Structural characterization of quaternary selenites of tungsten(VI), A₂W₃SeO₁₂ (A = NH₄, Cs, Rb, K or Tl)

The quaternary A₂W₃SeO₁₂ (A = NH₄, Cs, Rb, K or Tl) selenites have been prepared in the form of single crystals by hydro­thermal and novel solid-state reactions. They were characterized by X-ray diffraction, thermal and spectroscopic studies. All of them have a hexa­gonal tungsten oxide (HTO) related [W₃SeO₁₂]²⁻ anionic framework with pyramidally coordinated Se⁴⁺ ions. The known A₂W₃SeO₁₂ (A = NH₄, Cs or Rb) compounds are isostructural with the Cs₂W₃TeO₁₂ compound and have a non-centrosymmetric layered structure containing intra-layer Se—O bonds. The new compound K₂W₃SeO₁₂(α) is isostructural with the K₂W₃TeO₁₂ compound and has a centrosymmetric three-dimensional structure containing inter­layer Se—O bonds. It is inferred that the new Tl₂W₃SeO₁₂ compound has the same three-dimensional structure as K₂W₃SeO₁₂(α).

1. Chemical context

Non-centrosymmetric (NCS) compounds are widely studied as they have potentially useful symmetry-dependent properties such as piezoelectricity, ferroelectricity and second-order non-linear optical (NLO) behaviour (Halasyamani & Poeppelmeier 1998). Many crystalline selenites and tellurites containing d⁰ transition-metal ions such as V⁵⁺, Mo⁶⁺, W⁶⁺ are non-centrosymmetric compounds. The solid-state chemistry of these oxides is inter­esting from the point of view of both structural diversity and second harmonic generation (SHG) activity. They have two types of second-order Jahn–Teller (SOJT) distortion. One is the distorted octa­hedral coordination of the d⁰ transition-metal ion and the other is pyramidal, disphenoidal and square-pyramidal coordinations of Se⁴⁺ and Te⁴⁺, which have stereoactive lone pairs. Both SOJT distortions lead to acentric coordination environments that are conducive for NCS structures (Halasyamani 2004). For example, Cs₂Mo₃TeO₁₂ (Vidyavathy Balraj & Vidyasagar, 1998) and YVSe₂O₈ (Kim et al., 2014) have non-centrosymmetric layered structures with these SOJT distortions and exhibit SHG activity. It needs to be mentioned that quaternary selenites and tellurites containing d⁰ transition-metal ions, such as YVTe₂O₈ (Kim et al., 2014), are also known to have centrosymmetric structures and exhibit no SHG activity.

A₂Mo₃SeO₁₂ (A = NH₄, Cs, Rb, Tl) (Harrison et al., 1994; Dussack et al., 1996; Chang et al., 2010), A₂W₃SeO₁₂ (A = NH₄, Cs, Rb, K) (Harrison et al., 1995; Huang et al., 2014a,b) and Na₂W₃SeO₁₂·2H₂O (Nguyen & Halasyamani 2013), A₂Mo₃TeO₁₂ (A = Cs, NH₄) (Vidyavathy Balraj & Vidyasagar 1998), A₂W₃TeO₁₂ (A = K, Rb and Cs) (Goodey et al., 2003; Zhao et al., 2015) are the 14 quaternary selenites and tellurites of hexa­valent molybdenum and tungsten that have hexa­gonal tungsten oxide (HTO) related [M₃XO₁₂]²⁻ (M = Mo, W; X = Se, Te) anionic frameworks with pyramidally coordinated Se⁴⁺ and Te⁴⁺ ions. The single-crystal X-ray structures were determined for all except for the A₂W₃SeO₁₂ (A = NH₄, Cs, Rb) compounds, which were synthesized in polycrystalline form by the hydro­thermal method; the structures of the (NH₄)₂W₃SeO₁₂ and Cs₂W₃SeO₁₂ compounds were determined by powder neutron diffraction (Harrison et al., 1995). K₂W₃TeO₁₂ has a centrosymmetric three-dimensional structure (Goodey et al., 2003), whereas all of the others exhibit a non-centrosymmetric two-dimensional structure and show SHG response. It is noteworthy that the tellurites were synthesized by both hydro­thermal and solid-state reactions, whereas the selenites were synthesized only by the hydro­thermal method.

Ag₂Mo₃SeO₁₂ (Ling & Albrecht-Schmitt 2007), Li₂Mo₃TeO₁₂ (Oh et al., 2018) and A₄Mo₆Te₂O₂₄·6H₂O (A = Rb, K) (Vidyavathy Balraj & Vidyasagar 1998) compounds are quaternary selenite and tellurites of molybdenum, whose [Mo₃XO₁₂]²⁻ (X = Se, Te) anionic framework structures are not related to HTO. They have centrosymmetric layered and zero-dimensional structures and contain pyramidally coordinated Se⁴⁺ and pyramidally and disphenoidally coordinated Te⁴⁺ ions.

In this context, the structural characterization of new and known quaternary A₂W₃SeO₁₂ (A = NH₄, Cs, Rb, K, Tl) selenites of tungsten(VI) by single-crystal X-ray diffraction was considered necessary for their complete structural study and, therefore, was undertaken. This report is concerned with crystal growth by solid-state reactions and structural characterization of the known compounds A₂W₃SeO₁₂ [A = NH₄ (1), Cs (2) and Rb (3)] and new compounds K₂W₃SeO₁₂ (4α) and Tl₂W₃SeO₁₂ (5).

2. Structural commentary

The structures of compounds 1–5 are of two types, which contain a hexa­gonal tungsten oxide (HTO) related [W₃SeO₁₂]²⁻ anionic framework. (NH₄)₂W₃SeO₁₂ (1), Cs₂W₃SeO₁₂ (2) and Rb₂W₃SeO₁₂ (3) crystallize in the P6₃ space group and have the structure of Cs₂W₃TeO₁₂ (Zhao et al., 2015). They contain ammonium/caesium/rubidium ions between non-centrosymmetric HTO-related [W₃SeO₁₂]²⁻ layers, which have only intra-layer type Se—O bonds. The absolute structure configuration of the rubidium compound (3) is the inverse of that of the ammonium (1) and caesium (2) compounds.

As an illustrative example, the structure of Rb₂W₃SeO₁₂ (3) is discussed. Its asymmetric unit content of Rb_2/3WTe_1/3O₄ has two, one, one and four crystallographically distinct rubidium, tungsten, selenium and oxygen atoms, respectively. The tungsten atom is octa­hedrally coordinated to the apical O1 and O2 atoms and two each of equatorial O3 and O4 atoms (Fig. 1). The WO₆ octa­hedron resides near the threefold rotation axis located at the Wyckoff site 2a and shares its two cis O3 equatorial oxygen atoms with two such octa­hedra to form a W₃O₁₅ moiety. Such trinuclear moieties are connected to one another through sharing of equatorial O4 atoms, forming a hexa­gonal–tungsten–oxide (HTO) layer of composition WO₄ or W₃O₁₂. In other words, the HTO layer of WO₄ is formed from the sharing of four equatorial O3 and O4 atoms of every WO₆ octa­hedron with four such octa­hedra. The HTO layer of WO₄ has three-ring holes made of either O3 or O4 atoms and six-ring holes made of alternating O3 and O4 atoms. The selenium atom resides on a threefold rotation axis located at the 2a site and has a pyramidal coordination of C_3V symmetry, with three equivalent Se—O1 bonds. Thus, only three-ring holes of O3 are capped on one side of the layer, by bonding of the selenium atom to apical O1 oxygen atoms, to give rise to an asymmetric (W₃SeO₁₂)²⁻ layer. These layers are stacked, as shown in Fig. 1, along the crystallographic c-axis direction in the ABAB… fashion because adjacent layers are rotated with respect to each other such that the six-ring hole of one layer is above the uncapped three-ring hole of the next layer. As the other apical oxygen O2 atoms are not bonded to selenium, the Se—O bonding is described as intra-layer bonding and, therefore, the structure is two-dimensional. The pyramidal SeO₃ moieties and the lone-pair of electrons of Se⁴⁺ are respectively parallel and perpendicular to the HTO layers of WO₄. The selenites 1–5 of the present study are found to contain the same staggered stacking of the HTO-related WO₄ layers.

Figure 1 Polyhedral representation of (left) the unit-cell structure viewed along the a axis and (right) a (W3SeO12)^2− layer along with the Rb^+ counter-cations, viewed along the c axis, of Rb2W3SeO12 (3). A W3O15 moiety with a pyramidal selenium atom is indicated by a dashed red line and the net dipole directions of the WO6 octa­hedra and pyramidal SeO3 are shown.

K₂W₃SeO₁₂ (β) was reported (Huang et al., 2014a,b) to be obtained under hydro­thermal conditions and found to contain similar non-centrosymmetric HTO-related [W₃SeO₁₂]²⁻ layers with intra-layer Se—O bonds. On the other hand, K₂W₃SeO₁₂ (4α) of the present study was prepared by solid-state reaction and is isostructural with the reported K₂W₃TeO₁₂ (Goodey et al., 2003). Its centrosymmetric, three-dimensional HTO-related [W₃SeO₁₂]²⁻ framework contains inter-layer Se—O bonds (Fig. 2) and its asymmetric unit has one formula unit. The three W1—W3 atoms are octa­hedrally coordinated to six apical O1–O6 and six equatorial O7–O12 oxygen atoms. The three WO₆ octa­hedra in the trinuclear W1W2W3O₁₅ moieties share equatorial O7–O9 oxygen atoms and these moieties are connected to one another through the other equatorial O10–O12 oxygen atoms to form the WO₄ layer. The Se atom forms inter­layer Se—O bonds, by bonding to the apical O7, O10 and O12 oxygen atoms of W1W2W3O₁₅ moieties of adjacent HTO layers (Fig. 2) and thus the [W₃SeO₁₂]²⁻ framework is three-dimensional in nature.

Figure 2 Polyhedral representation of (left) the unit-cell structure viewed along the −a axis and (right) a segment of the (W3SeO12)^2− structure along with the K^+ counter-cations, viewed along the −b axis, of K2W3SeO12 (4α). A W1W2W3O15 moiety with pyramidal selenium is indicated by a dashed red line and the net dipole directions of octa­hedral WO6 and pyramidal SeO3 are shown.

Tl₂W₃SeO₁₂ (5) has an ortho­rhom­bic unit cell with a_o = 11.5962 (10) Å, b_o = 12.7206 (5) Å and c_o = 7.2362 (9) Å. The structure refinements in the non-centrosymmetric Pna2₁ and centrosymmetric Pnam space groups led to the respective structure agreement factor values of 6.37% and 15.98%; the structure refinements were unsatisfactory, mostly due to X-ray absorption. Its single crystal X-ray structure solution model is found to be same as the three-dimensional structure of K₂W₃SeO₁₂ (4α) and its observed powder XRD pattern (Figure S1b in the supporting information) agrees reasonably with the one simulated on the basis of this model structure. Moreover, the powder XRD patterns and unit-cell parameters of these two compounds are similar. The ortho­rhom­bic unit-cell parameters of the thallium (5) compound are related to the monoclinic unit-cell parameters of the potassium (4α) compound as follows: a_o ≃ b_m, b_o ≃ c_m, c_o ≃ a_m and α_o = 90° ≃ β_m. The single-crystal X-ray data for the thallium compound (5) in the centrosymmetric P2₁/n space group, corresponding to the potassium compound (4α), led to the same structure model and a high value of 19.18% for the structure-agreement factor. It is inferred from these observations that the Tl₂W₃SeO₁₂ compound (5) has the same three-dimensional structure as K₂W₃SeO₁₂ (4α).

In the structurally characterized compounds 1–4α of the present study, the WO₆ octa­hedra have C₃ distortion as three W—O bonds are <1.9 Å long and their three trans W—O bonds are >1.9 Å long; the values of WO₆ intra­octa­hedral distortions (Halasyamani 2004), Δ_d, are calculated to be in the 0.73–0.86 range (Table S1). The Se⁴⁺ ions have pyramidal coordination. The W—O and Se—O bond-length values are in the 1.703 (17)–2.184 (9) Å and 1.695 (10)–1.739 (10) Å ranges, respectively. The ammonium and alkali metal ions are found to be six- to nine-coordinated (Figure S2), when the cut-off value of 3.6 Å is considered for N⋯O non-bonding distances and A—O bond lengths. The calculated values (Brese & O'Keeffe 1991) of bond-valence sums for W⁶⁺, Se⁴⁺ and monovalent alkali metal ions are in the 6.079–6.283, 3.807–3.975 and 0.060–1.275 ranges, respectively. The respective values of 3.210, 3.322 and 3.207 Å for the shortest inter­layer O⋯O non-bonding distances of compounds 1–3 with intra-layer Se—O bonds are significantly higher than the corresponding value of 2.563 Å for compound 4α with inter­layer Se—O bonds.

The net dipole moment values for the WO₆ and SeO₃ polyhedra were calculated by vector summation of the dipole moments (Maggard et al., 2003; Ok & Halasyamani 2005; Galy et al., 1975) of six W—O bonds and three Se—O bonds and found to be in the 0.79–1.85 D and 5.73–9.13 D ranges, respectively (Tables S1–S3). The net dipole for the WO₆ octa­hedron points towards the triangular face of three oxygen atoms with W—O bonds >1.9 Å long, whereas the net dipoles for the SeO₃ polyhedra point opposite to the lone pair of electrons of selenium. In compounds 1–3, as shown for Rb₂W₃SeO₁₂ (3) in Fig. 1, the intra-layer SeO₃ dipole is oriented along the c-axis direction and perpendicular to the HTO layer. For the WO₆ octa­hedra, the net dipole moment components along the a and b axes cancel one another, whereas the c-axis component is anti­parallel and additive to the net dipole moment of pyramidal SeO₃. In the case of centrosymmetric three-dimensional K₂W₃SeO₁₂ (4α), as shown in Fig. 2, the net dipole moments of the WO₆ and SeO₃ polyhedra macroscopically cancel one another and result in a zero net dipole moment.

The solid state UV–Visible absorption spectra (Fig. 3) of compounds 1–5 reveal that their band gap values are in the range 2.7–3.5 eV (Kubelka & Munk, 1931). The additional absorption edge observed for the Tl₂W₃SeO₁₂ compound (5) corresponds to band gap value of 2.0 eV. When compared to Cs₂W₃SeO₁₂ (2), the corresponding Cs₂W₃TeO₁₂ tellurite (Zhao et al., 2015) has a lower band gap of 2.89 eV.

Figure 3 Solid state UV–visible absorption spectra for the A2W3SeO12 [A = NH4 (1), Cs (2), Rb (3), K (4α) and Tl (5)] compounds.

Rb₂W₃SeO₁₂ (3), K₂W₃SeO₁₂ (4α) and Tl₂W₃SeO₁₂ (5) undergo thermal decompositions and give rise to endothermic peaks at ∼600, ∼575 and ∼575°C and their respective observed weight losses of 10.0%, 12.3% and 9.0% compare well with those calculated for the loss of SeO₂ (Figure S3). The other endothermic peaks at ∼850 and 750°C could not be assigned. It was reported (Harrison et al., 1995) that a similar thermal loss of SeO₂ occurs in a single step between 500 and 600°C for Cs₂W₃SeO₁₂ (2) and in two steps at 350 and 450°C for (NH₄)₂W₃SeO₁₂ (1). When compared to the tungsten selenites 1–5, analogous A₂W₃TeO₁₂ (A = K, Rb, Cs) tellurites of tungsten (Goodey et al., 2003; Zhao et al., 2015) and A₂Mo₃SeO₁₂ (A = Rb, Tl) selenites of molybdenum (Chang et al., 2010) undergo single-step thermal decomposition at higher and lower temperatures of >700 and 300°C, respectively.

3. Syntheses and crystallization

Cs₂CO₃ (Alfa Aesar), Rb₂CO₃ (Alfa Aesar), TlNO₃ (Sigma Aldrich), H₂WO₄ (Sigma Aldrich), SeO₂ (Sigma Aldrich), NH₄Cl (Sarabhai M Chemicals) of >99% purity, NH₄OH (Fischer Scientific) of 25% dilution, WO₃ and Tl₂WO₄ were used for the synthesis and crystal growth of compounds 1–5. WO₃ was obtained by heating H₂WO₄ in the open air. Tl₂WO₄ was prepared by heating a stoichiometric mixture of TlNO₃ and H₂WO₄. Teflon-lined stainless steel acid digestion vessels of 23 mL capacity were employed for the hydro­thermal reactions.

The reactants and their qu­anti­ties, the temperature and duration of heating and the yields of products for the synthesis and crystal growth of compounds 1–5 are presented in Table S4. The ammonium compound (1) was synthesized by the hydro­thermal method, with or without NH₄Cl as mineralizer. The other four compounds (2–5) were obtained by solid-state reactions. The reactant mixtures were heated first in the open air and later in evacuated sealed silica ampoules. After the reaction, the solid product contents were washed with water to dissolve away the excess SeO₂.

The hydro­thermal and solid-state synthetic methods enabled the growth and isolation of single crystals of compounds 1–5. The utilization of excess SeO₂ as flux in the novel solid-state synthetic procedure facilitated the growth of single crystals of compounds 2–5. The powder XRD patterns of compounds 1–5 are presented in Figures S1a and S1b. (NH₄)₂W₃SeO₁₂ (1), Rb₂W₃SeO₁₂ (3) and Tl₂W₃SeO₁₂ (5) were obtained as homogeneous phases, as their observed powder XRD patterns compare reasonably well with the simulated ones. The powder XRD patterns of Cs₂W₃SeO₁₂ (2), Rb₂W₃SeO₁₂ (3) and K₂W₃SeO₁₂ (4α) contained two or three additional reflections of <10% intensity due to WO₃ or an unidentified phase; however, the homogeneous polycrystalline sample of Rb₂W₃SeO₁₂ (3) could be obtained (Figure S1b), under a different set of solid-state synthetic conditions mentioned in Table S4. Cs₂W₃SeO₁₂ (2) was prepared in polycrystalline form by the reported hydro­thermal method (Harrison et al., 1995). It is evident from the scanning electron micrographs (Figure S4) that crystallites of compounds 1 and 2 have a hexa­gonal prism shape and compounds 3–5 have block-shaped morphologies. The EDXA analyses confirmed the expected ratios of metal contents for all compounds 1–5.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 1. The crystals of the ammonium (1) and rubidium (3) compounds are twinned by merohedry (Spek 2020) by the [−1 0 0 1 1 0 0 0 − 1] and [1 0 0 − 1 −1 0 0 0 − 1] twin laws and their twinned lattices are generated through twofold rotation of the primary lattices about the [120] direction and the b axis, respectively. The crystal of the potassium (4α) compound is twinned by pseudo-merohedry (Spek 2020) by the twin law [−1 0 0 0 − 1 0 0 0 1] and the twinned lattice is generated through twofold rotation of the primary lattice about the c axis, as the value of the β angle of its monoclinic system is very close to 90°. The respective values of refined batch scale factor for the ammonium (1), rubidium (3) and potassium (4α) compounds are 0.029, 0.192 and 0.385. The hydrogen atoms of the NH₄⁺ ions in the ammonium compound (1) were not located in the difference-Fourier maps but are included in the formula. The final difference-Fourier maps did not show any chemically significant features and the Fourier difference peaks with an electron density of >1 e Å⁻³ were found to be ghosts. No reasonable structure solutions and refinements in the centrosymmetric P6₃/m space group were found for compounds 1–3.

Table 1
Experimental details

	1	2	3	4
Crystal data
Chemical formula	(NH4)2W3SeO12	Cs2W3SeO12	Rb2W3SeO12	K2W3SeO12
Mr	858.59	1088.33	993.40	900.66
Crystal system, space group	Hexagonal, P63	Hexagonal, P63	Hexagonal, P63	Monoclinic, P21/n
Temperature (K)	297	293	293	293
a, b, c (Å)	7.2303 (3), 7.2303 (3), 12.1491 (5)	7.2580 (3), 7.2580 (3), 12.5291 (5)	7.2380 (1), 7.2380 (1), 12.1115 (3)	7.2310 (2), 11.4863 (4), 12.6486 (4)
α, β, γ (°)	90, 90, 120	90, 90, 120	90, 90, 120	90, 90.096 (2), 90
V (Å^3)	550.03 (5)	571.59 (5)	549.50 (2)	1050.56 (6)
Z	2	2	2	4
Radiation type	Mo Kα	Mo Kα	Mo Kα	Mo Kα
μ (mm^−1)	34.67	39.63	43.49	37.09
Crystal size (mm)	0.10 × 0.10 × 0.05	0.10 × 0.08 × 0.05	0.10 × 0.05 × 0.05	0.08 × 0.05 × 0.02
Data collection
Diffractometer	Bruker APEXII CCD	Bruker APEXII CCD	Bruker APEXII CCD	Bruker APEXII CCD
Absorption correction	Multi-scan (SADABS; Krause et al., 2015)	Multi-scan (SADABS; Krause et al., 2015)	Multi-scan (SADABS; Krause et al., 2015)	Multi-scan (SADABS; Krause et al., 2015)
Tmin, Tmax	0.129, 0.276	0.110, 0.242	0.098, 0.220	0.155, 0.524
No. of measured, independent and observed [I > 2σ(I)] reflections	14419, 1079, 1069	2825, 831, 730	3497, 675, 654	26562, 4026, 3456
Rint	0.049	0.058	0.033	0.073
(sin θ/λ)max (Å^−1)	0.702	0.643	0.666	0.770
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.023, 0.052, 1.27	0.029, 0.054, 1.02	0.018, 0.033, 1.06	0.032, 0.105, 1.15
No. of reflections	1079	831	675	4026
No. of parameters	57	56	57	165
No. of restraints	1	13	7	24
H-atom treatment	H-atom parameters not defined	–	–	–
Δρmax, Δρmin (e Å^−3)	2.63, −2.37	1.90, −1.65	0.90, −1.14	3.94, −3.11
Absolute structure	Flack x determined using 492 quotients [(I^+)−(I^−)]/[(I^+)+(I^−)] (Parsons et al., 2013)	Flack x determined using 297 quotients [(I^+)−(I^−)]/[(I^+)+(I^−)] (Parsons et al., 2013)	Flack x determined using 182 quotients [(I^+)−(I^−)]/[(I^+)+(I^−)] (Parsons et al., 2013)
Absolute structure parameter	0.015 (13)	0.00 (3)	−0.08 (3)	–
Computer programs: APEX2 and SAINT (Bruker, 2004), SHELXT (Sheldrick, 2015a), SHELXL2013 (Sheldrick, 2015b), SHELXL (Sheldrick, 2015b), ORTEP-3 for Windows (Farrugia, 2012), DIAMOND (Pennington, 1999) and SHELXL97 (Sheldrick, 2008).

The powder X-ray diffraction (XRD) patterns of compounds 1–5 were recorded on a Bruker D8 Advanced powder X-ray diffractometer using Cu Kα (λ = 1.5418 Å) radiation. The monophasic nature of each of these compounds was verified by comparing their powder XRD patterns with those simulated, using Mercury (Macrae et al., 2020), on the basis of their single crystal X-ray structures.

Supporting information

Computing details

For all structures, data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004). Program(s) used to solve structure: SHELXT2013 (Sheldrick, 2015a) for NH42W3SeO121; SHELXT2014/7 (Sheldrick, 2015a) for Cs2W3SeO122, Rb2W3SeO123, K2W3SeO124. Program(s) used to refine structure: SHELXL2013 (Sheldrick, 2015b) for NH42W3SeO121; SHELXL2014/7 (Sheldrick, 2015b) for Cs2W3SeO122, K2W3SeO124; SHELXL2018/3 (Sheldrick, 2015b) for Rb2W3SeO123. For all structures, molecular graphics: ORTEP-3 for Windows (Farrugia, 2012) and DIAMOND (Pennington, 1999); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Diammonium tritungsten selenite (NH42W3SeO121)

Crystal data

(NH4)2W3SeO12	Dx = 5.184 Mg m^−3
Mr = 858.59	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P63	Cell parameters from 7856 reflections
a = 7.2303 (3) Å	θ = 3.3–30.4°
c = 12.1491 (5) Å	µ = 34.67 mm^−1
V = 550.03 (5) Å^3	T = 297 K
Z = 2	Block, colourless
F(000) = 748	0.10 × 0.10 × 0.05 mm

Data collection

Bruker APEXII CCD diffractometer	1069 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.049
φ and ω scans	θmax = 30.0°, θmin = 3.4°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −10→10
Tmin = 0.129, Tmax = 0.276	k = −10→10
14419 measured reflections	l = −17→17
1079 independent reflections

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0097P)^2 + 8.3615P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.023	Δρmax = 2.63 e Å^−3
wR(F^2) = 0.052	Δρmin = −2.37 e Å^−3
S = 1.27	Extinction correction: SHELXL-2018/3 (Sheldrick 2015b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
1079 reflections	Extinction coefficient: 0.0100 (5)
57 parameters	Absolute structure: Flack x determined using 492 quotients [(I^+)-(I^-)]/[(I^+)+(I^-)] (Parsons et al., 2013)
1 restraint	Absolute structure parameter: 0.015 (13)
H-atom parameters not defined

Special details

Experimental. Single crystals of compounds 1–5 were obtained along with the polycrystalline sample and the crystals were hand-picked for XRD study and mounted on thin glass fibres with epoxy glue and optically aligned on a Bruker APEXII charge-coupled device X-ray diffractometer using a digital camera. Intensity data were measured at 25 ^°C using Mo Kα (λ = 0.7103 Å) radiation. APEX II software (Bruker AXS) was used for preliminary determination of the cell constants and data collection control. The determination of integral intensities and global refinement were performed using SAINT-plus (Bruker AXS). A semi-empirical absorption correction was subsequently applied using SADABS. Space group determination, structure solution and least-squares refinement were carried out using SHELXTL (Sheldrick 2008) program. DIAMOND 3.0 (PENNINGTON 1999) and ORTEP-3 (Farrugia 1997) for windows were the graphic programs employed to draw the structures. The structures were solved by direct methods and refined by full matrix least squares on F².

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refined as a two-component twin

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
N1	0.333333	0.666667	0.115 (3)	0.042 (8)
N2	0.666667	0.333333	0.237 (2)	0.025 (5)
W	0.19142 (6)	0.33979 (5)	0.40000 (10)	0.00766 (15)
Se	0.000000	0.000000	0.16680 (15)	0.0102 (5)
O1	0.1264 (15)	0.2465 (16)	0.2271 (7)	0.0134 (17)
O2	0.4083 (16)	0.1964 (16)	0.0370 (8)	0.0137 (18)
O3	0.2494 (12)	0.1188 (12)	0.4103 (12)	0.0101 (19)
O4	0.0850 (15)	0.5365 (14)	0.3526 (8)	0.0111 (16)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
N1	0.052 (13)	0.052 (13)	0.023 (14)	0.026 (7)	0.000	0.000
N2	0.025 (8)	0.025 (8)	0.024 (12)	0.012 (4)	0.000	0.000
W	0.0069 (2)	0.00476 (19)	0.0108 (2)	0.00250 (14)	−0.0007 (3)	−0.0006 (3)
Se	0.0091 (5)	0.0091 (5)	0.0124 (12)	0.0045 (2)	0.000	0.000
O1	0.013 (4)	0.010 (4)	0.015 (4)	0.005 (4)	−0.004 (3)	0.001 (3)
O2	0.010 (4)	0.013 (5)	0.016 (4)	0.004 (4)	−0.001 (3)	0.002 (3)
O3	0.006 (3)	0.006 (3)	0.019 (5)	0.003 (2)	−0.002 (5)	0.005 (5)
O4	0.011 (4)	0.004 (4)	0.018 (4)	0.004 (3)	−0.003 (3)	−0.002 (3)

Geometric parameters (Å, º)

W—O2^i	1.722 (10)	W—O1	2.184 (9)
W—O3	1.848 (8)	Se—O1^iii	1.709 (10)
W—O4^ii	1.874 (9)	Se—O1	1.709 (10)
W—O3^iii	1.985 (8)	Se—O1^iv	1.709 (10)
W—O4	2.010 (9)
O2^i—W—O3	99.2 (6)	O3—W—O1	84.5 (5)
O2^i—W—O4^ii	99.3 (5)	O4^ii—W—O1	86.0 (4)
O3—W—O4^ii	96.7 (4)	O3^iii—W—O1	80.7 (5)
O2^i—W—O3^iii	93.4 (6)	O4—W—O1	81.0 (4)
O3—W—O3^iii	89.7 (4)	O1^iii—Se—O1	102.9 (4)
O4^ii—W—O3^iii	164.6 (5)	O1^iii—Se—O1^iv	102.9 (4)
O2^i—W—O4	94.7 (4)	O1—Se—O1^iv	102.9 (4)
O3—W—O4	164.5 (5)	Se—O1—W	130.9 (5)
O4^ii—W—O4	87.8 (6)	W—O3—W^iv	149.1 (5)
O3^iii—W—O4	82.6 (4)	W^v—O4—W	132.5 (5)
O2^i—W—O1	173.1 (4)

Symmetry codes: (i) x−y, x, z+1/2; (ii) −y+1, x−y+1, z; (iii) −y, x−y, z; (iv) −x+y, −x, z; (v) −x+y, −x+1, z.

Dicaesium tritungsten selenite (Cs2W3SeO122)

Crystal data

Cs2W3SeO12	Dx = 6.323 Mg m^−3
Mr = 1088.33	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P63	Cell parameters from 706 reflections
a = 7.2580 (3) Å	θ = 3.6–26.3°
c = 12.5291 (5) Å	µ = 39.63 mm^−1
V = 571.59 (5) Å^3	T = 293 K
Z = 2	Block, colourless
F(000) = 924	0.10 × 0.08 × 0.05 mm

Data collection

Bruker APEXII CCD diffractometer	730 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.058
phi and ω scans	θmax = 27.2°, θmin = 3.2°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −6→8
Tmin = 0.110, Tmax = 0.242	k = −9→9
2825 measured reflections	l = −16→14
831 independent reflections

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2)] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.029	Δρmax = 1.90 e Å^−3
wR(F^2) = 0.054	Δρmin = −1.65 e Å^−3
S = 1.02	Extinction correction: SHELXL2018/3 (Sheldrick 2015b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
831 reflections	Extinction coefficient: 0.0081 (4)
56 parameters	Absolute structure: Flack x determined using 297 quotients [(I^+)-(I^-)]/[(I^+)+(I^-)] (Parsons et al., 2013)
13 restraints	Absolute structure parameter: 0.00 (3)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Cs1	0.333333	0.666667	0.0902 (2)	0.0269 (9)
Cs2	0.666667	0.333333	0.22953 (19)	0.0143 (7)
W	0.14949 (10)	0.33884 (11)	0.39443 (8)	0.0056 (2)
Se	0.000000	0.000000	0.1700 (2)	0.0058 (7)
O1	0.125 (2)	0.250 (2)	0.2270 (11)	0.007 (3)
O2	0.401 (2)	0.207 (2)	0.0265 (14)	0.015 (3)
O3	0.2495 (18)	0.1279 (17)	0.4056 (14)	0.008 (3)
O4	0.088 (2)	0.549 (2)	0.3529 (11)	0.010 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Cs1	0.0277 (13)	0.0277 (13)	0.0251 (16)	0.0139 (6)	0.000	0.000
Cs2	0.0160 (10)	0.0160 (10)	0.0110 (13)	0.0080 (5)	0.000	0.000
W	0.0048 (4)	0.0031 (4)	0.0083 (4)	0.0016 (3)	0.0004 (5)	−0.0001 (5)
Se	0.0066 (9)	0.0066 (9)	0.0042 (18)	0.0033 (5)	0.000	0.000
O1	0.013 (8)	0.004 (7)	0.002 (6)	0.004 (7)	0.000 (6)	−0.001 (6)
O2	0.015 (8)	0.011 (9)	0.020 (9)	0.007 (7)	−0.010 (7)	0.003 (7)
O3	0.008 (3)	0.008 (3)	0.009 (3)	0.0042 (18)	0.0001 (14)	−0.0003 (14)
O4	0.009 (3)	0.009 (3)	0.010 (3)	0.0050 (19)	0.0000 (14)	−0.0001 (14)

Geometric parameters (Å, º)

Cs1—O1^i	3.132 (15)	Cs2—O4^ii	3.066 (14)
Cs1—O1	3.132 (15)	Cs2—O3^vi	3.427 (13)
Cs1—O1^ii	3.132 (15)	Cs2—O3	3.427 (13)
Cs1—O3^iii	3.497 (15)	Cs2—O3^vii	3.427 (13)
Cs1—O3^iv	3.497 (15)	Cs2—O1^vii	3.667 (13)
Cs1—O3^v	3.497 (15)	Cs2—O1	3.667 (13)
Cs1—O4^i	3.634 (14)	Cs2—O1^vi	3.667 (13)
Cs1—O4^ii	3.634 (14)	W—O2^x	1.703 (17)
Cs1—O4	3.634 (14)	W—O3^xi	1.840 (11)
Cs1—O2^i	3.695 (14)	W—O4	1.863 (13)
Cs1—O2^ii	3.695 (14)	W—O4^ii	2.000 (13)
Cs1—O2	3.695 (14)	W—O3	2.000 (10)
Cs2—O2	3.044 (16)	W—O1	2.176 (14)
Cs2—O2^vi	3.044 (16)	Se—O1^xi	1.723 (15)
Cs2—O2^vii	3.044 (16)	Se—O1	1.724 (15)
Cs2—O4^viii	3.066 (14)	Se—O1^ix	1.724 (15)
Cs2—O4^ix	3.066 (14)
O1^i—Cs1—O1	92.9 (4)	O4^ii—Cs2—O1^vi	143.4 (3)
O1^i—Cs1—O1^ii	92.9 (4)	O3^vi—Cs2—O1^vi	45.0 (3)
O1—Cs1—O1^ii	92.9 (4)	O3—Cs2—O1^vi	97.0 (3)
O1^i—Cs1—O3^iii	74.6 (3)	O3^vii—Cs2—O1^vi	127.0 (3)
O1—Cs1—O3^iii	132.9 (3)	O1^vii—Cs2—O1^vi	119.992 (7)
O1^ii—Cs1—O3^iii	132.1 (3)	O1—Cs2—O1^vi	119.993 (8)
O1^i—Cs1—O3^iv	132.1 (3)	O2^x—W—O3^xi	97.7 (8)
O1—Cs1—O3^iv	74.6 (3)	O2^x—W—O4	98.5 (7)
O1^ii—Cs1—O3^iv	132.9 (3)	O3^xi—W—O4	96.6 (5)
O3^iii—Cs1—O3^iv	81.0 (4)	O2^x—W—O4^ii	93.8 (6)
O1^i—Cs1—O3^v	132.9 (3)	O3^xi—W—O4^ii	167.0 (7)
O1—Cs1—O3^v	132.1 (3)	O4—W—O4^ii	87.4 (8)
O1^ii—Cs1—O3^v	74.6 (3)	O2^x—W—O3	92.3 (7)
O3^iii—Cs1—O3^v	81.0 (4)	O3^xi—W—O3	89.9 (7)
O3^iv—Cs1—O3^v	81.0 (4)	O4—W—O3	166.5 (7)
O1^i—Cs1—O4^i	48.2 (3)	O4^ii—W—O3	83.7 (5)
O1—Cs1—O4^i	81.9 (3)	O2^x—W—O1	172.7 (6)
O1^ii—Cs1—O4^i	47.2 (3)	O3^xi—W—O1	85.8 (7)
O3^iii—Cs1—O4^i	116.3 (3)	O4—W—O1	87.5 (6)
O3^iv—Cs1—O4^i	156.5 (3)	O4^ii—W—O1	82.1 (5)
O3^v—Cs1—O4^i	115.9 (3)	O3—W—O1	81.2 (6)
O1^i—Cs1—O4^ii	81.9 (3)	O2^x—W—Cs2^xii	123.2 (5)
O1—Cs1—O4^ii	47.2 (3)	O3^xi—W—Cs2^xii	57.3 (4)
O1^ii—Cs1—O4^ii	48.2 (3)	O4—W—Cs2^xii	46.0 (4)
O3^iii—Cs1—O4^ii	156.5 (3)	O4^ii—W—Cs2^xii	120.1 (4)
O3^iv—Cs1—O4^ii	115.9 (3)	O3—W—Cs2^xii	132.2 (4)
O3^v—Cs1—O4^ii	116.3 (3)	O1—W—Cs2^xii	64.1 (3)
O4^i—Cs1—O4^ii	43.1 (4)	O2^x—W—Cs1^xiii	59.3 (5)
O1^i—Cs1—O4	47.2 (3)	O3^xi—W—Cs1^xiii	53.6 (5)
O1—Cs1—O4	48.2 (3)	O4—W—Cs1^xiii	68.7 (4)
O1^ii—Cs1—O4	81.9 (3)	O4^ii—W—Cs1^xiii	138.9 (4)
O3^iii—Cs1—O4	115.9 (3)	O3—W—Cs1^xiii	124.3 (4)
O3^iv—Cs1—O4	116.3 (3)	O1—W—Cs1^xiii	127.4 (3)
O3^v—Cs1—O4	156.5 (3)	Cs2^xii—W—Cs1^xiii	65.81 (5)
O4^i—Cs1—O4	43.1 (4)	O2^x—W—Cs2	114.7 (5)
O4^ii—Cs1—O4	43.1 (4)	O3^xi—W—Cs2	127.9 (4)
O1^i—Cs1—O2^i	57.5 (4)	O4—W—Cs2	116.1 (4)
O1—Cs1—O2^i	91.3 (3)	O4^ii—W—Cs2	40.4 (4)
O1^ii—Cs1—O2^i	150.4 (4)	O3—W—Cs2	51.3 (4)
O3^iii—Cs1—O2^i	43.5 (3)	O1—W—Cs2	58.5 (3)
O3^iv—Cs1—O2^i	76.4 (3)	Cs2^xii—W—Cs2	120.63 (6)
O3^v—Cs1—O2^i	122.2 (4)	Cs1^xiii—W—Cs2	173.49 (5)
O4^i—Cs1—O2^i	104.7 (4)	O2^x—W—Cs1	138.0 (6)
O4^ii—Cs1—O2^i	121.5 (3)	O3^xi—W—Cs1	116.2 (5)
O4—Cs1—O2^i	79.1 (3)	O4—W—Cs1	55.9 (4)
O1^i—Cs1—O2^ii	91.3 (3)	O4^ii—W—Cs1	56.4 (4)
O1—Cs1—O2^ii	150.4 (4)	O3—W—Cs1	110.6 (5)
O1^ii—Cs1—O2^ii	57.5 (4)	O1—W—Cs1	43.4 (4)
O3^iii—Cs1—O2^ii	76.4 (3)	Cs2^xii—W—Cs1	65.44 (3)
O3^iv—Cs1—O2^ii	122.2 (4)	Cs1^xiii—W—Cs1	122.50 (3)
O3^v—Cs1—O2^ii	43.5 (3)	Cs2—W—Cs1	63.41 (3)
O4^i—Cs1—O2^ii	79.1 (3)	O2^x—W—Cs1^xiv	54.8 (5)
O4^ii—Cs1—O2^ii	104.7 (4)	O3^xi—W—Cs1^xiv	120.7 (4)
O4—Cs1—O2^ii	121.5 (3)	O4—W—Cs1^xiv	134.5 (4)
O2^i—Cs1—O2^ii	115.47 (19)	O4^ii—W—Cs1^xiv	62.2 (4)
O1^i—Cs1—O2	150.4 (4)	O3—W—Cs1^xiv	48.1 (4)
O1—Cs1—O2	57.5 (4)	O1—W—Cs1^xiv	117.9 (3)
O1^ii—Cs1—O2	91.3 (3)	Cs2^xii—W—Cs1^xiv	177.46 (4)
O3^iii—Cs1—O2	122.2 (4)	Cs1^xiii—W—Cs1^xiv	111.82 (6)
O3^iv—Cs1—O2	43.5 (3)	Cs2—W—Cs1^xiv	61.72 (4)
O3^v—Cs1—O2	76.4 (3)	Cs1—W—Cs1^xiv	117.06 (2)
O4^i—Cs1—O2	121.5 (3)	O1^xi—Se—O1	104.0 (5)
O4^ii—Cs1—O2	79.1 (3)	O1^xi—Se—O1^ix	104.0 (5)
O4—Cs1—O2	104.7 (4)	O1—Se—O1^ix	104.0 (5)
O2^i—Cs1—O2	115.47 (19)	O1^xi—Se—Cs2^xv	58.6 (4)
O2^ii—Cs1—O2	115.47 (19)	O1—Se—Cs2^xv	145.4 (5)
O2—Cs2—O2^vi	56.8 (5)	O1^ix—Se—Cs2^xv	58.6 (4)
O2—Cs2—O2^vii	56.8 (5)	O1^xi—Se—Cs2	145.4 (5)
O2^vi—Cs2—O2^vii	56.8 (5)	O1—Se—Cs2	58.6 (4)
O2—Cs2—O4^viii	153.5 (4)	O1^ix—Se—Cs2	58.6 (4)
O2^vi—Cs2—O4^viii	101.6 (4)	Cs2^xv—Se—Cs2	116.99 (3)
O2^vii—Cs2—O4^viii	99.6 (4)	O1^xi—Se—Cs2^xii	58.6 (4)
O2—Cs2—O4^ix	101.6 (4)	O1—Se—Cs2^xii	58.6 (4)
O2^vi—Cs2—O4^ix	99.6 (4)	O1^ix—Se—Cs2^xii	145.4 (5)
O2^vii—Cs2—O4^ix	153.5 (4)	Cs2^xv—Se—Cs2^xii	116.99 (3)
O4^viii—Cs2—O4^ix	96.8 (3)	Cs2—Se—Cs2^xii	116.99 (3)
O2—Cs2—O4^ii	99.6 (4)	O1^xi—Se—Cs1^xv	37.9 (5)
O2^vi—Cs2—O4^ii	153.5 (4)	O1—Se—Cs1^xv	122.6 (4)
O2^vii—Cs2—O4^ii	101.6 (4)	O1^ix—Se—Cs1^xv	122.6 (4)
O4^viii—Cs2—O4^ii	96.8 (3)	Cs2^xv—Se—Cs1^xv	64.012 (17)
O4^ix—Cs2—O4^ii	96.8 (3)	Cs2—Se—Cs1^xv	176.68 (9)
O2—Cs2—O3^vi	139.0 (3)	Cs2^xii—Se—Cs1^xv	64.014 (17)
O2^vi—Cs2—O3^vi	96.8 (4)	O1^xi—Se—Cs1	122.6 (4)
O2^vii—Cs2—O3^vi	137.8 (3)	O1—Se—Cs1	37.9 (5)
O4^viii—Cs2—O3^vi	50.0 (3)	O1^ix—Se—Cs1	122.6 (4)
O4^ix—Cs2—O3^vi	48.2 (3)	Cs2^xv—Se—Cs1	176.68 (9)
O4^ii—Cs2—O3^vi	109.7 (4)	Cs2—Se—Cs1	64.013 (17)
O2—Cs2—O3	96.8 (4)	Cs2^xii—Se—Cs1	64.013 (17)
O2^vi—Cs2—O3	137.8 (3)	Cs1^xv—Se—Cs1	114.79 (4)
O2^vii—Cs2—O3	139.0 (3)	O1^xi—Se—Cs1^xvi	122.6 (4)
O4^viii—Cs2—O3	109.7 (4)	O1—Se—Cs1^xvi	122.6 (4)
O4^ix—Cs2—O3	50.0 (3)	O1^ix—Se—Cs1^xvi	37.9 (5)
O4^ii—Cs2—O3	48.2 (3)	Cs2^xv—Se—Cs1^xvi	64.014 (17)
O3^vi—Cs2—O3	83.0 (4)	Cs2—Se—Cs1^xvi	64.013 (17)
O2—Cs2—O3^vii	137.8 (3)	Cs2^xii—Se—Cs1^xvi	176.68 (9)
O2^vi—Cs2—O3^vii	139.0 (3)	Cs1^xv—Se—Cs1^xvi	114.79 (4)
O2^vii—Cs2—O3^vii	96.8 (4)	Cs1—Se—Cs1^xvi	114.79 (4)
O4^viii—Cs2—O3^vii	48.2 (3)	Se—O1—W	129.4 (8)
O4^ix—Cs2—O3^vii	109.7 (4)	Se—O1—Cs1	122.3 (6)
O4^ii—Cs2—O3^vii	50.0 (3)	W—O1—Cs1	108.1 (5)
O3^vi—Cs2—O3^vii	83.0 (4)	Se—O1—Cs2	97.7 (5)
O3—Cs2—O3^vii	83.0 (4)	W—O1—Cs2	91.2 (4)
O2—Cs2—O1^vii	114.5 (4)	Cs1—O1—Cs2	83.4 (3)
O2^vi—Cs2—O1^vii	95.0 (4)	Se—O1—Cs2^xii	97.7 (5)
O2^vii—Cs2—O1^vii	58.5 (4)	W—O1—Cs2^xii	83.6 (4)
O4^viii—Cs2—O1^vii	47.1 (3)	Cs1—O1—Cs2^xii	83.4 (3)
O4^ix—Cs2—O1^vii	143.4 (3)	Cs2—O1—Cs2^xii	163.5 (5)
O4^ii—Cs2—O1^vii	83.8 (3)	W^xvii—O2—Cs2	159.8 (9)
O3^vi—Cs2—O1^vii	97.0 (3)	W^xvii—O2—Cs1	97.3 (5)
O3—Cs2—O1^vii	127.0 (3)	Cs2—O2—Cs1	84.1 (4)
O3^vii—Cs2—O1^vii	45.0 (3)	W^xvii—O2—Cs1^xvi	103.6 (6)
O2—Cs2—O1	58.5 (4)	Cs2—O2—Cs1^xvi	82.6 (3)
O2^vi—Cs2—O1	114.5 (4)	Cs1—O2—Cs1^xvi	152.0 (6)
O2^vii—Cs2—O1	95.0 (4)	W^ix—O3—W	148.6 (7)
O4^viii—Cs2—O1	143.4 (3)	W^ix—O3—Cs2	95.8 (5)
O4^ix—Cs2—O1	83.8 (3)	W—O3—Cs2	101.6 (5)
O4^ii—Cs2—O1	47.1 (3)	W^ix—O3—Cs1^xiv	101.4 (5)
O3^vi—Cs2—O1	127.0 (3)	W—O3—Cs1^xiv	106.7 (5)
O3—Cs2—O1	45.0 (3)	Cs2—O3—Cs1^xiv	81.5 (2)
O3^vii—Cs2—O1	97.0 (3)	W—O4—W^i	135.7 (8)
O1^vii—Cs2—O1	119.993 (7)	W—O4—Cs2^xii	108.0 (5)
O2—Cs2—O1^vi	95.0 (4)	W^i—O4—Cs2^xii	114.6 (5)
O2^vi—Cs2—O1^vi	58.5 (4)	W—O4—Cs1	99.0 (5)
O2^vii—Cs2—O1^vi	114.5 (4)	W^i—O4—Cs1	96.3 (5)
O4^viii—Cs2—O1^vi	83.8 (3)	Cs2^xii—O4—Cs1	84.8 (3)
O4^ix—Cs2—O1^vi	47.1 (3)

Symmetry codes: (i) −x+y, −x+1, z; (ii) −y+1, x−y+1, z; (iii) y, −x+y+1, z−1/2; (iv) x−y, x, z−1/2; (v) −x+1, −y+1, z−1/2; (vi) −y+1, x−y, z; (vii) −x+y+1, −x+1, z; (viii) x+1, y, z; (ix) −x+y, −x, z; (x) x−y, x, z+1/2; (xi) −y, x−y, z; (xii) x−1, y, z; (xiii) −x, −y+1, z+1/2; (xiv) −x+1, −y+1, z+1/2; (xv) x−1, y−1, z; (xvi) x, y−1, z; (xvii) y, −x+y, z−1/2.

Dirubidium tritungsten selenite (Rb2W3SeO123)

Crystal data

Rb2W3SeO12	Dx = 6.004 Mg m^−3
Mr = 993.40	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P63	Cell parameters from 19378 reflections
a = 7.2380 (1) Å	θ = 3.3–28.2°
c = 12.1115 (3) Å	µ = 43.49 mm^−1
V = 549.50 (2) Å^3	T = 293 K
Z = 2	Block, colourless
F(000) = 852	0.10 × 0.05 × 0.05 mm

Data collection

Bruker APEXII CCD diffractometer	654 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.033
phi and ω scans	θmax = 28.3°, θmin = 1.7°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −9→8
Tmin = 0.098, Tmax = 0.220	k = −8→9
3497 measured reflections	l = −11→16
675 independent reflections

Refinement

Refinement on F^2	w = 1/[σ^2(Fo^2) + (0.0065P)^2 + 2.2061P] where P = (Fo^2 + 2Fc^2)/3
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F^2 > 2σ(F^2)] = 0.018	Δρmax = 0.90 e Å^−3
wR(F^2) = 0.033	Δρmin = −1.14 e Å^−3
S = 1.06	Extinction correction: SHELXL2018/3 (Sheldrick 2015b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
675 reflections	Extinction coefficient: 0.0058 (2)
57 parameters	Absolute structure: Flack x determined using 182 quotients [(I^+)-(I^-)]/[(I^+)+(I^-)] (Parsons et al., 2013)
7 restraints	Absolute structure parameter: −0.08 (3)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refined as a two-component twin

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Rb1	0.666667	0.333333	0.8979 (2)	0.0389 (9)
Rb2	0.333333	0.666667	0.77053 (18)	0.0181 (6)
W	0.80778 (6)	0.66034 (6)	0.60562 (3)	0.00482 (12)
Se	1.000000	1.000000	0.83669 (14)	0.0057 (4)
O1	0.8727 (15)	0.7523 (15)	0.7767 (6)	0.0106 (18)
O2	0.5942 (14)	0.8028 (15)	0.9677 (7)	0.0106 (17)
O3	0.7494 (12)	0.8784 (12)	0.5928 (8)	0.0084 (16)
O4	0.9117 (13)	0.4617 (13)	0.6512 (6)	0.0069 (15)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Rb1	0.0433 (13)	0.0433 (13)	0.0300 (16)	0.0216 (7)	0.000	0.000
Rb2	0.0202 (9)	0.0202 (9)	0.0139 (11)	0.0101 (4)	0.000	0.000
W	0.0036 (2)	0.0027 (2)	0.00779 (17)	0.00128 (19)	0.0005 (4)	−0.0003 (3)
Se	0.0062 (5)	0.0062 (5)	0.0047 (10)	0.0031 (3)	0.000	0.000
O1	0.016 (5)	0.008 (5)	0.010 (4)	0.008 (4)	0.003 (4)	0.003 (4)
O2	0.002 (4)	0.011 (5)	0.015 (4)	0.000 (4)	−0.003 (3)	−0.004 (4)
O3	0.007 (3)	0.006 (4)	0.012 (5)	0.004 (3)	0.000 (4)	0.001 (4)
O4	0.0065 (18)	0.0069 (19)	0.0077 (18)	0.0038 (12)	−0.0003 (12)	−0.0002 (12)

Geometric parameters (Å, º)

Rb1—O1^i	3.009 (9)	Rb2—O4^i	3.012 (8)
Rb1—O1	3.009 (9)	Rb2—O3	3.382 (8)
Rb1—O1^ii	3.009 (9)	Rb2—O3^vi	3.382 (8)
Rb1—O4^ii	3.360 (8)	Rb2—O3^vii	3.382 (8)
Rb1—O4^i	3.360 (8)	Rb2—W	3.9926 (11)
Rb1—O4	3.360 (8)	Rb2—W^vii	3.9926 (11)
Rb1—O3^iii	3.518 (9)	Rb2—W^vi	3.9926 (11)
Rb1—O3^iv	3.518 (9)	W—O2^x	1.726 (8)
Rb1—O3^v	3.518 (9)	W—O3	1.833 (8)
Rb1—W	4.094 (2)	W—O4^i	1.860 (8)
Rb1—W^i	4.094 (2)	W—O4	2.005 (8)
Rb1—W^ii	4.094 (2)	W—O3^xi	2.011 (8)
Rb2—O2	2.894 (8)	W—O1	2.155 (8)
Rb2—O2^vi	2.894 (8)	Se—O1^ix	1.714 (9)
Rb2—O2^vii	2.894 (8)	Se—O1	1.714 (9)
Rb2—O4^viii	3.012 (8)	Se—O1^xi	1.714 (9)
Rb2—O4^ix	3.012 (8)
O1^i—Rb1—O1	98.2 (2)	O4^ix—Rb2—O3^vii	111.8 (2)
O1^i—Rb1—O1^ii	98.2 (2)	O4^i—Rb2—O3^vii	48.78 (18)
O1—Rb1—O1^ii	98.2 (2)	O3—Rb2—O3^vii	83.8 (2)
O1^i—Rb1—O4^ii	51.2 (2)	O3^vi—Rb2—O3^vii	83.8 (2)
O1—Rb1—O4^ii	88.0 (2)	O2—Rb2—W	89.89 (19)
O1^ii—Rb1—O4^ii	50.2 (2)	O2^vi—Rb2—W	147.69 (19)
O1^i—Rb1—O4^i	50.2 (2)	O2^vii—Rb2—W	113.3 (2)
O1—Rb1—O4^i	51.2 (2)	O4^viii—Rb2—W	114.82 (16)
O1^ii—Rb1—O4^i	88.0 (2)	O4^ix—Rb2—W	75.92 (16)
O4^ii—Rb1—O4^i	46.7 (2)	O4^i—Rb2—W	26.34 (16)
O1^i—Rb1—O4	88.0 (2)	O3—Rb2—W	27.21 (13)
O1—Rb1—O4	50.2 (2)	O3^vi—Rb2—W	105.50 (16)
O1^ii—Rb1—O4	51.2 (2)	O3^vii—Rb2—W	70.55 (14)
O4^ii—Rb1—O4	46.7 (2)	O2—Rb2—W^vii	147.69 (19)
O4^i—Rb1—O4	46.7 (2)	O2^vi—Rb2—W^vii	113.3 (2)
O1^i—Rb1—O3^iii	130.6 (2)	O2^vii—Rb2—W^vii	89.89 (19)
O1—Rb1—O3^iii	130.6 (2)	O4^viii—Rb2—W^vii	26.34 (16)
O1^ii—Rb1—O3^iii	71.3 (2)	O4^ix—Rb2—W^vii	114.82 (16)
O4^ii—Rb1—O3^iii	114.97 (19)	O4^i—Rb2—W^vii	75.92 (16)
O4^i—Rb1—O3^iii	159.4 (2)	O3—Rb2—W^vii	105.50 (16)
O4—Rb1—O3^iii	115.6 (2)	O3^vi—Rb2—W^vii	70.55 (14)
O1^i—Rb1—O3^iv	130.6 (2)	O3^vii—Rb2—W^vii	27.21 (13)
O1—Rb1—O3^iv	71.3 (2)	W—Rb2—W^vii	97.16 (4)
O1^ii—Rb1—O3^iv	130.6 (2)	O2—Rb2—W^vi	113.3 (2)
O4^ii—Rb1—O3^iv	159.4 (2)	O2^vi—Rb2—W^vi	89.89 (19)
O4^i—Rb1—O3^iv	115.6 (2)	O2^vii—Rb2—W^vi	147.69 (19)
O4—Rb1—O3^iv	115.0 (2)	O4^viii—Rb2—W^vi	75.92 (16)
O3^iii—Rb1—O3^iv	79.9 (2)	O4^ix—Rb2—W^vi	26.34 (16)
O1^i—Rb1—O3^v	71.3 (2)	O4^i—Rb2—W^vi	114.82 (16)
O1—Rb1—O3^v	130.6 (2)	O3—Rb2—W^vi	70.55 (14)
O1^ii—Rb1—O3^v	130.6 (2)	O3^vi—Rb2—W^vi	27.21 (13)
O4^ii—Rb1—O3^v	115.6 (2)	O3^vii—Rb2—W^vi	105.50 (16)
O4^i—Rb1—O3^v	114.97 (19)	W—Rb2—W^vi	97.16 (4)
O4—Rb1—O3^v	159.4 (2)	W^vii—Rb2—W^vi	97.16 (4)
O3^iii—Rb1—O3^v	79.9 (2)	O2^x—W—O3	98.3 (4)
O3^iv—Rb1—O3^v	79.9 (2)	O2^x—W—O4^i	99.3 (4)
O1^i—Rb1—W	76.74 (18)	O3—W—O4^i	97.5 (3)
O1—Rb1—W	30.77 (17)	O2^x—W—O4	93.8 (4)
O1^ii—Rb1—W	79.82 (18)	O3—W—O4	166.2 (4)
O4^ii—Rb1—W	57.35 (14)	O4^i—W—O4	87.0 (5)
O4^i—Rb1—W	26.63 (15)	O2^x—W—O3^xi	91.7 (5)
O4—Rb1—W	29.14 (14)	O3—W—O3^xi	90.0 (4)
O3^iii—Rb1—W	142.01 (14)	O4^i—W—O3^xi	165.5 (4)
O3^iv—Rb1—W	102.05 (14)	O4—W—O3^xi	83.0 (3)
O3^v—Rb1—W	138.07 (13)	O2^x—W—O1	172.2 (4)
O1^i—Rb1—W^i	30.77 (17)	O3—W—O1	85.6 (4)
O1—Rb1—W^i	79.82 (18)	O4^i—W—O1	86.8 (3)
O1^ii—Rb1—W^i	76.74 (17)	O4—W—O1	81.6 (3)
O4^ii—Rb1—W^i	26.63 (14)	O3^xi—W—O1	81.4 (4)
O4^i—Rb1—W^i	29.14 (15)	O2^x—W—Rb2	123.2 (3)
O4—Rb1—W^i	57.35 (14)	O3—W—Rb2	57.5 (3)
O3^iii—Rb1—W^i	138.07 (13)	O4^i—W—Rb2	45.9 (2)
O3^iv—Rb1—W^i	142.01 (14)	O4—W—Rb2	120.2 (2)
O3^v—Rb1—W^i	102.05 (14)	O3^xi—W—Rb2	133.0 (3)
W—Rb1—W^i	51.57 (3)	O1—W—Rb2	64.6 (2)
O1^i—Rb1—W^ii	79.82 (18)	O2^x—W—Rb1	135.6 (3)
O1—Rb1—W^ii	76.73 (17)	O3—W—Rb1	118.2 (3)
O1^ii—Rb1—W^ii	30.77 (17)	O4^i—W—Rb1	54.1 (2)
O4^ii—Rb1—W^ii	29.14 (15)	O4—W—Rb1	54.7 (2)
O4^i—Rb1—W^ii	57.35 (14)	O3^xi—W—Rb1	111.4 (3)
O4—Rb1—W^ii	26.63 (14)	O1—W—Rb1	45.6 (3)
O3^iii—Rb1—W^ii	102.05 (14)	Rb2—W—Rb1	66.84 (2)
O3^iv—Rb1—W^ii	138.07 (13)	O2^x—W—Rb1^xii	59.3 (3)
O3^v—Rb1—W^ii	142.01 (14)	O3—W—Rb1^xii	53.8 (3)
W—Rb1—W^ii	51.57 (3)	O4^i—W—Rb1^xii	70.4 (2)
W^i—Rb1—W^ii	51.57 (3)	O4—W—Rb1^xii	139.6 (2)
O2—Rb2—O2^vi	58.6 (3)	O3^xi—W—Rb1^xii	123.7 (2)
O2—Rb2—O2^vii	58.6 (3)	O1—W—Rb1^xii	127.9 (3)
O2^vi—Rb2—O2^vii	58.6 (3)	Rb2—W—Rb1^xii	66.06 (5)
O2—Rb2—O4^viii	153.0 (2)	Rb1—W—Rb1^xii	123.06 (2)
O2^vi—Rb2—O4^viii	97.5 (2)	O2^x—W—Rb2^xiii	113.1 (3)
O2^vii—Rb2—O4^viii	99.5 (3)	O3—W—Rb2^xiii	128.1 (3)
O2—Rb2—O4^ix	97.5 (2)	O4^i—W—Rb2^xiii	115.7 (2)
O2^vi—Rb2—O4^ix	99.5 (2)	O4—W—Rb2^xiii	39.5 (2)
O2^vii—Rb2—O4^ix	153.0 (2)	O3^xi—W—Rb2^xiii	50.7 (2)
O4^viii—Rb2—O4^ix	98.91 (18)	O1—W—Rb2^xiii	59.5 (2)
O2—Rb2—O4^i	99.5 (2)	Rb2—W—Rb2^xiii	122.13 (5)
O2^vi—Rb2—O4^i	153.0 (2)	Rb1—W—Rb2^xiii	64.26 (2)
O2^vii—Rb2—O4^i	97.5 (2)	Rb1^xii—W—Rb2^xiii	171.73 (3)
O4^viii—Rb2—O4^i	98.91 (18)	O1^ix—Se—O1	103.3 (3)
O4^ix—Rb2—O4^i	98.91 (18)	O1^ix—Se—O1^xi	103.3 (3)
O2—Rb2—O3	95.1 (2)	O1—Se—O1^xi	103.3 (3)
O2^vi—Rb2—O3	138.5 (3)	Se—O1—W	130.6 (5)
O2^vii—Rb2—O3	137.5 (3)	Se—O1—Rb1	125.7 (4)
O4^viii—Rb2—O3	111.8 (2)	W—O1—Rb1	103.7 (3)
O4^ix—Rb2—O3	48.78 (18)	W^xiv—O2—Rb2	159.3 (5)
O4^i—Rb2—O3	51.09 (19)	W—O3—W^ix	148.3 (5)
O2—Rb2—O3^vi	137.5 (3)	W—O3—Rb2	95.3 (3)
O2^vi—Rb2—O3^vi	95.1 (2)	W^ix—O3—Rb2	101.9 (3)
O2^vii—Rb2—O3^vi	138.5 (2)	W—O3—Rb1^xii	101.4 (3)
O4^viii—Rb2—O3^vi	48.78 (18)	W^ix—O3—Rb1^xii	107.3 (3)
O4^ix—Rb2—O3^vi	51.09 (19)	Rb2—O3—Rb1^xii	81.68 (17)
O4^i—Rb2—O3^vi	111.8 (2)	W^ii—O4—W	134.3 (4)
O3—Rb2—O3^vi	83.8 (2)	W^ii—O4—Rb2^xiii	107.7 (3)
O2—Rb2—O3^vii	138.5 (2)	W—O4—Rb2^xiii	115.5 (3)
O2^vi—Rb2—O3^vii	137.5 (3)	W^ii—O4—Rb1	99.3 (3)
O2^vii—Rb2—O3^vii	95.1 (2)	W—O4—Rb1	96.2 (3)
O4^viii—Rb2—O3^vii	51.09 (19)	Rb2^xiii—O4—Rb1	88.54 (18)

Symmetry codes: (i) −y+1, x−y, z; (ii) −x+y+1, −x+1, z; (iii) y, −x+y, z+1/2; (iv) x−y+1, x, z+1/2; (v) −x+1, −y+1, z+1/2; (vi) −y+1, x−y+1, z; (vii) −x+y, −x+1, z; (viii) x−1, y, z; (ix) −x+y+1, −x+2, z; (x) x−y+1, x, z−1/2; (xi) −y+2, x−y+1, z; (xii) −x+1, −y+1, z−1/2; (xiii) x+1, y, z; (xiv) y, −x+y+1, z+1/2.

Dipotassium tritungsten selenite (K2W3SeO124)

Crystal data

K2W3SeO12	F(000) = 1559
Mr = 900.66	Dx = 5.694 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71073 Å
a = 7.2310 (2) Å	Cell parameters from 9566 reflections
b = 11.4863 (4) Å	θ = 3.2–33.2°
c = 12.6486 (4) Å	µ = 37.09 mm^−1
β = 90.096 (2)°	T = 293 K
V = 1050.56 (6) Å^3	Block, colourless
Z = 4	0.08 × 0.05 × 0.02 mm

Data collection

Bruker APEXII CCD diffractometer	3456 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.073
phi and ω scans	θmax = 33.2°, θmin = 3.2°
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	h = −11→11
Tmin = 0.155, Tmax = 0.524	k = −17→17
26562 measured reflections	l = −19→19
4026 independent reflections

Refinement

Refinement on F^2	24 restraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0554P)^2] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.032	(Δ/σ)max < 0.001
wR(F^2) = 0.105	Δρmax = 3.94 e Å^−3
S = 1.15	Δρmin = −3.11 e Å^−3
4026 reflections	Extinction correction: SHELXL2018/3 (Sheldrick 2015b), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
165 parameters	Extinction coefficient: 0.00176 (12)

Special details

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Refinement. Refined as a two-component twin

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
K1	0.2501 (5)	0.4522 (3)	0.9115 (3)	0.0223 (6)
K2	0.2548 (5)	0.0822 (3)	0.8952 (3)	0.0234 (7)
W1	0.22893 (7)	0.79646 (4)	0.08433 (4)	0.00612 (10)
W2	0.01720 (7)	0.75074 (4)	0.82437 (4)	0.00629 (11)
W3	0.50663 (8)	0.75947 (4)	0.84420 (4)	0.00583 (11)
Se	0.25041 (19)	0.49742 (10)	0.17926 (9)	0.0078 (2)
O1	0.2536 (13)	0.6087 (8)	0.0913 (8)	0.0164 (19)
O2	0.2387 (16)	0.9444 (8)	0.0619 (7)	0.016 (2)
O3	0.0634 (14)	0.4225 (9)	0.1258 (9)	0.013 (2)
O4	0.0680 (14)	0.8954 (9)	0.7993 (9)	0.014 (2)
O5	0.4324 (14)	0.4206 (9)	0.1236 (8)	0.012 (2)
O6	0.4376 (14)	0.8956 (9)	0.8021 (9)	0.015 (2)
O7	0.0615 (15)	0.7625 (9)	0.9781 (9)	0.012 (2)
O8	0.2548 (14)	0.6902 (7)	0.8102 (7)	0.0093 (16)
O9	0.4378 (15)	0.7668 (9)	0.9828 (8)	0.0100 (19)
O10	0.9354 (14)	0.7050 (10)	0.6903 (8)	0.014 (2)
O11	0.7529 (15)	0.7855 (8)	0.8637 (7)	0.0096 (16)
O12	0.0599 (14)	0.7924 (9)	0.1938 (8)	0.0110 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0208 (14)	0.0264 (14)	0.0197 (14)	0.0030 (13)	−0.0020 (17)	0.0005 (13)
K2	0.0269 (17)	0.0211 (14)	0.0223 (16)	0.0007 (14)	−0.0005 (14)	0.0060 (12)
W1	0.00737 (19)	0.00678 (18)	0.00421 (17)	0.00057 (16)	−0.00022 (19)	0.00021 (17)
W2	0.0049 (2)	0.0084 (2)	0.0056 (2)	−0.0003 (2)	−0.00087 (18)	0.00082 (15)
W3	0.0047 (2)	0.0074 (2)	0.0054 (2)	0.00025 (19)	0.00025 (19)	−0.00006 (16)
Se	0.0090 (5)	0.0065 (4)	0.0078 (5)	0.0005 (4)	−0.0003 (5)	0.0003 (4)
O1	0.017 (2)	0.016 (2)	0.016 (2)	0.0001 (10)	0.0001 (10)	0.0005 (10)
O2	0.030 (6)	0.006 (4)	0.012 (4)	0.001 (4)	−0.005 (4)	0.002 (3)
O3	0.008 (4)	0.010 (4)	0.021 (5)	0.002 (4)	−0.009 (4)	−0.002 (4)
O4	0.013 (2)	0.014 (2)	0.014 (2)	0.0003 (10)	0.0000 (10)	0.0001 (10)
O5	0.011 (4)	0.010 (4)	0.016 (5)	0.003 (4)	0.003 (4)	0.003 (4)
O6	0.013 (5)	0.005 (4)	0.025 (6)	0.000 (4)	−0.002 (4)	0.008 (4)
O7	0.012 (2)	0.012 (2)	0.011 (2)	0.0002 (10)	−0.0004 (10)	0.0002 (10)
O8	0.003 (4)	0.010 (4)	0.015 (4)	0.003 (4)	−0.003 (4)	−0.001 (3)
O9	0.010 (2)	0.010 (2)	0.010 (2)	−0.0002 (10)	0.0005 (10)	−0.0004 (10)
O10	0.006 (4)	0.026 (6)	0.008 (5)	0.005 (4)	−0.004 (3)	0.000 (4)
O11	0.008 (4)	0.011 (4)	0.009 (4)	−0.002 (4)	−0.003 (4)	−0.004 (3)
O12	0.007 (4)	0.019 (5)	0.007 (4)	0.006 (4)	0.000 (3)	0.001 (4)

Geometric parameters (Å, º)

K1—O3^i	2.726 (10)	K2—W1^ii	3.993 (4)
K1—O5^ii	2.757 (11)	W1—O2	1.724 (9)
K1—O1^iii	2.899 (10)	W1—O7^x	1.849 (11)
K1—O5^iii	3.009 (11)	W1—O12	1.849 (10)
K1—O8	3.019 (9)	W1—O10^xi	2.005 (10)
K1—O4^iv	3.046 (11)	W1—O9^x	2.013 (11)
K1—O3^iii	3.050 (12)	W1—O1	2.166 (9)
K1—O6^iv	3.091 (12)	W2—O4	1.731 (11)
K1—Se^iii	3.427 (4)	W2—O8	1.863 (10)
K1—Se^ii	3.835 (4)	W2—O10^xii	1.870 (10)
K1—Se^i	3.839 (3)	W2—O7	1.975 (11)
K1—W2	3.975 (3)	W2—O11^xii	2.016 (11)
K2—O2^v	2.639 (9)	W2—O3^i	2.167 (10)
K2—O6^vi	2.780 (11)	W3—O6	1.726 (10)
K2—O4^vi	2.809 (11)	W3—O11	1.822 (11)
K2—O10^vii	2.861 (11)	W3—O9	1.825 (11)
K2—O8^iv	2.879 (9)	W3—O12^xiii	2.031 (10)
K2—O12^i	2.918 (10)	W3—O8	2.032 (10)
K2—O9^viii	3.213 (11)	W3—O5^ii	2.153 (10)
K2—O7^ix	3.316 (12)	Se—O1	1.695 (10)
K2—O11^viii	3.408 (9)	Se—O5	1.735 (10)
K2—W2^iv	3.767 (3)	Se—O3	1.739 (10)
K2—W1^i	3.775 (4)
O3^i—K1—O5^ii	112.6 (3)	O12—W1—K2^i	49.0 (3)
O3^i—K1—O1^iii	79.3 (3)	O10^xi—W1—K2^i	130.3 (3)
O5^ii—K1—O1^iii	78.0 (3)	O9^x—W1—K2^i	143.4 (3)
O3^i—K1—O5^iii	125.5 (3)	O1—W1—K2^i	116.2 (3)
O5^ii—K1—O5^iii	81.0 (3)	O2—W1—K2^ii	68.2 (4)
O1^iii—K1—O5^iii	51.1 (3)	O7^x—W1—K2^ii	137.1 (4)
O3^i—K1—O8	57.2 (3)	O12—W1—K2^ii	125.4 (3)
O5^ii—K1—O8	56.1 (3)	O10^xi—W1—K2^ii	42.7 (3)
O1^iii—K1—O8	76.8 (3)	O9^x—W1—K2^ii	53.0 (3)
O5^iii—K1—O8	118.8 (3)	O1—W1—K2^ii	105.6 (3)
O3^i—K1—O4^iv	108.8 (3)	K2^i—W1—K2^ii	137.13 (9)
O5^ii—K1—O4^iv	67.2 (3)	O2—W1—K2^xiv	26.6 (3)
O1^iii—K1—O4^iv	144.7 (3)	O7^x—W1—K2^xiv	76.9 (3)
O5^iii—K1—O4^iv	124.4 (3)	O12—W1—K2^xiv	119.5 (3)
O8—K1—O4^iv	79.5 (3)	O10^xi—W1—K2^xiv	111.4 (3)
O3^i—K1—O3^iii	81.0 (3)	O9^x—W1—K2^xiv	74.1 (3)
O5^ii—K1—O3^iii	124.9 (3)	O1—W1—K2^xiv	145.5 (3)
O1^iii—K1—O3^iii	51.3 (3)	K2^i—W1—K2^xiv	77.64 (8)
O5^iii—K1—O3^iii	52.3 (2)	K2^ii—W1—K2^xiv	73.29 (8)
O8—K1—O3^iii	118.9 (3)	O4—W2—O8	98.3 (4)
O4^iv—K1—O3^iii	161.2 (3)	O4—W2—O10^xii	99.8 (5)
O3^i—K1—O6^iv	66.2 (3)	O8—W2—O10^xii	95.6 (4)
O5^ii—K1—O6^iv	109.6 (3)	O4—W2—O7	94.6 (5)
O1^iii—K1—O6^iv	145.0 (3)	O8—W2—O7	88.4 (4)
O5^iii—K1—O6^iv	160.9 (3)	O10^xii—W2—O7	164.3 (5)
O8—K1—O6^iv	79.9 (3)	O4—W2—O11^xii	93.2 (4)
O4^iv—K1—O6^iv	51.6 (3)	O8—W2—O11^xii	166.7 (4)
O3^iii—K1—O6^iv	124.0 (3)	O10^xii—W2—O11^xii	88.9 (4)
O3^i—K1—Se^iii	95.2 (2)	O7—W2—O11^xii	84.0 (4)
O5^ii—K1—Se^iii	94.6 (2)	O4—W2—O3^i	172.6 (4)
O1^iii—K1—Se^iii	29.60 (19)	O8—W2—O3^i	86.2 (4)
O5^iii—K1—Se^iii	30.4 (2)	O10^xii—W2—O3^i	85.5 (4)
O8—K1—Se^iii	106.4 (2)	O7—W2—O3^i	79.6 (4)
O4^iv—K1—Se^iii	153.9 (2)	O11^xii—W2—O3^i	81.6 (4)
O3^iii—K1—Se^iii	30.43 (19)	O4—W2—K2^xv	105.4 (4)
O6^iv—K1—Se^iii	153.6 (2)	O8—W2—K2^xv	48.1 (3)
O3^i—K1—Se^ii	130.7 (3)	O10^xii—W2—K2^xv	47.6 (3)
O5^ii—K1—Se^ii	24.1 (2)	O7—W2—K2^xv	133.7 (3)
O1^iii—K1—Se^ii	97.7 (2)	O11^xii—W2—K2^xv	134.4 (3)
O5^iii—K1—Se^ii	82.7 (2)	O3^i—W2—K2^xv	82.0 (3)
O8—K1—Se^ii	74.0 (2)	O4—W2—K1	142.1 (3)
O4^iv—K1—Se^ii	50.4 (2)	O8—W2—K1	46.7 (3)
O3^iii—K1—Se^ii	134.5 (2)	O10^xii—W2—K1	98.2 (3)
O6^iv—K1—Se^ii	100.5 (2)	O7—W2—K1	73.6 (3)
Se^iii—K1—Se^ii	105.89 (9)	O11^xii—W2—K1	120.3 (3)
O3^i—K1—Se^i	23.8 (2)	O3^i—W2—K1	40.7 (3)
O5^ii—K1—Se^i	131.1 (2)	K2^xv—W2—K1	64.86 (8)
O1^iii—K1—Se^i	98.5 (2)	O4—W2—K1^xv	40.9 (4)
O5^iii—K1—Se^i	134.1 (2)	O8—W2—K1^xv	76.3 (3)
O8—K1—Se^i	75.4 (2)	O10^xii—W2—K1^xv	68.4 (3)
O4^iv—K1—Se^i	100.3 (2)	O7—W2—K1^xv	127.3 (3)
O3^iii—K1—Se^i	82.19 (19)	O11^xii—W2—K1^xv	117.0 (3)
O6^iv—K1—Se^i	50.05 (19)	O3^i—W2—K1^xv	146.4 (3)
Se^iii—K1—Se^i	105.76 (9)	K2^xv—W2—K1^xv	64.97 (7)
Se^ii—K1—Se^i	140.87 (10)	K1—W2—K1^xv	120.66 (4)
O3^i—K1—W2	31.2 (2)	O6—W3—O11	100.1 (4)
O5^ii—K1—W2	81.4 (2)	O6—W3—O9	100.1 (5)
O1^iii—K1—W2	71.7 (2)	O11—W3—O9	97.5 (5)
O5^iii—K1—W2	122.4 (2)	O6—W3—O12^xiii	91.8 (5)
O8—K1—W2	26.7 (2)	O11—W3—O12^xiii	89.3 (4)
O4^iv—K1—W2	97.2 (2)	O9—W3—O12^xiii	165.0 (4)
O3^iii—K1—W2	98.9 (2)	O6—W3—O8	91.8 (4)
O6^iv—K1—W2	75.8 (2)	O11—W3—O8	165.4 (4)
Se^iii—K1—W2	98.21 (8)	O9—W3—O8	88.6 (4)
Se^ii—K1—W2	100.71 (8)	O12^xiii—W3—O8	81.8 (4)
Se^i—K1—W2	52.29 (5)	O6—W3—O5^ii	171.1 (4)
O2^v—K2—O6^vi	84.1 (3)	O11—W3—O5^ii	86.1 (4)
O2^v—K2—O4^vi	82.2 (3)	O9—W3—O5^ii	85.3 (4)
O6^vi—K2—O4^vi	57.1 (3)	O12^xiii—W3—O5^ii	81.8 (4)
O2^v—K2—O10^vii	129.3 (4)	O8—W3—O5^ii	81.2 (4)
O6^vi—K2—O10^vii	81.2 (3)	O6—W3—K1	135.8 (3)
O4^vi—K2—O10^vii	126.1 (3)	O11—W3—K1	124.0 (3)
O2^v—K2—O8^iv	168.0 (3)	O9—W3—K1	73.4 (3)
O6^vi—K2—O8^iv	87.8 (3)	O12^xiii—W3—K1	91.6 (3)
O4^vi—K2—O8^iv	85.9 (3)	O8—W3—K1	45.4 (2)
O10^vii—K2—O8^iv	57.6 (3)	O5^ii—W3—K1	38.9 (3)
O2^v—K2—O12^i	124.7 (4)	O6—W3—K2^xv	95.1 (4)
O6^vi—K2—O12^i	126.0 (3)	O11—W3—K2^xv	129.0 (3)
O4^vi—K2—O12^i	80.6 (3)	O9—W3—K2^xv	127.2 (3)
O10^vii—K2—O12^i	102.8 (3)	O12^xiii—W3—K2^xv	41.6 (3)
O8^iv—K2—O12^i	54.6 (3)	O8—W3—K2^xv	40.4 (3)
O2^v—K2—O9^viii	88.4 (3)	O5^ii—W3—K2^xv	75.9 (3)
O6^vi—K2—O9^viii	106.9 (3)	K1—W3—K2^xv	61.03 (7)
O4^vi—K2—O9^viii	162.1 (3)	O6—W3—K2^viii	88.1 (4)
O10^vii—K2—O9^viii	51.2 (3)	O11—W3—K2^viii	54.1 (3)
O8^iv—K2—O9^viii	102.5 (3)	O9—W3—K2^viii	47.8 (3)
O12^i—K2—O9^viii	117.2 (3)	O12^xiii—W3—K2^viii	142.7 (3)
O2^v—K2—O7^ix	84.6 (3)	O8—W3—K2^viii	135.5 (3)
O6^vi—K2—O7^ix	161.5 (3)	O5^ii—W3—K2^viii	100.7 (3)
O4^vi—K2—O7^ix	106.7 (3)	K1—W3—K2^viii	113.79 (7)
O10^vii—K2—O7^ix	117.3 (3)	K2^xv—W3—K2^viii	174.68 (8)
O8^iv—K2—O7^ix	100.8 (3)	O1—Se—O5	96.1 (5)
O12^i—K2—O7^ix	51.9 (3)	O1—Se—O3	97.5 (5)
O9^viii—K2—O7^ix	87.4 (3)	O5—Se—O3	100.4 (4)
O2^v—K2—O11^viii	63.4 (3)	O1—Se—K1^x	57.7 (3)
O6^vi—K2—O11^viii	137.0 (3)	O5—Se—K1^x	61.4 (3)
O4^vi—K2—O11^viii	135.9 (3)	O3—Se—K1^x	62.7 (4)
O10^vii—K2—O11^viii	97.6 (3)	O1—Se—K1^ii	71.1 (3)
O8^iv—K2—O11^viii	127.9 (3)	O5—Se—K1^ii	40.5 (3)
O12^i—K2—O11^viii	96.4 (3)	O3—Se—K1^ii	133.7 (4)
O9^viii—K2—O11^viii	48.8 (3)	K1^x—Se—K1^ii	74.10 (9)
O7^ix—K2—O11^viii	46.8 (3)	O1—Se—K1^i	72.8 (3)
O2^v—K2—W2^iv	156.5 (3)	O5—Se—K1^i	132.1 (4)
O6^vi—K2—W2^iv	82.8 (2)	O3—Se—K1^i	39.3 (3)
O4^vi—K2—W2^iv	106.6 (2)	K1^x—Se—K1^i	74.24 (9)
O10^vii—K2—W2^iv	28.8 (2)	K1^ii—Se—K1^i	140.87 (10)
O8^iv—K2—W2^iv	28.8 (2)	Se—O1—W1	141.0 (6)
O12^i—K2—W2^iv	78.7 (2)	Se—O1—K1^x	92.7 (4)
O9^viii—K2—W2^iv	76.9 (2)	W1—O1—K1^x	125.8 (4)
O7^ix—K2—W2^iv	112.5 (2)	W1—O2—K2^xiv	136.4 (5)
O11^viii—K2—W2^iv	115.99 (18)	Se—O3—W2^i	123.4 (5)
O2^v—K2—W1^i	97.2 (3)	Se—O3—K1^i	116.9 (5)
O6^vi—K2—W1^i	139.0 (2)	W2^i—O3—K1^i	108.1 (4)
O4^vi—K2—W1^i	82.3 (2)	Se—O3—K1^x	86.8 (4)
O10^vii—K2—W1^i	124.7 (2)	W2^i—O3—K1^x	118.7 (4)
O8^iv—K2—W1^i	83.2 (2)	K1^i—O3—K1^x	99.0 (3)
O12^i—K2—W1^i	28.6 (2)	W2—O4—K2^xvi	139.1 (5)
O9^viii—K2—W1^i	114.1 (2)	W2—O4—K1^xv	117.3 (5)
O7^ix—K2—W1^i	29.32 (19)	K2^xvi—O4—K1^xv	90.3 (3)
O11^viii—K2—W1^i	76.0 (2)	Se—O5—W3^ii	124.5 (5)
W2^iv—K2—W1^i	105.51 (8)	Se—O5—K1^ii	115.3 (5)
O2^v—K2—W1^ii	101.5 (3)	W3^ii—O5—K1^ii	111.7 (4)
O6^vi—K2—W1^ii	81.5 (2)	Se—O5—K1^x	88.2 (4)
O4^vi—K2—W1^ii	138.0 (2)	W3^ii—O5—K1^x	112.0 (4)
O10^vii—K2—W1^ii	28.4 (2)	K1^ii—O5—K1^x	99.0 (3)
O8^iv—K2—W1^ii	85.9 (2)	W3—O6—K2^xvi	134.9 (6)
O12^i—K2—W1^ii	125.5 (2)	W3—O6—K1^xv	125.9 (5)
O9^viii—K2—W1^ii	30.0 (2)	K2^xvi—O6—K1^xv	90.0 (3)
O7^ix—K2—W1^ii	115.2 (2)	W1^iii—O7—W2	146.6 (6)
O11^viii—K2—W1^ii	78.6 (2)	W1^iii—O7—K2^ix	89.2 (4)
W2^iv—K2—W1^ii	57.20 (5)	W2—O7—K2^ix	113.7 (4)
W1^i—K2—W1^ii	137.13 (9)	W2—O8—W3	131.3 (5)
O2—W1—O7^x	96.6 (5)	W2—O8—K2^xv	103.1 (4)
O2—W1—O12	100.1 (5)	W3—O8—K2^xv	112.3 (4)
O7^x—W1—O12	96.1 (4)	W2—O8—K1	106.6 (4)
O2—W1—O10^xi	95.0 (5)	W3—O8—K1	106.0 (3)
O7^x—W1—O10^xi	166.0 (5)	K2^xv—O8—K1	89.6 (3)
O12—W1—O10^xi	89.5 (4)	W3—O9—W1^iii	145.8 (6)
O2—W1—O9^x	91.8 (5)	W3—O9—K2^viii	107.3 (4)
O7^x—W1—O9^x	89.5 (4)	W1^iii—O9—K2^viii	96.9 (4)
O12—W1—O9^x	166.1 (4)	W2^xvii—O10—W1^xiii	147.4 (6)
O10^xi—W1—O9^x	82.3 (4)	W2^xvii—O10—K2^xviii	103.6 (4)
O2—W1—O1	169.9 (4)	W1^xiii—O10—K2^xviii	109.0 (4)
O7^x—W1—O1	82.7 (4)	W3—O11—W2^xvii	149.4 (5)
O12—W1—O1	89.9 (4)	W3—O11—K2^viii	100.2 (4)
O10^xi—W1—O1	84.4 (4)	W2^xvii—O11—K2^viii	109.0 (4)
O9^x—W1—O1	78.2 (4)	W1—O12—W3^xi	146.7 (5)
O2—W1—K2^i	71.7 (4)	W1—O12—K2^i	102.4 (4)
O7^x—W1—K2^i	61.4 (3)	W3^xi—O12—K2^i	110.9 (4)

Symmetry codes: (i) −x, −y+1, −z+1; (ii) −x+1, −y+1, −z+1; (iii) x, y, z+1; (iv) −x+1/2, y−1/2, −z+3/2; (v) x, y−1, z+1; (vi) x, y−1, z; (vii) −x+3/2, y−1/2, −z+3/2; (viii) −x+1, −y+1, −z+2; (ix) −x, −y+1, −z+2; (x) x, y, z−1; (xi) x−1/2, −y+3/2, z−1/2; (xii) x−1, y, z; (xiii) x+1/2, −y+3/2, z+1/2; (xiv) x, y+1, z−1; (xv) −x+1/2, y+1/2, −z+3/2; (xvi) x, y+1, z; (xvii) x+1, y, z; (xviii) −x+3/2, y+1/2, −z+3/2.