambient conditions, we were mainly guided by the single-crystal X-ray diffraction data. However, seeing a very complex coordination mode in the “V4OSe6I3” structure, we have carefully analyzed the structure from the positions of symmetry and chemical synthesis in this system. The “new structure” was recognized as the complex superposition of the structure of another compound with composition “V4OSe6I10” just found in the same experiment. We outlined the course of observations, reasoning and solutions to the symmetry false estimation problem, which we believe to be of interest to readers dealing with X-ray diffraction analysis.

1. Introduction

For more than 100 years, physico-chemical analysis [1,2] has been one of the most effective ways to study near-equilibrium systems. However, due to ever-increasing complexity of studied objects and required details of their characterization, more and more new methods of physico-chemical investigation are currently being proposed [3]. In particularly difficult cases, classical methods of investigation without isolation of individual phases (thermal analysis and calorimetry, X-ray phase analysis, measurement of physico-mechanical and electrical properties) based on the study of a bulk of matter can be significantly extended with “local” methods (X-ray or electron diffractometry, electron or atomic force microscopy, X-ray spectroscopy fluorescence or electronic photoemission, etc.).
Diffraction methods and, primarily, single crystal X-ray diffraction analysis (SC XRD), are the most common ways to characterize the connectivity (i.e., topological dimensionality of a bond network) and periodicity of materials at the atomic level. Methods of analysis of diffraction beyond Bragg peaks also allows touch parameters of the crystalline domains of dimensions [4] and local-range order [5] (italics mark three different characteristics of “dimensionality”, which are often poorly distinguished in chemical texts [6]).
Frequently, even approximate data on the structure of phases provide valuable information, allowing both correcting synthetic approaches and predicting a number of their physico-chemical parameters. It is especially helpful because modern diffraction studies can be carried out for small samples (X-ray diffraction—100-0.1 microns, electron diffraction—down to ~10 nm). In this regard, it becomes tempting to interpret diffraction data measured on preliminary test samples, which are often of “low-quality” (both by the degree of localization of diffraction effects and by the signal-to-noise ratio) to obtain any advance information about the system under study. However, when conducting structural analysis of data, the quality of which is “on the verge of acceptable” one should expect false solutions and carefully verify the obtained structural models. In most cases, in order to attribute a particular model to a false one, it is enough to have a basic “chemical intuition” (by uncharacteristic coordination or the presence of “impossible” chemical bonds) or empirical methods of analysis (for example, using the bond valence method [7,8,9]). Another major barrier for the false structure models is an analysis of their symmetry [10,11,12], and deeper theoretical considerations of entire classes of crystal structures or abstract structure-related constructions [13,14,15,16,17]. However, in rare cases some faults can “break through” these barriers, and sometimes “live” in the scientific community for a long time. However, even they could play the positive role in the development of the chemical science (e.g., an example of wrong XRD hydrogen atoms attribution, demonstrated by Dr. Alison Edwards at AsCA-2019 [18]: [M2X8]-cluster structure described in [19] at first, was then successively corrected and used by F. A. Cotton to illustrate his theory of multiple metal–metal bonds [20,21]).
Another non-trivial example of the SC XRD faults occurred during physico-chemical characterization of a reaction product, which was obtained during our exploration of new types of compounds realized in halogen (Hal)—chalcogen (Q)—transition elements (M) systems. To date, a large number of compounds in the M-Q-Hal-(O) systems were obtained for niobium, tantalum, molybdenum, tungsten and rhenium [22,23,24,25], while those for titanium, zirconium, hafnium and vanadium are much less known. However, for any of the systems, a thorough and exhaustive search of possible phases is crucial both for understanding of the fundamental chemistry of the elements [26,27] and for development of novel, “greener” and “smarter” materials [28,29]. The completion of the ideas about the phase diversity is expected to serve as a reliable foundation for the development of the computational chemistry of transition elements in complex oxidation states [30,31], and the analysis of specific intermolecular interactions [32].
Our work on the search for vanadium chalcohalides for the first time revealed the conditions for the formation of an O-centered tetra-nuclear complex [V4O(µ-Se2)4I4(µ-I)2]0d [33,34] (hereinafter nd superscript will denote the connectivity of the coordination fragments), which is arranged similarly to molecular titanium complexes [35,36]. There is a μ4-O connected V4-core in the shape of a distorted tetrahedron, which is additionally bridged by four diselenide (Se2)2− and two iodide ligands; four terminal iodides coordinate V atoms additionally. On the other hand, it was known for titanium and niobium to form extended structures (polymeric chains), which are constructed from such tetra-nuclear units [37,38,39]. In order to approach vanadium selenoiodide with a polymeric structure, we screened the conditions of the syntheses using an evacuated ampoule method, in a narrow temperature range. As a result, we obtained a unique product containing (seemingly) three new different phases possessing a common structural fragment {V4O(µ-Se2)4I4(µ-I)2}, surprisingly having topologically different structures of molecular (0D), chain (1D) and layer (2D) types. It took quite a large series of experiments to confirm finally the existence of the molecular phase, to show that the chain phase is not as simple as it seemed at the beginning, and to recognize the layer phase as a non-trivial fault of the X-ray diffraction interpretation. This work is devoted just to the “closure” of the last phase, while the description of the characteristics of the other phases will be given in their “primary” version, only to understand the difficulties that arose during the process of structural analysis.

2. Materials and Methods

2.1. Synthetic Procedure

2.1.1. Chemical Materials

Vanadium powder (99%) purchased from SibMetallTorg (Russia) was preliminarily washed in 7 M hydrochloric acid and dried under dynamic vacuum. Powder selenium (99.99%, particles size 50 μm) was purchased from SibMetallTorg (Russia). Iodine in granules (99%) was obtained from the Scientific and production association Iodobrom (Russia). Vanadium diselenide was synthesized by the direct reaction of elementary substances in evacuated glass ampoule at 750 °C. Selenium dioxide was synthesized by two-step synthesis: in the first reaction, we oxidized elemental selenium by excess of H2O2 to produce H2SeO3, in the second reaction we decomposed H2SeO3 by heating it under dynamic vacuum at 250 °C. To avoid formation of H2SeO3, the product was stored in desiccator with P2O5.

2.1.2. Chemical Synthesis

The assembly of different crystals was found in a product of the following experiment. VSe2 powder (0.448 g, 2.14 mmol), SeO2 powder (0.032 g, 0.288 mmol) and iodine granules (0.831 g, 3.27 mmol) were thoroughly mixed and grounded in a mortar and then put into a 20 mL glass ampoule (10 cm in length). The ampoule was evacuated and sealed. The ampoule was heated up to 250 °C in 10 h and kept at this temperature for 48 h. After that, the ampoule was cooled with the furnace for ca. 3 h. Some quantity of unreacted iodine and presumably selenium dioxide were evaporated from the mixture of products, to another end of the ampoule, by heating it in a sand bath (T = 150 °C) for 10 h. Product formed in the bottom part of the ampoule as a number of crystals in the form of small black plates mixed with black needles. Crystals for X-ray single crystal structure determination was taken from this mixture manually at ambient conditions. SEM/EDX elemental analysis for two specimens gave V4Se6.9I9.5 (needle crystal) and V4Se6.6I9.1 (plate crystal), Figure S1 of SI.

2.2. X-ray Diffraction Structure Studies

Single crystal X-ray diffraction data for three specimens were collected on a Bruker D8 Duo diffractometer (APEX II CCD detector, fine-focus Mo tube, graphite monochromated MoKα radiation λ = 0.71073 Å) at room temperature via 0.5° ω- and φ-scan techniques. Experimental data reductions were performed using the APEX2 suite [40]. Scaling and absorption corrections of the experimental intensities were performed by SADABS empirically (3 odd and 6 even orders for spherical harmonics) [41]. The structures were solved by SHELXT [42] and refined using the full-matrix least-squares by SHELXL [43] assisted with Olex2 GUI [44]. While all the data were of a poor quality, refined parameters of the structure models will be refined further in Section 3.2. The crystallographic characteristics, experimental data and structure refinement indicators are collected in Table S1 of SI, and more detailed in associated CIF and HTML files. Since they aimed at describing problems at the initial stages of phase analysis, they were not deposited in any crystal structure database and cannot be cited out of this context.

2.3. X-ray Powder Diffractometry

X-ray powder diffraction (XRPD) pattern was collected with a Philips PW 1830/1710 automated diffractometer (CuKα radiation, 40 kV/35 mA, secondary graphite monochromator, silicon as an external standard). The sample was grinded in a mortar in hexane and deposed on polished side of a quartz-glass holder as a thin (ca. 0.1 mm) layer. Qualitative comparison (Topas Academic v.6 [45]) of the experimental pattern with ones, calculated (Mercury 2022.3 [46]) for the reagents and possible products was used for the phase analysis.

2.4. Electron Microscopy and EDX

Electron microscopy and energy-dispersive spectroscopy was performed with a Hitachi TM3000 scanning electron microscope equipped with a Bruker QUANTAX 70 Energy Dispersive X-ray spectrometer (Figure S1 of SI).

2.5. 3D-DFT

Unrestricted DFT structure refinement with 3D periodic boundary conditions via CP2K v.8.2 package [47] were used to verify an arrangement of N-bonded H atoms of the 3,5-dimethylpyrazole molecules. Gaussian plane wave [48] calculations were conducted within PBE functional [49] with D3(BJ) correction [50,51]. Valence electrons were described by TZVP-MOLOPT-GTH basis sets [52], atomic core electrons were described by Goedecker–Teter–Hutter (GTH) pseudopotentials [53,54,55]. The fragments under refinement contain all atoms of the corresponding unit cells with fixed lattice dimensions. Computational details are listed in Table S2 of SI and associated files.

3. Results

3.1. Discussion of the Chemical Syntheses

In the course of the synthetic experiments, we found that the precise temperature control is the crucial factor for successful synthesis. In a narrow temperature region of 220–250 °C several similar compounds could be formed and even a slight deviation from required conditions may change a product. The second most important factor in the synthesis may be a pressure of volatile components in the reaction medium. Thus, using an excess of iodine increases the yield of the vanadium selenoiodides.
Two previously obtained compounds of V4OSe8I6·X (X = I2, hereinafter referred to as M1, or 3,5-dimethylpyrazole) contained O-centered molecules [V4O(μ-Se2)4I4(μ-I)2]0d. From the further syntheses, we expected the formation of new coordination motifs, which would include this unit, possibly with changes in number of the ligands. This could happen due to the formation of extended coordination structures, for instance, as in chain compounds such as Ti4Se9I6 [56] or M4OTe9I4 (M = Ti [37], Nb [38], Ta [39]), or the layer structure similar to V4S9Br4 [57]. We carried out a synthetic procedure at the temperature of 250 °C from the mixture of VSe2, SeO2 and I2, which has resulted in a black and dark-grey crystalline product.

3.2. Crystal Structures Estimation

3.2.1. The Crystal Structure of V4OSe8I6·2I2 (M2)

M2 (Figure 1) was found to have molecular crystal structure with co-crystallized [V4O(μ-Se2)4I4(μ-I)2]0d clusters and diiodine molecules. The structure is monoclinic (space group C 2/c) with β = 90.5(3)°. All non-O atoms were localized via the intrinsic phasing method. Atomic displacements were refined anisotropically for I atoms, and isotropically for V and Se. The central O atom could not be reliably localized due to high noise on the electron density map. The cluster molecules are located on 2-fold axes (special position 4e). The final refinement indicators are Rint = 14.6%, <I/σ(I)> = 4.0 up to 0.90 Å, R1 = 15.7%, wR2 = 45.3%, goodness of fit of 1.15 and residual electron density max/min +4.2/−4.6 e/ų.

3.2.2. The Crystal Structure of V4OSe8I5 (C)

C was found to have polymeric structure with [V4O(μ-Se2)4I4(μ2+2-I)2/2]1d monomeric units, which are linked via μ4 iodine bridges in chains (Figure 2). The structure is also monoclinic (space group C 2/c) with the chains, directed along b axis. All atoms were localized via intrinsic phasing method. Atomic displacements were refined anisotropically for all non-O atoms, and isotropically for O. The cluster molecules are located on 2-fold axes (special position 4e). The final refinement indicators are Rint = 9.2%, <I/σ(I)> = 3.2 up to 0.90 Å, R1 = 8.4%, wR2 = 19.2%, goodness of fit of 0.92 and residual electron density max/min +1.8/−1.7 e/ų.

3.2.3. The Crystal Structure of V4OSe6I3 (L)

L was found to have polymeric structure with [V4O(μ-Se2)2(μ2+2-Se2/2)4(μ1+1-I)4/2(μ2+2-I)2/2]2d monomeric units, which are linked via μ4-iodide bridging ligands in one direction and via μ4-diselenide and μ-iodide bridging ligands in another one (Figure 3). The resulting layers form orthorhombic crystal structure (space group P ccm) with the layer planes perpendicular to the b axis. All atoms were localized via intrinsic phasing method. Atomic displacements were refined anisotropically for all non-O atoms, and isotropically for O. The cluster molecules are located around special positions with 222 point symmetry (Wykoff symbol 2h). The refinement indicators are Rint = 14.2%, <I/σ(I)> = 8.8 up to 0.90 Å, R1 = 13.0%, wR2 = 39.9%, goodness of fit of 1.54 and residual electron density max/min +5.3/−3.2 e/ų.
The structure model (Figure 4a) shows anomalous large atomic displacements for V and O atoms, as well as highly elongated ellipsoids for Se atoms of sidelong diselenide ligands. Additionally, the bond length of this ligand in the model appears to be abnormally high—2.59 Å vs. statistically averaged 2.38(18)Å (quartiles values are 2.31/2.34/2.37 Å) for 182 metal-coordinated diselenide fragments from CSD v.5.43 (November 2021) [58].
Attempts to reduce V and O atomic displacements by refining occupancies of the positions led to significant decrease in R values (R1 decreased from 13.0% to 9.4%, Figure 4b). Additional improvement, down to R1 = 8.3%, was achieved via description of the sidelong diselenides as superpositions of diselenides and diiodine (or diiodide ligands), depicted in Figure 4c. These improvements explicitly show the obtained structure is an overlay of something else and the original structure model is just a simulation, caused by incorrect symmetry accounting. Unfortunately, all of these “modifications” were performed just before the manuscript writing, while the actual nature of the “L” phase was disclosed in more complex way!

3.3. Powder X-ray Diffraction

The experimental diffraction pattern of the product shown is a poor match with calculated patterns of both reagent phases and potential products (Figure 5; the crystal structures of M2, C and L are estimated in this work, one for M1 was taken from [33]). There are no observable peaks, which would correspond to reagents. On the other hand, only the pattern of M2 is a vague match for the experimental one. However, there are a number of strong predicted peaks, which are distinctly absent in the experimental pattern. The admixture of still unknown phase(s) combined with severe preferred orientation of M2 crystals could explain the observed diffraction pattern.
One more observation worth noting is the close similarity of the simulated patterns for M2 and L. Indeed, one could observe that the diffraction of L looks similar to M2. There are only three strong peaks at 11.35°, 16.96° and 24.40° that are missing, which could be explained by higher symmetry of the former structure. This suggests that these structures could be related; alternatively, the crystal structure of L phase is just an over-symmetrized variant of the one for M2!

3.4. Computational Simulations

3.4.1. Oxidation States and Spin Multiplicities Assumptions

Based on the results of our previous work on M1, all vanadium atoms in the molecular cluster [V4O(μ-Se2)4I4(μ-I)2]0d have oxidation state +4 and one unpaired electron, with uncorrelated spins. For the structure geometry optimization, we used high-spin states with four unpaired electrons per the cluster fragment. An oxygen atom was placed in the geometrical center of the cluster “manually” by analogy with the known O-centered fragments and was confirmed by DFT calculations.
Formation of the chained structure [V4O(μ-Se2)4I4(μ2+2-I)2/2]1d should result in the averaged oxidation state of vanadium of +3.75, which may be presented as superposition of three V+4 and one V+3 in each cluster unit. The more probable alternative is formation of “mixed valence” states of vanadium atoms. In fact, now we have some reasons to consider this model as oversimplified. Therefore, a quantum chemical simulation of this phase will be discussed in a dedicated work.
The further polymerization of the cluster units into [V4O(μ-Se2)2(μ2+2-Se2)2/2(μ1+1-I)4/2(μ2+2-I)2/2]2d layers should result in the further lowering of oxidation states of vanadium. The formal estimation of one in assumption of conserving of the oxidation states of ligands (−2 for O, −1 for Se in diselenide and −1 for I) gives an oxidation state of vanadium of +2.75. This may be presented as the sum of V+2 and V+3 atoms in a 1:3 ratio. While the lowest and the highest spin state for vanadium in these oxidation states should account for one to three and zero to two unpaired electrons, respectively, we tried to perform geometry optimization of the crystal structures with one to nine unpaired electrons per the cluster unit.

3.4.2. Geometry Optimization for V4OSe8I6·2I2 (M2)

The M2 crystal structure model with inserted μ4-O atom was refined successfully. Only minor shifts of the atoms were observed. This confirms our interpretation of M2, with the SC XRD model comprising [V4O(μ-Se2)4I4(μ-I)2]0d, instead of [V4(μ-Se2)4I4(μ-I)2]0d.

3.4.3. Geometry Optimization for V4OSe6I3 (L)

Among the five L crystal structure models, each having different spin multiplicities, the one with three unpaired electrons per cluster unit has the lowest total energy value. There are significant geometry changes relative to the SC XRD crystal structure. They are (1) reduction of the sidelong diselenide Se–Se distance down to expected value of 2.34 Å, (2) significant shift of the μ1+1-I atoms without considerable changing of V–I distances and (3) increasing of Se–Se distances in the cluster-bridging μ2+2 diselenides up to 2.99 Å. The last means formation of a couple of μ2+2-monoselenide ligands instead of each diselenide one and transformation of the structure into [V4O(μ-Se2)2(μ2+2-Se)4/2(μ1+1-I)4/2(μ2+2-I)2/2]2d (Figure 6) with the formal oxidation state of vanadium of +3.25. While up to this moment we collected enough evidence to consider the L structure as an SC XRD fault, we did not perform further geometry optimization and investigation of the stability of this hypothetical structure.

3.4.4. Symmetry Consideration of M2 and L Crystal Structures

Based on the previous results, one can conclude the layer structure of L is an artefact of symmetry overestimation, and the structures of M2 and L are in some relationship. Comparison of their unit cell dimensions (C 2/c a = 20.2, b = 11.8, c = 12.1 Å, β = 90.5(3)°, V = 2900 ų for M2, and P ccm a = 5.9, b = 10.2, c = 12.1 Å, V = 730 ų for L) shows 1.99:1 volume ratio of their primitive unit cells. There is also a certain pairwise similarity of the unit cell parameters: aM2~2·bL, bM2~2·aL, cM2~cL. These observations suggest that the addition of some extra symmetry operators can lead to the “obtaining” of the structure of L from one of M2. Indeed, if one applied additional symmetry, generated by translation (1/2b) and a mirror plane (..m) to the structure of M2, preliminarily adjusted the β value to 90°, one could achieve the crystal structure of L (Figure 7). This construction with regard to the results of 3.2.3, 3.3, 3.4.3 and synthetic consideration discussed further clearly indicates that the L structure is a false solution.

4. Discussion

Since the structures of M2 (V4OSe8I6·2I2) and C (V4OSe8I5) include an O-centered fragment {V4O}, these compounds can be assigned to a vast group of so-called anion-centered compounds. The representatives of this group are numerous minerals which structures are described in terms of different coordination of fragments {M4O} (M = Cu, Pb, Ln, Bi, Hg) bearing molecular (0D) or oligomeric structures as well as infinite coordination motifs—chains (1D), layers (2D), as well as framework structures (3D) [59]. On the other side, M2 and C, as well as a few of the related compounds [33,34], possess a more complex fragment, {M4O(Q2)4} (Q2 for dichalcogenide ligand), which can be considered as a structural building block. The similar building blocks are also observed in various oxochalcohalides of 3–6 period transition elements with molecular structure Ti4OS8Hal6 (Hal = Cl [35], Br [36]), Ti4OSe8Br6 [60], as well as with chain structure M4OTe9I4 (M = Ti [37], Nb [38], Ta [39]). Despite the general {M4O} compounds, or the only known layer {M4Q(Q2)4} [57], no evidence of structures with a higher connectivity is known for the compounds with the {M4O(Q2)4} building blocks. Thus, discover of L (“V4OSe6I3”) structure with layer structure could open a new branch in the chemistry of these compounds.
Having obtained a small series of selenium-iodide vanadium complexes, we noticed that heating of similar ratios of starting species (most often metal vanadium, selenium, iodine and water as an oxygen source) at a temperature of 220 °C results in the formation of various molecular compounds containing an O-centered tetra-nuclear fragment V4OSe8I6 [33,34]. In their crystal structures molecules V4OSe8I6 form non-covalent contacts with iodine or 3,5-dimethylpyrazole molecules. When the synthesis temperature was increased to 280–300 °C, we obtained crystals in which tetranuclear complexes V4OSe8I5 form polymeric chains, organized by bridging via iodide ligands.
The initially assumed layer structure with the composition V4OSe6I3 was characterized by a rather complex way of binding of the tetra-nuclear fragments, which could even be called redundant. First, bridging iodine atoms were observed in two directions, similar to a chain structure, but in addition to this, diselenide groups also became bridging in one of these directions. We could expect such a complex binding of the tetra-nuclear fragments at a synthesis temperature higher than the synthesis temperature of chain compounds V4OSe8I5+x. The binding of vanadium fragments in this way looked for us incredible for a crystal obtained at the temperature of 220 °C, at which previously we obtained only compounds with isolated V4OSe8I6 complex molecules. After a number of various considerations, the structure was recognized as incorrect, caused by a symmetry overestimation.
As other related examples of ambiguous SC XRD results, it is possible to list some useful (or currently seeming to be such) structural models that turned out to be inaccurate or incomplete. In addition to the previously mentioned case with an incorrect assessment of the oxidation state due to incorrect determination of hydrogen atoms [19], in our practice, structural models with largely incomplete localization of atoms have been encountered [61]. In general, this situation is typical in the structural chemistry of metal-organic frameworks (MOF’s) [62,63,64] and other classes of compounds with the presence of unequally connected parts of the crystal structure. Complete and accurate (at least according to formal criteria) structural models that obviously do not fully describe the structure of real phases are also very common in X-ray diffraction analysis of octahedral cluster compounds [65], the real diffraction from which surprisingly often contains noticeable diffuse scattering. Moreover, even qualitative consideration of diffuse scattering sometimes makes it possible to interpret the local structure of phases with complex disordering [66].
On the other hand, there are cases when well-established ideas about the compositions of phases obtained from the data of classical physico-chemical analysis, on the contrary, make correctly defined crystal structures questionable, which is why their publication requires tougher than usual evidence of their correctness (e.g., [67] vs. [68]). In the rarest cases, contradictions, sometimes apparent, may arise between the results obtained only by X-ray diffraction analysis, as in the case of the implementation in the system of two polymorphic modifications with extremely similar parameters of elementary cells [69].

5. Conclusions

We demonstrated here obtaining critical information about the structure and phase composition of complex samples from the system V-Se-I-O. An interesting case of obtaining a false solution and the way taken to its “closure” are discussed.
A variety of coordination modes of halogen and chalcogen atoms, as well as the possibility of increasing connectivity in the structure, allowed us to believe in the existence of a structure V4OSe6I3 (L) built of coordinating polymeric layers. However, from the standpoint of the synthetic conditions, realization of this kind of connectivity turns out to be unlikely: for the transition from molecular to polymeric structure in this system, it is necessary to increase the synthesis temperature from 220 to 280 °C, which almost exhausts the temperature range for the existence of these tetra-nuclear vanadium fragments. These considerations inspired the work on the revision of the V4OSe6I3 crystal structure, which was found to be an over-symmetrized model of V4OSe8I6·2I2 (M2) with I2 co-crystallization molecules disguised as diselenide ligands.
Thus, we would like to recognize that the publication of “bad” structures (i.e., structural models of quality deviating from the requirements of the IUCr), as well as a critical description of anomalies that are not explained by the published models, can be useful for the development of both theoretical and experimental chemistry. In the end, to refute nontrivial false solutions, deep development of new methods of analysis may be necessary.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/sym15020508/s1, Figure S1: SEM picture of two specimens from a product of synthesis, described in Section 2.1.2 of the article. (a) A stick, V:Se:I = 4:6.9:9.5; (b) a plate, V:Se:I = 4:6.6:9.1.; Table S1: Crystal data and structure refinement details for M2, C and L (three variants); Table S2: Main indicators of unrestricted Kohn–Sham DFT with periodic boundary conditions for structures of M1, M2 and L.

Author Contributions

Conceptualization, V.K.; Data curation, V.K.; Formal analysis, V.K.; Funding acquisition, S.A.; Investigation, V.K. and R.G.; Methodology, V.K. and R.G.; Project administration, S.A.; Resources, R.G.; Visualization, V.K., R.G. and S.A.; Writing—original draft, V.K., R.G. and S.A.; Writing—review and editing, V.K. and S.A. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Russian Science Foundation (project RSF No. 21-13-00274, https://rscf.ru/project/21-13-00274/, accessed on 19 April 2021). The authors also thank XRD Facility of Nikolaev Institute of Inorganic Chemistry SB RAS for the SC XRD data collection (Ministry of Science and Higher Education of the Russian Federation, N 121031700313-8).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

No data are available in public databases due to their unfinished character.

Acknowledgments

The authors thank Novosibirsk State University Supercomputer Center for providing supercomputer facility. The authors also thank Taisiya Sukhikh for graphic presentation of the principal question in this manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

References

  1. Gibbs, J.W. On the Equilibrium of Heterogeneous Substances. Trans. Connect. Acad. Arts Sci. 1879, 3, 343–524. [Google Scholar] [CrossRef]
  2. Kuznetsov, N.T.; Novotortsev, V.M. Nikolai Semenovich Kurnakov (to the 150th Anniversary of His Birthday). Russ. J. Inorg. Chem. 2010, 55, 1668–1679. [Google Scholar] [CrossRef]
  3. Zhao, J.-C. Phase Diagram Determination Using Diffusion Multiples. In Methods for Phase Diagram Determination; Elsevier: Amsterdam, The Netherlands, 2007; pp. 246–272. ISBN 978-0-08-044629-5. [Google Scholar]
  4. Egami, T.; Billinge, S.J.L. Underneath the Bragg Peaks: Structural Analysis of Complex Materials; T. Egami, S.J.L.B., Ed.; Elsevier: Amsterdam, The Netherlands, 2012; ISBN 0080426980. [Google Scholar]
  5. Welberry, T.R. Diffuse X-Ray Scattering and Models of Disorder; IUCr Monog.; Oxford University Press: Oxford, UK, 2022; ISBN 9780198862482. [Google Scholar]
  6. Nespolo, M. Lattice versus Structure, Dimensionality versus Periodicity: A Crystallographic Babel? J. Appl. Crystallogr. 2019, 52, 451–456. [Google Scholar] [CrossRef]
  7. Urusov, V.S. Theoretical Analysis and Empirical Manifestation of the Distortion Theorem. Zeitschrift für Krist. Mater. 2003, 218, 709–719. [Google Scholar] [CrossRef]
  8. Brown, I.D. Recent Developments in the Methods and Applications of the Bond Valence Model. Chem. Rev. 2009, 109, 6858–6919. [Google Scholar] [CrossRef] [PubMed]
  9. Chen, H.; Adams, S. Bond Softness Sensitive Bond-Valence Parameters for Crystal Structure Plausibility Tests. IUCrJ 2017, 4, 614–625. [Google Scholar] [CrossRef]
  10. Zwart, P.H.; Grosse-Kunstleve, R.W.; Lebedev, A.A.; Murshudov, G.N.; Adams, P.D. Surprises and Pitfalls Arising from (Pseudo)Symmetry. Acta Crystallogr. Sect. D 2008, 64, 99–107. [Google Scholar] [CrossRef]
  11. Lombardo, G.M.; Punzo, F. False Asymmetry, Pseudosymmetry, Disorder, Polymorphism and Atomic Displacement Parameters. J. Mol. Struct. 2014, 1078, 158–164. [Google Scholar] [CrossRef]
  12. Clegg, W. Some Reflections on Symmetry: Pitfalls of Automation and Some Illustrative Examples. Acta Crystallogr. Sect. E 2019, 75, 1812–1819. [Google Scholar] [CrossRef] [PubMed]
  13. Dornberger-Schiff, K. On Order-Disorder Structures (OD-Structures). Acta Crystallogr. 1956, 9, 593–601. [Google Scholar] [CrossRef]
  14. Belokoneva, E.L. Borate Crystal Chemistry in Terms of the Extended OD Theory: Topology and Symmetry Analysis. Crystallogr. Rev. 2005, 11, 151–198. [Google Scholar] [CrossRef]
  15. Friedrichs, O.D.; Dress, A.W.M.; Huson, D.H.; Klinowski, J.; Mackay, A.L. Systematic Enumeration of Crystalline Networks. Nature 1999, 400, 644–647. [Google Scholar] [CrossRef]
  16. Komarov, V.Y.; Solodovnikov, S.F.; Grachev, E.V.; Kosyakov, V.I.; Manakov, A.Y.; Kurnosov, A.V.; Shestakov, V.A. Phase Formation and Structure of High-Pressure Gas Hydrates and Modeling of Tetrahedral Frameworks with Uniform Polyhedral Cavities. Crystallogr. Rev. 2007, 13, 257–297. [Google Scholar] [CrossRef]
  17. Nespolo, M. Does Mathematical Crystallography Still Have a Role in the XXI Century? Acta Crystallogr. Sect. A 2008, 64, 96–111. [Google Scholar] [CrossRef] [PubMed]
  18. Tiekink, E. 16th Conferense of the Asian Crystallographic Association (AsCA2019). 2020. Available online: https://www.iucr.org/news/newsletter/volume-28/number-3/16th-conference-of-the-asian-crystallographic-association-asca2019 (accessed on 28 August 2020).
  19. Kuznetsov, V.G.; Koz’min, P.A. A Study of the Structure of (PyH) HReCl4. J. Struct. Chem. 1963, 4, 49–55. [Google Scholar] [CrossRef]
  20. Cotton, A.F.; Matonic, J.H.; Silva, D.d.O. Crystallographic Disorder of the M2 Units in [M2Cl8]N− (M = Mo, Re) Compounds. Inorg. Chim. Acta 1995, 234, 115–125. [Google Scholar] [CrossRef]
  21. Cotton, F.A.; Murillo, C.A.; Walton, R.A. Multiple Bonds between Metal Atoms, 3rd ed.; Cotton, F.A., Murillo, C.A., Walton, R.A., Eds.; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2005; ISBN 0387250840. [Google Scholar]
  22. Fedorov, V.E.; Mishchenko, A.V.; Fedin, V.P. Cluster Transition Metal Chalcogenide Halides. Russ. Chem. Rev. 1985, 54, 408. [Google Scholar] [CrossRef]
  23. Gabriel, J.-C.P.; Boubekeur, K.; Uriel, S.; Batail, P. Chemistry of Hexanuclear Rhenium Chalcohalide Clusters. Chem. Rev. 2001, 101, 2037–2066. [Google Scholar] [CrossRef] [PubMed]
  24. Gushchin, A.L.; Laricheva, Y.A.; Sokolov, M.N.; Llusar, R. Tri- and Tetranuclear Molybdenum and Tungsten Chalcogenide Clusters: On the Way to New Materials and Catalysts. Russ. Chem. Rev. 2018, 87, 670. [Google Scholar] [CrossRef]
  25. Lee, S.C.; Holm, R.H. Nonmolecular Metal Chalcogenide/Halide Solids and Their Molecular Cluster Analogues. Angew. Chemie Int. Ed. English 1990, 29, 840–856. [Google Scholar] [CrossRef]
  26. Artemkina, S.B.; Grayfer, E.D.; Ivanova, M.N.; Ledneva, A.Y.; Poltarak, A.A.; Poltarak, P.A.; Yarovoi, S.S.; Kozlova, S.G.; Fedorov, V.E. Structural and Chemical Features of Chalcogenides of Early Transition Metals. J. Struct. Chem. 2022, 63, 1079–1100. [Google Scholar] [CrossRef]
  27. Fedorov, V.E.; Mironov, Y.V.; Naumov, N.G.; Sokolov, M.N.; Fedin, V.P. Chalcogenide Clusters of Group 5–7 Metals. Russ. Chem. Rev. 2007, 76, 529–552. [Google Scholar] [CrossRef]
  28. Feliz, M.; Guillamón, E.; Llusar, R.; Vicent, C.; Stiriba, S.; Pérez-Prieto, J.; Barberis, M. Unprecedented Stereoselective Synthesis of Catalytically Active Chiral Mo3CuS4 Clusters. Chem. Eur. J. 2006, 12, 1486–1492. [Google Scholar] [CrossRef] [PubMed]
  29. Chang, Y.-P.; Hector, A.L.; Levason, W.; Reid, G. Chalcogenoether Complexes of Nb(v) Thio- and Seleno-Halides as Single Source Precursors for Low Pressure Chemical Vapour Deposition of NbS2 and NbSe2 Thin Films. Dalt. Trans. 2017, 46, 9824–9832. [Google Scholar] [CrossRef]
  30. Cramer, C.J.; Truhlar, D.G. Density Functional Theory for Transition Metals and Transition Metal Chemistry. Phys. Chem. Chem. Phys. 2009, 11, 10757–10816. [Google Scholar] [CrossRef]
  31. Gimferrer, M.; Van der Mynsbrugge, J.; Bell, A.T.; Salvador, P.; Head-Gordon, M. Facing the Challenges of Borderline Oxidation State Assignments Using State-of-the-Art Computational Methods. Inorg. Chem. 2020, 59, 15410–15420. [Google Scholar] [CrossRef]
  32. Bartashevich, E.; Yushina, I.; Kropotina, K.; Muhitdinova, S.; Tsirelson, V. Testing the Tools for Revealing and Characterizing the Iodine-Iodine Halogen Bond in Crystals. Acta Crystallogr. Sect. B 2017, 73, 217–226. [Google Scholar] [CrossRef]
  33. Artemkina, S.; Galiev, R.; Poltarak, P.; Komarov, V.; Gayfulin, Y.; Lavrov, A.; Fedorov, V. Vanadium O-Centered Selenoiodide Complex: Synthesis and Structure of V4O(Se2)4I6·I2. Inorg. Chem. 2021, 60, 17627–17634. [Google Scholar] [CrossRef]
  34. Artemkina, S.B.; Galiev, R.R.; Komarov, V.Y.; Fedorov, V.E.; Ledneva, A.Y.; Khisamov, R. Characterization of the O-Centered Vanadium Selenoiodides V4OSe8I6· X (X = I2, Dmp). Inorganica Chim. Acta, 2022; 121366, in press. [Google Scholar] [CrossRef]
  35. Cotton, F.A.; Feng, X.; Kibala, P.A.; Sandor, R.B.W. An Oxygen-Centered Tetranuclear Titanium Compound Ti4O(S2)4Cl6. J. Am. Chem. Soc. 1989, 111, 2148–2151. [Google Scholar] [CrossRef]
  36. Cotton, F.A.; Kibala, P.A.; Sandor, R.B.W. Synthesis and Crystal Structures of Ti4O(S2)4Br6. Eur. J. Solid State Inorg. Chem. 1988, 25, 631–636. [Google Scholar]
  37. Liu, S.X.; Huang, D.P.; Huang, C.C.; Xu, H.D.; Huang, J.L. A New Extended Tetranuclear Titanium Cluster: Ti4O(Te2)4Tel4. J. Solid State Chem. 1996, 123, 273–276. [Google Scholar] [CrossRef]
  38. Tremel, W. Nb4OTe9I4: A One-Dimensional Chain Compound Containing Tetranuclear Oxygen-Centred Niobium Clusters. J. Chem. Soc. Chem. Commun. 1992, 709–710. [Google Scholar] [CrossRef]
  39. Huang, D.P.; Huang, C.C.; Liu, S.X.; Xu, H.D.; Huang, J.L. An Oxygen-Centred Tetranuclear Tantalum Cluster: Ta4O(Te2)4TeI4. Acta Crystallogr. Sect. C Cryst. Struct. Commun. 1998, 54, 893–895. [Google Scholar] [CrossRef]
  40. Bruker APEX2 Software Suite, APEX2 v.2013.6-2, SADABS v. 2012/1, SAINT v. 8.32b; Bruker AXS Inc.: Madison, WI, USA, 2006.
  41. Krause, L.; Herbst-Irmer, R.; Sheldrick, G.M.; Stalke, D. Comparison of Silver and Molybdenum Microfocus X-Ray Sources for Single-Crystal Structure Determination. J. Appl. Crystallogr. 2015, 48, 3–10. [Google Scholar] [CrossRef]
  42. Sheldrick, G.M. SHELXT—Integrated Space-Group and Crystal-Structure Determination. Acta Crystallogr. Sect. A Found. Crystallogr. 2015, 71, 3–8. [Google Scholar] [CrossRef]
  43. Sheldrick, G.M. Crystal Structure Refinement with SHELXL. Acta Crystallogr. Sect. C Struct. Chem. 2015, 71, 3–8. [Google Scholar] [CrossRef]
  44. Dolomanov, O.V.; Bourhis, L.J.; Gildea, R.J.; Howard, J.A.K.; Puschmann, H. OLEX2: A Complete Structure Solution, Refinement and Analysis Program. J. Appl. Crystallogr. 2009, 42, 339–341. [Google Scholar] [CrossRef]
  45. Coelho, A. TOPAS and TOPAS-Academic: An Optimization Program Integrating Computer Algebra and Crystallographic Objects Written in C++. J. Appl. Crystallogr. 2018, 51, 210–218. [Google Scholar] [CrossRef]
  46. Macrae, C.F.; Sovago, I.; Cottrell, S.J.; Galek, P.T.A.; McCabe, P.; Pidcock, E.; Platings, M.; Shields, G.P.; Stevens, J.S.; Towler, M.; et al. Mercury 4.0: From Visualization to Analysis, Design and Prediction. J. Appl. Crystallogr. 2020, 53, 226–235. [Google Scholar] [CrossRef]
  47. Kühne, T.D.; Iannuzzi, M.; Del Ben, M.; Rybkin, V.V.; Seewald, P.; Stein, F.; Laino, T.; Khaliullin, R.Z.; Schütt, O.; Schiffmann, F. CP2K: An Electronic Structure and Molecular Dynamics Software Package-Quickstep: Efficient and Accurate Electronic Structure Calculations. J. Chem. Phys. 2020, 152, 194103. [Google Scholar] [CrossRef] [PubMed]
  48. Lippert, G.; Parrinello, M.; Jurg, H. A Hybrid Gaussian and Plane Wave Density Functional Scheme. Mol. Phys. 1997, 92, 477–488. [Google Scholar] [CrossRef]
  49. Perdew, J.P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. [Google Scholar] [CrossRef]
  50. Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. [Google Scholar] [CrossRef] [PubMed]
  51. Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456–1465. [Google Scholar] [CrossRef]
  52. VandeVondele, J.; Hutter, J. Gaussian Basis Sets for Accurate Calculations on Molecular Systems in Gas and Condensed Phases. J. Chem. Phys. 2007, 127, 114105. [Google Scholar] [CrossRef]
  53. Goedecker, S.; Teter, M.; Hutter, J. Separable Dual-Space Gaussian Pseudopotentials. Phys. Rev. B 1996, 54, 1703. [Google Scholar] [CrossRef]
  54. Hartwigsen, C.; Gœdecker, S.; Hutter, J. Relativistic Separable Dual-Space Gaussian Pseudopotentials from H to Rn. Phys. Rev. B 1998, 58, 3641. [Google Scholar] [CrossRef]
  55. Krack, M. Pseudopotentials for H to Kr Optimized for Gradient-Corrected Exchange-Correlation Functionals. Theor. Chem. Acc. 2005, 114, 145–152. [Google Scholar] [CrossRef]
  56. Poltarak, P.A.; Komarov, V.Y.; Kozlova, S.G.; Sukhikh, A.S.; Artemkina, S.B.; Fedorov, V.E. First Titanium Square Fragment {Ti4(Μ4-Se)(Μ2-Se2)4} in Its Selenoiodide: Synthesis and Structure of Ti4Se9I6. Inorganica Chim. Acta 2019, 488, 285–291. [Google Scholar] [CrossRef]
  57. Mironov, Y.V.; Yarovoi, S.S.; Naumov, D.Y.; Kozlova, S.G.; Ikorsky, V.N.; Kremer, R.K.; Simon, A.; Fedorov, V.E. V4S9Br4: A Novel High-Spin Vanadium Cluster Thiobromide with Square-Planar Metal Core. J. Phys. Chem. B 2005, 109, 23804–23807. [Google Scholar] [CrossRef] [PubMed]
  58. Groom, C.R.; Bruno, I.J.; Lightfoot, M.P.; Ward, S.C. The Cambridge Structural Database. Acta Crystallogr. Sect. B 2016, 72, 171–179. [Google Scholar] [CrossRef] [PubMed]
  59. Krivovichev, S.V.; Mentré, O.; Siidra, O.I.; Colmont, M.; Filatov, S.K. Anion-Centered Tetrahedra in Inorganic Compounds. Chem. Rev. 2013, 113, 6459–6535. [Google Scholar] [CrossRef] [PubMed]
  60. Poltarak, P.A.; Komarov, V.Y.; Gayfulin, Y.M.; Artemkina, S.B.; Fedorov, V.E. New O-Centered Titanium Chalcohalide: Synthesis and Structure of Ti4O(Se2)4Br6. Z. Fuer Anorg. Und Allg. Chem. 2021, 647, 1729–1734. [Google Scholar] [CrossRef]
  61. Rodionova, T.V.; Komarov, V.Y.; Villevald, G.V.; Karpova, T.D.; Kuratieva, N.V.; Manakov, A.Y. Calorimetric and Structural Studies of Tetrabutylammonium Bromide Ionic Clathrate Hydrates. J. Phys. Chem. B 2013, 117, 10677–10685. [Google Scholar] [CrossRef]
  62. Dybtsev, D.N.; Yutkin, M.P.; Samsonenko, D.G.; Fedin, V.P.; Nuzhdin, A.L.; Bezrukov, A.A.; Bryliakov, K.P.; Talsi, E.P.; Belosludov, R.V.; Mizuseki, H. Modular, Homochiral, Porous Coordination Polymers: Rational Design, Enantioselective Guest Exchange Sorption and Ab Initio Calculations of Host–Guest Interactions. Chem. Eur. J. 2010, 16, 10348–10356. [Google Scholar] [CrossRef] [PubMed]
  63. Lysova, A.A.; Samsonenko, D.G.; Dorovatovskii, P.V.; Lazarenko, V.A.; Khrustalev, V.N.; Kovalenko, K.A.; Dybtsev, D.N.; Fedin, V.P. Tuning the Molecular and Cationic Affinity in a Series of Multifunctional Metal–Organic Frameworks Based on Dodecanuclear Zn(II) Carboxylate Wheels. J. Am. Chem. Soc. 2019, 141, 17260–17269. [Google Scholar] [CrossRef]
  64. Lysova, A.A.; Samsonenko, D.G.; Kovalenko, K.A.; Nizovtsev, A.S.; Dybtsev, D.N.; Fedin, V.P. A Series of Mesoporous Metal-Organic Frameworks with Tunable Windows Sizes and Exceptionally High Ethane over Ethylene Adsorption Selectivity. Angew. Chemie Int. Ed. 2020, 59, 20561–20567. [Google Scholar] [CrossRef]
  65. Mikhaylov, M.A.; Abramov, P.A.; Komarov, V.Y.; Sokolov, M.N. Cluster Aqua/Hydroxocomplexes Supporting Extended Hydrogen Bonding Networks. Preparation and Structure of a Unique Series of Cluster Hydrates [Mo6I8(OH)4(H2O)2]·nH2O (N = 2, 12, 14). Polyhedron 2017, 122, 241–246. [Google Scholar] [CrossRef]
  66. Yarovoy, S.S.; Ivanova, M.; Sukhikh, T.S.; Ryzhikov, M.R.; Fedorov, V.E.; Naumov, N.G. Replenishment in the Family of Rhenium Chalcobromides; Synthesis and Structure of Molecular {Re4S4}Br8(TeBr2)4, Dimeric [{Re4S4}Br8(TeBr2)3]2, and Polymeric {Re4S4}Br8 Compounds Based on the {Re4S4}8+ Tetrahedral Cluster Core. Inorg. Chem. 2022, 61, 20472–20479. [Google Scholar] [CrossRef]
  67. Dyadin, Y.A.; Yakovlev, I.I.; Bondaryuk, I.V.; Zelenina, L.S. Water—Tetra n-Butylammonium Bromide System. Clathrate Hydrates. Dokl. Akad. Nauk SSSR 1972, 203, 1068–1071. [Google Scholar]
  68. Lipkowski, J.; Komarov, V.Y.; Rodionova, T.V.; Dyadin, Y.A.; Aladko, L.S. The Structure of Tetrabutylammonium Bromide Hydrate (C4H9)4NBr·21/3H2O. J. Supramol. Chem. 2002, 2, 435–439. [Google Scholar] [CrossRef]
  69. Vasilyev, E.S.; Bizyaev, S.N.; Komarov, V.Y.; Tkachev, A. V Syntheses of Chiral Fused 4, 5-Diazafluorene–Bis (Nopinane) Derivatives. Mendeleev Commun. 2019, 29, 584–586. [Google Scholar] [CrossRef]
Symmetry 15 00508 g001 550
Figure 1. (a) Molecular and (b) crystal structure of [V4O(µ-Se2)4I4(µ-I)2] [I2]2, M2. Atomic displacements are shown at 50% probability. The missing O atom is shown as a connection point of dashed bonds.
Figure 1. (a) Molecular and (b) crystal structure of [V4O(µ-Se2)4I4(µ-I)2] [I2]2, M2. Atomic displacements are shown at 50% probability. The missing O atom is shown as a connection point of dashed bonds.
Symmetry 15 00508 g001
Symmetry 15 00508 g002 550
Figure 2. (a) Molecular and (b) crystal structure of [V4O(µ-Se2)4I4(µ2+2-I)2/2]1d, C. Atomic displacements are shown at 50% probability.
Figure 2. (a) Molecular and (b) crystal structure of [V4O(µ-Se2)4I4(µ2+2-I)2/2]1d, C. Atomic displacements are shown at 50% probability.
Symmetry 15 00508 g002
Symmetry 15 00508 g003 550
Figure 3. (a) Molecular and (b) crystal structure of [V4O(µ-Se2)2(µ2+2-Se2/2)4(µ1+1-I)4/2(µ2+2-I)2/2]2d, L. Atomic displacements are shown at 50% probability.
Figure 3. (a) Molecular and (b) crystal structure of [V4O(µ-Se2)2(µ2+2-Se2/2)4(µ1+1-I)4/2(µ2+2-I)2/2]2d, L. Atomic displacements are shown at 50% probability.
Symmetry 15 00508 g003
Symmetry 15 00508 g004 550
Figure 4. Steps of improvement of the orthorhombic crystal structure of L: (a) original model, (b) refinement of V and O positions occupancies, (c) splitting of the sidelong diselenide ligand. Stars mark partially occupied positions. Atomic displacements are shown for 50% probability.
Figure 4. Steps of improvement of the orthorhombic crystal structure of L: (a) original model, (b) refinement of V and O positions occupancies, (c) splitting of the sidelong diselenide ligand. Stars mark partially occupied positions. Atomic displacements are shown for 50% probability.
Symmetry 15 00508 g004
Symmetry 15 00508 g005 550
Figure 5. (a) Heat map representation (intensities coded via blue-green-red-yellow-purple color palette) of the experimental X-ray powder diffraction pattern of the crystalline precipitate and computed ones for reagents and known products (M1 is for the structure of [V4O(µ−Se2)4I4(µ-I)2]0d [I2]; M2, L and C are for the structures of this work). (b) Comparison of the experimental diffraction pattern of the crystalline precipitate (top) and simulated one for M2 (bottom).
Figure 5. (a) Heat map representation (intensities coded via blue-green-red-yellow-purple color palette) of the experimental X-ray powder diffraction pattern of the crystalline precipitate and computed ones for reagents and known products (M1 is for the structure of [V4O(µ−Se2)4I4(µ-I)2]0d [I2]; M2, L and C are for the structures of this work). (b) Comparison of the experimental diffraction pattern of the crystalline precipitate (top) and simulated one for M2 (bottom).
Symmetry 15 00508 g005
Symmetry 15 00508 g006 550
Figure 6. Overlaying of the SC XRD (element-colored) and UKS-optimized (green) fragments of L crystal structure in two orthogonal projections (a) along a direction, (b) along b direction.
Figure 6. Overlaying of the SC XRD (element-colored) and UKS-optimized (green) fragments of L crystal structure in two orthogonal projections (a) along a direction, (b) along b direction.
Symmetry 15 00508 g006
Symmetry 15 00508 g007 550
Figure 7. Symmetrical relationships between crystal structure models of M2 and L. M2 on the left (a,c), L-imitation, obtained from M2 by adding the symmetry elements, on the right (b,d). Projections of the structures along L “layers” on top (a,b), a slab of the “layers” on bottom.
Figure 7. Symmetrical relationships between crystal structure models of M2 and L. M2 on the left (a,c), L-imitation, obtained from M2 by adding the symmetry elements, on the right (b,d). Projections of the structures along L “layers” on top (a,b), a slab of the “layers” on bottom.
Symmetry 15 00508 g007
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Komarov, V.; Galiev, R.; Artemkina, S. 2d, or Not 2d: An Almost Perfect Mock of Symmetry. Symmetry 2023, 15, 508. https://doi.org/10.3390/sym15020508

AMA Style

Komarov V, Galiev R, Artemkina S. 2d, or Not 2d: An Almost Perfect Mock of Symmetry. Symmetry. 2023; 15(2):508. https://doi.org/10.3390/sym15020508

Chicago/Turabian Style

Komarov, Vladislav, Ruslan Galiev, and Sofya Artemkina. 2023. "2d, or Not 2d: An Almost Perfect Mock of Symmetry" Symmetry 15, no. 2: 508. https://doi.org/10.3390/sym15020508

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop