Vadim M Kovrugin
email: kovrugin_vm@hotmail.com

Marie Colmont

Oleg I Siidra

Dmitry O Charkin

Almaz Aliev

Sergey V Krivovichev

Olivier Mentré

Keywords: bismuth, crystal structure, manganese, mixedligand coordination, selenites, single crystal XRD

Single crystals of new Mn 2 [Bi 2 O](SeO 3 ) 4 (I), MnBi(SeO 3 ) 2 Cl (II), Mn II Mn III (SeO 3 ) 2 Cl (III), Mn 5 (SeO 3 ) 2 Cl 6 (IV), and Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V) have been synthesized by chemical vapour transport and hydrothermal methods. They have been structurally characterized by single crystal X-ray diffraction analysis. The compounds II-V are the first Mn selenite chlorides, while the I, II and V compounds are the first Bi-containing Mn oxoselenites. Structural relationships of the new phases with other compounds are discussed. An overview of the mixed-ligand MnO m Cl n polyhedra in inorganic compounds is given.

Introduction

Over the last two decades, the chemistry of selenites (Se IV ) and selenates (Se VI ) has been intensively developed [START_REF] Choudhury | Three-dimensional organically templated open-framework transition metal selenites[END_REF][2][START_REF] Zhao | BiCuSeO oxyselenides: new promising thermoelectric materials[END_REF][START_REF] Kovrugin | pH-controlled pathway and systematic hydrothermal phase diagram for elaboration of synthetic lead nickel selenites[END_REF][START_REF] Song | Rich structural chemistry in scandium selenium/tellurium oxides: mixed-valent seleniteselenates, Sc 2 (SeO 3 ) 2 (SeO 4 ) and Sc 2 (TeO 3 )(SeO 3 )(SeO 4 ), and ternary tellurite, Sc 2 (TeO 3 ) 3[END_REF]. Metal oxyhalides with selenite anions demonstrate a rich and diverse crystal chemistry due to the interplay between soft-soft and hard-hard interactions involving selenite groups, metals and halide ions [START_REF] Berdonosov | Transition metal selenite halides: a fascinating family of magnetic compounds[END_REF][START_REF] Aliev | Mentré, Revised bismuth chloroselenite system: evidence of a noncentrosymmmetric structure with a giant unit cell[END_REF][START_REF] Kovrugin | Pathways for synthesis of new selenium-containing oxo-compounds: chemical vapor transport reactions, hydrothermal techniques and evaporation method[END_REF][START_REF] Charkin | Polar BaCl(ClO 4 ) • H 2 O layered chloride perchlorate[END_REF][START_REF] Kovrugin | Oxocentered Cu(ii) lead selenite honeycomb lattices hosting Cu(i)Cl 2 groups obtained by chemical vapor transport reactions[END_REF][START_REF] Kovrugin | Dimers of oxocentred [OCu 4 ] 6+ tetrahedra in two novel copper selenite chlorides, K[Cu 3 O](SeO 3 ) 2 Cl and Na 2 [Cu 7 O 2 ] (SeO 3 ) 4 Cl 4 , and related minerals and inorganic compounds[END_REF][12]. Note, that the crystal structures of most of them consist of Cu cations. This fascinating family of versatile structural architectures of selenite halides has been recently reviewed by Berdonosov in Ref. [START_REF] Berdonosov | Transition metal selenite halides: a fascinating family of magnetic compounds[END_REF]. For several phases, magnetic properties have been studied [START_REF] Berdonosov | Crystal structures and variable magnetism of PbCu 2 (XO 3 ) 2 Cl 2 with X = Se[END_REF][START_REF] Janson | CaCu 2 (SeO 3 ) 2 Cl 2 : spin-1/2 Heisenberg chain compound with complex frustrated interchain couplings[END_REF][START_REF] Badrtdinov | Magnetism of coupled spin tetrahedra in ilinskite-type KCu 5 O 2 (SeO 3 ) 2 Cl 3[END_REF][START_REF] Berdonosov | Crystal structure, physical properties, and electronic and magnetic structure of the spin S = 5/2 zigzag chain compound Bi 2 Fe(SeO 3 ) 2 OCl 3[END_REF]. For example, a series of well-studied francisite-type Cu 3 M(SeO 3 ) 2 O 2 X (M = Bi, La, Sm, Yb; X = Cl, Br) compounds demonstrates various magnetic behavior depending on M and X ions [START_REF] Markina | Static and dynamic magnetic properties of two synthetic francisites Cu 3 La(SeO 3 ) 2 O 2 X (X = Br and Cl)[END_REF][START_REF] Constable | Magnetic and dielectric order in the kagomelike francisite Cu 3 Bi(SeO 3 ) 2 O 2 Cl[END_REF][START_REF] Gnezdilov | Lattice and magnetic instabilities in Cu 3 Bi(SeO 3 ) 2 O 2 X (X = Br, Cl)[END_REF][START_REF] Wu | Anisotropic spin-flip-induced multiferroic behavior in kagome Cu 3 Bi(SeO 3 ) 2 O 2 Cl[END_REF][START_REF] Prishchenko | Antiferroelectric instability in the kagome francisite Cu 3 Bi(SeO 3 ) 2 O 2 X (X = Cl, Br)[END_REF][START_REF] Zakharov | Magnetic, resonance, and optical properties of Cu 3 Sm(SeO 3 ) 2 O 2 Cl: a rare-earth francisite compound[END_REF][START_REF] Zakharov | Thermodynamic properties, electron spin resonance, and underlying spin model in Cu 3 Y(SeO 3 ) 2 O 2[END_REF][START_REF] Wu | Anisotropic pressure effects on the Kagome Cu 3 Bi(SeO 3 ) 2 O 2 Cl metamagnet[END_REF]. Also relevant is the crystal chemistry of (SeO 3 ) 2-groups, which have been recently shown to be similar to those of (HPO 3 ) 2- phosphite groups, where H δ-can substitute the electron lone pair of the selenites [START_REF] Kovrugin | Bonding scheme, hydride character, and magnetic paths of (HPO 3 ) 2versus (SeO 3 ) 2building units in solids[END_REF].

In that frame, Bi III ions are of special interest, since they have a strong affinity to specific oxocentered topologies [START_REF] Krivovichev | Anion-centered tetrahedra in inorganic compounds[END_REF][27][START_REF] Lü | Multidimensional open-frameworks: combinations of one-dimensional channels and two-dimensional layers in novel Bi/M oxo-chlorides[END_REF][29], and therefore its combination with asymmetric selenite groups may result in unique non-centrosymmetric structural architectures [START_REF] Aliev | Mentré, Revised bismuth chloroselenite system: evidence of a noncentrosymmmetric structure with a giant unit cell[END_REF][START_REF] Liang | BiFSeO 3 : an excellent SHG material designed by aliovalent substitution[END_REF][START_REF] Geng | BaBi(SeO 3 ) 2 Cl: a new polar material showing high second-harmonic generation efficiency enhanced by constructive alignment of chloride ions[END_REF] with non-linear optical properties of respective materials. For example, the second-harmonic generation (SHG) efficiency of Bi(SeO 3 )F exhibiting the largest SHG response among all reported oxoselenites [START_REF] Liang | BiFSeO 3 : an excellent SHG material designed by aliovalent substitution[END_REF] compares well to that of BiO(IO 3 ) (SHG efficiency: 12.5 × KDP); the unique β-Bi(SeO 3 )Cl with a giant (V = 19792 Å 3 ) unit cell (SHG efficiency: 2 × KDP) possesses an exceptionally complex structure [START_REF] Aliev | Mentré, Revised bismuth chloroselenite system: evidence of a noncentrosymmmetric structure with a giant unit cell[END_REF].

Incorporation of transition metals into the crystal structures of bismuth selenite oxyhalides sometimes results in unusual physical properties. In particular, the Fe-containing Bi 2 Fe(SeO 3 ) 2 OCl 3 material is an interesting example of the quasi-one-dimensional magnetic system [START_REF] Berdonosov | Crystal structure, physical properties, and electronic and magnetic structure of the spin S = 5/2 zigzag chain compound Bi 2 Fe(SeO 3 ) 2 OCl 3[END_REF]. We have been encouraged to explore the manganesecontaining bismuth selenite-oxychloride system, which has never been reported yet. Here, unconventional magnetoelectric properties motivated us, since the mixed valence halide-free [Mn 3+x O 7 ][Bi 4 O 4.5-y ] phase with a mapleleaf lattice is an unusual 2D antiferromagnet [START_REF] Aliev | Two-dimensional antiferromagnetism in the [Mn 3+x O 7 ][Bi 4 O 4.5-y ] compound with a maple-leaf lattice[END_REF], while the well-known multiferroic BiMnO 3 shows a complex magnetic phase diagram [START_REF] Chou | Multiple magnetic transitions in multiferroic BiMnO 3[END_REF].

In order to fill this gap, we report on the syntheses and structural characterization of five novel phases, namely, Mn II 2 [Bi 2 O](SeO 3 ) 4 (I), Mn II Bi(SeO 3 ) 2 Cl (II), Mn II Mn III (SeO 3 ) 2 Cl (III), Mn II 5 (SeO 3 ) 2 Cl 6 (IV), and Mn II 4 (Mn II 5 ,Bi)(SeO 3 ) [START_REF] Kovrugin | Pathways for synthesis of new selenium-containing oxo-compounds: chemical vapor transport reactions, hydrothermal techniques and evaporation method[END_REF] Cl 5 (V). The compounds III and IV are the first Mn selenite chlorides without alien cations; while the compounds I, II and V are the first examples of Mn-Bi selenites and selenite-chlorides. Structural relationships of the new classes of materials with other compounds will also be discussed.

Experimental Synthesis

New compounds reported in this work have been synthesized by two different methods.

The Mn 2 [Bi 2 O](SeO 3 ) 4 (I) compound has been obtained from the hydrothermal reaction of SeO 2 (2.5 mmol), MnO 2 (2.0 mmol), Mn 2 O 3 (0.25 mmol), and BiOCl (3.0 mmol) carried out in 6 mL of distilled water. The reaction was run in a 23 mL Parr hydrothermal autoclave at 200 °C for 2 days and the autoclave was slowly cooled to room temperature at a rate of 3.7 °C/h. The resulting precipitate was filtered through a filter paper. Transparent brownish single crystals of I were found in association with dark brown single crystals of Mn 3 O(SeO 3 ) 3 [START_REF] Wildner | Crystal structure of Mn(II)Mn(III) 2 O(SeO 3 ) 3[END_REF] in white powder of mixed Bi 2 (SeO 3 ) 3 [START_REF] Rademacher | Crystal structure of bismuth selenite, Bi 2 (SeO 3 ) 3 . Z. Kristallogr[END_REF] and BiOCl [START_REF] Keramidas | The crystal structure of BiOCl[END_REF] composition.

The other phases have been prepared using the chemical vapour transport (CVT) method, which has already demonstrated its efficiency for the synthesis of novel selenium-based oxyhalides [START_REF] Kovrugin | Pathways for synthesis of new selenium-containing oxo-compounds: chemical vapor transport reactions, hydrothermal techniques and evaporation method[END_REF][START_REF] Charkin | Chemical vapor transport and solid-state exchange synthesis of new copper selenite bromides[END_REF]. Interestingly, the new MnBi(SeO 3 ) 2 Cl (II), Mn II Mn III (SeO 3 ) 2 Cl (III), and Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V) phases were grown as a result of the CVT reaction of precursors mixed in the same molar ratio as the following: SeO 2 (4.0 mmol), Mn 2 O 3 (1.0 mmol), Bi 2 O 3 (1.0 mmol) and BiCl 3 (2.0 mmol). Mn 5 (SeO 3 ) 2 Cl 6 (IV) was obtained from the mixture of Bi 2 (SeO 3 ) 3 :MnCl 2 = 1:1. The mixtures of precursors were loaded into glass tubes (15 × 0.9 cm), which were evacuated (10 -2 mbar) and sealed. The tubes were placed horizontally in a tubular furnace so that the precursor-filled ('hot') zone was situated in the central part of the furnace, while the opposite precursor-free ('deposition') zone was turned out toward the furnace edge. This edge remained uncapped during the experiment to create a temperature gradient of about 50 °C between the two zones of the tubes. Different thermal treatment programs were applied for the preparation of the new compounds as listed in Table 1. The furnace was switched off after slow cooling to 200 °C. At the end of reactions, brown single crystals of II-V were observed in association with single crystals of additional phases in the deposition zones of the tubes. It is worthy to note that the crystal growth of the new phases shows a strong dependence on the temperature conditions of the syntheses.

In order to prepare pure bulk polycrystalline samples of the new compounds, we tried to increase the duration of thermal treatment.

It resulted in preparation of pure phases with maximum yield of approximately 60% based on hydrated MnCl 2 for the compound IV with optimal heating time of 216 h.

Single crystal X-ray diffraction

Single crystals of new compounds were mounted on thin glass fibers for X-ray diffraction (XRD) analysis and tested using a Bruker DUO APEX II CCD four-circle diffractometer with a IμS micro-focus tube delivering a MoK α radiation, λ = 0.71073 Å at 50 kV and 40 mA. More than a hemisphere of three-dimensional XRD data was collected for each compound with frame widths of 0.5° in ω, and a 30 s count time for each frame. The diffraction data were integrated and corrected for absorption using a multi-scan type model integrated in the APEX2 and SAD-ABS Bruker programs. The unit cell parameters were determined and refined by least-squares techniques. The crystal structures of Mn 2 [Bi 2 O] (SeO 3 ) 4 (I), MnBi(SeO 3 ) 2 Cl (II), Mn II Mn III (SeO 3 ) 2 Cl (III), Mn II 5 (SeO 3 ) 2 Cl 6 (IV), and Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V) were solved by direct methods using the SHELXL-2013 program [START_REF] Sheldrick | Crystal structure refinement with SHELXL[END_REF] and refined to the agreement factors (R 1 [I > 2σ(I)]) of 2.9%, 2.1%, 4.9%, 2.8%, and 2.2%, respectively.

The final structural models include coordinates and anisotropic displacement parameters for all atoms. Data collection refinement parameters and detailed crystallographic information are provided in Table 2. Fractional atomic coordinates, atomic displacement parameters, and selected bond distances are listed in Tables S1-S5, S6-S10, and S11-S15, respectively. The results of the bond-valence sum (BVS) analysis are given in Tables S16-S20. Empirical bond valence parameters required for the BVS calculations for Mn and Se were taken from Ref. [START_REF] Brese | Bond-valence parameters for solids[END_REF] and for Bi from Ref. [START_REF] Krivovichev | Derivation of bond-valence parameters for some cation-oxygen pairs on the basis of empirical relationships between r o and b[END_REF]. Further details of the crystal structure investigations may be obtained from FIZ Karlsruhe (crysdata@fiz-karlsruhe.de) on quoting the deposition numbers CSD-434425, CSD-434426, CSD-434427, CSD-434428, and CSD-424429 for Mn 2 [Bi 2 O](SeO 3 ) 4 , MnBi(SeO 3 ) 2 Cl, Mn II Mn III (SeO 3 ) 2 Cl, Mn II 5 (SeO 3 ) 2 Cl 6 , and Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 , respectively.

Results

Crystal structure of Mn 2 [Bi 2 O](SeO 3 ) 4 (I)

In contrast to the other phases reported in this work, Mn 2 [Bi 2 O](SeO 3 ) 4 (I) does not contain any halide anions. Its crystal structure contains one Bi site coordinated by eight oxygen atoms with the average <Bi-O> distance equal to 2.481 Å. The coordination polyhedron of Bi III can Tab. 1: Experimental parameters of the CVT reactions (transport agent: Cl -). One crystallographically independent Mn II cation site has a distorted octahedral environment with the Mn-O bond lengths in the range of 2.138-2.309 Å. A bond valence sum calculation gives a value of 1.93 v.u. (valence units) for this site, confirming an oxidation state of 2 for Mn cations. Each MnO 6 octahedron shares two edges with adjacent octahedra thus forming [MnO 4 ] 6-zigzag chains running along the c-axis (Figure 1c). The Mn • • • Mn distance is 3.498(1) Å.

Heating time

Tab. 2: Crystallographic data and refinement parameters for Mn 2 [Bi 2 O](SeO 3 ) 4 (I), MnBi(SeO 3 ) 2 Cl (II), Mn II Mn III (SeO 3 ) 2 Cl (III), Mn II 5 (SeO 3 ) 2 Cl 6 (IV), and Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V). Two crystallographically independent Se IV sites adopt a typical triangular pyramidal coordination with Se atoms located at the apices, in agreement with the stereochemical activity of lone electron pairs. The average <Se-O> bond lengths are 1.702 and 1.700 Å for Se1 and Se2, respectively.

I II III IV V M r (g
In the 3D framework of I, the [Bi 2 O] 4+ chains are linked through SeO 3 groups and [MnO 4 ] 6-chains resulting in a formation of pseudo-tetrahedral [Se] IV empty channels along the c-axis occupied by lone electron pairs of Se IV cations as demonstrated in Figure 1d.

Crystal structure of MnBi(SeO 3 ) 2 Cl (II)

In the crystal structure of MnBi(SeO 3 ) 2 Cl (II), there is one symmetrically unique Mn site occupied by Mn II cations. Mn II have mixed-ligand coordination environments (calculated BVS equals 1.84 v.u.), thus, forming (MnO 4 Cl 2 ) 8- octahedra (<Mn-O> = 2.242 Å), which are interconnected via common Cl • • • Cl and O • • • O edges producing infinite zigzag chains running along the a-axis with the Mn • • • Mn distance of 3.705(1) Å. The chains are further linked by selenite groups into sheets parallel to (001) (Figure 2a). One symmetrically unique Bi III cation has a distorted nine-fold coordination by eight oxygen atoms (<Bi-O> = 2.534 Å) and one chlorine atom (Bi-Cl = 2.936(1) Å). The Bi III cations provide linkage between the sheets and compensate for their negative charge (Figure 2b).

During the structure solution and refinement, two possible orientations of the Se2-based selenite anion were observed due to the disorder of three O sites, which may lead to a local twist of the SeO 3 ion (Figure 2c). The refinement of the occupancies gave the ratio of 0.67/0.33 for each pair of the disordered O sites. Thus, we consider two possible sets of the Se2 environment by the O atoms: O5A, O4A, O6A ( 1 Se2-O = 1.654, 1.687, 1.808 Å; < 1 Se2-O> = 1.716 Å; weight = 67%) and O6B, O4B, O5B ( 2 Se2-O = 1.472, 1.730, 1.795 Å, < 2 Se2-O> = 1.666 Å; weight = 33%). The average <Se1-O> bond length and the occupancy-weighted <Se2-O> bond length are 1.702 and 1.700 Å, respectively.

Crystal structure of Mn II Mn III (SeO 3 ) 2 Cl (III)

Chemically, the compound III corresponds to the substitution of Bi III for Mn II in the formula of the phase II. Unsurprisingly, the different anionic affinities of the two cations lead to very different topologies. The crystal structure of Mn II Mn III (SeO 3 ) 2 Cl (III) is based upon 2D electroneutral sheets separated by lone electron pairs of selenite groups and interacting with each other due to weak secondary interactions only (Figure 3a). In the structure of III, there are two crystallographically independent Mn sites occupied by Mn II respectively. The calculated bond valence sums give 3.15 and 2.03 v.u. for Mn1 and Mn2, respectively, in good agreement with the Mn1 III and Mn2 II charge ordering. An overview of coordination geometry of mixed-ligand MnO n Cl m coordination polyhedra observed in Mn-containing inorganic compounds is discussed below in details. It is noteworthy that this mixed valence compounds result from CVT experiments, while divalent Mn II species are stable in our hydrothermal conditions. The structure of III contains two independent Se IV cations in their typical (SeO 3 ) 2-triangular pyramids. The average <Se-O> distance is 1.702 and 1.708 Å for the Se1 and Se2, respectively.

The electroneutral sheets of III are formed by (Mn II 2 O 10 ) 16-and (Mn III 2 O 8 Cl 2 ) 12-dimers sharing oxygenbased edges (Figure 3b). Dimers are connected to each other in 2D slabs by oxygen corner sharing. Additional linkage between the Mn-centered octahedra is provided by the SeO 3 groups (Figure 3c) with the lone pairs of electrons oriented toward the interstitial space between the plane of the sheet.

Crystal structure of Mn 5 (SeO 3 ) 2 Cl 6 (IV)

In the structure of Mn 5 (SeO 3 ) 2 Cl 6 (IV), there are three crystallographically inequivalent octahedrally coordinated Mn sites. The Mn1 and Mn3 sites are surrounded by two oxygen and four chlorine anions each with the average <Mn-O> bond lengths of 2.073 and 2.157 Å for Mn1 and Mn3, respectively. The average <Mn-Cl> distance is 2.594 Å for both sites. The Mn2 site forms a strongly distorted octahedron by 4 O 2-and 2 Cl -with the average <Mn-O> and <Mn-Cl> lengths of 2.226 and 2.552 Å, respectively. The BVS analysis for the Mn sites indicates 2.09, 1.88, and 1.91 v.u. (valence units) for Mn1, Mn2 and Mn3, which is well consistent with Mn II species. The structure of IV also contains one inequivalent Se site adopting a typical triangular pyramidal coordination with stereochemicaly active lone pair of electrons. The average <Se-O> bond length is 1.704 Å. Note that the SeO 3 groups are 'chelating' sharing a common O • • • O edge with the Mn2O 2 Cl 4 octahedra, which is rather rare in transitional-metal selenites (Figure 4). Similar 'chelating' feature

Crystal structure of Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V)

The compound Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V) demonstrates a partially Bi/Mn disordered structure. Its crystal structure can be described as based upon 2D blocks composed of distorted square antiprisms of four crystallographically inequivalent mixed sites statistically occupied by Mn II and Bi III cations. The edge-sharing antiprisms are arranged in a staggered manner (Figure 6a). A refinement of the mixed sites gave the following cationic distributions: 0.97Mn II /0.03Bi III , 0.92Mn II /0.08Bi III , 0.87Mn II /0.13Bi III , and 0.37Mn II /0.63Bi III for Mn3, Mn4, Mn5, and Bi6, respectively, under the restraints of a total neutral charge. In the structure of V, there are also two fully ordered Mn II sites (Mn1 and Mn2), which are octahedrally coordinated by three oxygen (<Mn1-O> = 2.143 Å, <Mn2-O> = 2.130 Å) and three chlorine (<Mn1-Cl> = 2.640 Å, <Mn2-Cl> = 2.623 Å) atoms each. Two octahedra share their common Cl 3 face to form a dimer, which is further linked through one of its Cl corners with an adjacent dimer into a square-like tetrameric unit. Four symmetrically inequivalent Se IV triangular pyramids (<Se-O> = 1.702, 1.702, 1.697, and 1.692 Å for Se1, Se2, Se3, and Se4) are connected to the O corners of the tetrameric unit as shown in Figure 6d. The inspection of Fourier difference electron-density maps showed that two of the five crystallographically independent Cl -sites are disordered. The refinement of their occupancies indicated identical 0.58/0.42 ratios for both Cl1A/ Cl1B and Cl2A/Cl2B sites. The arrangement of the tetrameric units in the structure of V is shown in Figure 6b. This Cl disorder reflects the influence of the local Mn II /Bi III occurrence in the layers with locally different oxygen coordination. As can be seen from Table 3, the disordering of the two aliovalent metal sites is in good agreement with our BVS calculations and differences of ionic radii (r Bi III (octa) = 1.03 Å, r Mn II (HS, octa) = 0.83 Å). Such significant differences suggest local configurations depending on the involved cations while the average structure is refined. Therefore, for all mixed sites Bi III seem over-bonded (BVS in range of 3.40-3.80 v.u. for the Bi3-Bi6 sites), while Mn II appear under-bonded (BVS in range of 1.58-1.84 v.u. for the Mn3-Mn6 sites). The deviations from the ideal values is consistent with the refined Mn/Bi ratio for each of these sites.

The tetrameric units are connected to the 2D sheets via sharing common O • • • O edges of octahedra or selenite pyramids with the square antiprisms resulting in a complex 3D framework with large pseudo-tetragonal empty channels occupied by lone electron pairs of Se IV cations along the a-axis (Figure 6c).

Discussion

The structural edifices of the new compounds reveal a remarkable variety of their different structure types. Four of them (I, III-V) are new and have never been observed in reported inorganic compounds to the best of our knowledge. Nevertheless, some relations to the crystal structures of already reported phases can be evaluated.

The structural motif of Mn 2 [Bi where n is the chain multiplicity [START_REF] Krivovichev | Anion-centered tetrahedra in inorganic compounds[END_REF]. For example, in the crystal structures of [Tb 2 O](SeO 3 ) 2 [START_REF] Wontcheu | Tb 2 Se 2 O 7 : terbium(III) oxide oxoselenate(IV) according to Tb 2 O[SeO 3 ] 2 with a "lone-pair" channel structure[END_REF] and [M 3 O 2 ](SeO 3 ) 2 Cl (M III = Tb [START_REF] Wontcheu | Tb 3 O 2 Cl[SeO 3 ] 2 and Tb 5 O 4 Cl 3[END_REF] and Y [START_REF] Zitzer | Synthesis, crystal structure and spectroscopic properties of Y 3 O 2 Cl[SeO 3 ] 2 : Eu 3+[END_REF]) with n equaled 1 and 2, respectively, the single [Tb 2 O] 4+ and double [M [START_REF] Zhao | BiCuSeO oxyselenides: new promising thermoelectric materials[END_REF] O 2 ] 5+ chains of oxocentered tetrahedra are linked via selenite anions into similar 3D frameworks (Figure 7b,c). Tab. 3: Calculated BVS of cations in Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V). Despite the similarity in their chemical formulae, the crystal structures of MnBi(SeO 3 ) 2 Cl (II) and Mn II Mn III (SeO 3 ) 2 Cl (III) belong to different structure types. The structure of MnBi(SeO 3 ) 2 Cl (II) is isotypic with the previously reported MnSm(SeO 3 ) 2 Cl, CoSm(SeO 3 ) 2 Cl, and CuGd(SeO 3 ) 2 Cl [START_REF] Wickleder | CoSm(SeO 3 ) 2 Cl, CuGd(SeO 3 ) 2 Cl, MnSm(SeO 3 ) 2 Cl, CuGd 2 (SeO 3 ) 4 und CuSm 2 (SeO 3 ) 4 : Übergangsmetallhaltige Selenite von Samarium und Gadolinum[END_REF], whereas the structure type of III is reported here for the first time. It is of interest, however, that, in the Mn 5 (TeO 3 ) 4 Cl 2 [START_REF] Zimmermann | A synthetic route toward layered materials: introducing stereochemically active lone-pairs into transition metal oxohalides[END_REF] and Mn 4 (TeO 3 )(SiO 4 )X 2 (X = Cl, Be) [START_REF] Zimmermann | Two isostructural layered oxohalide compounds containing Mn 2+ , Te 4+ and Si 4+ ; crystal structure and magnetic susceptibility[END_REF] compounds, chloride ions and lone electron pairs of Te IV protrude from the sheets in a similar way as observed in the structure of III, which means that the sheets are interconnected by the weak interactions only.

Atom

One of the interesting features of the crystal structure of Mn 5 (SeO 3 ) 2 Cl 6 (IV) is the presence of honeycomb sheets composed of edge-sharing (MnO 2 Cl 4 ) octahedra (similar Mn II coordination has previously been reported in Mn 9 Sb 8 O [START_REF] Berdonosov | Crystal structure, physical properties, and electronic and magnetic structure of the spin S = 5/2 zigzag chain compound Bi 2 Fe(SeO 3 ) 2 OCl 3[END_REF] Cl 10 [START_REF] Zimmermann | A synthetic route toward layered materials: introducing stereochemically active lone-pairs into transition metal oxohalides[END_REF]). The honeycomb sheets based on triangular lattices are of interest in terms of enhanced electron transport and 2D-magnetic frustration owing to significant M • • • M interactions [START_REF] Richter | Quantum magnetism in two dimensions: from semi-classical Neel order to magnetic disorder[END_REF]. For example, the structures of Bi 3 Mn 4 O 12 (NO 3 ) and BiMnTeO 6 based upon honeycomb sheets of Mn IV and Mn III cations, respectively, are good model compounds of honeycomb antiferromagnets [START_REF] Smirnova | Synthesis, crystal structure, and magnetic properties of Bi 3 Mn 4 O 12 (NO 3 ) oxynitrate comprising S = 3/2 honeycomb lattice[END_REF][START_REF] Kim | Structure and magnetic behavior of layered honeycomb tellurates, BiM(III)TeO 6 (M = Cr, Mn, Fe)[END_REF]. From this point of view, the further magnetic studies of the IV phase would be of interest, and efforts are now provided to prepare the single-phase material.

Regarding the unusual structure of Mn 4 (Mn 5 ,Bi) (SeO 3 ) 8 Cl 5 (V), its remarkable structural complexity (Figure 6) comes to our attention first. A quantitative evaluation of the structural complexity of the structure V can be done using the amount of Shannon information measured in bits per atom (I G in bits/atom) and per unit cell (I G,total in bits/cell), according to Krivovichev approach [START_REF] Krivovichev | Structural complexity of minerals: information storage and processing in the mineral world[END_REF][START_REF] Krivovichev | Topological complexity of crystal structures: quantitative approach[END_REF][START_REF] Krivovichev | Ladders of information: what contributes to the structural complexity of inorganic crystals[END_REF]. The calculations using the ToposPro [START_REF] Blatov | Applied topological analysis of crystal structures with the program package ToposPro[END_REF] software gave the structural information amounts, I G and I G,total , 4.704 bits/atom and 884.263 bits/cell for the V compound, which allows classification of its structure as complex (only 0.03% of all reported inorganic compounds) [START_REF] Krivovichev | Which inorganic structures are the most complex?[END_REF]. The estimated structural complexity values for I-V compounds are given in Table 2.

Note that the compound V bears a structural analogy to the Na 2 Ln 3 (TeO 3 ) 4 X 3 phases [START_REF] Charkin | Synthesis, structures, and luminescent properties of sodium rare-earth metal(III) chloride oxotellurates(IV), Na 2 Ln 3 Cl 3 [TeO 3 ] 4[END_REF]. In their structures, there are layered blocks of distorted square LnO 8 antiprisms arranged in check-wise fashion very similar to the blocks of Mn/BiO 8 antiprisms found in Mn 4 (Mn 5 ,Bi) (SeO 3 ) 8 Cl 5 (Figure 7a). The phase V is the only one selenite with such structural motif, and it is a unique example of Mn II occupying sites more typical for Ln III , to the best of our knowledge. It may be the Se IV /Mn II and Te IV /Ln III ratio which would favor such arrangement.

It is worth paying special attention also to four 8e sites in the structure of V, which are statistically occupied by Mn II and Bi III atoms. This relatively rare aliovalent substitution of Mn II -based polyanionic compounds for Bi III has been previously found in Bi~1 .2 Mn~1 .2 PO 5.5 [START_REF] Abraham | Crystal structure approach of the disordered new compounds Bi~1 .2 M~1 .2 PO 5.5 (M = Mn, Co, Zn): the role of oxygen-centered tetrahedra linkage in the structure of bismuth-transition metal oxy-phosphates[END_REF]. Note also that despite the larger ionic radius of 6-coordinated Mn II (0.9 Å) compared to Mn III (0.685 Å), isovalent doping of Bi III (1.17 Å) by Mn III has been reported so far in the sillenitetype Bi 12 (Bi 0.53 Mn 0.47 )O 20 phase [START_REF] Neov | Neutrondiffraction study of Bi 12 MO 20 single crystals with sillenite structure[END_REF]. Meanwhile, the diversity of other aliovalent M II (Cd, Cu, Zn, Mg, Co) cations incorporating mainly into oxocentered O(Bi,M) 4 tetrahedra is also known [START_REF] Aliev | Labile degree of disorder in bismuth-oxophosphate compounds: illustration through three new structural types[END_REF][START_REF] Colmont | Bi 2 O 3 -CuO-P 2 O 5 system: two novel compounds built from the intergrowths oxocentered polycationic 1D-ribbons[END_REF][START_REF] Endara | Novel tailormade Bi 4 MO 4 (PO 4 ) 2 structural type (M=Mg, Zn)[END_REF][START_REF] Endara | Inorganic polar blocks into controlled acentric assemblies[END_REF][START_REF] Colmont | Double (n = 2) and triple (n = 3) [M 4 Bi 2n-2 O 2n ] x+ polycationic ribbons in the new Bi~3Cd~3 .72 M~1[END_REF].

One of the interesting structural features of all the new phases is the presence of mixed-ligand MnO n Cl m coordination polyhedra. Figure 8 summarizes all encountered

Coordination number

Geometry

Average bond lengths and distortion Site Formula Ref.

<Mn-O> (Å) <Mn-Cl > (Å) ∆ d , 10 six-fold anionic environments of Mn cations in the crystal structures I-V. The remarkable versatility of the Mn coordination in five compounds reported herein encouraged us to investigate the mixed-ligand environments of Mn cations in the structures of all reported inorganic compounds. Table 4 provides an overview of the observed MnO n Cl m polyhedra.

Eleven and two stereochemically different mixed-ligand geometries correspond to Mn II and Mn III cations, respectively, while no mixed-ligand environments were found for Mn IV so far. All observed polyhedra can be described as octahedra with various degrees of distortion except the Mn coordination polyhedron in the structure of CsMn 2 (V 2 O 7 )Cl, which is rather a trigonal prism than an octahedron [START_REF] Queen | The versatile chemistry and noncentrosymmetric crystal structures of salt-inclusion vanadate hybrids[END_REF]. MnO 4 Cl 2 octahedra are most common, whereas MnOCl 5 configurations are very rare. In order to quantify the degree of distortions for the mixed-ligand polyhedra, we used the ∆ d parameter defined previously by Alonso et al. for perovskites [START_REF] Alonso | Evolution of the Jahn-Teller distortion of MnO 6 octahedra in RMnO 3 perovskites (R = Pr[END_REF]. This parameter concerns the deviation of Mn-O/Cl distances with respect to its average value for each octahedron and can be calculated as follows ∆ d = (1/6) • Σ n=1,6 [(d n - 〈d〉)/〈d〉] 2 , where 〈d〉 is the average Mn-O/Cl distance in a octahedron. Unsurprisingly, there is an increase of the distortion of polyhedra with the elongation of the Mn-Cl distances. The geometries of the polyhedra show essential variabilities for each type of MnO n Cl m polyhedra. In particular, two chloride anions in MnO 4 Cl 2 octahedra may be located opposite to each other and complement the MnO 4 squares ([(4O) + (2Cl)]) (trans-position) or be in cis-position ([(3O + Cl) + (O + Cl)] octahedra). The average bond lengths in the mixed-ligand polyhedra for all the structures under consideration are: <Mn II -O> = 2.180 Å and <Mn II -Cl> = 2.645 Å.

Conclusion

Five new compounds belonging to novel chemical families of materials (Mn selenite chlorides and Bi-Mn selenites and oxoselenites) have been synthesized and structurally characterized by single crystal X-ray diffraction analysis for the first time. Four of them (II-V) containing chloride anions have been prepared by the CVT method, whereas crystals of the compound I were grown hydrothermally. The combination of asymmetric selenite group with stereoactive lone pairs of electrons, chloride anions, transition-metal and bismuth cations provides an example of a promising chemical system for search of new materials with novel structure types. The crystal growth in the system is strongly dependent upon the synthesis conditions, which is manifested in the formation of three different phases from the same initial mixture with the only difference in a temperature regime of the applied thermal treatment. Hence, further efforts in the synthesis of novel Bi and Mn oxoselenites by the CVT method may be focused on the investigation of the temperature influence upon the crystal growth. The structural variety, complexity, and the presence of a transition metal in the new phases provide a broad field for the further studies of their physical pro perties. Nevertheless, the difficulties to choose the optimal experimental conditions for the preparation of sufficient amount of bulk phase should be considered.

  be described as a strongly distorted square antiprism. The interesting feature of the crystal structure of I is the presence of an 'additional' oxygen atom (O7), which is coordinated solely by four Bi III cations forming oxocentered (OBi 4 ) 10+ tetrahedra[START_REF] Krivovichev | Anion-centered tetrahedra in inorganic compounds[END_REF]. The OBi 4 tetrahedra share trans-oriented edges to form infinite [Bi 2 O] 4+ chains elongated along the c-axis (Figure1b). The O7 • • • O7 distance is 2.753(3) Å. The Bi • • • Bi edge-lengths are of 3.751(5) Å. Such chains are rather common in Bi(III) oxysalts, e.g. in [Bi 2 O](AuO 4 )[START_REF] Geb | Bi 2 AuO 5 and Bi 4 Au 2 O 9 , two novel ternary oxoaurates[END_REF].

Fig. 1 :

 1 Fig. 1: Projection of the crystal structure of Mn 2 [Bi 2 O](SeO 3 ) 4 (I) (a) built up from [Bi 2 O] 4+ (b) and [MnO 4 ] 6-chains (c); pseudo-tetrahedral channels filled by lone electron pairs (LP, green) of Se cations (d).

  and Mn III cations. Both sites have irregular octahedral environments formed by five O and one Cl for Mn1 and six O for Mn2, with the average Mn-O bond lengths of 2.084 and 2.226 Å for the Mn1 and Mn2 sites,

Fig. 2 :

 2 Fig. 2: General projections of the crystal structure of MnBi(SeO 3 ) 2 Cl (II) along [010] -(a) and [110] -(b) (disordered O sites and selenite groups in b are omitted for clarity); anionic arrangement of cations in the structure -(c).

Fig. 3 :

 3 Fig. 3: General projection of the crystal structure of Mn II Mn III (SeO 3 ) 2 Cl (III) along [010] -(a) and its sheet -(b) (selenite groups are omitted for clarity); anionic arrangement of metal cations in the structure -(c).

Fig. 4 :

 4 Fig. 4: Fragment of Mn 5 (SeO 3 ) 2 Cl 6 (IV) showing the cationic arrangement. The shortest interatomic distances are given.

Fig. 5 :

 5 Fig. 5: General projection of the crystal structure of Mn 5 (SeO 3 ) 2 Cl 6 (IV) along [010] -(b) and two Mn-based 2D-blocks (a) and (c).

Fig. 6 :

 6 Fig. 6: Projection of the crystal structure of Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V) along [100] -(c), the sheets of square antiprisms -(a), the tetrameric unit -(d), and their arrangement in the structure -(b).

  2 O](SeO 3 ) 4 (I) is closely related to the one observed in the structure of Cu[Bi 2 O] (SeO 3 ) 3 (H 2 O) [45], which is also a transitional-metal selenite with [Bi 2 O] chains of trans-edge-sharing OBi 4 tetrahedra. Here the [Bi 2 O] 4+ chains are linked through (CuO 5 ) 8-square pyramids and (SeO 3 ) 2-triangular pyramids to form a 3D framework with channels occupied by the lone electron pairs on the Se IV cations (Figure 7a). Interestingly, the condensation of the [M 2 O] m+ single chains through the equatorial edges of (OM 4 ) tetrahedra produces the family of chains with the general formula [M n+1 O n ] m+ ,

Fig. 7 :

 7 Fig. 7: Projections of the crystal structures of Cu[Bi 2 O](SeO 3 ) 2 (H 2 O) [45] (a), [Tb 2 O](SeO 3 ) 2 [46] (b) and [Tb 3 O 2 ](SeO 3 ) 2 Cl [47] (c).

Fig. 8 :Tab. 4 :

 84 Fig. 8: Coordination polyhedra of the Mn II/III -filled sites in the structures of I-V.

Temp. Dwell time Target temp. Cooling time Cooling rate Main products Additional products

	2 h	400 °C 24 h	200 °C 100 h	2.0 °C/h MnBi(SeO 3 ) 2 Cl (II) (brown plates)	Bi 6 (SeO 3 ) 4 Cl 10 [7] (transparent plates)
	2 h	400 °C 24 h	200 °C 72 h	2.8 °C/h Mn II Mn III (SeO 3 ) 2 Cl (III) (brown prisms)	Bi 6 (SeO 3 ) 4 Cl 10 [7] (transparent plates)
	3 h	450 °C 216 h 200 °C 100 h	2.5 °C/h Mn 5 (SeO 3 ) 2 Cl 6 (IV) (brown plates)	Bi 6 (SeO 3 ) 4 Cl 10 [7] (transparent plates)
	3 h	450 °C 48 h	200 °C 100 h	2.5 °C/h Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5 (V) (brown prisms) γ-Bi(SeO 3 )Cl [38] (transparent plates)

  4

	Tab. 4 (continued)
	Coordination	Geometry	Average bond lengths and distortion	Site	Formula	Ref.
	number		<Mn-O> (Å) <Mn-Cl > (Å)	∆ d , 10 4
	Oxidation state of Mn: +3	2.041	2.741	193	Mn1	Cs 2 Mn(VO 3 ) 2 Cl 2	[81]
	6 = [5O-1Cl]	[(4O) + (O + Cl)]	2.084 2.176	2.242 2.531	87	48	Mn1 Mn1	Mn II Mn III (SeO 3 ) 2 Cl K 2 MnCl 4 (H 2 O) 2	a [96]
	6 = [4O-2Cl]	[(4O) + (2Cl)]	1.895 2.080	2.702 2.560	323	89	Mn1 Mn1	Ba 2 Mn(Si 2 O 7 )Cl Rb 2 MnCl 4 (H 2 O) 2	[68] [97]
			1.891 2.128	2.905 2.543	461	66	Mn1 Mn1	FeMn 7 O 10 Cl 3 Cs 2 MnCl 4 (H 2 O) 2	[69] [97]
			1.890 2.200	2.831 2.545	406	45	Mn1 Mn1	Mn 8 O 10 Cl 3 (NH 4 ) 2 MnCl 4 (H 2 O) 2	[70] [98]
	6 = [2O-4Cl] Oxidation state of Mn: +2 [(2O + 2Cl)-cis + (2Cl)] b 6 = [6O-0Cl] [(4O) + (2O)] 6 = [2O-4Cl] [(4Cl) + (2O)]	1.890 2.176 2.215 2.157 2.226 2.073	2.846 2.541 -2.594 -2.594	433 6 119 51 39 107	Mn2 Mn1 Mn1 Mn3 Mn2 Mn1	Mn 8 O 10 Cl 3 α-RbMnCl 3 (H 2 O) 2 Mn 5 (SeO 3 ) 2 Cl 6 Mn 2 [Bi 2 O](SeO 3 ) 4 Mn II Mn III (SeO 3 ) 2 Cl Mn 5 (SeO 3 ) 2 Cl 6	[70] [94] a a a a
	6 = [5O-1Cl] 6 = [1O-5Cl]	[(4O) + (O + Cl)] [(O + 3Cl) + (2Cl)]	2.178 2.078 2.223 2.268 2.218 2.259	2.574 2.550 2.490 2.550 2.654 2.540	48 42 86	53 18 20	Mn1 Mn1 Mn1 Mn1 Mn1 Mn2	MnCl 2 (H 2 O) (NH 4 ) 2 MnB 2 P 3 O 11 (OH) 2 Cl CrMnCl 5 (NH 3 ) 6 (H 2 O) MnSb 2 O 3 (OH)Cl Mn 2 (PO 4 )Cl CrMnCl 5 (NH 3 ) 6 (H 2 O)	[71] [99] [72] [100] [73] [100]
			2.198	2.475	25		Mn1	Mn 3 (Sb 2 O 2 )(VO 4 ) 1.9 (SbO 3 ) 0.1 Cl 2	[74]
			2.168	2.919	152		Mn1	Na 2 RbMn 3 (P 2 O 7 ) 2 Cl	[75]
			2.173	2.951	161		Mn1	Na 2 CsMn 3 (P 2 O 7 ) 2 Cl	[75]
			2.171	2.570	46		Mn1	Na 13 Mn 4 Se 6 W 24 O 151 ClH 114	[76]
			2.173	2.978	175		Mn3	Mn 3.5 (AsO 4 ) 2 Cl	[77]
			2.166	2.962	189		Mn2	Mn 4 (TeO 3 )(SiO 4 )Cl 2	[51]
			2.234	2.557	44		Mn2	Mn 5 (AsO 4 ) 3 Cl	[77]
			2.251	2.500	37		Mn2	Mn 5 (PO 4 ) 3 Cl 0.9 (OH) 0.1	[78]
			2.276	2.163	8		Mn6	Mn 7 Fe 0.6 Mg 0.4 Si 6 O 15 Cl 2 (OH) 8	[79]
			2.217	2.589	41		Mn5	Mn 8 Si 6 O 24 ClH 9	[79, 80]
			2.284	2.587	107		Mn6	Mn 11 (AsO 4 ) 7 Cl	[77]
	6 = [4O-2Cl]	[(4O) + (2Cl)]	2.115	2.648	129		Mn1	CsMn 2 (V 2 O 7 )Cl	[81]
			2.134	3.081	448		Mn1	Mn 3 (B 7 O 13 )Cl	[82]
			2.121	3.070	442		Mn2	Mn 3 (B 7 O 13 )Cl	[82]
			2.130	3.074	431		Mn3	Mn 3 (B 7 O 13 )Cl	[82]
			2.154	2.546	67		Mn2	Mn 3 (Sb 2 O 2 )(VO 4 ) 1.9 (SbO 3 ) 0.1 Cl 2	[74]
			2.165	2.620	111		Mn2	Na 2 RbMn 3 (P 2 O 7 ) 2 Cl	[75]
			2.171	2.641	123		Mn2	Na 2 CsMn 3 (P 2 O 7 ) 2 Cl	[75]
			2.144	2.685	121		Mn2	K 2 CsMn 3 (P 2 O 7 ) 2 Cl	[75]
			2.244	2.489	25		Mn4	Mn 3.5 (AsO 4 ) 2 Cl	[77]
			2.225	2.392	42		Mn5	Mn 7 Fe 0.6 Mg 0.4 Si 6 O 15 Cl 2 (OH) 8	[79]
	6 = [4O-2Cl]	[(3O + Cl) + (O + Cl)]	2.186	2.660	97		Mn1	MnSm(SeO 3 ) 2 Cl	[49]
			2.242	2.627	83		Mn1	MnBi(SeO 3 ) 2 Cl	a
			2.114	2.731	165		Mn1	Mn 3.5 (AsO 4 ) 2 Cl	[77]
			2.226	2.552	45		Mn2	Mn 5 (SeO 3 ) 2 Cl 6	a
			2.244	2.543	36		Mn2	Mn 7 Fe 0.6 Mg 0.4 Si 6 O 15 Cl 2 (OH) 8	[79]
			2.242	2.544	37		Mn2	Mn 8 Si 6 O 24 ClH 9	[79, 80]
			2.097	2.960	328		Mn1	Mn 11 (AsO 4 ) 7 Cl	[77]
	6 = [4O-2Cl]	[(2O + 2Cl)-cis + (2O)]	2.193	2.500	40		Mn1	CuMn(HSeO 3 ) 2 Cl 2 (H 2 O) 4	[83]
			2.183	2.534	47		Mn1	CsMnCl 3 (H 2 O) 2	[84-86]
			2.201	2.488	35		Mn1	MnCl 2 (H 2 O) 4	[87-89]
			2.227	2.563	77		Mn2	Mn 2 (PO 4 )Cl	[73]
	6 = [4O-2Cl]	[(2O + Cl) + (2O + Cl)]	2.122	2.867	222		Mn2	CsMn 2 (V 2 O 7 )Cl	[81]
	6 = [3O-3Cl]	[(2O + 2Cl)-cis + (O + Cl)]	2.143	2.640	62		Mn1	Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5	a
			2.130	2.623	68		Mn2	Mn 4 (Mn 5 ,Bi)(SeO 3 ) 8 Cl 5	a
	6 = [3O-3Cl]	[(2O + 2Cl)-trans + (O + Cl)]	2.335	2.629	217		Mn1	Mn 4 (TeO 3 )(SiO 4 )Cl 2	[51]
	6 = [2O-4Cl]	[(4Cl) + (2O)]	2.193	2.584	57		Mn1	MnCl 2 (H 2 O) 2	[90, 91]
			2.186	2.536	49		Mn1	KMnCl 3 (H 2 O) 2	[92, 93]
			2.216	2.539	43		Mn1	β-RbMnCl 3 (H 2 O) 2	[94, 95]
			2.048	2.648	142		Mn1	Rb 2 Mn(VO 3 ) 2 Cl 2	[81]

a This work. b Mn-O bong lengths in MnO 6 are given for the I and III compounds for comparison.

Acknowledgements: This work was carried out within the project of the Russian Foundation for Basic Research through the grant 16-35-00191 mol_a for VMK. OIS thanks the President grant MD-5229.2018.5. We also thank an anonymous referee for his/her constructive comments and useful suggestions.

Supplementary Material:

The online version of this article offers supplementary material (https://doi.org/10.1515/zkri-2018-2088).