Structural characterization of quaternary selenites of tungsten(VI), A 2W3SeO12 (A = NH4, Cs, Rb, K or Tl).

The quaternary A 2W3SeO12 (A = NH4, Cs, Rb, K or Tl) selenites have been prepared in the form of single crystals by hydro-thermal and novel solid-state reactions. They were characterized by X-ray diffraction, thermal and spectroscopic studies. All of them have a hexa-gonal tungsten oxide (HTO) related [W3SeO12]2- anionic framework with pyramidally coordinated Se4+ ions. The known A 2W3SeO12 (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 inter-layer Se-O bonds. It is inferred that the new Tl2W3SeO12 compound has the same three-dimensional structure as K2W3SeO12(α). © Balisetty and Vidyasagar 2021.

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 d 0 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 d 0 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 d 0 transition-metal ions, such as YVTe2O8 (Kim et al., 2014 ▸), are also known to have centrosymmetric structures and exhibit no SHG activity.

A 2Mo3SeO12 (A = NH4, Cs, Rb, Tl) (Harrison et al., 1994 ▸; Dussack et al., 1996 ▸; Chang et al., 2010 ▸), A 2W3SeO12 (A = NH4, Cs, Rb, K) (Harrison et al., 1995 ▸; Huang et al., 2014a ▸,b ▸) and Na2W3SeO12·2H2O (Nguyen & Halasyamani 2013 ▸), A 2Mo3TeO12 (A = Cs, NH4) (Vidyavathy Balraj & Vidyasagar 1998 ▸), A 2W3TeO12 (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 [M 3 XO12]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 A 2W3SeO12 (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 A 4Mo6Te2O24·6H2O (A = Rb, K) (Vidyavathy Balraj & Vidyasagar 1998 ▸) compounds are quaternary selenite and tellurites of molybdenum, whose [Mo3 XO12]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 A 2W3SeO12 (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 A 2W3SeO12 [A = NH4 (1), Cs (2) and Rb (3)] and new compounds K2W3SeO12 (4α) and Tl2W3SeO12 (5).

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 Rb2/3WTe1/3O4 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 3 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 (4 ) 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 (4 ), 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 C 3 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, 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 A 2W3SeO12 [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 A 2W3TeO12 (A = K, Rb, Cs) tellurites of tungsten (Goodey et al., 2003 ▸; Zhao et al., 2015 ▸) and A 2Mo3SeO12 (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.

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.

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 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
M r	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 (Å3)	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 ▸)
T min, T max	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
R int	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.

Crystal structure: contains datablock(s) global, NH42W3SeO121, Cs2W3SeO122, Rb2W3SeO123, K2W3SeO124. DOI: 10.1107/S2056989021002735/ru2074sup1.cif

Structure factors: contains datablock(s) NH42W3SeO121. DOI: 10.1107/S2056989021002735/ru2074NH42W3SeO121sup2.hkl

Supporting information file. DOI: 10.1107/S2056989021002735/ru2074sup6.pdf

Rietveld powder data: contains datablock(s) NH42W3SeO121. DOI: 10.1107/S2056989021002735/ru2074NH42W3SeO121sup7.rtv

Structure factors: contains datablock(s) Cs2W3SeO122. DOI: 10.1107/S2056989021002735/ru2074Cs2W3SeO122sup3.hkl

Rietveld powder data: contains datablock(s) Cs2W3SeO122. DOI: 10.1107/S2056989021002735/ru2074Cs2W3SeO122sup8.rtv

Structure factors: contains datablock(s) Rb2W3SeO123. DOI: 10.1107/S2056989021002735/ru2074Rb2W3SeO123sup4.hkl

Rietveld powder data: contains datablock(s) Rb2W3SeO123. DOI: 10.1107/S2056989021002735/ru2074Rb2W3SeO123sup9.rtv

Rietveld powder data: contains datablock(s) K2W3SeO124. DOI: 10.1107/S2056989021002735/ru2074K2W3SeO124sup10.rtv

Structure factors: contains datablock(s) K2W3SeO124. DOI: 10.1107/S2056989021002735/ru2074K2W3SeO124sup5.hkl

CCDC references: 2000910, 2000899, 2000898, 2000897

Additional supporting information: crystallographic information; 3D view; checkCIF report

(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) Å3	T = 297 K
Z = 2	Block, colourless
F(000) = 748	0.10 × 0.10 × 0.05 mm

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 on F2	w = 1/[σ2(Fo2) + (0.0097P)2 + 8.3615P] where P = (Fo2 + 2Fc2)/3
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F2 > 2σ(F2)] = 0.023	Δρmax = 2.63 e Å−3
wR(F2) = 0.052	Δρmin = −2.37 e Å−3
S = 1.27	Extinction correction: SHELXL-2018/3 (Sheldrick 2015b), Fc*=kFc[1+0.001xFc2λ3/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

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

	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)

	U11	U22	U33	U12	U13	U23
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)

W—O2i	1.722 (10)	W—O1	2.184 (9)
W—O3	1.848 (8)	Se—O1iii	1.709 (10)
W—O4ii	1.874 (9)	Se—O1	1.709 (10)
W—O3iii	1.985 (8)	Se—O1iv	1.709 (10)
W—O4	2.010 (9)
O2i—W—O3	99.2 (6)	O3—W—O1	84.5 (5)
O2i—W—O4ii	99.3 (5)	O4ii—W—O1	86.0 (4)
O3—W—O4ii	96.7 (4)	O3iii—W—O1	80.7 (5)
O2i—W—O3iii	93.4 (6)	O4—W—O1	81.0 (4)
O3—W—O3iii	89.7 (4)	O1iii—Se—O1	102.9 (4)
O4ii—W—O3iii	164.6 (5)	O1iii—Se—O1iv	102.9 (4)
O2i—W—O4	94.7 (4)	O1—Se—O1iv	102.9 (4)
O3—W—O4	164.5 (5)	Se—O1—W	130.9 (5)
O4ii—W—O4	87.8 (6)	W—O3—Wiv	149.1 (5)
O3iii—W—O4	82.6 (4)	Wv—O4—W	132.5 (5)
O2i—W—O1	173.1 (4)

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) Å3	T = 293 K
Z = 2	Block, colourless
F(000) = 924	0.10 × 0.08 × 0.05 mm

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 on F2	w = 1/[σ2(Fo2)] where P = (Fo2 + 2Fc2)/3
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F2 > 2σ(F2)] = 0.029	Δρmax = 1.90 e Å−3
wR(F2) = 0.054	Δρmin = −1.65 e Å−3
S = 1.02	Extinction correction: SHELXL2018/3 (Sheldrick 2015b), Fc*=kFc[1+0.001xFc2λ3/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)

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.

	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)

	U11	U22	U33	U12	U13	U23
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)

Cs1—O1i	3.132 (15)	Cs2—O4ii	3.066 (14)
Cs1—O1	3.132 (15)	Cs2—O3vi	3.427 (13)
Cs1—O1ii	3.132 (15)	Cs2—O3	3.427 (13)
Cs1—O3iii	3.497 (15)	Cs2—O3vii	3.427 (13)
Cs1—O3iv	3.497 (15)	Cs2—O1vii	3.667 (13)
Cs1—O3v	3.497 (15)	Cs2—O1	3.667 (13)
Cs1—O4i	3.634 (14)	Cs2—O1vi	3.667 (13)
Cs1—O4ii	3.634 (14)	W—O2x	1.703 (17)
Cs1—O4	3.634 (14)	W—O3xi	1.840 (11)
Cs1—O2i	3.695 (14)	W—O4	1.863 (13)
Cs1—O2ii	3.695 (14)	W—O4ii	2.000 (13)
Cs1—O2	3.695 (14)	W—O3	2.000 (10)
Cs2—O2	3.044 (16)	W—O1	2.176 (14)
Cs2—O2vi	3.044 (16)	Se—O1xi	1.723 (15)
Cs2—O2vii	3.044 (16)	Se—O1	1.724 (15)
Cs2—O4viii	3.066 (14)	Se—O1ix	1.724 (15)
Cs2—O4ix	3.066 (14)
O1i—Cs1—O1	92.9 (4)	O4ii—Cs2—O1vi	143.4 (3)
O1i—Cs1—O1ii	92.9 (4)	O3vi—Cs2—O1vi	45.0 (3)
O1—Cs1—O1ii	92.9 (4)	O3—Cs2—O1vi	97.0 (3)
O1i—Cs1—O3iii	74.6 (3)	O3vii—Cs2—O1vi	127.0 (3)
O1—Cs1—O3iii	132.9 (3)	O1vii—Cs2—O1vi	119.992 (7)
O1ii—Cs1—O3iii	132.1 (3)	O1—Cs2—O1vi	119.993 (8)
O1i—Cs1—O3iv	132.1 (3)	O2x—W—O3xi	97.7 (8)
O1—Cs1—O3iv	74.6 (3)	O2x—W—O4	98.5 (7)
O1ii—Cs1—O3iv	132.9 (3)	O3xi—W—O4	96.6 (5)
O3iii—Cs1—O3iv	81.0 (4)	O2x—W—O4ii	93.8 (6)
O1i—Cs1—O3v	132.9 (3)	O3xi—W—O4ii	167.0 (7)
O1—Cs1—O3v	132.1 (3)	O4—W—O4ii	87.4 (8)
O1ii—Cs1—O3v	74.6 (3)	O2x—W—O3	92.3 (7)
O3iii—Cs1—O3v	81.0 (4)	O3xi—W—O3	89.9 (7)
O3iv—Cs1—O3v	81.0 (4)	O4—W—O3	166.5 (7)
O1i—Cs1—O4i	48.2 (3)	O4ii—W—O3	83.7 (5)
O1—Cs1—O4i	81.9 (3)	O2x—W—O1	172.7 (6)
O1ii—Cs1—O4i	47.2 (3)	O3xi—W—O1	85.8 (7)
O3iii—Cs1—O4i	116.3 (3)	O4—W—O1	87.5 (6)
O3iv—Cs1—O4i	156.5 (3)	O4ii—W—O1	82.1 (5)
O3v—Cs1—O4i	115.9 (3)	O3—W—O1	81.2 (6)
O1i—Cs1—O4ii	81.9 (3)	O2x—W—Cs2xii	123.2 (5)
O1—Cs1—O4ii	47.2 (3)	O3xi—W—Cs2xii	57.3 (4)
O1ii—Cs1—O4ii	48.2 (3)	O4—W—Cs2xii	46.0 (4)
O3iii—Cs1—O4ii	156.5 (3)	O4ii—W—Cs2xii	120.1 (4)
O3iv—Cs1—O4ii	115.9 (3)	O3—W—Cs2xii	132.2 (4)
O3v—Cs1—O4ii	116.3 (3)	O1—W—Cs2xii	64.1 (3)
O4i—Cs1—O4ii	43.1 (4)	O2x—W—Cs1xiii	59.3 (5)
O1i—Cs1—O4	47.2 (3)	O3xi—W—Cs1xiii	53.6 (5)
O1—Cs1—O4	48.2 (3)	O4—W—Cs1xiii	68.7 (4)
O1ii—Cs1—O4	81.9 (3)	O4ii—W—Cs1xiii	138.9 (4)
O3iii—Cs1—O4	115.9 (3)	O3—W—Cs1xiii	124.3 (4)
O3iv—Cs1—O4	116.3 (3)	O1—W—Cs1xiii	127.4 (3)
O3v—Cs1—O4	156.5 (3)	Cs2xii—W—Cs1xiii	65.81 (5)
O4i—Cs1—O4	43.1 (4)	O2x—W—Cs2	114.7 (5)
O4ii—Cs1—O4	43.1 (4)	O3xi—W—Cs2	127.9 (4)
O1i—Cs1—O2i	57.5 (4)	O4—W—Cs2	116.1 (4)
O1—Cs1—O2i	91.3 (3)	O4ii—W—Cs2	40.4 (4)
O1ii—Cs1—O2i	150.4 (4)	O3—W—Cs2	51.3 (4)
O3iii—Cs1—O2i	43.5 (3)	O1—W—Cs2	58.5 (3)
O3iv—Cs1—O2i	76.4 (3)	Cs2xii—W—Cs2	120.63 (6)
O3v—Cs1—O2i	122.2 (4)	Cs1xiii—W—Cs2	173.49 (5)
O4i—Cs1—O2i	104.7 (4)	O2x—W—Cs1	138.0 (6)
O4ii—Cs1—O2i	121.5 (3)	O3xi—W—Cs1	116.2 (5)
O4—Cs1—O2i	79.1 (3)	O4—W—Cs1	55.9 (4)
O1i—Cs1—O2ii	91.3 (3)	O4ii—W—Cs1	56.4 (4)
O1—Cs1—O2ii	150.4 (4)	O3—W—Cs1	110.6 (5)
O1ii—Cs1—O2ii	57.5 (4)	O1—W—Cs1	43.4 (4)
O3iii—Cs1—O2ii	76.4 (3)	Cs2xii—W—Cs1	65.44 (3)
O3iv—Cs1—O2ii	122.2 (4)	Cs1xiii—W—Cs1	122.50 (3)
O3v—Cs1—O2ii	43.5 (3)	Cs2—W—Cs1	63.41 (3)
O4i—Cs1—O2ii	79.1 (3)	O2x—W—Cs1xiv	54.8 (5)
O4ii—Cs1—O2ii	104.7 (4)	O3xi—W—Cs1xiv	120.7 (4)
O4—Cs1—O2ii	121.5 (3)	O4—W—Cs1xiv	134.5 (4)
O2i—Cs1—O2ii	115.47 (19)	O4ii—W—Cs1xiv	62.2 (4)
O1i—Cs1—O2	150.4 (4)	O3—W—Cs1xiv	48.1 (4)
O1—Cs1—O2	57.5 (4)	O1—W—Cs1xiv	117.9 (3)
O1ii—Cs1—O2	91.3 (3)	Cs2xii—W—Cs1xiv	177.46 (4)
O3iii—Cs1—O2	122.2 (4)	Cs1xiii—W—Cs1xiv	111.82 (6)
O3iv—Cs1—O2	43.5 (3)	Cs2—W—Cs1xiv	61.72 (4)
O3v—Cs1—O2	76.4 (3)	Cs1—W—Cs1xiv	117.06 (2)
O4i—Cs1—O2	121.5 (3)	O1xi—Se—O1	104.0 (5)
O4ii—Cs1—O2	79.1 (3)	O1xi—Se—O1ix	104.0 (5)
O4—Cs1—O2	104.7 (4)	O1—Se—O1ix	104.0 (5)
O2i—Cs1—O2	115.47 (19)	O1xi—Se—Cs2xv	58.6 (4)
O2ii—Cs1—O2	115.47 (19)	O1—Se—Cs2xv	145.4 (5)
O2—Cs2—O2vi	56.8 (5)	O1ix—Se—Cs2xv	58.6 (4)
O2—Cs2—O2vii	56.8 (5)	O1xi—Se—Cs2	145.4 (5)
O2vi—Cs2—O2vii	56.8 (5)	O1—Se—Cs2	58.6 (4)
O2—Cs2—O4viii	153.5 (4)	O1ix—Se—Cs2	58.6 (4)
O2vi—Cs2—O4viii	101.6 (4)	Cs2xv—Se—Cs2	116.99 (3)
O2vii—Cs2—O4viii	99.6 (4)	O1xi—Se—Cs2xii	58.6 (4)
O2—Cs2—O4ix	101.6 (4)	O1—Se—Cs2xii	58.6 (4)
O2vi—Cs2—O4ix	99.6 (4)	O1ix—Se—Cs2xii	145.4 (5)
O2vii—Cs2—O4ix	153.5 (4)	Cs2xv—Se—Cs2xii	116.99 (3)
O4viii—Cs2—O4ix	96.8 (3)	Cs2—Se—Cs2xii	116.99 (3)
O2—Cs2—O4ii	99.6 (4)	O1xi—Se—Cs1xv	37.9 (5)
O2vi—Cs2—O4ii	153.5 (4)	O1—Se—Cs1xv	122.6 (4)
O2vii—Cs2—O4ii	101.6 (4)	O1ix—Se—Cs1xv	122.6 (4)
O4viii—Cs2—O4ii	96.8 (3)	Cs2xv—Se—Cs1xv	64.012 (17)
O4ix—Cs2—O4ii	96.8 (3)	Cs2—Se—Cs1xv	176.68 (9)
O2—Cs2—O3vi	139.0 (3)	Cs2xii—Se—Cs1xv	64.014 (17)
O2vi—Cs2—O3vi	96.8 (4)	O1xi—Se—Cs1	122.6 (4)
O2vii—Cs2—O3vi	137.8 (3)	O1—Se—Cs1	37.9 (5)
O4viii—Cs2—O3vi	50.0 (3)	O1ix—Se—Cs1	122.6 (4)
O4ix—Cs2—O3vi	48.2 (3)	Cs2xv—Se—Cs1	176.68 (9)
O4ii—Cs2—O3vi	109.7 (4)	Cs2—Se—Cs1	64.013 (17)
O2—Cs2—O3	96.8 (4)	Cs2xii—Se—Cs1	64.013 (17)
O2vi—Cs2—O3	137.8 (3)	Cs1xv—Se—Cs1	114.79 (4)
O2vii—Cs2—O3	139.0 (3)	O1xi—Se—Cs1xvi	122.6 (4)
O4viii—Cs2—O3	109.7 (4)	O1—Se—Cs1xvi	122.6 (4)
O4ix—Cs2—O3	50.0 (3)	O1ix—Se—Cs1xvi	37.9 (5)
O4ii—Cs2—O3	48.2 (3)	Cs2xv—Se—Cs1xvi	64.014 (17)
O3vi—Cs2—O3	83.0 (4)	Cs2—Se—Cs1xvi	64.013 (17)
O2—Cs2—O3vii	137.8 (3)	Cs2xii—Se—Cs1xvi	176.68 (9)
O2vi—Cs2—O3vii	139.0 (3)	Cs1xv—Se—Cs1xvi	114.79 (4)
O2vii—Cs2—O3vii	96.8 (4)	Cs1—Se—Cs1xvi	114.79 (4)
O4viii—Cs2—O3vii	48.2 (3)	Se—O1—W	129.4 (8)
O4ix—Cs2—O3vii	109.7 (4)	Se—O1—Cs1	122.3 (6)
O4ii—Cs2—O3vii	50.0 (3)	W—O1—Cs1	108.1 (5)
O3vi—Cs2—O3vii	83.0 (4)	Se—O1—Cs2	97.7 (5)
O3—Cs2—O3vii	83.0 (4)	W—O1—Cs2	91.2 (4)
O2—Cs2—O1vii	114.5 (4)	Cs1—O1—Cs2	83.4 (3)
O2vi—Cs2—O1vii	95.0 (4)	Se—O1—Cs2xii	97.7 (5)
O2vii—Cs2—O1vii	58.5 (4)	W—O1—Cs2xii	83.6 (4)
O4viii—Cs2—O1vii	47.1 (3)	Cs1—O1—Cs2xii	83.4 (3)
O4ix—Cs2—O1vii	143.4 (3)	Cs2—O1—Cs2xii	163.5 (5)
O4ii—Cs2—O1vii	83.8 (3)	Wxvii—O2—Cs2	159.8 (9)
O3vi—Cs2—O1vii	97.0 (3)	Wxvii—O2—Cs1	97.3 (5)
O3—Cs2—O1vii	127.0 (3)	Cs2—O2—Cs1	84.1 (4)
O3vii—Cs2—O1vii	45.0 (3)	Wxvii—O2—Cs1xvi	103.6 (6)
O2—Cs2—O1	58.5 (4)	Cs2—O2—Cs1xvi	82.6 (3)
O2vi—Cs2—O1	114.5 (4)	Cs1—O2—Cs1xvi	152.0 (6)
O2vii—Cs2—O1	95.0 (4)	Wix—O3—W	148.6 (7)
O4viii—Cs2—O1	143.4 (3)	Wix—O3—Cs2	95.8 (5)
O4ix—Cs2—O1	83.8 (3)	W—O3—Cs2	101.6 (5)
O4ii—Cs2—O1	47.1 (3)	Wix—O3—Cs1xiv	101.4 (5)
O3vi—Cs2—O1	127.0 (3)	W—O3—Cs1xiv	106.7 (5)
O3—Cs2—O1	45.0 (3)	Cs2—O3—Cs1xiv	81.5 (2)
O3vii—Cs2—O1	97.0 (3)	W—O4—Wi	135.7 (8)
O1vii—Cs2—O1	119.993 (7)	W—O4—Cs2xii	108.0 (5)
O2—Cs2—O1vi	95.0 (4)	Wi—O4—Cs2xii	114.6 (5)
O2vi—Cs2—O1vi	58.5 (4)	W—O4—Cs1	99.0 (5)
O2vii—Cs2—O1vi	114.5 (4)	Wi—O4—Cs1	96.3 (5)
O4viii—Cs2—O1vi	83.8 (3)	Cs2xii—O4—Cs1	84.8 (3)
O4ix—Cs2—O1vi	47.1 (3)

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) Å3	T = 293 K
Z = 2	Block, colourless
F(000) = 852	0.10 × 0.05 × 0.05 mm

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 on F2	w = 1/[σ2(Fo2) + (0.0065P)2 + 2.2061P] where P = (Fo2 + 2Fc2)/3
Least-squares matrix: full	(Δ/σ)max < 0.001
R[F2 > 2σ(F2)] = 0.018	Δρmax = 0.90 e Å−3
wR(F2) = 0.033	Δρmin = −1.14 e Å−3
S = 1.06	Extinction correction: SHELXL2018/3 (Sheldrick 2015b), Fc*=kFc[1+0.001xFc2λ3/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)

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

	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)

	U11	U22	U33	U12	U13	U23
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)

Rb1—O1i	3.009 (9)	Rb2—O4i	3.012 (8)
Rb1—O1	3.009 (9)	Rb2—O3	3.382 (8)
Rb1—O1ii	3.009 (9)	Rb2—O3vi	3.382 (8)
Rb1—O4ii	3.360 (8)	Rb2—O3vii	3.382 (8)
Rb1—O4i	3.360 (8)	Rb2—W	3.9926 (11)
Rb1—O4	3.360 (8)	Rb2—Wvii	3.9926 (11)
Rb1—O3iii	3.518 (9)	Rb2—Wvi	3.9926 (11)
Rb1—O3iv	3.518 (9)	W—O2x	1.726 (8)
Rb1—O3v	3.518 (9)	W—O3	1.833 (8)
Rb1—W	4.094 (2)	W—O4i	1.860 (8)
Rb1—Wi	4.094 (2)	W—O4	2.005 (8)
Rb1—Wii	4.094 (2)	W—O3xi	2.011 (8)
Rb2—O2	2.894 (8)	W—O1	2.155 (8)
Rb2—O2vi	2.894 (8)	Se—O1ix	1.714 (9)
Rb2—O2vii	2.894 (8)	Se—O1	1.714 (9)
Rb2—O4viii	3.012 (8)	Se—O1xi	1.714 (9)
Rb2—O4ix	3.012 (8)
O1i—Rb1—O1	98.2 (2)	O4ix—Rb2—O3vii	111.8 (2)
O1i—Rb1—O1ii	98.2 (2)	O4i—Rb2—O3vii	48.78 (18)
O1—Rb1—O1ii	98.2 (2)	O3—Rb2—O3vii	83.8 (2)
O1i—Rb1—O4ii	51.2 (2)	O3vi—Rb2—O3vii	83.8 (2)
O1—Rb1—O4ii	88.0 (2)	O2—Rb2—W	89.89 (19)
O1ii—Rb1—O4ii	50.2 (2)	O2vi—Rb2—W	147.69 (19)
O1i—Rb1—O4i	50.2 (2)	O2vii—Rb2—W	113.3 (2)
O1—Rb1—O4i	51.2 (2)	O4viii—Rb2—W	114.82 (16)
O1ii—Rb1—O4i	88.0 (2)	O4ix—Rb2—W	75.92 (16)
O4ii—Rb1—O4i	46.7 (2)	O4i—Rb2—W	26.34 (16)
O1i—Rb1—O4	88.0 (2)	O3—Rb2—W	27.21 (13)
O1—Rb1—O4	50.2 (2)	O3vi—Rb2—W	105.50 (16)
O1ii—Rb1—O4	51.2 (2)	O3vii—Rb2—W	70.55 (14)
O4ii—Rb1—O4	46.7 (2)	O2—Rb2—Wvii	147.69 (19)
O4i—Rb1—O4	46.7 (2)	O2vi—Rb2—Wvii	113.3 (2)
O1i—Rb1—O3iii	130.6 (2)	O2vii—Rb2—Wvii	89.89 (19)
O1—Rb1—O3iii	130.6 (2)	O4viii—Rb2—Wvii	26.34 (16)
O1ii—Rb1—O3iii	71.3 (2)	O4ix—Rb2—Wvii	114.82 (16)
O4ii—Rb1—O3iii	114.97 (19)	O4i—Rb2—Wvii	75.92 (16)
O4i—Rb1—O3iii	159.4 (2)	O3—Rb2—Wvii	105.50 (16)
O4—Rb1—O3iii	115.6 (2)	O3vi—Rb2—Wvii	70.55 (14)
O1i—Rb1—O3iv	130.6 (2)	O3vii—Rb2—Wvii	27.21 (13)
O1—Rb1—O3iv	71.3 (2)	W—Rb2—Wvii	97.16 (4)
O1ii—Rb1—O3iv	130.6 (2)	O2—Rb2—Wvi	113.3 (2)
O4ii—Rb1—O3iv	159.4 (2)	O2vi—Rb2—Wvi	89.89 (19)
O4i—Rb1—O3iv	115.6 (2)	O2vii—Rb2—Wvi	147.69 (19)
O4—Rb1—O3iv	115.0 (2)	O4viii—Rb2—Wvi	75.92 (16)
O3iii—Rb1—O3iv	79.9 (2)	O4ix—Rb2—Wvi	26.34 (16)
O1i—Rb1—O3v	71.3 (2)	O4i—Rb2—Wvi	114.82 (16)
O1—Rb1—O3v	130.6 (2)	O3—Rb2—Wvi	70.55 (14)
O1ii—Rb1—O3v	130.6 (2)	O3vi—Rb2—Wvi	27.21 (13)
O4ii—Rb1—O3v	115.6 (2)	O3vii—Rb2—Wvi	105.50 (16)
O4i—Rb1—O3v	114.97 (19)	W—Rb2—Wvi	97.16 (4)
O4—Rb1—O3v	159.4 (2)	Wvii—Rb2—Wvi	97.16 (4)
O3iii—Rb1—O3v	79.9 (2)	O2x—W—O3	98.3 (4)
O3iv—Rb1—O3v	79.9 (2)	O2x—W—O4i	99.3 (4)
O1i—Rb1—W	76.74 (18)	O3—W—O4i	97.5 (3)
O1—Rb1—W	30.77 (17)	O2x—W—O4	93.8 (4)
O1ii—Rb1—W	79.82 (18)	O3—W—O4	166.2 (4)
O4ii—Rb1—W	57.35 (14)	O4i—W—O4	87.0 (5)
O4i—Rb1—W	26.63 (15)	O2x—W—O3xi	91.7 (5)
O4—Rb1—W	29.14 (14)	O3—W—O3xi	90.0 (4)
O3iii—Rb1—W	142.01 (14)	O4i—W—O3xi	165.5 (4)
O3iv—Rb1—W	102.05 (14)	O4—W—O3xi	83.0 (3)
O3v—Rb1—W	138.07 (13)	O2x—W—O1	172.2 (4)
O1i—Rb1—Wi	30.77 (17)	O3—W—O1	85.6 (4)
O1—Rb1—Wi	79.82 (18)	O4i—W—O1	86.8 (3)
O1ii—Rb1—Wi	76.74 (17)	O4—W—O1	81.6 (3)
O4ii—Rb1—Wi	26.63 (14)	O3xi—W—O1	81.4 (4)
O4i—Rb1—Wi	29.14 (15)	O2x—W—Rb2	123.2 (3)
O4—Rb1—Wi	57.35 (14)	O3—W—Rb2	57.5 (3)
O3iii—Rb1—Wi	138.07 (13)	O4i—W—Rb2	45.9 (2)
O3iv—Rb1—Wi	142.01 (14)	O4—W—Rb2	120.2 (2)
O3v—Rb1—Wi	102.05 (14)	O3xi—W—Rb2	133.0 (3)
W—Rb1—Wi	51.57 (3)	O1—W—Rb2	64.6 (2)
O1i—Rb1—Wii	79.82 (18)	O2x—W—Rb1	135.6 (3)
O1—Rb1—Wii	76.73 (17)	O3—W—Rb1	118.2 (3)
O1ii—Rb1—Wii	30.77 (17)	O4i—W—Rb1	54.1 (2)
O4ii—Rb1—Wii	29.14 (15)	O4—W—Rb1	54.7 (2)
O4i—Rb1—Wii	57.35 (14)	O3xi—W—Rb1	111.4 (3)
O4—Rb1—Wii	26.63 (14)	O1—W—Rb1	45.6 (3)
O3iii—Rb1—Wii	102.05 (14)	Rb2—W—Rb1	66.84 (2)
O3iv—Rb1—Wii	138.07 (13)	O2x—W—Rb1xii	59.3 (3)
O3v—Rb1—Wii	142.01 (14)	O3—W—Rb1xii	53.8 (3)
W—Rb1—Wii	51.57 (3)	O4i—W—Rb1xii	70.4 (2)
Wi—Rb1—Wii	51.57 (3)	O4—W—Rb1xii	139.6 (2)
O2—Rb2—O2vi	58.6 (3)	O3xi—W—Rb1xii	123.7 (2)
O2—Rb2—O2vii	58.6 (3)	O1—W—Rb1xii	127.9 (3)
O2vi—Rb2—O2vii	58.6 (3)	Rb2—W—Rb1xii	66.06 (5)
O2—Rb2—O4viii	153.0 (2)	Rb1—W—Rb1xii	123.06 (2)
O2vi—Rb2—O4viii	97.5 (2)	O2x—W—Rb2xiii	113.1 (3)
O2vii—Rb2—O4viii	99.5 (3)	O3—W—Rb2xiii	128.1 (3)
O2—Rb2—O4ix	97.5 (2)	O4i—W—Rb2xiii	115.7 (2)
O2vi—Rb2—O4ix	99.5 (2)	O4—W—Rb2xiii	39.5 (2)
O2vii—Rb2—O4ix	153.0 (2)	O3xi—W—Rb2xiii	50.7 (2)
O4viii—Rb2—O4ix	98.91 (18)	O1—W—Rb2xiii	59.5 (2)
O2—Rb2—O4i	99.5 (2)	Rb2—W—Rb2xiii	122.13 (5)
O2vi—Rb2—O4i	153.0 (2)	Rb1—W—Rb2xiii	64.26 (2)
O2vii—Rb2—O4i	97.5 (2)	Rb1xii—W—Rb2xiii	171.73 (3)
O4viii—Rb2—O4i	98.91 (18)	O1ix—Se—O1	103.3 (3)
O4ix—Rb2—O4i	98.91 (18)	O1ix—Se—O1xi	103.3 (3)
O2—Rb2—O3	95.1 (2)	O1—Se—O1xi	103.3 (3)
O2vi—Rb2—O3	138.5 (3)	Se—O1—W	130.6 (5)
O2vii—Rb2—O3	137.5 (3)	Se—O1—Rb1	125.7 (4)
O4viii—Rb2—O3	111.8 (2)	W—O1—Rb1	103.7 (3)
O4ix—Rb2—O3	48.78 (18)	Wxiv—O2—Rb2	159.3 (5)
O4i—Rb2—O3	51.09 (19)	W—O3—Wix	148.3 (5)
O2—Rb2—O3vi	137.5 (3)	W—O3—Rb2	95.3 (3)
O2vi—Rb2—O3vi	95.1 (2)	Wix—O3—Rb2	101.9 (3)
O2vii—Rb2—O3vi	138.5 (2)	W—O3—Rb1xii	101.4 (3)
O4viii—Rb2—O3vi	48.78 (18)	Wix—O3—Rb1xii	107.3 (3)
O4ix—Rb2—O3vi	51.09 (19)	Rb2—O3—Rb1xii	81.68 (17)
O4i—Rb2—O3vi	111.8 (2)	Wii—O4—W	134.3 (4)
O3—Rb2—O3vi	83.8 (2)	Wii—O4—Rb2xiii	107.7 (3)
O2—Rb2—O3vii	138.5 (2)	W—O4—Rb2xiii	115.5 (3)
O2vi—Rb2—O3vii	137.5 (3)	Wii—O4—Rb1	99.3 (3)
O2vii—Rb2—O3vii	95.1 (2)	W—O4—Rb1	96.2 (3)
O4viii—Rb2—O3vii	51.09 (19)	Rb2xiii—O4—Rb1	88.54 (18)

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) Å3	Block, colourless
Z = 4	0.08 × 0.05 × 0.02 mm

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 on F2	24 restraints
Least-squares matrix: full	w = 1/[σ2(Fo2) + (0.0554P)2] where P = (Fo2 + 2Fc2)/3
R[F2 > 2σ(F2)] = 0.032	(Δ/σ)max < 0.001
wR(F2) = 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+0.001xFc2λ3/sin(2θ)]-1/4
165 parameters	Extinction coefficient: 0.00176 (12)

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

	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)

	U11	U22	U33	U12	U13	U23
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)

K1—O3i	2.726 (10)	K2—W1ii	3.993 (4)
K1—O5ii	2.757 (11)	W1—O2	1.724 (9)
K1—O1iii	2.899 (10)	W1—O7x	1.849 (11)
K1—O5iii	3.009 (11)	W1—O12	1.849 (10)
K1—O8	3.019 (9)	W1—O10xi	2.005 (10)
K1—O4iv	3.046 (11)	W1—O9x	2.013 (11)
K1—O3iii	3.050 (12)	W1—O1	2.166 (9)
K1—O6iv	3.091 (12)	W2—O4	1.731 (11)
K1—Seiii	3.427 (4)	W2—O8	1.863 (10)
K1—Seii	3.835 (4)	W2—O10xii	1.870 (10)
K1—Sei	3.839 (3)	W2—O7	1.975 (11)
K1—W2	3.975 (3)	W2—O11xii	2.016 (11)
K2—O2v	2.639 (9)	W2—O3i	2.167 (10)
K2—O6vi	2.780 (11)	W3—O6	1.726 (10)
K2—O4vi	2.809 (11)	W3—O11	1.822 (11)
K2—O10vii	2.861 (11)	W3—O9	1.825 (11)
K2—O8iv	2.879 (9)	W3—O12xiii	2.031 (10)
K2—O12i	2.918 (10)	W3—O8	2.032 (10)
K2—O9viii	3.213 (11)	W3—O5ii	2.153 (10)
K2—O7ix	3.316 (12)	Se—O1	1.695 (10)
K2—O11viii	3.408 (9)	Se—O5	1.735 (10)
K2—W2iv	3.767 (3)	Se—O3	1.739 (10)
K2—W1i	3.775 (4)
O3i—K1—O5ii	112.6 (3)	O12—W1—K2i	49.0 (3)
O3i—K1—O1iii	79.3 (3)	O10xi—W1—K2i	130.3 (3)
O5ii—K1—O1iii	78.0 (3)	O9x—W1—K2i	143.4 (3)
O3i—K1—O5iii	125.5 (3)	O1—W1—K2i	116.2 (3)
O5ii—K1—O5iii	81.0 (3)	O2—W1—K2ii	68.2 (4)
O1iii—K1—O5iii	51.1 (3)	O7x—W1—K2ii	137.1 (4)
O3i—K1—O8	57.2 (3)	O12—W1—K2ii	125.4 (3)
O5ii—K1—O8	56.1 (3)	O10xi—W1—K2ii	42.7 (3)
O1iii—K1—O8	76.8 (3)	O9x—W1—K2ii	53.0 (3)
O5iii—K1—O8	118.8 (3)	O1—W1—K2ii	105.6 (3)
O3i—K1—O4iv	108.8 (3)	K2i—W1—K2ii	137.13 (9)
O5ii—K1—O4iv	67.2 (3)	O2—W1—K2xiv	26.6 (3)
O1iii—K1—O4iv	144.7 (3)	O7x—W1—K2xiv	76.9 (3)
O5iii—K1—O4iv	124.4 (3)	O12—W1—K2xiv	119.5 (3)
O8—K1—O4iv	79.5 (3)	O10xi—W1—K2xiv	111.4 (3)
O3i—K1—O3iii	81.0 (3)	O9x—W1—K2xiv	74.1 (3)
O5ii—K1—O3iii	124.9 (3)	O1—W1—K2xiv	145.5 (3)
O1iii—K1—O3iii	51.3 (3)	K2i—W1—K2xiv	77.64 (8)
O5iii—K1—O3iii	52.3 (2)	K2ii—W1—K2xiv	73.29 (8)
O8—K1—O3iii	118.9 (3)	O4—W2—O8	98.3 (4)
O4iv—K1—O3iii	161.2 (3)	O4—W2—O10xii	99.8 (5)
O3i—K1—O6iv	66.2 (3)	O8—W2—O10xii	95.6 (4)
O5ii—K1—O6iv	109.6 (3)	O4—W2—O7	94.6 (5)
O1iii—K1—O6iv	145.0 (3)	O8—W2—O7	88.4 (4)
O5iii—K1—O6iv	160.9 (3)	O10xii—W2—O7	164.3 (5)
O8—K1—O6iv	79.9 (3)	O4—W2—O11xii	93.2 (4)
O4iv—K1—O6iv	51.6 (3)	O8—W2—O11xii	166.7 (4)
O3iii—K1—O6iv	124.0 (3)	O10xii—W2—O11xii	88.9 (4)
O3i—K1—Seiii	95.2 (2)	O7—W2—O11xii	84.0 (4)
O5ii—K1—Seiii	94.6 (2)	O4—W2—O3i	172.6 (4)
O1iii—K1—Seiii	29.60 (19)	O8—W2—O3i	86.2 (4)
O5iii—K1—Seiii	30.4 (2)	O10xii—W2—O3i	85.5 (4)
O8—K1—Seiii	106.4 (2)	O7—W2—O3i	79.6 (4)
O4iv—K1—Seiii	153.9 (2)	O11xii—W2—O3i	81.6 (4)
O3iii—K1—Seiii	30.43 (19)	O4—W2—K2xv	105.4 (4)
O6iv—K1—Seiii	153.6 (2)	O8—W2—K2xv	48.1 (3)
O3i—K1—Seii	130.7 (3)	O10xii—W2—K2xv	47.6 (3)
O5ii—K1—Seii	24.1 (2)	O7—W2—K2xv	133.7 (3)
O1iii—K1—Seii	97.7 (2)	O11xii—W2—K2xv	134.4 (3)
O5iii—K1—Seii	82.7 (2)	O3i—W2—K2xv	82.0 (3)
O8—K1—Seii	74.0 (2)	O4—W2—K1	142.1 (3)
O4iv—K1—Seii	50.4 (2)	O8—W2—K1	46.7 (3)
O3iii—K1—Seii	134.5 (2)	O10xii—W2—K1	98.2 (3)
O6iv—K1—Seii	100.5 (2)	O7—W2—K1	73.6 (3)
Seiii—K1—Seii	105.89 (9)	O11xii—W2—K1	120.3 (3)
O3i—K1—Sei	23.8 (2)	O3i—W2—K1	40.7 (3)
O5ii—K1—Sei	131.1 (2)	K2xv—W2—K1	64.86 (8)
O1iii—K1—Sei	98.5 (2)	O4—W2—K1xv	40.9 (4)
O5iii—K1—Sei	134.1 (2)	O8—W2—K1xv	76.3 (3)
O8—K1—Sei	75.4 (2)	O10xii—W2—K1xv	68.4 (3)
O4iv—K1—Sei	100.3 (2)	O7—W2—K1xv	127.3 (3)
O3iii—K1—Sei	82.19 (19)	O11xii—W2—K1xv	117.0 (3)
O6iv—K1—Sei	50.05 (19)	O3i—W2—K1xv	146.4 (3)
Seiii—K1—Sei	105.76 (9)	K2xv—W2—K1xv	64.97 (7)
Seii—K1—Sei	140.87 (10)	K1—W2—K1xv	120.66 (4)
O3i—K1—W2	31.2 (2)	O6—W3—O11	100.1 (4)
O5ii—K1—W2	81.4 (2)	O6—W3—O9	100.1 (5)
O1iii—K1—W2	71.7 (2)	O11—W3—O9	97.5 (5)
O5iii—K1—W2	122.4 (2)	O6—W3—O12xiii	91.8 (5)
O8—K1—W2	26.7 (2)	O11—W3—O12xiii	89.3 (4)
O4iv—K1—W2	97.2 (2)	O9—W3—O12xiii	165.0 (4)
O3iii—K1—W2	98.9 (2)	O6—W3—O8	91.8 (4)
O6iv—K1—W2	75.8 (2)	O11—W3—O8	165.4 (4)
Seiii—K1—W2	98.21 (8)	O9—W3—O8	88.6 (4)
Seii—K1—W2	100.71 (8)	O12xiii—W3—O8	81.8 (4)
Sei—K1—W2	52.29 (5)	O6—W3—O5ii	171.1 (4)
O2v—K2—O6vi	84.1 (3)	O11—W3—O5ii	86.1 (4)
O2v—K2—O4vi	82.2 (3)	O9—W3—O5ii	85.3 (4)
O6vi—K2—O4vi	57.1 (3)	O12xiii—W3—O5ii	81.8 (4)
O2v—K2—O10vii	129.3 (4)	O8—W3—O5ii	81.2 (4)
O6vi—K2—O10vii	81.2 (3)	O6—W3—K1	135.8 (3)
O4vi—K2—O10vii	126.1 (3)	O11—W3—K1	124.0 (3)
O2v—K2—O8iv	168.0 (3)	O9—W3—K1	73.4 (3)
O6vi—K2—O8iv	87.8 (3)	O12xiii—W3—K1	91.6 (3)
O4vi—K2—O8iv	85.9 (3)	O8—W3—K1	45.4 (2)
O10vii—K2—O8iv	57.6 (3)	O5ii—W3—K1	38.9 (3)
O2v—K2—O12i	124.7 (4)	O6—W3—K2xv	95.1 (4)
O6vi—K2—O12i	126.0 (3)	O11—W3—K2xv	129.0 (3)
O4vi—K2—O12i	80.6 (3)	O9—W3—K2xv	127.2 (3)
O10vii—K2—O12i	102.8 (3)	O12xiii—W3—K2xv	41.6 (3)
O8iv—K2—O12i	54.6 (3)	O8—W3—K2xv	40.4 (3)
O2v—K2—O9viii	88.4 (3)	O5ii—W3—K2xv	75.9 (3)
O6vi—K2—O9viii	106.9 (3)	K1—W3—K2xv	61.03 (7)
O4vi—K2—O9viii	162.1 (3)	O6—W3—K2viii	88.1 (4)
O10vii—K2—O9viii	51.2 (3)	O11—W3—K2viii	54.1 (3)
O8iv—K2—O9viii	102.5 (3)	O9—W3—K2viii	47.8 (3)
O12i—K2—O9viii	117.2 (3)	O12xiii—W3—K2viii	142.7 (3)
O2v—K2—O7ix	84.6 (3)	O8—W3—K2viii	135.5 (3)
O6vi—K2—O7ix	161.5 (3)	O5ii—W3—K2viii	100.7 (3)
O4vi—K2—O7ix	106.7 (3)	K1—W3—K2viii	113.79 (7)
O10vii—K2—O7ix	117.3 (3)	K2xv—W3—K2viii	174.68 (8)
O8iv—K2—O7ix	100.8 (3)	O1—Se—O5	96.1 (5)
O12i—K2—O7ix	51.9 (3)	O1—Se—O3	97.5 (5)
O9viii—K2—O7ix	87.4 (3)	O5—Se—O3	100.4 (4)
O2v—K2—O11viii	63.4 (3)	O1—Se—K1x	57.7 (3)
O6vi—K2—O11viii	137.0 (3)	O5—Se—K1x	61.4 (3)
O4vi—K2—O11viii	135.9 (3)	O3—Se—K1x	62.7 (4)
O10vii—K2—O11viii	97.6 (3)	O1—Se—K1ii	71.1 (3)
O8iv—K2—O11viii	127.9 (3)	O5—Se—K1ii	40.5 (3)
O12i—K2—O11viii	96.4 (3)	O3—Se—K1ii	133.7 (4)
O9viii—K2—O11viii	48.8 (3)	K1x—Se—K1ii	74.10 (9)
O7ix—K2—O11viii	46.8 (3)	O1—Se—K1i	72.8 (3)
O2v—K2—W2iv	156.5 (3)	O5—Se—K1i	132.1 (4)
O6vi—K2—W2iv	82.8 (2)	O3—Se—K1i	39.3 (3)
O4vi—K2—W2iv	106.6 (2)	K1x—Se—K1i	74.24 (9)
O10vii—K2—W2iv	28.8 (2)	K1ii—Se—K1i	140.87 (10)
O8iv—K2—W2iv	28.8 (2)	Se—O1—W1	141.0 (6)
O12i—K2—W2iv	78.7 (2)	Se—O1—K1x	92.7 (4)
O9viii—K2—W2iv	76.9 (2)	W1—O1—K1x	125.8 (4)
O7ix—K2—W2iv	112.5 (2)	W1—O2—K2xiv	136.4 (5)
O11viii—K2—W2iv	115.99 (18)	Se—O3—W2i	123.4 (5)
O2v—K2—W1i	97.2 (3)	Se—O3—K1i	116.9 (5)
O6vi—K2—W1i	139.0 (2)	W2i—O3—K1i	108.1 (4)
O4vi—K2—W1i	82.3 (2)	Se—O3—K1x	86.8 (4)
O10vii—K2—W1i	124.7 (2)	W2i—O3—K1x	118.7 (4)
O8iv—K2—W1i	83.2 (2)	K1i—O3—K1x	99.0 (3)
O12i—K2—W1i	28.6 (2)	W2—O4—K2xvi	139.1 (5)
O9viii—K2—W1i	114.1 (2)	W2—O4—K1xv	117.3 (5)
O7ix—K2—W1i	29.32 (19)	K2xvi—O4—K1xv	90.3 (3)
O11viii—K2—W1i	76.0 (2)	Se—O5—W3ii	124.5 (5)
W2iv—K2—W1i	105.51 (8)	Se—O5—K1ii	115.3 (5)
O2v—K2—W1ii	101.5 (3)	W3ii—O5—K1ii	111.7 (4)
O6vi—K2—W1ii	81.5 (2)	Se—O5—K1x	88.2 (4)
O4vi—K2—W1ii	138.0 (2)	W3ii—O5—K1x	112.0 (4)
O10vii—K2—W1ii	28.4 (2)	K1ii—O5—K1x	99.0 (3)
O8iv—K2—W1ii	85.9 (2)	W3—O6—K2xvi	134.9 (6)
O12i—K2—W1ii	125.5 (2)	W3—O6—K1xv	125.9 (5)
O9viii—K2—W1ii	30.0 (2)	K2xvi—O6—K1xv	90.0 (3)
O7ix—K2—W1ii	115.2 (2)	W1iii—O7—W2	146.6 (6)
O11viii—K2—W1ii	78.6 (2)	W1iii—O7—K2ix	89.2 (4)
W2iv—K2—W1ii	57.20 (5)	W2—O7—K2ix	113.7 (4)
W1i—K2—W1ii	137.13 (9)	W2—O8—W3	131.3 (5)
O2—W1—O7x	96.6 (5)	W2—O8—K2xv	103.1 (4)
O2—W1—O12	100.1 (5)	W3—O8—K2xv	112.3 (4)
O7x—W1—O12	96.1 (4)	W2—O8—K1	106.6 (4)
O2—W1—O10xi	95.0 (5)	W3—O8—K1	106.0 (3)
O7x—W1—O10xi	166.0 (5)	K2xv—O8—K1	89.6 (3)
O12—W1—O10xi	89.5 (4)	W3—O9—W1iii	145.8 (6)
O2—W1—O9x	91.8 (5)	W3—O9—K2viii	107.3 (4)
O7x—W1—O9x	89.5 (4)	W1iii—O9—K2viii	96.9 (4)
O12—W1—O9x	166.1 (4)	W2xvii—O10—W1xiii	147.4 (6)
O10xi—W1—O9x	82.3 (4)	W2xvii—O10—K2xviii	103.6 (4)
O2—W1—O1	169.9 (4)	W1xiii—O10—K2xviii	109.0 (4)
O7x—W1—O1	82.7 (4)	W3—O11—W2xvii	149.4 (5)
O12—W1—O1	89.9 (4)	W3—O11—K2viii	100.2 (4)
O10xi—W1—O1	84.4 (4)	W2xvii—O11—K2viii	109.0 (4)
O9x—W1—O1	78.2 (4)	W1—O12—W3xi	146.7 (5)
O2—W1—K2i	71.7 (4)	W1—O12—K2i	102.4 (4)
O7x—W1—K2i	61.4 (3)	W3xi—O12—K2i	110.9 (4)