A polymorph of K₄Ge₄Se₁₀

A new monoclinic polymorph, β-K₄Ge₄Se₁₀ (tetra­potassium deca­selenidotetra­germanate), that crystallizes in space group P2₁/c has been isolated. The structure contains isolated super-tetra­hedral adamantane [Ge₄Se₁₀]⁴⁻ clusters identical to those in the known K₄Ge₄Se₁₀ polymorph (P2₁/m), held together in in the crystal structure by ionic inter­action with the K⁺ ions. The adamantane unit, [Ge₄Se₁₀]⁴⁻, is formed by corner-sharing of four GeSe₄ tetra­hedra, with average Ge—Se distances of 2.378 and 2.281 Å for (Ge—Se)_endo and (Ge—Se)_exo, respectively. There are four crystallographically distinct K⁺ ions in β-K₄Ge₄Se₁₀ having coordination numbers of 5, 7 and 8 (× 2), with K—Se distances in the range 2.986 (2)–3.888 (1) Å, while the coordination numbers of the three unique K⁺ ions in the known K₄Ge₄Se₁₀ (P2₁/m) vary between 5 and 7. Besides the differences in coordination numbers of K⁺ ions, the two polymorphs also exhibit a different packing of the adamantane units.

Key indicators

• Single-crystal X-ray study
• T = 100 K
• Mean [sigma](e-Ge) = 0.001 Å
• R factor = 0.041
• wR factor = 0.103
• Data-to-parameter ratio = 29.4

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S1. Comment

The structure determination of K₄Ge₄Se₁₀ was first carried out by Eisenmann and Hansa (1993). The compound was synthesized by stoichiometric combination of elements in an evacuated graphitized silica ampoule at 1073 K. It crystallizes in space group P2₁/m with cell parameters a = 10.202 (6) Å, b = 11.544 (6) Å, c = 9.806 (6) Å, β = 90.6 (1)°, V = 1154.8 ų. Wachhold & Kanatzidis (2000) reported the synthesis of K₄Ge₄Se₁₀ starting with K₂Se, Ge and Se, following the same route by which we have synthesized K₄Ge₄Se₁₀ and determined its crystal structure at 100 K, which reveals that the cell pararmeters are different from those reported by Eisenmann and Hansa (1993). The present β-structure crystallizes in the monoclinic system but with a different space group (P2₁/c); although there is an obvious metric relationship between the unit cells of the two structures, their symmetries do not allow to transform one structure into another.

Complementary views of the two polymorphs are given in Fig. 1. The structure of β-K₄Ge₄Se₁₀ contains isolated adamantane-like [Ge₄Se₁₀]^4- units formed by four corner-shared GeSe₄ tetrahedra similar to K₄Ge₄Se₁₀—P2₁/m. However, these units are arranged differently in the two polymorphs. In both the structures, anionic adamantane units are stacked one over the other along the c- and b axis for K₄Ge₄Se₁₀—P2₁/m and β-K₄Ge₄Se₁₀, respectively, held together by K⁺ cations to form a column. Such columns are placed side by side in a layer like arrangement parallel to the ac- and ab-plane, for K₄Ge₄Se₁₀—P2₁/m and β-K₄Ge₄Se₁₀, respectively. In K₄Ge₄Se₁₀—P2₁/m the adamantane units are arranged such that [Ge₄Se₁₀]^4- super tetrahedra are face up in one layer while they are placed face down in the next layer, which means the Se atoms are arranged in opposite directions in alternate layer. However, in the new polymorph, β-K₄Ge₄Se₁₀, the directions of the super tetrahedra (arrangement of Se atoms) alternate in every two layers (Fig. 1). Thus in β-K₄Ge₄Se₁₀ the c axis is approximately doubled the length of the b axis in K₄Ge₄Se₁₀—P2₁/m. The average Ge—Se distances (d(Ge—Se)_endo = 2.378, d(Ge—Se)_exo = 2.281 Å; Table 1) and the coordination number of the K⁺ ions (CN = 5–8) of β-K₄Ge₄Se₁₀ are comparable to that of K₄Ge₄Se₁₀—P2₁/m.

Related literature

For the first polymorph (P2₁/m) of this composition, see: Eisenmann & Hansa (1993); for preparation, see: Wachhold & Kanatzidis (2000); Wachhold et al. (2000).

S2. Experimental

The synthesis of β-K₄Ge₄Se₁₀ was carried out according to the reported procedure (Wachhold and Kanatzidis, 2000) but with a longer heating time, 48 hrs compared to 32 hrs. Orange needles of K₄Ge₄Se₁₀ were obtained from a solid-state reaction of K₂Se, Ge, and Se by mixing stoichiometric amounts (1:2:4) of 471.46 mg K₂Se (prepared following the reported procedure, Wachhold and Kanatzidis, 2000), 435.6 mg Ge (Cerac, 99.999%), and 947.5 mg of Se (Aldrich, 99.5%). The reactants were loaded into a fused-silica tube under N₂ atmosphere in a glovebox. The tube was torch-sealed under vacuum and then placed in a furnace. The sample was heated to 1123 K at a rate of 35 K/h, held at 1123 k for 48 h, and then cooled to room temperature at a cooling rate of 35 K/h. The tube was opened under N₂, the product was ground and powder X-ray diffraction (PXRD) was carried out. The PXRD did not match with the simulated pattern from the atomic coordinates of known K₄Ge₄Se₁₀ (P2₁/m) (Eisenmann and Hansa, 1993). This led us to believe that the current product could be a polymorphic modification and subsequent single-crystal X-ray data revealed different cell parameters and structure solution indicated a new polymorph of K₄Ge₄Se₁₀ (in P2₁/c space group, β-phase). The experimental PXRD was in good agreement with the simulated pattern of β-K₄Ge₄Se₁₀. The finely ground product was air sensitive and decomposed after 20–30 minutes of exposure in air. The single-crystal X-ray data was collected at low temperature (100 K) under a flow of liquid N₂ and the crystal did not show any sign of decomposition during the period of data collection. Although β-K₄Ge₄Se₁₀ was obtained following the reported synthesis procedure (Wachhold and Kanatzidis, 2000; Wachhold et al., 2000), however, they did not report a detailed crystallographic characterization of their K₄Ge₄Se₁₀ and hence it is unclear whether they also obtained the same polymorph as reported here.

S3. Refinement

The highest peak and the deepest hole in the final Fourier map are 0.96 Å from Ge4 and 2.16 Å from Se10, respectively.

Computing details

Data collection: SMART (Bruker, 2000); cell refinement: SAINT (Bruker, 2000); data reduction: SAINT; program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: DIAMOND (Brandenburg, 2005); software used to prepare material for publication: SHELXL97.

Figures

Fig. 1. Ball and stick representation of the packing of adamantane units in the two polymorphs: K4Ge4Se10—P21/m (left), β-K4Ge4Se10 (right).

tetrapotassium decaselenidotetragermanate

Crystal data

K4Ge4Se10	F(000) = 2176
Mr = 1236.36	Dx = 3.669 Mg m^−3
Monoclinic, P21/c	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2ybc	Cell parameters from 5478 reflections
a = 9.9796 (8) Å	θ = 2.3–28.3°
b = 9.7047 (8) Å	µ = 22.31 mm^−1
c = 23.184 (2) Å	T = 100 K
β = 94.508 (2)°	Irregular, orange
V = 2238.4 (3) Å^3	0.26 × 0.12 × 0.06 mm
Z = 4

Data collection

Bruker SMART CCD area detector diffractometer	4823 independent reflections
Radiation source: fine-focus sealed tube	3896 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.069
φ and ω scans	θmax = 27.0°, θmin = 1.8°
Absorption correction: multi-scan (SADABS; Sheldrick, 1996)	h = −12→12
Tmin = 0.054, Tmax = 0.262	k = −12→12
19344 measured reflections	l = −29→29

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)] = 0.042	w = 1/[σ^2(Fo^2) + (0.0511P)^2 + 6.4498P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.103	(Δ/σ)max < 0.001
S = 1.04	Δρmax = 1.72 e Å^−3
4823 reflections	Δρmin = −1.47 e Å^−3
164 parameters	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00274 (12)

Special details

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
Ge1	0.05608 (7)	0.77088 (7)	0.37483 (3)	0.01313 (18)
Ge2	0.84125 (7)	0.08752 (7)	0.37930 (3)	0.01123 (17)
Ge3	0.72783 (7)	0.75584 (7)	0.30709 (3)	0.01103 (17)
Ge4	0.73792 (7)	0.77065 (7)	0.47074 (3)	0.01166 (17)
Se1	0.61852 (7)	0.67644 (7)	0.39529 (3)	0.01264 (16)
Se2	0.96086 (7)	0.68890 (7)	0.46503 (3)	0.01607 (18)
Se3	0.27457 (7)	0.70088 (7)	0.36540 (3)	0.01702 (18)
Se4	0.83817 (7)	0.32038 (7)	0.37588 (3)	0.01580 (18)
Se5	0.71983 (7)	0.00069 (7)	0.30260 (3)	0.01306 (17)
Se6	0.72631 (7)	0.01489 (7)	0.46832 (3)	0.01402 (17)
Se7	0.95299 (7)	0.67889 (7)	0.29407 (3)	0.01363 (17)
Se8	0.06604 (7)	0.01348 (7)	0.37121 (3)	0.01835 (18)
Se9	0.61132 (7)	0.68152 (7)	0.23270 (3)	0.01788 (18)
Se10	0.62389 (7)	0.69187 (7)	0.55318 (3)	0.01533 (17)
K1	0.84052 (16)	0.61928 (16)	0.65528 (7)	0.0223 (4)
K2	0.43100 (16)	0.99728 (15)	0.39359 (7)	0.0163 (3)
K3	0.31801 (17)	0.62238 (16)	0.50104 (7)	0.0221 (4)
K4	0.67980 (19)	0.35486 (18)	0.26208 (8)	0.0288 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ge1	0.0119 (4)	0.0106 (3)	0.0157 (4)	0.0012 (3)	−0.0064 (3)	−0.0001 (3)
Ge2	0.0138 (4)	0.0092 (3)	0.0098 (4)	0.0003 (3)	−0.0052 (3)	0.0017 (3)
Ge3	0.0121 (3)	0.0108 (3)	0.0090 (4)	0.0009 (3)	−0.0063 (3)	−0.0009 (3)
Ge4	0.0156 (4)	0.0089 (3)	0.0095 (4)	0.0005 (3)	−0.0049 (3)	0.0021 (3)
Se1	0.0125 (3)	0.0121 (3)	0.0126 (4)	−0.0010 (3)	−0.0044 (3)	0.0010 (3)
Se2	0.0167 (4)	0.0141 (3)	0.0159 (4)	0.0015 (3)	−0.0083 (3)	0.0043 (3)
Se3	0.0112 (3)	0.0153 (3)	0.0232 (4)	0.0008 (3)	−0.0072 (3)	−0.0019 (3)
Se4	0.0232 (4)	0.0098 (3)	0.0133 (4)	−0.0009 (3)	−0.0058 (3)	0.0013 (3)
Se5	0.0165 (4)	0.0111 (3)	0.0105 (3)	0.0018 (3)	−0.0065 (3)	0.0016 (3)
Se6	0.0233 (4)	0.0092 (3)	0.0092 (3)	0.0015 (3)	−0.0013 (3)	0.0009 (3)
Se7	0.0133 (3)	0.0132 (3)	0.0136 (4)	0.0016 (3)	−0.0038 (3)	−0.0020 (3)
Se8	0.0141 (4)	0.0122 (3)	0.0275 (4)	−0.0011 (3)	−0.0063 (3)	0.0022 (3)
Se9	0.0203 (4)	0.0177 (4)	0.0137 (4)	0.0009 (3)	−0.0113 (3)	−0.0038 (3)
Se10	0.0239 (4)	0.0116 (3)	0.0101 (3)	−0.0014 (3)	−0.0017 (3)	0.0020 (3)
K1	0.0240 (8)	0.0184 (8)	0.0233 (9)	−0.0021 (7)	−0.0057 (7)	−0.0017 (7)
K2	0.0188 (8)	0.0150 (7)	0.0143 (8)	−0.0010 (6)	−0.0045 (6)	−0.0027 (6)
K3	0.0275 (9)	0.0182 (8)	0.0196 (8)	0.0035 (7)	−0.0052 (7)	−0.0052 (7)
K4	0.0406 (11)	0.0204 (8)	0.0220 (9)	−0.0030 (7)	−0.0190 (8)	0.0049 (7)

Geometric parameters (Å, º)

Ge1—Se7^i	2.2492 (10)	Se8—K1^v	3.7468 (18)
Ge1—Se3	2.3105 (10)	Se9—K4	3.3027 (19)
Ge1—Se8^ii	2.3583 (10)	Se9—K4^vi	3.368 (2)
Ge1—Se2^i	2.4943 (11)	Se9—K2^x	3.4284 (17)
Ge2—Se5	2.2366 (9)	Se9—K1^iv	3.5827 (19)
Ge2—Se4	2.2613 (9)	Se10—K1	3.1574 (17)
Ge2—Se8^iii	2.3769 (10)	Se10—K3	3.2640 (18)
Ge2—Se6	2.5384 (10)	Se10—K2^xi	3.3211 (17)
Ge3—Se9	2.1288 (9)	Se10—K3^v	3.3663 (17)
Ge3—Se5^ii	2.3795 (10)	K1—Se3^v	3.3341 (17)
Ge3—Se7	2.4092 (10)	K1—Se4^vii	3.3929 (19)
Ge3—Se1	2.5131 (10)	K1—Se9^xii	3.5827 (19)
Ge3—K1^iv	3.9678 (19)	K1—Se7^vii	3.6904 (17)
Ge4—Se1	2.2335 (9)	K1—Se8^v	3.7468 (18)
Ge4—Se6^ii	2.3735 (9)	K1—Se7^xii	3.8577 (17)
Ge4—Se2	2.3755 (10)	K1—Se5^xiii	3.8882 (19)
Ge4—Se10	2.4238 (10)	K1—Ge3^xii	3.9678 (19)
Ge4—K3^v	3.9173 (18)	K1—K3^v	4.499 (2)
Se1—K2	3.6314 (16)	K1—K2^xi	4.689 (2)
Se1—K3^v	3.7879 (18)	K1—K4^vii	5.021 (2)
Se2—Ge1^iii	2.4943 (11)	K2—Se6^ii	3.3035 (16)
Se2—K3^iii	3.6537 (18)	K2—Se10^xi	3.3211 (17)
Se3—K3	3.2317 (18)	K2—Se9^vi	3.4284 (17)
Se3—K2	3.3133 (16)	K2—Se8^ii	3.6418 (17)
Se3—K1^v	3.3341 (17)	K2—Se6^v	3.6768 (18)
Se3—K4^vi	3.374 (2)	K2—Se5^ii	3.7034 (18)
Se4—K4	2.9859 (17)	K2—K4^vi	3.941 (2)
Se4—K1^vii	3.3929 (19)	K2—K3	4.600 (2)
Se4—K3^v	3.4028 (19)	K2—K1^xi	4.689 (2)
Se5—Ge3^viii	2.3795 (10)	K2—K3^xi	4.990 (2)
Se5—K4	3.5773 (18)	K3—Se10^v	3.3663 (17)
Se5—K2^viii	3.7034 (18)	K3—Se4^v	3.4028 (19)
Se5—K1^ix	3.8882 (19)	K3—Se6^v	3.6252 (17)
Se6—Ge4^viii	2.3735 (9)	K3—Se2^i	3.6537 (18)
Se6—K2^viii	3.3035 (16)	K3—Se1^v	3.7879 (18)
Se6—K3^v	3.6252 (17)	K3—Ge4^v	3.9173 (18)
Se6—K2^v	3.6768 (18)	K3—K3^v	4.344 (3)
Se7—Ge1^iii	2.2492 (10)	K3—K1^v	4.499 (2)
Se7—K1^vii	3.6904 (17)	K3—K2^xi	4.990 (2)
Se7—K1^iv	3.8577 (17)	K4—Se9^x	3.368 (2)
Se8—Ge1^viii	2.3583 (10)	K4—Se3^x	3.374 (2)
Se8—Ge2^i	2.3769 (10)	K4—K2^x	3.941 (2)
Se8—K2^viii	3.6418 (17)	K4—K1^vii	5.021 (2)
Se7^i—Ge1—Se3	100.24 (4)	Se10—K1—K4^vii	148.33 (6)
Se7^i—Ge1—Se8^ii	112.61 (4)	Se3^v—K1—K4^vii	114.13 (4)
Se3—Ge1—Se8^ii	104.32 (4)	Se4^vii—K1—K4^vii	35.31 (3)
Se7^i—Ge1—Se2^i	113.08 (4)	Se9^xii—K1—K4^vii	114.14 (4)
Se3—Ge1—Se2^i	114.21 (4)	Se7^vii—K1—K4^vii	54.97 (3)
Se8^ii—Ge1—Se2^i	111.60 (4)	Se8^v—K1—K4^vii	76.87 (3)
Se5—Ge2—Se4	110.10 (4)	Se7^xii—K1—K4^vii	56.64 (3)
Se5—Ge2—Se8^iii	106.21 (4)	Se5^xiii—K1—K4^vii	91.81 (4)
Se4—Ge2—Se8^iii	108.04 (4)	Ge3^xii—K1—K4^vii	88.53 (4)
Se5—Ge2—Se6	106.89 (4)	K3^v—K1—K4^vii	126.72 (5)
Se4—Ge2—Se6	107.47 (4)	K2^xi—K1—K4^vii	124.61 (4)
Se8^iii—Ge2—Se6	118.02 (4)	Se6^ii—K2—Se3	122.37 (5)
Se9—Ge3—Se5^ii	106.77 (4)	Se6^ii—K2—Se10^xi	85.67 (4)
Se9—Ge3—Se7	104.41 (4)	Se3—K2—Se10^xi	140.62 (6)
Se5^ii—Ge3—Se7	109.42 (4)	Se6^ii—K2—Se9^vi	117.77 (5)
Se9—Ge3—Se1	108.11 (4)	Se3—K2—Se9^vi	105.06 (4)
Se5^ii—Ge3—Se1	109.06 (4)	Se10^xi—K2—Se9^vi	80.26 (4)
Se7—Ge3—Se1	118.41 (3)	Se6^ii—K2—Se1	66.48 (3)
Se9—Ge3—K1^iv	63.87 (4)	Se3—K2—Se1	59.48 (3)
Se5^ii—Ge3—K1^iv	70.55 (3)	Se10^xi—K2—Se1	151.02 (5)
Se7—Ge3—K1^iv	69.59 (3)	Se9^vi—K2—Se1	119.03 (5)
Se1—Ge3—K1^iv	170.69 (4)	Se6^ii—K2—Se8^ii	155.99 (5)
Se1—Ge4—Se6^ii	111.61 (4)	Se3—K2—Se8^ii	63.83 (3)
Se1—Ge4—Se2	105.31 (4)	Se10^xi—K2—Se8^ii	79.71 (4)
Se6^ii—Ge4—Se2	112.11 (4)	Se9^vi—K2—Se8^ii	78.53 (3)
Se1—Ge4—Se10	103.52 (4)	Se1—K2—Se8^ii	123.18 (4)
Se6^ii—Ge4—Se10	107.97 (4)	Se6^ii—K2—Se6^v	88.25 (4)
Se2—Ge4—Se10	116.00 (4)	Se3—K2—Se6^v	85.24 (4)
Se1—Ge4—K3^v	70.00 (3)	Se10^xi—K2—Se6^v	67.14 (3)
Se6^ii—Ge4—K3^v	165.69 (4)	Se9^vi—K2—Se6^v	136.72 (5)
Se2—Ge4—K3^v	80.24 (3)	Se1—K2—Se6^v	102.59 (4)
Se10—Ge4—K3^v	58.62 (3)	Se8^ii—K2—Se6^v	68.58 (3)
Ge4—Se1—Ge3	105.83 (4)	Se6^ii—K2—Se5^ii	66.18 (3)
Ge4—Se1—K2	84.27 (3)	Se3—K2—Se5^ii	105.73 (4)
Ge3—Se1—K2	89.12 (3)	Se10^xi—K2—Se5^ii	111.23 (4)
Ge4—Se1—K3^v	76.36 (3)	Se9^vi—K2—Se5^ii	63.77 (3)
Ge3—Se1—K3^v	133.58 (4)	Se1—K2—Se5^ii	65.82 (3)
K2—Se1—K3^v	136.35 (4)	Se8^ii—K2—Se5^ii	137.13 (5)
Ge4—Se2—Ge1^iii	111.12 (3)	Se6^v—K2—Se5^ii	154.29 (5)
Ge4—Se2—K3^iii	161.33 (4)	Se6^ii—K2—K4^vi	132.29 (6)
Ge1^iii—Se2—K3^iii	79.56 (4)	Se3—K2—K4^vi	54.62 (4)
Ge1—Se3—K3	91.87 (4)	Se10^xi—K2—K4^vi	128.04 (5)
Ge1—Se3—K2	99.19 (4)	Se9^vi—K2—K4^vi	52.69 (4)
K3—Se3—K2	89.29 (4)	Se1—K2—K4^vi	79.42 (4)
Ge1—Se3—K1^v	88.32 (4)	Se8^ii—K2—K4^vi	71.29 (4)
K3—Se3—K1^v	86.48 (4)	Se6^v—K2—K4^vi	132.68 (5)
K2—Se3—K1^v	171.51 (4)	Se5^ii—K2—K4^vi	69.90 (4)
Ge1—Se3—K4^vi	98.40 (4)	Se6^ii—K2—K3	90.20 (4)
K3—Se3—K4^vi	160.00 (5)	Se3—K2—K3	44.63 (3)
K2—Se3—K4^vi	72.21 (4)	Se10^xi—K2—K3	117.56 (5)
K1^v—Se3—K4^vi	110.82 (5)	Se9^vi—K2—K3	148.88 (5)
Ge2—Se4—K4	98.50 (4)	Se1—K2—K3	57.59 (3)
Ge2—Se4—K1^vii	99.76 (4)	Se8^ii—K2—K3	80.00 (4)
K4—Se4—K1^vii	103.65 (5)	Se6^v—K2—K3	50.46 (3)
Ge2—Se4—K3^v	98.03 (4)	Se5^ii—K2—K3	123.40 (4)
K4—Se4—K3^v	118.50 (5)	K4^vi—K2—K3	98.95 (5)
K1^vii—Se4—K3^v	130.79 (4)	Se6^ii—K2—K1^xi	124.08 (4)
Ge2—Se5—Ge3^viii	109.10 (3)	Se3—K2—K1^xi	112.76 (4)
Ge2—Se5—K4	83.63 (4)	Se10^xi—K2—K1^xi	42.26 (3)
Ge3^viii—Se5—K4	166.82 (4)	Se9^vi—K2—K1^xi	49.44 (3)
Ge2—Se5—K2^viii	87.00 (4)	Se1—K2—K1^xi	166.05 (5)
Ge3^viii—Se5—K2^viii	89.49 (3)	Se8^ii—K2—K1^xi	51.60 (3)
K4—Se5—K2^viii	94.72 (4)	Se6^v—K2—K1^xi	87.58 (4)
Ge2—Se5—K1^ix	128.71 (4)	Se5^ii—K2—K1^xi	108.43 (4)
Ge3^viii—Se5—K1^ix	74.21 (3)	K4^vi—K2—K1^xi	86.66 (4)
K4—Se5—K1^ix	95.33 (4)	K3—K2—K1^xi	126.65 (5)
K2^viii—Se5—K1^ix	143.75 (4)	Se6^ii—K2—K3^xi	46.55 (3)
Ge4^viii—Se6—Ge2	105.79 (3)	Se3—K2—K3^xi	161.67 (5)
Ge4^viii—Se6—K2^viii	90.04 (4)	Se10^xi—K2—K3^xi	40.30 (3)
Ge2—Se6—K2^viii	91.69 (4)	Se9^vi—K2—K3^xi	93.19 (4)
Ge4^viii—Se6—K3^v	166.30 (4)	Se1—K2—K3^xi	112.99 (4)
Ge2—Se6—K3^v	87.68 (4)	Se8^ii—K2—K3^xi	119.72 (4)
K2^viii—Se6—K3^v	92.03 (4)	Se6^v—K2—K3^xi	80.20 (4)
Ge4^viii—Se6—K2^v	88.32 (3)	Se5^ii—K2—K3^xi	83.63 (4)
Ge2—Se6—K2^v	165.46 (4)	K4^vi—K2—K3^xi	143.28 (5)
K2^viii—Se6—K2^v	91.75 (4)	K3—K2—K3^xi	117.06 (4)
K3^v—Se6—K2^v	78.09 (4)	K1^xi—K2—K3^xi	77.86 (3)
Ge1^iii—Se7—Ge3	98.20 (4)	Se3—K3—Se10	111.20 (6)
Ge1^iii—Se7—K1^vii	80.73 (4)	Se3—K3—Se10^v	82.19 (4)
Ge3—Se7—K1^vii	134.92 (4)	Se10—K3—Se10^v	98.16 (5)
Ge1^iii—Se7—K1^iv	125.24 (4)	Se3—K3—Se4^v	137.92 (6)
Ge3—Se7—K1^iv	74.58 (3)	Se10—K3—Se4^v	97.61 (4)
K1^vii—Se7—K1^iv	141.46 (3)	Se10^v—K3—Se4^v	124.39 (5)
Ge1^viii—Se8—Ge2^i	104.85 (4)	Se3—K3—Se6^v	87.29 (4)
Ge1^viii—Se8—K2^viii	89.79 (3)	Se10—K3—Se6^v	81.47 (4)
Ge2^i—Se8—K2^viii	160.28 (4)	Se10^v—K3—Se6^v	168.57 (6)
Ge1^viii—Se8—K1^v	165.28 (5)	Se4^v—K3—Se6^v	66.81 (3)
Ge2^i—Se8—K1^v	88.51 (4)	Se3—K3—Se2^i	71.47 (4)
K2^viii—Se8—K1^v	78.78 (4)	Se10—K3—Se2^i	156.24 (5)
Ge3—Se9—K4	93.85 (4)	Se10^v—K3—Se2^i	105.56 (4)
Ge3—Se9—K4^vi	102.68 (4)	Se4^v—K3—Se2^i	70.12 (4)
K4—Se9—K4^vi	129.58 (4)	Se6^v—K3—Se2^i	75.01 (3)
Ge3—Se9—K2^x	153.05 (4)	Se3—K3—Se1^v	143.22 (5)
K4—Se9—K2^x	71.65 (4)	Se10—K3—Se1^v	79.53 (4)
K4^vi—Se9—K2^x	104.03 (4)	Se10^v—K3—Se1^v	61.20 (3)
Ge3—Se9—K1^iv	83.89 (4)	Se4^v—K3—Se1^v	69.98 (4)
K4—Se9—K1^iv	119.43 (5)	Se6^v—K3—Se1^v	129.49 (5)
K4^vi—Se9—K1^iv	109.57 (5)	Se2^i—K3—Se1^v	113.06 (5)
K2^x—Se9—K1^iv	83.93 (4)	Se3—K3—Ge4^v	112.46 (5)
Ge4—Se10—K1	108.99 (5)	Se10—K3—Ge4^v	106.30 (4)
Ge4—Se10—K3	104.87 (4)	Se10^v—K3—Ge4^v	37.93 (2)
K1—Se10—K3	142.83 (5)	Se4^v—K3—Ge4^v	86.46 (4)
Ge4—Se10—K2^xi	96.19 (4)	Se6^v—K3—Ge4^v	153.08 (6)
K1—Se10—K2^xi	92.71 (4)	Se2^i—K3—Ge4^v	93.50 (4)
K3—Se10—K2^xi	98.54 (4)	Se1^v—K3—Ge4^v	33.65 (2)
Ge4—Se10—K3^v	83.45 (4)	Se3—K3—K3^v	99.58 (6)
K1—Se10—K3^v	87.13 (4)	Se10—K3—K3^v	50.10 (4)
K3—Se10—K3^v	81.84 (5)	Se10^v—K3—K3^v	48.06 (3)
K2^xi—Se10—K3^v	179.54 (5)	Se4^v—K3—K3^v	122.49 (6)
Se10—K1—Se3^v	83.82 (4)	Se6^v—K3—K3^v	130.41 (6)
Se10—K1—Se4^vii	113.87 (5)	Se2^i—K3—K3^v	153.60 (7)
Se3^v—K1—Se4^vii	116.80 (5)	Se1^v—K3—K3^v	59.34 (4)
Se10—K1—Se9^xii	80.14 (4)	Ge4^v—K3—K3^v	66.40 (4)
Se3^v—K1—Se9^xii	110.40 (5)	Se3—K3—K1^v	47.71 (3)
Se4^vii—K1—Se9^xii	131.67 (5)	Se10—K3—K1^v	131.72 (5)
Se10—K1—Se7^vii	138.23 (5)	Se10^v—K3—K1^v	44.51 (3)
Se3^v—K1—Se7^vii	59.50 (3)	Se4^v—K3—K1^v	127.26 (5)
Se4^vii—K1—Se7^vii	71.92 (4)	Se6^v—K3—K1^v	128.57 (5)
Se9^xii—K1—Se7^vii	128.77 (5)	Se2^i—K3—K1^v	68.47 (4)
Se10—K1—Se8^v	80.18 (4)	Se1^v—K3—K1^v	98.21 (4)
Se3^v—K1—Se8^v	161.84 (6)	Ge4^v—K3—K1^v	65.24 (3)
Se4^vii—K1—Se8^v	63.21 (3)	K3^v—K3—K1^v	86.98 (5)
Se9^xii—K1—Se8^v	75.27 (4)	Se3—K3—K2	46.08 (3)
Se7^vii—K1—Se8^v	131.15 (5)	Se10—K3—K2	77.01 (4)
Se10—K1—Se7^xii	130.48 (5)	Se10^v—K3—K2	117.23 (5)
Se3^v—K1—Se7^xii	131.87 (5)	Se4^v—K3—K2	118.23 (5)
Se4^vii—K1—Se7^xii	82.65 (4)	Se6^v—K3—K2	51.46 (3)
Se9^xii—K1—Se7^xii	57.56 (3)	Se2^i—K3—K2	90.73 (4)
Se7^vii—K1—Se7^xii	90.81 (4)	Se1^v—K3—K2	155.97 (5)
Se8^v—K1—Se7^xii	66.04 (3)	Ge4^v—K3—K2	154.80 (5)
Se10—K1—Se5^xiii	118.96 (5)	K3^v—K3—K2	100.70 (6)
Se3^v—K1—Se5^xiii	73.76 (4)	K1^v—K3—K2	93.54 (4)
Se4^vii—K1—Se5^xiii	127.01 (5)	Se3—K3—K2^xi	109.01 (5)
Se9^xii—K1—Se5^xiii	57.82 (3)	Se10—K3—K2^xi	41.16 (3)
Se7^vii—K1—Se5^xiii	71.91 (3)	Se10^v—K3—K2^xi	139.32 (5)
Se8^v—K1—Se5^xiii	121.81 (5)	Se4^v—K3—K2^xi	73.39 (4)
Se7^xii—K1—Se5^xiii	60.61 (3)	Se6^v—K3—K2^xi	41.42 (3)
Se10—K1—Ge3^xii	111.83 (5)	Se2^i—K3—K2^xi	115.10 (4)
Se3^v—K1—Ge3^xii	107.08 (5)	Se1^v—K3—K2^xi	101.72 (4)
Se4^vii—K1—Ge3^xii	118.34 (4)	Ge4^v—K3—K2^xi	135.32 (4)
Se9^xii—K1—Ge3^xii	32.24 (2)	K3^v—K3—K2^xi	91.26 (5)
Se7^vii—K1—Ge3^xii	98.47 (4)	K1^v—K3—K2^xi	155.67 (5)
Se8^v—K1—Ge3^xii	86.93 (4)	K2—K3—K2^xi	62.94 (4)
Se7^xii—K1—Ge3^xii	35.83 (2)	Se4—K4—Se9	112.11 (5)
Se5^xiii—K1—Ge3^xii	35.24 (2)	Se4—K4—Se9^x	108.09 (6)
Se10—K1—K3^v	48.36 (3)	Se9—K4—Se9^x	108.77 (5)
Se3^v—K1—K3^v	45.81 (3)	Se4—K4—Se3^x	128.74 (6)
Se4^vii—K1—K3^v	101.35 (5)	Se9—K4—Se3^x	106.52 (5)
Se9^xii—K1—K3^v	119.14 (5)	Se9^x—K4—Se3^x	89.23 (4)
Se7^vii—K1—K3^v	89.99 (4)	Se4—K4—Se5	67.66 (4)
Se8^v—K1—K3^v	116.11 (5)	Se9—K4—Se5	173.44 (7)
Se7^xii—K1—K3^v	175.97 (5)	Se9^x—K4—Se5	65.76 (4)
Se5^xiii—K1—K3^v	115.98 (5)	Se3^x—K4—Se5	77.56 (4)
Ge3^xii—K1—K3^v	140.14 (5)	Se4—K4—K2^x	159.96 (7)
Se10—K1—K2^xi	45.02 (3)	Se9—K4—K2^x	55.66 (4)
Se3^v—K1—K2^xi	121.25 (5)	Se9^x—K4—K2^x	91.57 (4)
Se4^vii—K1—K2^xi	110.45 (5)	Se3^x—K4—K2^x	53.18 (4)
Se9^xii—K1—K2^xi	46.64 (3)	Se5—K4—K2^x	126.51 (5)
Se7^vii—K1—K2^xi	175.36 (5)	Se4—K4—K1^vii	41.05 (3)
Se8^v—K1—K2^xi	49.62 (3)	Se9—K4—K1^vii	101.91 (4)
Se7^xii—K1—K2^xi	85.61 (4)	Se9^x—K4—K1^vii	144.16 (5)
Se5^xiii—K1—K2^xi	103.70 (4)	Se3^x—K4—K1^vii	99.56 (5)
Ge3^xii—K1—K2^xi	76.90 (4)	Se5—K4—K1^vii	82.21 (4)
K3^v—K1—K2^xi	93.39 (4)	K2^x—K4—K1^vii	121.49 (5)

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