Dipotassium tetra­chromate(VI), K₂Cr₄O₁₃

The structure of dipotassium tetra­chromium(VI) trideca­oxide, K₂Cr₄O₁₃, has been determined from single-crystal X-ray data collected at 173 (2) K on a racemically twinned crystal with monoclinic Pc space-group symmetry. The structure is composed of discrete [Cr₄O₁₃]^2- zigzag chains held together by the charge-balancing potassium ions. The conformations adopted by the tetra­chromate anion in alkali metal salts and Cr₈O₂₁ are different and can be divided into three categories.

S1. Comment

CrO₃ derivatives are a field of current interest for surface finishing which proceeds in systems containing CrO₃ dissolved in water. The structure of the predominant species in chromium electroplating baths has been investigated extensively (Radnai & Dorgai, 1992; Šarmaitis et al., 1996; Çengeloglu et al., 2003). These compounds are also continuing to attract interest (Carlsen et al., 1995; Islam et al., 2005; Karunakaran & Suresh, 2004) as they represent the most widely used group of oxidizing agents in organic chemistry, able to oxidize almost every organic functional group (Cainelli & Cardillo, 1984). Chromic acid is a common reagent but the active species in the oxidizing solutions may vary depending on the reaction conditions. The polymerization of the CrO₄²⁻ units into corner-sharing dimers, trimers or longer chains is pH and concentration dependent (Šarmaitis et al., 1996). The deformation of the CrO₄ tetrahedra increases with the length of the chains (Gili & Lorenzo-Louis, 1999). Pressprich et al. (1988) studied and compared the Cr—O bond lengths within anions of the formula [Cr_nO_{(3n + 1)}]²⁻. They found that, with increasing polymerization, the average bridging bond length increases, while the average non-bridging bond length decreases. The structure of CrO₃ (Hanic & Štempelová, 1960; Stephens & Cruickshank, 1970) consists of infinite chains of corner-sharing CrO₄ tetrahedra with the bridging Cr—O distances 0.15 Å longer than the mean terminal distance, resulting in deformed CrO₄ units. The structures of trichromate compounds consist of [Cr₃O₁₀]²⁻ anions, together with inorganic cations (Mattes & Meschede, 1973; Kolitsch, 2003; Blum et al., 1979; Blum & Guitel, 1980; Löfgren, 1974) or organic cations (Ding et al., 2004; Stepien & Grabowski, 1977; Garrison et al., 2001; Luis et al., 1995; Fossé et al., 2001). In these structures, the [Cr₃O₁₀]²⁻ units adopt different conformations as a result of the diversity in packing (Casari & Langer, 2005).

Four compounds containing the tetrachromate unit have been structurally characterized before now, including three alkali metal salts and one mixed valence binary oxide. The chemical analogues K₂Cr₄O₁₃ (Golovachev et al., 1970; Kuz'min et al., 1972), Rb₂Cr₄O₁₃ (Löfgren, 1971, 1973) and Cs₂Cr₄O₁₃ (Kolitsch, 2004) all belong to the monoclinic system, with space groups Pc, P2₁/c and P2₁/n, respectively. Blum & Tran Qui (1979) reported indexed powder diffraction data on (NH₄)₂Cr₄O₁₃ and assigned the space group to be P2₁/c, as determined for Rb₂Cr₄O₁₃ (Löfgren, 1973) and unpublished work on K₂Cr₄O₁₃ by Löfgren. Doubts about both the space-group assignment and the unit-cell parameters of the K₂Cr₄O₁₃ structure were expressed by Kolitsch (2004). Furthermore, neither s.u. values nor anisotropic displacement parameters are given in the papers (Golovachev et al., 1970; Kuz'min et al., 1972), and an R value of 0.108 was reported, based on film data. We present here a redetermination of the structure of K₂Cr₄O₁₃.

The K₂Cr₄O₁₃ structure belongs to the non-centrosymmetric space group Pc, while the other three chemical analogues belong to space group P2₁/c with unit cells doubled in the a direction (Löfgren, 1973; Kolitsch, 2004; Blum & Tran Qui, 1979). The reciprocal space was searched carefully for weak extra reflections, especially for h = (2n − 1)/2, but without success. The crystal under investigation was twinned by an inversion operation and the twin volume ratio was refined to 0.64 (3)/0.36 (3).

There are one discrete chromate tetramer and two non equivalent potassium ions in the asymmetric unit of K₂Cr₄O₁₃ (Fig. 1). The tetrachromate ion, [Cr₄O₁₃]²⁻, is composed of a chain of four CrO₄ tetrahedra, joined by shared corners. The Cr—O bridging distances, can be divided into two groups (Table 1). The two terminal CrO₄ units have longer Cr—O bridging distances [mean 1.834 (4) Å] than the two inner units [mean 1.74 (4) Å]. The non-bridging Cr—O bonding distances are significantly shorter [mean 1.605 (6) Å] (Fig. 1 and Table 1). Despite the variation of bond lengths, the mean Cr—O distance within the individual tetrahedra remains constant [1.66 (5) Å]. The [Cr₄O₁₃]²⁻ anions form isolated zigzag chains in the c direction, whose charge is counterbalanced by the intercalating potassium ions (Fig. 2).

The two cations, K1 and K2, are irregularly coordinated (within 3.28 Å) by 11 and ten O atoms, respectively (Table 1), but have similar mean K—O bond lengths [2.96 (3) Å]. The O atoms neighbouring each potassium ion belong to six different tetrachromate chains. The relatively high potassium coordination, compared with the ninefold coordination in K₂Cr₃O₁₀ (Blum et al., 1979), may be attributed to the high oxygen/potassium ratio (Löfgren, 1973) or to the packing features, as in the case of the 11-coordinate ammonium ions in α-(NH₄)₂Cr₃O₁₀ (Casari & Langer, 2005).

Comparing the structural arrangement in the tetrachromate analogues, it is evident that Cs₂Cr₄O₁₃ (Fig. 3a) differs from Rb₂Cr₄O₁₃ and K₂Cr₄O₁₃ (Fig. 3b and 3c). The latter are quite similar but contain different cation–cation distances for the Rb1—Rb1, Rb2—Rb2, K1—K1 and K2—K2 pairs (Fig. 3b and 3c). These distances vary by 0.111 (3) Å in Rb₂Cr₄O₁₃ and 0.038 (4) Å in K₂Cr₄O₁₃. Furthermore, every other tetrachromate group is rotated in Rb₂Cr₄O₁₃ compared with K₂Cr₄O₁₃, but the shapes of the tetrachromate chains are almost the same (Fig. 4a). In Cs₂Cr₄O₁₃, the packing of the [Cr₄O₁₃]²⁻ anions and cations different, as is the shape of the chromate chain (Fig. 4b). Structural data have so far been determined for only one other compound containing the [Cr₄O₁₃]²⁻ unit, i.e. the mixed valence Cr₈O₂₁ oxide, which is better described as Cr^III₂(Cr^VIO₄)₂(Cr^VI₄O₁₃) (Norby et al., 1991). In this compound, the tetrachromate chain adopts a third conformation (Fig. 4c), resembling a section of the one-dimensional chains in CrO₃ (Hanic & Štempelová, 1960), except for the Cr—O—Cr angle of 180.0 (7)°.

Values of the Cr1—Cr2—Cr3—Cr4 torsion angles, and the Cr1—Cr2—Cr3 and Cr2—Cr3—Cr4 angles in tetrachromate structures, are presented in Table 2. In the nearly planar tetrachromate units, the Cr1—Cr2—Cr3 and Cr2—Cr3—Cr4 angles seem to occur in pairs of a small and a large angle. A combination of two extreme values [86.48 (2) and 127.29 (2)°] is encountered in the Cs₂Cr₄O₁₃ structure (Kolitsch, 2004). The Cr1—Cr2—Cr3 angles have also been examined in trichromates (Casari & Langer, 2005) which interestingly showed a range of angles between 86.85 (2) and 127.73 (4)°.

In summary, the structure of K₂Cr₃O₁₃ has been redetermined from a racemic twinned crystal and it has been shown that, even if the structure shows similarities with Rb₂Cr₃O₁₃ (Löfgren, 1973), the compounds are different enough to lead to a different unit cell and space group.

S2. Experimental

Crystals of K₂Cr₄O₁₃ were formed during an attempt to prepare Ce(CrO₄)₂·H₂O and/or Ce(CrO₄)₂·2H₂O. Ce(SO₄)₂·4H₂O (1.50 g, 3.75 mmol) was dissolved in water (10 ml) and Ce(OH)₄ was precipitated with 15 M ammonia. Ce(OH)₄ (0.12 g 0.76 mmol) was added to a saturated solution of KCrO₄ (1.5 ml), and then concentrated sulfuric acid was added until the cerium hydroxide was completely dissolved. This particular sample was left covered and unguarded and, after nine months, dark orange–red crystals of K₂Cr₄O₁₃, suitable for single-crystal X-analysis, were obtained.

Computing details

Data collection: SMART (Siemens, 1995); cell refinement: SAINT (Siemens, 1995); data reduction: SAINT and SADABS (Sheldrick, 2002); program(s) used to solve structure: SHELXTL (Bruker, 2001); program(s) used to refine structure: SHELXTL; molecular graphics: DIAMOND (Brandenburg, 2000); software used to prepare material for publication: SHELXTL.

Figures

	Fig. 1. The asymmetric unit of K2Cr4O13, with atomic displacement ellipsoids drawn at the 50% probability level.
	Fig. 2. The packing in K2Cr4O13.
	Fig. 3. A comparison of the packing in (a) Cs2Cr4O13 (Kolitsch, 2004), (b) Rb2Cr4O13 (Löfgren, 1973) and (c) K2Cr4O13 (this work). The numbers 1 and 2 denote M1–M1 and M2–M2 cation pairs in (b) and (c).
	Fig. 4. The configuration of [Cr4O13]^2− chains in (a) K2Cr4O13 (this paper), (b) Cs2Cr4O13 (Kolitsch, 2004) and (c) Cr8O21 (Norby et al., 1991).

dipotassium tetrachromium(VI) tridecaoxide

Crystal data

K2Cr4O13	F(000) = 476
Mr = 494.20	Dx = 2.750 Mg m^−3
Monoclinic, Pc	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P -2yc	Cell parameters from 3954 reflections
a = 8.6165 (2) Å	θ = 2.4–33.0°
b = 7.4725 (1) Å	µ = 4.30 mm^−1
c = 9.2811 (3) Å	T = 173 K
β = 92.746 (2)°	Rhombic, orange–red
V = 596.89 (3) Å^3	0.06 × 0.06 × 0.04 mm
Z = 2

Data collection

Siemens SMART 1K CCD area-detector diffractometer	4076 independent reflections
Radiation source: fine-focus sealed tube	3268 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.045
ω scans	θmax = 33.0°, θmin = 2.4°
Absorption correction: multi-scan (SADABS; Sheldrick, 2002)	h = −13→13
Tmin = 0.782, Tmax = 0.847	k = −11→10
7800 measured reflections	l = −14→13

Refinement

Refinement on F^2	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.048	w = 1/[σ^2(Fo^2) + (0.0471P)^2 + 0.0614P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.105	(Δ/σ)max < 0.001
S = 1.01	Δρmax = 0.69 e Å^−3
4076 reflections	Δρmin = −0.84 e Å^−3
173 parameters	Absolute structure: Flack (1983), 1935 Friedel pairs
2 restraints	Absolute structure parameter: 0.64 (3)

Special details

Experimental. Data were collected at low temperature using a Siemens SMART CCD diffractometer equiped with a LT-2 device. A full sphere of reciprocal space was scanned by 0.3° steps in ω with a crystal–to–detector distance of 3.97 cm, xx s per frame. Preliminary orientation matrix was obtained from the first 100 frames using SMART (Siemens, 1995). The collected frames were integrated using the preliminary orientation matrix which was updated every 100 frames. Final cell parameters were obtained by refinement on the position of 3954 reflections with I>10σ(I) after integration of all the frames data using SAINT (Siemens, 1995).

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

Refinement. Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > σ(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	Uiso*/Ueq
K1	−0.18218 (15)	0.40208 (18)	0.24453 (13)	0.0189 (3)
K2	0.53715 (15)	−0.10604 (18)	0.10280 (13)	0.0186 (3)
Cr1	0.51828 (9)	0.43180 (11)	−0.03277 (9)	0.01284 (18)
Cr2	0.17134 (10)	0.44328 (11)	0.01327 (9)	0.01418 (17)
Cr3	0.18289 (10)	0.10769 (11)	0.24480 (9)	0.01196 (16)
Cr4	−0.14713 (9)	−0.07133 (12)	0.36963 (9)	0.01249 (17)
O11	0.5276 (5)	0.2597 (6)	0.0691 (5)	0.0269 (10)
O12	0.3431 (5)	0.5592 (5)	0.0063 (5)	0.0161 (8)
O13	0.6639 (5)	0.5616 (5)	0.0006 (5)	0.0189 (8)
O14	0.5104 (5)	0.3757 (7)	−0.1998 (5)	0.0293 (11)
O21	0.0276 (5)	0.5770 (6)	−0.0043 (5)	0.0266 (11)
O22	0.1642 (5)	0.3017 (6)	−0.1148 (5)	0.0263 (10)
O23	0.1608 (5)	0.3304 (6)	0.1782 (4)	0.0193 (9)
O31	0.3379 (5)	0.0952 (6)	0.3427 (5)	0.0222 (9)
O32	0.1982 (5)	−0.0274 (6)	0.1164 (4)	0.0232 (9)
O41	−0.1339 (5)	−0.1544 (6)	0.5295 (5)	0.0266 (10)
O42	−0.1635 (5)	−0.2270 (6)	0.2508 (5)	0.0256 (10)
O43	0.0251 (5)	0.0658 (5)	0.3416 (4)	0.0166 (8)
O44	−0.2953 (5)	0.0606 (5)	0.3511 (5)	0.0210 (9)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
K1	0.0229 (6)	0.0181 (6)	0.0159 (5)	0.0021 (5)	0.0015 (5)	−0.0022 (5)
K2	0.0227 (6)	0.0148 (6)	0.0183 (6)	0.0022 (5)	0.0001 (5)	0.0017 (5)
Cr1	0.0129 (4)	0.0114 (4)	0.0144 (4)	0.0006 (3)	0.0024 (3)	−0.0001 (3)
Cr2	0.0130 (4)	0.0153 (4)	0.0143 (4)	−0.0010 (3)	0.0012 (3)	0.0037 (3)
Cr3	0.0119 (4)	0.0135 (4)	0.0106 (3)	−0.0003 (3)	0.0013 (3)	0.0013 (3)
Cr4	0.0121 (4)	0.0111 (4)	0.0143 (4)	−0.0017 (3)	0.0011 (3)	0.0024 (3)
O11	0.025 (2)	0.016 (2)	0.040 (3)	0.0013 (18)	0.0086 (19)	0.0105 (19)
O12	0.0168 (18)	0.0135 (18)	0.018 (2)	0.0023 (15)	0.0012 (15)	−0.0001 (15)
O13	0.0153 (19)	0.0191 (19)	0.022 (2)	−0.0029 (16)	0.0013 (16)	−0.0012 (18)
O14	0.026 (2)	0.040 (3)	0.022 (2)	0.002 (2)	0.0025 (18)	−0.017 (2)
O21	0.016 (2)	0.032 (3)	0.032 (3)	0.0062 (19)	0.0048 (19)	0.011 (2)
O22	0.029 (2)	0.030 (3)	0.020 (2)	−0.0108 (19)	0.0014 (17)	−0.0029 (18)
O23	0.024 (2)	0.019 (2)	0.0153 (19)	−0.0030 (17)	0.0029 (16)	0.0013 (15)
O31	0.016 (2)	0.028 (2)	0.022 (2)	−0.0033 (17)	−0.0032 (16)	0.0035 (17)
O32	0.031 (2)	0.023 (2)	0.0165 (19)	0.0010 (18)	0.0025 (17)	0.0001 (17)
O41	0.018 (2)	0.036 (3)	0.025 (2)	−0.0046 (19)	0.0005 (18)	0.014 (2)
O42	0.024 (2)	0.020 (2)	0.033 (2)	−0.0045 (17)	−0.0002 (18)	−0.010 (2)
O43	0.020 (2)	0.014 (2)	0.0163 (19)	−0.0044 (15)	0.0057 (16)	0.0000 (14)
O44	0.0159 (19)	0.021 (2)	0.027 (2)	0.0039 (16)	0.0046 (17)	0.0000 (17)

Geometric parameters (Å, º)

Cr1—O11	1.596 (4)	K2—O14^vii	2.740 (5)
Cr1—O12	1.835 (4)	K2—O31^iv	2.896 (4)
Cr1—O13	1.605 (4)	K2—O31	3.246 (5)
Cr1—O14	1.604 (5)	K2—O32	2.988 (4)
Cr2—O12	1.719 (4)	K2—O42^viii	3.003 (5)
Cr2—O21	1.594 (4)	K2—O44^ix	2.825 (4)
Cr2—O22	1.590 (5)	K2—O44^viii	2.937 (5)
Cr2—O23	1.753 (4)	K1—Cr1^i	3.5635 (15)
Cr3—O23	1.783 (4)	K2—Cr4^viii	3.5993 (15)
Cr3—O31	1.582 (4)	K2—Cr1^vi	3.6765 (15)
Cr3—O32	1.572 (4)	Cr1—K1^viii	3.5634 (15)
Cr3—O43	1.694 (4)	Cr1—K1^x	3.6036 (15)
Cr4—O41	1.607 (5)	Cr1—K2^v	3.6766 (15)
Cr4—O42	1.604 (4)	Cr4—K2^i	3.5994 (15)
Cr4—O43	1.833 (4)	Cr4—K2^xi	3.7954 (15)
Cr4—O44	1.615 (4)	O11—K1^viii	3.106 (5)
K1—O11^i	3.106 (5)	O12—K2^v	3.116 (4)
K1—O13^ii	2.790 (5)	O13—K1^x	2.790 (5)
K1—O13^i	2.831 (5)	O13—K1^viii	2.831 (5)
K1—O14^ii	3.189 (5)	O13—K2^v	2.892 (4)
K1—O21^iii	2.884 (5)	O14—K2^iv	2.740 (5)
K1—O21	3.273 (5)	O14—K1^x	3.189 (5)
K1—O23	3.094 (4)	O21—K1^xii	2.885 (5)
K1—O41^iv	2.768 (5)	O31—K2^vii	2.896 (4)
K1—O42^v	2.777 (5)	O41—K1^vii	2.768 (5)
K1—O43	3.188 (4)	O42—K1^vi	2.777 (5)
K1—O44	2.921 (4)	O42—K2^i	3.003 (5)
K2—O11	2.751 (5)	O44—K2^xi	2.825 (4)
K2—O12^vi	3.116 (4)	O44—K2^i	2.937 (5)
K2—O13^vi	2.892 (4)
O41^iv—K1—O42^v	132.22 (14)	O12^vi—K2—Cr4^viii	129.27 (9)
O41^iv—K1—O13^ii	140.66 (14)	O31—K2—Cr4^viii	84.37 (8)
O42^v—K1—O13^ii	85.09 (13)	O14^vii—K2—Cr1^vi	62.25 (12)
O41^iv—K1—O13^i	77.63 (13)	O11—K2—Cr1^vi	153.31 (12)
O42^v—K1—O13^i	67.74 (13)	O44^ix—K2—Cr1^vi	81.14 (9)
O13^ii—K1—O13^i	114.63 (15)	O13^vi—K2—Cr1^vi	24.78 (9)
O41^iv—K1—O21^iii	120.59 (14)	O31^iv—K2—Cr1^vi	74.11 (9)
O42^v—K1—O21^iii	83.99 (13)	O44^viii—K2—Cr1^vi	132.74 (9)
O13^ii—K1—O21^iii	67.13 (12)	O32—K2—Cr1^vi	99.90 (9)
O13^i—K1—O21^iii	150.99 (13)	O42^viii—K2—Cr1^vi	84.07 (9)
O41^iv—K1—O44	73.99 (13)	O12^vi—K2—Cr1^vi	29.92 (8)
O42^v—K1—O44	152.23 (13)	O31—K2—Cr1^vi	130.83 (8)
O13^ii—K1—O44	67.46 (11)	Cr4^viii—K2—Cr1^vi	108.83 (4)
O13^i—K1—O44	119.17 (14)	O11—Cr1—O14	111.1 (3)
O21^iii—K1—O44	88.86 (13)	O11—Cr1—O13	110.9 (2)
O41^iv—K1—O23	64.07 (12)	O14—Cr1—O13	109.9 (3)
O42^v—K1—O23	97.00 (13)	O11—Cr1—O12	108.6 (2)
O13^ii—K1—O23	133.15 (13)	O14—Cr1—O12	109.2 (2)
O13^i—K1—O23	109.20 (12)	O13—Cr1—O12	106.9 (2)
O21^iii—K1—O23	66.59 (12)	O11—Cr1—K1^viii	60.52 (18)
O44—K1—O23	104.69 (12)	O14—Cr1—K1^viii	132.64 (18)
O41^iv—K1—O11^i	62.48 (13)	O13—Cr1—K1^viii	50.61 (16)
O42^v—K1—O11^i	113.42 (13)	O12—Cr1—K1^viii	117.63 (14)
O13^ii—K1—O11^i	94.38 (13)	O11—Cr1—K1^x	126.88 (16)
O13^i—K1—O11^i	52.45 (12)	O14—Cr1—K1^x	62.23 (18)
O21^iii—K1—O11^i	154.13 (13)	O13—Cr1—K1^x	47.73 (17)
O44—K1—O11^i	66.73 (12)	O12—Cr1—K1^x	123.57 (13)
O23—K1—O11^i	126.08 (12)	K1^viii—Cr1—K1^x	85.52 (3)
O41^iv—K1—O43	64.86 (12)	O11—Cr1—K2^v	123.66 (19)
O42^v—K1—O43	138.56 (13)	O14—Cr1—K2^v	125.1 (2)
O13^ii—K1—O43	96.82 (11)	O13—Cr1—K2^v	49.07 (15)
O13^i—K1—O43	142.41 (11)	O12—Cr1—K2^v	57.89 (13)
O21^iii—K1—O43	59.56 (12)	K1^viii—Cr1—K2^v	78.04 (3)
O44—K1—O43	53.65 (11)	K1^x—Cr1—K2^v	81.46 (3)
O23—K1—O43	52.58 (10)	O22—Cr2—O21	109.8 (3)
O11^i—K1—O43	107.72 (11)	O22—Cr2—O12	108.0 (2)
O41^iv—K1—O14^ii	128.29 (14)	O21—Cr2—O12	110.3 (2)
O42^v—K1—O14^ii	61.63 (13)	O22—Cr2—O23	109.3 (2)
O13^ii—K1—O14^ii	51.61 (12)	O21—Cr2—O23	108.6 (2)
O13^i—K1—O14^ii	63.23 (12)	O12—Cr2—O23	110.8 (2)
O21^iii—K1—O14^ii	109.51 (13)	O22—Cr2—K1	111.27 (16)
O44—K1—O14^ii	96.13 (12)	O21—Cr2—K1	58.10 (16)
O23—K1—O14^ii	158.58 (13)	O12—Cr2—K1	140.60 (14)
O11^i—K1—O14^ii	67.00 (13)	O23—Cr2—K1	52.79 (14)
O43—K1—O14^ii	145.40 (11)	O32—Cr3—O31	107.4 (2)
O41^iv—K1—O21	69.57 (13)	O32—Cr3—O43	112.5 (2)
O42^v—K1—O21	65.34 (12)	O31—Cr3—O43	111.2 (2)
O13^ii—K1—O21	149.72 (12)	O32—Cr3—O23	110.4 (2)
O13^i—K1—O21	61.37 (11)	O31—Cr3—O23	109.1 (2)
O21^iii—K1—O21	101.70 (14)	O43—Cr3—O23	106.35 (19)
O44—K1—O21	142.41 (12)	O32—Cr3—K2	50.15 (16)
O23—K1—O21	50.47 (11)	O31—Cr3—K2	59.77 (16)
O11^i—K1—O21	102.99 (13)	O43—Cr3—K2	142.85 (14)
O43—K1—O21	101.15 (11)	O23—Cr3—K2	110.59 (13)
O14^ii—K1—O21	113.42 (11)	O32—Cr3—K1	117.78 (16)
O41^iv—K1—Cr1^i	69.49 (10)	O31—Cr3—K1	134.70 (17)
O42^v—K1—Cr1^i	89.56 (10)	O43—Cr3—K1	55.10 (14)
O13^ii—K1—Cr1^i	104.59 (10)	O23—Cr3—K1	52.47 (13)
O13^i—K1—Cr1^i	25.98 (8)	K2—Cr3—K1	157.98 (4)
O21^iii—K1—Cr1^i	169.85 (10)	O42—Cr4—O41	110.7 (3)
O44—K1—Cr1^i	93.28 (10)	O42—Cr4—O44	109.1 (2)
O23—K1—Cr1^i	122.18 (8)	O41—Cr4—O44	110.8 (2)
O11^i—K1—Cr1^i	26.57 (8)	O42—Cr4—O43	110.7 (2)
O43—K1—Cr1^i	129.05 (8)	O41—Cr4—O43	109.0 (2)
O14^ii—K1—Cr1^i	60.40 (9)	O44—Cr4—O43	106.56 (19)
O21—K1—Cr1^i	82.57 (9)	O42—Cr4—K2^i	55.70 (17)
O14^vii—K2—O11	143.45 (16)	O41—Cr4—K2^i	128.69 (16)
O14^vii—K2—O44^ix	134.75 (14)	O44—Cr4—K2^i	53.37 (16)
O11—K2—O44^ix	78.47 (13)	O43—Cr4—K2^i	122.23 (13)
O14^vii—K2—O13^vi	68.47 (14)	O42—Cr4—K1	118.07 (18)
O11—K2—O13^vi	145.64 (14)	O41—Cr4—K1	130.89 (18)
O44^ix—K2—O13^vi	67.42 (12)	O44—Cr4—K1	48.45 (15)
O14^vii—K2—O31^iv	120.81 (14)	O43—Cr4—K1	58.64 (13)
O11—K2—O31^iv	82.19 (14)	K2^i—Cr4—K1	78.87 (3)
O44^ix—K2—O31^iv	67.26 (13)	O42—Cr4—K2^xi	127.11 (16)
O13^vi—K2—O31^iv	88.21 (12)	O41—Cr4—K2^xi	68.27 (17)
O14^vii—K2—O44^viii	80.86 (14)	O44—Cr4—K2^xi	42.54 (16)
O11—K2—O44^viii	71.29 (13)	O43—Cr4—K2^xi	119.55 (13)
O44^ix—K2—O44^viii	110.27 (13)	K2^i—Cr4—K2^xi	83.03 (3)
O13^vi—K2—O44^viii	116.25 (13)	K1—Cr4—K2^xi	78.28 (3)
O31^iv—K2—O44^viii	153.11 (12)	Cr1—O11—K2	150.3 (3)
O14^vii—K2—O32	90.15 (13)	Cr1—O11—K1^viii	92.91 (19)
O11—K2—O32	77.61 (13)	K2—O11—K1^viii	105.17 (15)
O44^ix—K2—O32	123.41 (13)	Cr2—O12—Cr1	117.6 (2)
O13^vi—K2—O32	124.63 (13)	Cr2—O12—K2^v	147.6 (2)
O31^iv—K2—O32	59.20 (12)	Cr1—O12—K2^v	92.19 (17)
O44^viii—K2—O32	109.16 (12)	Cr1—O13—K1^x	107.1 (2)
O14^vii—K2—O42^viii	64.58 (13)	Cr1—O13—K1^viii	103.41 (18)
O11—K2—O42^viii	111.80 (14)	K1^x—O13—K1^viii	119.91 (17)
O44^ix—K2—O42^viii	87.29 (13)	Cr1—O13—K2^v	106.2 (2)
O13^vi—K2—O42^viii	64.01 (13)	K1^x—O13—K2^v	113.47 (14)
O31^iv—K2—O42^viii	148.41 (13)	K1^viii—O13—K2^v	105.61 (15)
O44^viii—K2—O42^viii	52.37 (12)	Cr1—O14—K2^iv	146.8 (3)
O32—K2—O42^viii	149.29 (13)	Cr1—O14—K1^x	91.3 (2)
O14^vii—K2—O12^vi	62.66 (14)	K2^iv—O14—K1^x	100.22 (14)
O11—K2—O12^vi	138.75 (14)	Cr2—O21—K1^xii	124.8 (2)
O44^ix—K2—O12^vi	98.47 (12)	Cr2—O21—K1	97.48 (18)
O13^vi—K2—O12^vi	54.70 (12)	K1^xii—O21—K1	104.25 (15)
O31^iv—K2—O12^vi	59.62 (12)	Cr2—O23—Cr3	138.0 (2)
O44^viii—K2—O12^vi	143.38 (12)	Cr2—O23—K1	100.39 (17)
O32—K2—O12^vi	70.00 (12)	Cr3—O23—K1	100.34 (16)
O42^viii—K2—O12^vi	109.09 (12)	Cr3—O31—K2^vii	158.1 (2)
O14^vii—K2—O31	79.51 (13)	Cr3—O31—K2	95.33 (19)
O11—K2—O31	66.67 (12)	K2^vii—O31—K2	105.83 (13)
O44^ix—K2—O31	145.06 (12)	Cr3—O32—K2	106.0 (2)
O13^vi—K2—O31	147.53 (12)	Cr4—O41—K1^vii	156.5 (3)
O31^iv—K2—O31	104.29 (12)	Cr4—O42—K1^vi	137.8 (3)
O44^viii—K2—O31	61.42 (11)	Cr4—O42—K2^i	98.1 (2)
O32—K2—O31	47.89 (11)	K1^vi—O42—K2^i	104.07 (14)
O42^viii—K2—O31	107.26 (12)	Cr3—O43—Cr4	148.7 (2)
O12^vi—K2—O31	105.96 (11)	Cr3—O43—K1	99.06 (16)
O14^vii—K2—Cr4^viii	71.22 (11)	Cr4—O43—K1	91.96 (15)
O11—K2—Cr4^viii	91.39 (11)	Cr4—O44—K2^xi	114.7 (2)
O44^ix—K2—Cr4^viii	99.26 (10)	Cr4—O44—K1	107.11 (19)
O13^vi—K2—Cr4^viii	90.15 (10)	K2^xi—O44—K1	111.53 (14)
O31^iv—K2—Cr4^viii	165.94 (10)	Cr4—O44—K2^i	100.44 (18)
O44^viii—K2—Cr4^viii	26.19 (8)	K2^xi—O44—K2^i	116.64 (15)
O32—K2—Cr4^viii	131.67 (9)	K1—O44—K2^i	105.31 (14)
O42^viii—K2—Cr4^viii	26.19 (8)

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