Dinuclear oxofluorometallates as a new structural type of d⁰ transition metal oxofluoride compound

Five isomorphous d⁰ transition metal oxofluoride compounds A₃[M₂O_xF_11 - x]·(AF)_0.333 (A = K, Rb, NH₄; M = Nb, Mo, W; x = 2, 4) have been synthesized from acid fluoride solutions, and their crystal structures have been determined by single-crystal X-ray diffraction. The basic structural building units are dinuclear M₂X₁₁ (dimers) formed from NbOF₅ or Mo(W)O₂F₄ octahedra connected by the fluorine bridging atom. In the Nb₂O₂F₉ dimer, the O atoms occupy apical corners. In the M₂O₄F₇ (M = Mo, W) dimers two O atoms are also apically placed, whereas the other two O atoms are statistically disordered in equatorial planes. The arrangement of dimers is so that the hexagonal tunnels containing `free' fluoride ions are formed. During the irradiation process the orthorhombic structure of K₃Nb₂O₂F₉·(KF)_0.333 transforms into a pseudo-trigonal one with a = 23.15 Å, which is the [101] diagonal of the orthorhombic unit cell. The other four trigonal crystals are merohedral twins.

Computing details

Data collection: Bruker Smart v5.054 (Bruker, 1998) for (II), (III), (IV), (V). Cell refinement: Bruker SAINT v6.02a (Bruker, 2000) for (II), (III), (IV), (V). Data reduction: Bruker SAINT v6.02a (Bruker, 2000) for (II), (III), (IV), (V). Program(s) used to solve structure: SHELXS97 (Sheldrick, 1990) for (I); Bruker SHELXTL v5.1 (Bruker, 1998) for (II), (III), (IV), (V). Program(s) used to refine structure: SHELXL97 (Sheldrick, 1997) for (I); Bruker SHELXTL v5.1 (Bruker, 1998) for (II), (III), (IV), (V). Molecular graphics: Bruker SHELXTL v5.1 (Bruker, 1998) for (II), (III), (IV), (V). Software used to prepare material for publication: Bruker SHELXTL v5.1 (Bruker, 1998) for (II), (III), (IV), (V).

Figures

(I) potassium oxofluoroniobate

Crystal data

3(F9Nb2O2)·F·10(K)	F(000) = 1472
Mr = 1576.46	Dx = 2.902 Mg m^−3
Orthorhombic, Pmn21	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P2ac-2	Cell parameters from 512 reflections
a = 20.1095 (6) Å	θ = 2.7–31.9°
b = 7.8045 (2) Å	µ = 3.16 mm^−1
c = 11.4938 (4) Å	T = 223 K
V = 1803.89 (9) Å^3	Plate, colorless
Z = 6	0.32 × 0.28 × 0.18 mm

Data collection

Bruker P4 diffractometer	5889 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.019
Graphite monochromator	θmax = 31.9°, θmin = 2.8°
Absorption correction: multi-scan SADABS v.2.03; Bruker 1999	h = −28→29
Tmin = 0.431, Tmax = 0.600	k = −11→10
20107 measured reflections	l = −16→17
5975 independent reflections

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0447P)^2 + 4.7059P] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.031	(Δ/σ)max = 0.014
wR(F^2) = 0.093	Δρmax = 1.37 e Å^−3
S = 1.18	Δρmin = −0.78 e Å^−3
5889 reflections	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
239 parameters	Extinction coefficient: 0.00013 (10)
1 restraint	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: 0.05 (6)

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
Nb1	0.694119 (14)	0.54920 (4)	0.31782 (2)	0.02328 (5)
Nb2	0.802239 (12)	1.00119 (4)	0.42425 (2)	0.02032 (5)
Nb3	0.5000	0.07657 (5)	0.51913 (3)	0.02165 (7)
Nb4	0.5000	0.53236 (5)	0.73355 (3)	0.02077 (7)
K1	0.5000	0.54735 (18)	0.37941 (14)	0.0436 (3)
K2	0.64207 (5)	0.46945 (13)	0.00278 (8)	0.0435 (2)
K3	0.67135 (4)	0.76061 (8)	0.61290 (6)	0.02692 (13)
K4	0.87478 (4)	0.97010 (12)	0.76828 (7)	0.03550 (18)
K5	0.0000	0.93829 (15)	0.35489 (10)	0.0322 (2)
K6	0.83901 (4)	0.73830 (8)	0.14066 (6)	0.02574 (13)
F1	0.78186 (14)	0.4685 (4)	0.2716 (2)	0.0480 (7)
F2	0.69629 (14)	0.6967 (4)	0.1824 (2)	0.0473 (7)
F3	0.62425 (12)	0.6942 (3)	0.3809 (2)	0.0408 (6)
F4	0.70869 (13)	0.4663 (3)	0.47488 (19)	0.0376 (5)
F5	0.75475 (14)	0.7516 (3)	0.3912 (2)	0.0438 (6)
F6	0.87385 (13)	0.8739 (5)	0.3539 (3)	0.0739 (10)
F7	0.77051 (16)	1.0426 (4)	0.2683 (2)	0.0567 (8)
F8	0.71371 (12)	1.0506 (3)	0.4812 (3)	0.0441 (6)
F9	0.81935 (15)	0.8788 (4)	0.5676 (2)	0.0496 (7)
F10	0.56946 (10)	−0.0149 (3)	0.6199 (2)	0.0344 (5)
F11	0.56705 (10)	0.2271 (3)	0.4530 (2)	0.0344 (5)
F12	0.5000	0.2707 (4)	0.6564 (3)	0.0377 (8)
F13	0.5673 (3)	0.4272 (7)	0.8224 (5)	0.1565 (16)
F14	0.5645 (2)	0.5641 (5)	0.6136 (4)	0.1158 (12)
O1	0.6462 (2)	0.3870 (4)	0.2612 (3)	0.0631 (10)
O2	0.84304 (17)	1.1876 (4)	0.4493 (3)	0.0492 (8)
O3	0.5000	−0.0765 (5)	0.4103 (4)	0.0414 (10)
O4	0.5000	0.7276 (5)	0.7987 (4)	0.0497 (12)
F15	0.5000	0.1013 (9)	0.1186 (3)	0.084 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Nb1	0.03248 (12)	0.01998 (11)	0.01738 (9)	−0.00326 (10)	0.00528 (10)	−0.00175 (9)
Nb2	0.02055 (10)	0.02420 (11)	0.01620 (9)	−0.00367 (9)	0.00220 (9)	−0.00127 (8)
Nb3	0.01597 (13)	0.01967 (14)	0.02932 (17)	0.000	0.000	0.00198 (13)
Nb4	0.01802 (14)	0.01919 (14)	0.02511 (16)	0.000	0.000	0.00084 (13)
K1	0.0337 (5)	0.0368 (6)	0.0602 (8)	0.000	0.000	0.0055 (6)
K2	0.0531 (5)	0.0402 (4)	0.0372 (4)	−0.0021 (4)	−0.0104 (4)	−0.0014 (3)
K3	0.0320 (3)	0.0180 (2)	0.0307 (3)	0.0015 (2)	−0.0034 (3)	−0.0009 (2)
K4	0.0379 (4)	0.0362 (4)	0.0324 (3)	−0.0028 (3)	−0.0085 (3)	−0.0045 (3)
K5	0.0312 (5)	0.0325 (5)	0.0328 (5)	0.000	0.000	0.0021 (4)
K6	0.0338 (3)	0.0196 (2)	0.0238 (3)	−0.0054 (2)	−0.0013 (2)	−0.0004 (2)
F1	0.0541 (14)	0.0393 (12)	0.0506 (14)	0.0127 (11)	0.0240 (12)	−0.0007 (11)
F2	0.0596 (15)	0.0521 (15)	0.0303 (10)	−0.0053 (12)	−0.0004 (10)	0.0123 (11)
F3	0.0361 (10)	0.0455 (13)	0.0410 (11)	0.0099 (10)	0.0013 (9)	−0.0014 (10)
F4	0.0533 (13)	0.0353 (11)	0.0241 (9)	0.0023 (10)	0.0087 (9)	0.0084 (8)
F5	0.0534 (13)	0.0263 (10)	0.0517 (14)	−0.0127 (10)	−0.0101 (11)	0.0008 (9)
F6	0.0319 (11)	0.119 (2)	0.0707 (16)	−0.0041 (15)	0.0185 (11)	−0.0570 (17)
F7	0.0734 (17)	0.0608 (15)	0.0359 (11)	−0.0270 (14)	−0.0190 (12)	0.0208 (11)
F8	0.0331 (11)	0.0396 (12)	0.0597 (15)	0.0078 (10)	0.0143 (11)	−0.0073 (11)
F9	0.0729 (16)	0.0481 (14)	0.0279 (10)	0.0069 (14)	−0.0180 (11)	0.0043 (10)
F10	0.0214 (8)	0.0308 (10)	0.0509 (13)	0.0045 (7)	−0.0032 (9)	0.0084 (9)
F11	0.0273 (9)	0.0379 (11)	0.0379 (10)	−0.0074 (8)	0.0076 (8)	0.0065 (9)
F12	0.0595 (19)	0.0196 (12)	0.0339 (14)	0.000	0.000	−0.0012 (11)
F13	0.200 (3)	0.114 (3)	0.156 (3)	0.080 (3)	−0.145 (2)	−0.068 (3)
F14	0.132 (2)	0.080 (2)	0.135 (3)	−0.0669 (18)	0.100 (2)	−0.0600 (19)
O1	0.097 (2)	0.0439 (15)	0.0485 (17)	−0.0395 (17)	0.0126 (18)	−0.0171 (14)
O2	0.0542 (16)	0.0410 (15)	0.0526 (17)	−0.0226 (14)	−0.0003 (14)	−0.0096 (13)
O3	0.047 (2)	0.0306 (18)	0.046 (2)	0.000	0.000	−0.0107 (17)
O4	0.076 (3)	0.0228 (17)	0.050 (2)	0.000	0.000	−0.0110 (17)
F15	0.0131 (11)	0.229 (6)	0.0091 (10)	0.000	0.000	−0.004 (2)

Geometric parameters (Å, º)

Nb1—O1	1.718 (3)	K4—O1^i	2.820 (4)
Nb1—F2	1.937 (3)	K4—F11^i	2.871 (2)
Nb1—F4	1.940 (2)	K4—F3^x	2.922 (3)
Nb1—F3	1.945 (2)	K4—F7^x	2.923 (3)
Nb1—F1	1.947 (3)	K4—F8^x	3.030 (3)
Nb1—F5	2.166 (2)	K4—F15^i	3.100 (2)
Nb1—K3	3.7994 (8)	K4—O3^i	3.114 (3)
Nb1—K2	3.8203 (10)	K4—F2^x	3.127 (3)
Nb1—K6	3.8489 (8)	K5—F6^xi	2.586 (3)
Nb1—K2^i	3.9233 (11)	K5—F6^iii	2.586 (3)
Nb2—O2	1.695 (3)	K5—O4^xii	2.686 (4)
Nb2—F6	1.928 (3)	K5—F12^xiii	2.804 (3)
Nb2—F7	1.930 (3)	K5—F15^vii	3.047 (3)
Nb2—F9	1.936 (2)	K5—F10^xiii	3.099 (3)
Nb2—F8	1.936 (2)	K5—F10^v	3.099 (3)
Nb2—F5	2.203 (2)	K5—F13^xiii	3.179 (6)
Nb2—K3	3.8929 (8)	K5—F13^v	3.179 (6)
Nb2—K6	3.9217 (7)	K6—F4^vi	2.665 (2)
Nb2—K2^i	3.9447 (11)	K6—F8^ii	2.682 (3)
Nb2—K4^ii	3.9919 (9)	K6—F6	2.760 (3)
Nb3—O3	1.730 (4)	K6—F1	2.832 (3)
Nb3—F11	1.943 (2)	K6—F10^vi	2.847 (2)
Nb3—F11^iii	1.943 (2)	K6—F11^vi	2.880 (2)
Nb3—F10	1.950 (2)	K6—F2	2.928 (3)
Nb3—F10^iii	1.950 (2)	K6—F14^vi	3.071 (4)
Nb3—F12	2.188 (3)	K6—F13^vi	3.095 (6)
Nb3—K6^i	3.8104 (7)	K6—F7	3.113 (3)
Nb3—K6^iv	3.8104 (7)	K6—F12^vi	3.2432 (8)
Nb3—K4^v	3.8454 (9)	F1—F5	2.659 (4)
Nb3—K4^vi	3.8454 (9)	F1—F2	2.681 (4)
Nb4—O4	1.698 (4)	F1—F4	2.761 (3)
Nb4—F13	1.884 (5)	F1—O1	2.803 (5)
Nb4—F13^iii	1.884 (5)	F2—F3	2.703 (4)
Nb4—F14^iii	1.909 (4)	F2—F5	2.707 (4)
Nb4—F14	1.909 (4)	F2—O1	2.770 (4)
Nb4—F12	2.226 (3)	F3—F5	2.665 (4)
Nb4—K5^vii	3.9290 (13)	F3—F4	2.686 (4)
Nb4—K6^iv	4.0103 (8)	F3—O1	2.799 (4)
Nb4—K6^i	4.0103 (8)	F4—F5	2.596 (3)
Nb4—K1	4.0720 (17)	F4—O1	2.827 (4)
Nb4—K3	4.1195 (8)	F5—F9	2.605 (4)
Nb4—K3^iii	4.1195 (8)	F5—F6	2.614 (4)
K1—F3	2.749 (3)	F5—F8	2.683 (4)
K1—F3^iii	2.749 (3)	F5—F7	2.694 (4)
K1—O3^viii	2.957 (4)	F6—F9	2.691 (4)
K1—F11^iii	2.963 (3)	F6—O2	2.753 (5)
K1—F11	2.963 (3)	F7—F8	2.702 (4)
K1—F14	2.992 (5)	F7—O2	2.781 (4)
K1—F14^iii	2.992 (5)	F8—F9	2.701 (4)
K2—F13^ix	2.582 (5)	F8—O2	2.836 (4)
K2—O2^ii	2.763 (3)	F9—O2	2.808 (4)
K2—F9^vi	2.923 (3)	F10—F12	2.663 (3)
K2—F2	2.932 (3)	F10—F11	2.692 (3)
K2—F5^vi	2.987 (3)	F10—F10^iii	2.793 (4)
K2—O1	3.041 (4)	F10—O3	2.826 (5)
K2—F4^vi	3.059 (3)	F11—F12	2.721 (4)
K2—F1^vi	3.104 (3)	F12—F13	2.639 (5)
K2—F6^vi	3.195 (4)	F12—F13^iii	2.639 (5)
K3—F7^x	2.630 (3)	F12—F10^iii	2.663 (3)
K3—F14	2.639 (4)	F12—F14	2.678 (4)
K3—F10^viii	2.697 (2)	F12—F14^iii	2.678 (4)
K3—F1^i	2.722 (3)	F12—F11^iii	2.721 (4)
K3—F8	2.853 (3)	F13—F14	2.627 (7)
K3—F3	2.877 (3)	F13—F13^iii	2.707 (11)
K3—F4	2.890 (3)	F13—O4	2.721 (6)
K3—F5	3.051 (3)	F14—F14^iii	2.596 (8)
K3—F9	3.159 (3)	F14—O4	2.799 (6)
K4—F9	2.659 (3)
O1—Nb1—F2	98.40 (15)	O3—Nb3—F11	97.74 (13)
O1—Nb1—F4	101.04 (14)	O3—Nb3—F11^iii	97.74 (13)
F2—Nb1—F4	160.54 (12)	F11—Nb3—F11^iii	87.86 (13)
O1—Nb1—F3	99.48 (16)	O3—Nb3—F10	100.19 (13)
F2—Nb1—F3	88.28 (12)	F11—Nb3—F10	87.51 (9)
F4—Nb1—F3	87.49 (11)	F11^iii—Nb3—F10	161.93 (10)
O1—Nb1—F1	99.59 (16)	O3—Nb3—F10^iii	100.19 (13)
F2—Nb1—F1	87.29 (12)	F11—Nb3—F10^iii	161.93 (10)
F4—Nb1—F1	90.52 (12)	F11^iii—Nb3—F10^iii	87.51 (9)
F3—Nb1—F1	160.85 (12)	F10—Nb3—F10^iii	91.52 (14)
O1—Nb1—F5	179.23 (15)	O3—Nb3—F12	179.84 (17)
F2—Nb1—F5	82.37 (11)	F11—Nb3—F12	82.15 (9)
F4—Nb1—F5	78.20 (10)	F11^iii—Nb3—F12	82.15 (9)
F3—Nb1—F5	80.62 (11)	F10—Nb3—F12	79.92 (9)
F1—Nb1—F5	80.33 (11)	F10^iii—Nb3—F12	79.92 (9)
O2—Nb2—F6	98.74 (16)	O4—Nb4—F13	98.76 (19)
O2—Nb2—F7	100.01 (15)	O4—Nb4—F13^iii	98.76 (19)
F6—Nb2—F7	86.77 (14)	F13—Nb4—F13^iii	91.9 (4)
O2—Nb2—F9	101.13 (15)	O4—Nb4—F14^iii	101.63 (16)
F6—Nb2—F9	88.29 (14)	F13—Nb4—F14^iii	159.44 (19)
F7—Nb2—F9	158.79 (13)	F13^iii—Nb4—F14^iii	87.7 (2)
O2—Nb2—F8	102.52 (14)	O4—Nb4—F14	101.63 (16)
F6—Nb2—F8	158.72 (13)	F13—Nb4—F14	87.7 (2)
F7—Nb2—F8	88.67 (14)	F13^iii—Nb4—F14	159.44 (19)
F9—Nb2—F8	88.49 (13)	F14^iii—Nb4—F14	85.7 (3)
O2—Nb2—F5	176.73 (14)	O4—Nb4—F12	177.31 (18)
F6—Nb2—F5	78.21 (13)	F13—Nb4—F12	79.40 (16)
F7—Nb2—F5	81.08 (12)	F13^iii—Nb4—F12	79.40 (16)
F9—Nb2—F5	77.72 (11)	F14^iii—Nb4—F12	80.31 (13)
F8—Nb2—F5	80.55 (11)	F14—Nb4—F12	80.31 (13)

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

(II) ammonium oxofluoroniobate

Crystal data

3(F9Nb2O2)·F·10(NH4)	Dx = 2.272 Mg m^−3
Mr = 1325.56	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3m1	Cell parameters from 512 reflections
Hall symbol: -P 3 2	θ = 2.8–31.7°
a = 20.3757 (4) Å	µ = 1.88 mm^−1
c = 8.0851 (3) Å	T = 173 K
V = 2906.97 (13) Å^3	Shere, colorless
Z = 9	0.25 × 0.25 × 0.25 mm
F(000) = 1848

Data collection

Bruker P4 diffractometer	3484 independent reflections
Radiation source: fine-focus sealed tube	3158 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.025
Detector resolution: 8.33 pixels mm^-1	θmax = 31.9°, θmin = 2.8°
ω scans	h = −29→29
Absorption correction: multi-scan SADABS v.2.03; Bruker 1999	k = −28→29
Tmin = 0.651, Tmax = 0.651	l = −11→11
34445 measured reflections

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)] = 0.082	w = 1/[σ^2(Fo^2) + (0.1002P)^2 + 30.7776P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.224	(Δ/σ)max = 0.068
S = 1.08	Δρmax = 3.02 e Å^−3
3158 reflections	Δρmin = −2.19 e Å^−3
137 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00016 (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	Occ. (<1)
Nb1	0.53585 (3)	0.07171 (5)	0.78533 (10)	0.04191 (19)
Nb2	0.40677 (6)	0.20338 (3)	0.30603 (10)	0.04243 (18)
Nb3	0.26826 (5)	0.13413 (2)	0.74052 (10)	0.03681 (16)
N1	0.5818 (4)	0.4182 (4)	0.2623 (9)	0.064 (3)
N2	0.3335 (3)	0.3335 (3)	0.0000	0.0333 (13)
N3	0.5108 (4)	0.2554 (2)	0.7742 (10)	0.0407 (16)
N4	0.3329 (4)	0.3329 (4)	0.5000	0.0368 (14)
N5	0.0857 (3)	0.1714 (5)	0.7383 (10)	0.0490 (19)
F1	0.5671 (3)	−0.0018 (4)	0.7283 (8)	0.1019 (17)
F2	0.6271 (3)	0.1206 (3)	0.9204 (8)	0.0795 (18)
F3	0.5000	0.0000	1.0000	0.081 (3)
F4	0.3365 (3)	0.1002 (2)	0.2283 (5)	0.0686 (12)
F5	0.4526 (2)	0.1601 (2)	0.4482 (6)	0.0585 (11)
F6	0.3247 (4)	0.16237 (18)	0.5043 (7)	0.0573 (16)
F7	0.2238 (5)	0.0384 (3)	0.6568 (15)	0.235 (5)
F8	0.3471 (4)	0.1077 (4)	0.7761 (8)	0.119 (2)
O1	0.5678 (5)	0.1355 (9)	0.6309 (14)	0.129 (4)
O2	0.4739 (7)	0.2370 (4)	0.1510 (11)	0.096 (3)
O3	0.2185 (6)	0.1093 (3)	0.9301 (12)	0.088 (3)
F9	0.0000	0.0000	0.829 (7)	0.136 (17)	0.50
F10	0.6667	0.3333	0.751 (7)	0.34 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Nb1	0.03258 (19)	0.0696 (5)	0.0359 (4)	0.0348 (2)	0.00163 (18)	0.0033 (4)
Nb2	0.0757 (5)	0.03456 (19)	0.0308 (3)	0.0378 (3)	−0.0048 (4)	−0.00241 (18)
Nb3	0.0524 (4)	0.0314 (2)	0.0336 (3)	0.0262 (2)	−0.0037 (3)	−0.00184 (15)
N1	0.063 (3)	0.063 (3)	0.023 (3)	−0.001 (4)	0.011 (2)	−0.011 (2)
N2	0.0413 (15)	0.0413 (15)	0.018 (2)	0.0207 (19)	−0.0016 (11)	0.0016 (11)
N3	0.043 (4)	0.038 (2)	0.042 (4)	0.0217 (18)	0.002 (3)	0.0012 (16)
N4	0.0518 (16)	0.0518 (16)	0.0135 (19)	0.031 (2)	0.0032 (11)	−0.0032 (11)
N5	0.046 (2)	0.074 (5)	0.036 (3)	0.037 (3)	−0.0095 (18)	−0.019 (4)
F1	0.094 (2)	0.173 (3)	0.089 (4)	0.1054 (19)	−0.020 (3)	−0.051 (3)
F2	0.045 (2)	0.060 (2)	0.114 (5)	0.0114 (18)	−0.017 (3)	0.014 (3)
F3	0.086 (6)	0.050 (5)	0.095 (8)	0.025 (2)	0.016 (3)	0.031 (5)
F4	0.129 (3)	0.0503 (16)	0.0394 (18)	0.0550 (17)	−0.028 (2)	−0.0224 (14)
F5	0.0714 (17)	0.0615 (17)	0.061 (2)	0.0472 (14)	−0.013 (2)	−0.0010 (18)
F6	0.067 (4)	0.072 (3)	0.032 (2)	0.0333 (19)	−0.011 (3)	−0.0056 (14)
F7	0.227 (7)	0.047 (3)	0.305 (9)	−0.026 (4)	0.187 (7)	−0.050 (5)
F8	0.147 (3)	0.183 (4)	0.083 (4)	0.125 (3)	0.012 (3)	0.057 (3)
O1	0.109 (4)	0.235 (13)	0.086 (6)	0.118 (6)	0.046 (4)	0.093 (7)
O2	0.158 (10)	0.094 (4)	0.058 (4)	0.079 (5)	0.054 (6)	0.027 (3)
O3	0.078 (6)	0.120 (7)	0.053 (5)	0.039 (3)	−0.003 (5)	−0.002 (2)
F9	0.109 (16)	0.109 (16)	0.19 (5)	0.055 (8)	0.000	0.000
F10	0.033 (4)	0.033 (4)	0.95 (10)	0.0167 (18)	0.000	0.000

Geometric parameters (Å, º)

Nb1—O1	1.681 (12)	N4—F1^vii	2.736 (8)
Nb1—F2	1.946 (5)	N4—F5^vi	2.968 (4)
Nb1—F2^i	1.946 (5)	N4—F5^ii	2.968 (4)
Nb1—F1^i	1.953 (6)	N4—F4^ii	2.975 (5)
Nb1—F1	1.953 (6)	N4—F4^vi	2.975 (5)
Nb1—F3	2.1479 (9)	N4—F7^vi	2.983 (12)
Nb2—O2	1.724 (10)	N4—F7^ii	2.983 (12)
Nb2—F5^ii	1.947 (5)	N4—F8^vi	3.041 (8)
Nb2—F5	1.947 (5)	N4—F8^ii	3.041 (8)
Nb2—F4^ii	1.963 (4)	N5—F7^ii	2.762 (7)
Nb2—F4	1.963 (4)	N5—F7^x	2.762 (7)
Nb2—F6	2.160 (6)	N5—O3^xi	2.807 (13)
Nb3—O3	1.766 (10)	N5—F4^vi	3.237 (10)
Nb3—F7	1.822 (7)	N5—F4^xii	3.237 (10)
Nb3—F7^ii	1.822 (7)	N5—F6^vi	3.341 (11)
Nb3—F8	1.954 (7)	N5—F9	3.112 (17)
Nb3—F8^ii	1.954 (7)	F1—F3	2.597 (6)
Nb3—F6	2.154 (6)	F1—F2	2.661 (8)
N1—F5^iii	3.002 (6)	F1—F1^i	2.771 (10)
N1—F5^ii	3.002 (6)	F1—O1	2.900 (15)
N1—O1^iii	3.021 (13)	F2—F3	2.607 (4)
N1—F2^iv	3.173 (10)	F2—O1	2.720 (11)
N1—F2^v	3.173 (10)	F2—F2^i	2.720 (11)
N1—F1^vi	3.176 (12)	F3—F1^xiii	2.597 (6)
N1—F1^vii	3.176 (12)	F3—F1^i	2.597 (6)
N1—O2	3.340 (10)	F3—F1^xiv	2.597 (6)
N1—O2^iii	3.340 (10)	F3—F2^xiv	2.607 (4)
N2—F4^viii	2.730 (5)	F3—F2^i	2.607 (4)
N2—F4^ii	2.730 (5)	F3—F2^xiii	2.607 (4)
N2—F8^vi	2.750 (7)	F4—F6	2.635 (7)
N2—F8^v	2.750 (7)	F4—F5	2.712 (6)
N2—F1^vii	2.976 (8)	F4—F4^ii	2.773 (9)
N2—F1^iv	2.976 (8)	F4—O2	2.862 (12)
N2—F2^vii	3.013 (7)	F5—F6	2.666 (7)
N2—F2^iv	3.013 (7)	F5—F5^ii	2.695 (9)
N2—F3^iv	3.393 (7)	F5—O2	2.780 (9)
N3—F10	2.756 (9)	F6—F8^ii	2.604 (8)
N3—F2^i	2.845 (6)	F6—F8	2.604 (8)
N3—F2^iii	2.845 (6)	F6—F7^ii	2.634 (9)
N3—O2^ix	3.116 (12)	F6—F7	2.634 (9)
N3—F5	3.134 (9)	F6—F4^ii	2.635 (7)
N3—F5^ii	3.134 (9)	F6—F5^ii	2.666 (7)
N3—F8	3.185 (9)	F7—F8	2.385 (12)
N3—F8^ii	3.185 (9)	F7—O3	2.672 (13)
N3—O1^iii	3.390 (12)	F7—F7^ii	2.997 (17)
N3—O1	3.390 (12)	F8—F8^ii	2.682 (15)
N4—F1^iii	2.736 (8)	F8—O3	2.915 (12)
O1—Nb1—F2	96.9 (4)	F5—Nb2—F4	87.84 (19)
O1—Nb1—F2^i	96.9 (4)	F4^ii—Nb2—F4	89.9 (3)
F2—Nb1—F2^i	88.7 (4)	O2—Nb2—F6	178.7 (4)
O1—Nb1—F1^i	105.6 (4)	F5^ii—Nb2—F6	80.79 (18)
F2—Nb1—F1^i	157.3 (3)	F5—Nb2—F6	80.79 (18)
O1—Nb1—F1	105.6 (4)	F4^ii—Nb2—F6	79.31 (18)
F2—Nb1—F1	86.1 (2)	F4—Nb2—F6	79.31 (18)
F2^i—Nb1—F1	157.3 (3)	O3—Nb3—F7	96.2 (4)
O1—Nb1—F3	174.1 (5)	O3—Nb3—F7^ii	96.2 (4)
F2—Nb1—F3	78.93 (17)	F7—Nb3—F7^ii	110.7 (8)
F2^i—Nb1—F3	78.93 (17)	O3—Nb3—F8	103.1 (3)
F1^i—Nb1—F3	78.4 (2)	F7—Nb3—F8	78.3 (4)
F1—Nb1—F3	78.4 (2)	F7^ii—Nb3—F8	157.8 (4)
F1^i—Nb1—F1	90.4 (3)	O3—Nb3—F8^ii	103.1 (3)
O2—Nb2—F5^ii	98.3 (3)	F7—Nb3—F8^ii	157.8 (4)
O2—Nb2—F5	98.3 (3)	F7^ii—Nb3—F8^ii	78.3 (4)
F5^ii—Nb2—F5	87.6 (3)	F8—Nb3—F8^ii	86.7 (4)
O2—Nb2—F4^ii	101.6 (3)	O3—Nb3—F6	177.8 (4)
F5^ii—Nb2—F4^ii	87.84 (19)	F7—Nb3—F6	82.5 (3)
F5—Nb2—F4^ii	160.0 (2)	F7^ii—Nb3—F6	82.5 (3)
O2—Nb2—F4	101.6 (3)	F8—Nb3—F6	78.5 (2)
F5^ii—Nb2—F4	160.0 (2)	F8^ii—Nb3—F6	78.5 (2)

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

(III) rubidium oxofluorodiniobate

Crystal data

9(F9Nb2O2)·Cl·2(F)·30(Rb)	Dx = 3.442 Mg m^−3
Mr = 6136.93	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3m1	Cell parameters from 512 reflections
Hall symbol: -P 3 2	θ = 2.8–32.0°
a = 20.4958 (4) Å	µ = 14.11 mm^−1
c = 8.1385 (2) Å	T = 223 K
V = 2960.77 (11) Å^3	Prism, colorless
Z = 9	0.30 × 0.28 × 0.26 mm
F(000) = 2756

Data collection

Bruker P4 diffractometer	3800 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.052
Graphite monochromator	θmax = 34.0°, θmin = 2.8°
Detector resolution: 8.33 pixels mm^-1	h = −27→32
ω scans	k = −32→32
72081 measured reflections	l = −12→12
4318 independent reflections

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)] = 0.039	w = 1/[σ^2(Fo^2) + (0.0445P)^2 + 18.7832P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.104	(Δ/σ)max = 0.008
S = 1.09	Δρmax = 2.56 e Å^−3
3800 reflections	Δρmin = −1.75 e Å^−3
139 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00015 (5)

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	Occ. (<1)
Nb1	0.537402 (19)	0.07480 (4)	0.79084 (8)	0.01771 (12)
Nb2	0.40882 (4)	0.20441 (2)	0.30343 (11)	0.02379 (14)
Nb3	0.27454 (6)	0.13727 (3)	0.74899 (10)	0.03251 (19)
Rb1	0.57809 (3)	0.42191 (3)	0.26420 (13)	0.0403 (2)
Rb2	0.33914 (4)	0.33914 (4)	0.0000	0.02283 (15)
Rb3	0.50682 (7)	0.25341 (3)	0.76568 (14)	0.0417 (2)
Rb4	0.32760 (4)	0.32760 (4)	0.5000	0.02534 (16)
Rb5	0.09282 (3)	0.18564 (6)	0.72202 (15)	0.0409 (2)
F1	0.5689 (2)	0.0050 (3)	0.7184 (6)	0.0391 (9)
F2	0.6273 (2)	0.1235 (2)	0.9266 (6)	0.0354 (9)
F3	0.5000	0.0000	1.0000	0.046 (2)
F4	0.3400 (2)	0.1030 (2)	0.2259 (5)	0.0365 (9)
F5	0.4555 (2)	0.1614 (3)	0.4377 (6)	0.0444 (11)
F6	0.3269 (3)	0.16346 (17)	0.5038 (7)	0.0379 (13)
F7	0.2190 (4)	0.0415 (3)	0.6444 (10)	0.088 (2)
F8	0.3532 (4)	0.1107 (4)	0.7814 (9)	0.077 (2)
O1	0.5688 (3)	0.1375 (5)	0.6325 (9)	0.048 (2)
O2	0.4747 (5)	0.2374 (3)	0.1493 (12)	0.059 (2)
O3	0.2291 (10)	0.1146 (5)	0.9359 (12)	0.111 (5)
Cl1	0.0000	0.0000	0.0000	0.0356 (12)
F10	0.6667	0.3333	0.252 (4)	0.064 (8)	0.50
F11	0.6667	0.3333	0.981 (6)	0.084 (12)	0.50

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Nb1	0.01521 (17)	0.0239 (3)	0.0169 (3)	0.01193 (14)	0.00217 (11)	0.0043 (2)
Nb2	0.0276 (3)	0.01828 (19)	0.0286 (3)	0.01378 (16)	−0.0005 (3)	−0.00023 (13)
Nb3	0.0555 (5)	0.0319 (3)	0.0180 (3)	0.0278 (3)	−0.0022 (3)	−0.00111 (16)
Rb1	0.0366 (3)	0.0366 (3)	0.0320 (4)	0.0066 (4)	−0.0020 (2)	0.0020 (2)
Rb2	0.0257 (3)	0.0257 (3)	0.0172 (3)	0.0129 (3)	−0.00073 (13)	0.00073 (13)
Rb3	0.0581 (6)	0.0304 (3)	0.0459 (5)	0.0291 (3)	0.0012 (5)	0.0006 (2)
Rb4	0.0287 (3)	0.0287 (3)	0.0192 (3)	0.0149 (3)	0.00116 (14)	−0.00116 (14)
Rb5	0.0324 (3)	0.0358 (4)	0.0557 (7)	0.0179 (2)	−0.0034 (2)	−0.0069 (4)
F1	0.039 (2)	0.050 (2)	0.043 (2)	0.0332 (19)	0.0002 (18)	−0.013 (2)
F2	0.0212 (16)	0.036 (2)	0.044 (2)	0.0100 (15)	−0.0067 (16)	−0.0005 (17)
F3	0.049 (4)	0.036 (4)	0.049 (5)	0.018 (2)	0.014 (2)	0.029 (4)
F4	0.052 (2)	0.0222 (16)	0.036 (2)	0.0191 (16)	−0.0083 (18)	−0.0113 (15)
F5	0.037 (2)	0.048 (3)	0.061 (3)	0.030 (2)	−0.009 (2)	0.003 (2)
F6	0.038 (3)	0.046 (3)	0.027 (2)	0.0188 (15)	0.001 (2)	0.0004 (12)
F7	0.076 (4)	0.029 (2)	0.122 (6)	−0.002 (3)	0.034 (4)	−0.012 (3)
F8	0.081 (4)	0.074 (4)	0.093 (5)	0.050 (3)	−0.020 (4)	0.024 (4)
O1	0.050 (3)	0.062 (5)	0.035 (4)	0.031 (3)	0.0140 (19)	0.028 (4)
O2	0.057 (5)	0.060 (4)	0.057 (5)	0.029 (3)	0.028 (5)	0.014 (2)
O3	0.144 (14)	0.158 (11)	0.025 (4)	0.072 (7)	0.012 (7)	0.006 (3)
Cl1	0.0198 (12)	0.0198 (12)	0.067 (4)	0.0099 (6)	0.000	0.000
F10	0.040 (8)	0.040 (8)	0.11 (3)	0.020 (4)	0.000	0.000
F11	0.043 (10)	0.043 (10)	0.17 (4)	0.021 (5)	0.000	0.000

Geometric parameters (Å, º)

Nb1—O1	1.703 (7)	Nb3—F6	2.201 (6)
Nb1—F1^i	1.933 (4)	Rb1—F5^iii	2.931 (5)
Nb1—F1	1.933 (4)	Rb1—F5^ii	2.931 (5)
Nb1—F2	1.943 (4)	Rb1—F10	3.1460 (17)
Nb1—F2^i	1.943 (4)	Rb2—F8^iv	2.782 (6)
Nb1—F3	2.1589 (6)	Rb2—F8^v	2.782 (6)
Nb2—O2	1.715 (8)	Rb2—F4^vi	2.793 (4)
Nb2—F5^ii	1.931 (4)	Rb2—F4^ii	2.793 (4)
Nb2—F5	1.931 (4)	Rb3—F2^i	2.875 (4)
Nb2—F4	1.943 (4)	Rb3—F2^iii	2.875 (4)
Nb2—F4^ii	1.943 (4)	Rb3—F11	3.33 (2)
Nb2—F6	2.185 (6)	Rb4—F1^iii	2.808 (4)
Nb3—O3	1.721 (11)	Rb4—F1^vii	2.808 (4)
Nb3—F7	1.907 (6)	Rb5—F7^viii	2.748 (5)
Nb3—F7^ii	1.907 (6)	Rb5—F7^ii	2.748 (5)
Nb3—F8^ii	1.960 (6)	Rb5—O3^ix	2.889 (10)
Nb3—F8	1.960 (6)	Rb5—Cl1^x	3.9970 (12)
O1—Nb1—F1^i	100.9 (3)	F5—Nb2—F4	87.50 (19)
O1—Nb1—F1	100.9 (3)	O2—Nb2—F4^ii	101.0 (3)
F1^i—Nb1—F1	89.5 (3)	F4—Nb2—F4^ii	89.9 (3)
O1—Nb1—F2	98.0 (3)	O2—Nb2—F6	178.7 (4)
F1^i—Nb1—F2	161.1 (2)	F5^ii—Nb2—F6	82.11 (19)
F1—Nb1—F2	88.40 (18)	F4—Nb2—F6	79.86 (17)
F2—Nb1—F2^i	87.5 (3)	O3—Nb3—F7	98.8 (4)
O1—Nb1—F3	177.1 (3)	O3—Nb3—F7^ii	98.8 (4)
F1^i—Nb1—F3	81.15 (15)	F7—Nb3—F7^ii	93.9 (5)
F1—Nb1—F3	81.15 (15)	O3—Nb3—F8^ii	102.4 (4)
F2—Nb1—F3	79.95 (13)	F7—Nb3—F8^ii	158.7 (3)
F2^i—Nb1—F3	79.95 (13)	O3—Nb3—F8	102.4 (4)
O2—Nb2—F5^ii	97.0 (3)	F7—Nb3—F8	85.7 (3)
O2—Nb2—F5	97.0 (3)	F8^ii—Nb3—F8	87.1 (4)
F5^ii—Nb2—F5	89.5 (3)	O3—Nb3—F6	177.1 (6)
O2—Nb2—F4	101.0 (3)	F7—Nb3—F6	79.3 (2)
F5^ii—Nb2—F4	162.0 (2)	F8—Nb3—F6	79.7 (2)

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

(IV) rubidium oxofluoromolybdate

Crystal data

3(F7Mo2O4)·F·10(Rb)	Dx = 3.533 Mg m^−3
Mr = 2040.34	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3m1	Cell parameters from 512 reflections
Hall symbol: -P 3 2	θ = 2.8–31.7°
a = 20.2744 (2) Å	µ = 14.66 mm^−1
c = 8.0811 (1) Å	T = 243 K
V = 2876.72 (5) Å^3	Prism, colorless
Z = 9	0.38 × 0.29 × 0.20 mm
F(000) = 2748

Data collection

Bruker P4 diffractometer	4199 independent reflections
Radiation source: fine-focus sealed tube	3674 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.043
Detector resolution: 8.33 pixels mm^-1	θmax = 34.0°, θmin = 2.8°
ω scans	h = −31→31
Absorption correction: multi-scan SADABS v.2.03; Bruker 1999	k = −27→31
Tmin = 0.072, Tmax = 0.158	l = −12→12
65645 measured reflections

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) + (0.0671P)^2 + 14.0018P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.119	(Δ/σ)max = 0.016
S = 1.08	Δρmax = 3.58 e Å^−3
3674 reflections	Δρmin = −1.75 e Å^−3
139 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.00026 (5)

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	Occ. (<1)
Mo1	0.536270 (14)	0.07254 (3)	0.78655 (6)	0.02384 (9)
Mo2	0.40922 (3)	0.204609 (17)	0.30643 (8)	0.03274 (11)
Mo3	0.27359 (3)	0.136794 (16)	0.75362 (6)	0.02762 (10)
Rb1	0.57809 (2)	0.42191 (2)	0.25143 (9)	0.03932 (15)
Rb2	0.34062 (3)	0.34062 (3)	0.0000	0.02856 (12)
Rb3	0.50739 (5)	0.25369 (2)	0.75732 (10)	0.04097 (15)
Rb4	0.32677 (3)	0.32677 (3)	0.5000	0.02963 (12)
Rb5	0.09321 (2)	0.18643 (4)	0.70946 (10)	0.04012 (15)
F1	0.56736 (13)	0.00406 (17)	0.7207 (4)	0.0412 (6)
F2	0.62653 (13)	0.12305 (16)	0.9200 (4)	0.0360 (7)
F3	0.5000	0.0000	1.0000	0.0337 (12)
F4	0.33930 (17)	0.10465 (14)	0.2296 (4)	0.0389 (7)
F5	0.45503 (16)	0.16233 (17)	0.4366 (5)	0.0472 (8)
F6	0.3274 (3)	0.16372 (13)	0.5078 (5)	0.0397 (10)
F7	0.2197 (3)	0.0442 (2)	0.6401 (9)	0.115 (2)
F8	0.3486 (2)	0.1092 (2)	0.7873 (6)	0.0747 (12)
O1	0.56719 (16)	0.1344 (3)	0.6274 (6)	0.0430 (12)
O2	0.4723 (4)	0.23617 (18)	0.1487 (8)	0.0534 (15)
O3	0.2273 (5)	0.1137 (2)	0.9341 (9)	0.076 (3)
F9	0.0000	0.0000	0.0000	0.49 (7)
F10	0.6667	0.3333	0.240 (3)	0.068 (7)	0.50
F11	0.6667	0.3333	0.960 (5)	0.090 (10)	0.50

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Mo1	0.02277 (13)	0.0283 (2)	0.02231 (19)	0.01413 (10)	0.00432 (8)	0.00865 (16)
Mo2	0.0342 (3)	0.02748 (15)	0.0387 (3)	0.01712 (13)	0.0007 (2)	0.00036 (11)
Mo3	0.0375 (2)	0.02584 (14)	0.02339 (19)	0.01875 (12)	−0.00401 (18)	−0.00201 (9)
Rb1	0.03747 (16)	0.03747 (16)	0.0329 (3)	0.0111 (2)	−0.00131 (14)	0.00131 (14)
Rb2	0.02853 (12)	0.02853 (12)	0.0224 (2)	0.00959 (16)	−0.00086 (11)	0.00086 (11)
Rb3	0.0569 (4)	0.03170 (17)	0.0427 (3)	0.0285 (2)	0.0021 (3)	0.00106 (16)
Rb4	0.03007 (13)	0.03007 (13)	0.0222 (2)	0.01015 (16)	0.00380 (11)	−0.00380 (11)
Rb5	0.0383 (2)	0.0416 (3)	0.0415 (3)	0.02079 (17)	−0.00297 (14)	−0.0059 (3)
F1	0.0401 (9)	0.0549 (11)	0.0435 (14)	0.0349 (8)	−0.0024 (10)	−0.0178 (11)
F2	0.0209 (9)	0.0381 (12)	0.0450 (15)	0.0116 (8)	−0.0040 (10)	0.0015 (11)
F3	0.038 (2)	0.028 (2)	0.032 (2)	0.0140 (11)	0.0076 (10)	0.015 (2)
F4	0.0616 (13)	0.0231 (9)	0.0358 (13)	0.0240 (9)	−0.0080 (12)	−0.0073 (9)
F5	0.0513 (11)	0.0487 (12)	0.0573 (19)	0.0368 (9)	−0.0165 (13)	−0.0062 (13)
F6	0.051 (2)	0.0473 (17)	0.0221 (15)	0.0255 (12)	−0.0009 (17)	−0.0005 (9)
F7	0.105 (4)	0.0327 (18)	0.138 (5)	−0.018 (2)	0.048 (4)	−0.017 (3)
F8	0.0756 (18)	0.085 (2)	0.078 (3)	0.0505 (16)	−0.011 (2)	0.020 (2)
O1	0.0453 (19)	0.055 (3)	0.032 (2)	0.0275 (15)	0.0114 (11)	0.023 (2)
O2	0.052 (3)	0.062 (3)	0.043 (3)	0.0261 (17)	0.018 (3)	0.0089 (13)
O3	0.074 (5)	0.108 (5)	0.036 (3)	0.037 (2)	0.009 (3)	0.0044 (17)
F9	0.35 (5)	0.35 (5)	0.8 (2)	0.17 (2)	0.000	0.000
F10	0.051 (6)	0.051 (6)	0.103 (18)	0.025 (3)	0.000	0.000
F11	0.045 (7)	0.045 (7)	0.18 (3)	0.023 (3)	0.000	0.000

Geometric parameters (Å, º)

Mo1—O1	1.683 (5)	Rb3—F2^i	2.865 (3)
Mo1—F1^i	1.866 (3)	Rb3—F5^v	3.051 (4)
Mo1—F1	1.866 (3)	Rb3—F5	3.051 (4)
Mo1—F2	1.920 (3)	Rb3—F8^v	3.094 (4)
Mo1—F2^i	1.920 (3)	Rb3—F8	3.094 (4)
Mo1—F3	2.1442 (5)	Rb3—O2^xii	3.222 (6)
Mo1—Rb2^ii	3.8781 (5)	Rb3—F11	3.240 (19)
Mo1—Rb2^iii	3.8781 (5)	Rb4—F1^vi	2.823 (3)
Mo1—Rb3^iv	4.0048 (4)	Rb4—F1^x	2.823 (3)
Mo1—Rb3	4.0048 (4)	Rb4—F7^ix	2.957 (7)
Mo2—O2	1.689 (6)	Rb4—F7^v	2.957 (7)
Mo2—F5^v	1.871 (3)	Rb4—F4^v	2.967 (3)
Mo2—F5	1.871 (3)	Rb4—F4^ix	2.967 (3)
Mo2—F4^v	1.905 (2)	Rb4—F5^ix	3.049 (3)
Mo2—F4	1.905 (2)	Rb4—F5^v	3.049 (3)
Mo2—F6	2.170 (4)	Rb4—F8^ix	3.083 (5)
Mo2—Rb5^ii	3.9138 (10)	Rb4—F8^v	3.083 (5)
Mo2—Rb4	3.9390 (3)	Rb5—F7^v	2.740 (4)
Mo2—Rb4^ii	3.9390 (3)	Rb5—F7^xiii	2.740 (4)
Mo2—Rb1	4.0306 (5)	Rb5—O3^xiv	2.968 (7)
Mo3—O3	1.669 (7)	Rb5—F4^ix	3.030 (3)
Mo3—F7	1.873 (5)	Rb5—F4^xv	3.030 (3)
Mo3—F7^v	1.873 (5)	Rb5—F6^ix	3.035 (4)
Mo3—F8^v	1.884 (5)	Rb5—F7^ix	3.177 (7)
Mo3—F8	1.884 (5)	Rb5—F7^xv	3.177 (7)
Mo3—F6	2.200 (4)	F1—F3	2.618 (3)
Mo3—Rb4^ii	4.0056 (5)	F1—F2	2.638 (4)
Mo3—Rb4	4.0056 (5)	F1—F1^i	2.649 (5)
Mo3—Rb5^ii	4.0430 (9)	F1—O1	2.749 (6)
Rb1—F5^vi	2.965 (3)	F2—O1	2.714 (5)
Rb1—F5^v	2.965 (3)	F2—F3	2.612 (2)
Rb1—F2^vii	3.042 (3)	F2—F2^i	2.636 (6)
Rb1—F2^viii	3.042 (3)	F4—F6	2.614 (4)
Rb1—O1^vi	3.063 (5)	F4—F5	2.632 (4)
Rb1—F10	3.1118 (12)	F4—F4^v	2.636 (6)
Rb1—F1^ix	3.118 (3)	F4—O2	2.761 (6)
Rb1—F1^x	3.118 (3)	F5—F5^v	2.643 (7)
Rb2—F8^viii	2.743 (5)	F5—F6	2.664 (5)
Rb2—F8^ix	2.743 (5)	F5—O2	2.693 (7)
Rb2—F4^xi	2.829 (3)	F6—F7	2.548 (6)
Rb2—F4^v	2.829 (3)	F6—F8	2.642 (6)
Rb2—F1^x	2.956 (3)	F7—F8	2.556 (7)
Rb2—F1^vii	2.956 (3)	F7—F7^v	2.662 (11)
Rb2—F2^x	2.958 (3)	F7—O3	2.726 (9)
Rb2—F2^vii	2.958 (3)	F8—F8^v	2.640 (10)
Rb2—F3^vii	3.2314 (6)	F8—O3	2.772 (9)
Rb3—F2^vi	2.865 (3)
O1—Mo1—F1	101.40 (17)	F4^v—Mo2—F4	87.5 (2)
F1^i—Mo1—F1	90.42 (15)	O2—Mo2—F6	179.6 (2)
O1—Mo1—F2	97.53 (17)	F5—Mo2—F6	82.13 (13)
F1^i—Mo1—F2	160.90 (14)	F4—Mo2—F6	79.50 (12)
F1—Mo1—F2	88.31 (13)	O3—Mo3—F7	100.5 (3)
F2—Mo1—F2^i	86.7 (2)	F7—Mo3—F7^v	90.6 (5)
O1—Mo1—F3	176.3 (2)	F7—Mo3—F8^v	157.1 (2)
F1—Mo1—F3	81.19 (10)	O3—Mo3—F8	102.3 (2)
F2—Mo1—F3	79.78 (9)	F7—Mo3—F8	85.8 (3)
O2—Mo2—F5	98.17 (19)	F8^v—Mo3—F8	88.9 (3)
F5^v—Mo2—F5	89.9 (2)	O3—Mo3—F6	176.3 (3)
F5—Mo2—F4^v	161.61 (14)	F7—Mo3—F6	77.0 (2)
O2—Mo2—F4	100.20 (19)	F8—Mo3—F6	80.21 (17)
F5—Mo2—F4	88.37 (13)

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

(V) rubidium oxofluorotungstate

Crystal data

3(F7W2O4)·F·10(Rb)	Dx = 4.496 Mg m^−3
Mr = 2567.80	Mo Kα radiation, λ = 0.71073 Å
Trigonal, P3m1	Cell parameters from 512 reflections
Hall symbol: -P 3 2	θ = 2.8–30.2°
a = 20.1457 (7) Å	µ = 31.01 mm^−1
c = 8.0951 (5) Å	T = 203 K
V = 2845.2 (2) Å^3	Prism, colorless
Z = 9	0.32 × 0.26 × 0.20 mm
F(000) = 3324

Data collection

Bruker P4 diffractometer	3254 independent reflections
Radiation source: fine-focus sealed tube	2724 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.093
Detector resolution: 8.33 pixels mm^-1	θmax = 31.0°, θmin = 2.8°
ω scans	h = −28→29
Absorption correction: multi-scan SADABS v.2.03; Bruker 1999	k = −26→28
Tmin = 0.036, Tmax = 0.063	l = −11→11
32262 measured reflections

Refinement

Refinement on F^2	0 restraints
Least-squares matrix: full	Primary atom site location: structure-invariant direct methods
R[F^2 > 2σ(F^2)] = 0.057	Secondary atom site location: difference Fourier map
wR(F^2) = 0.150	w = 1/[σ^2(Fo^2) + (0.0713P)^2 + 119.5815P] where P = (Fo^2 + 2Fc^2)/3
S = 1.03	(Δ/σ)max = 0.018
2724 reflections	Δρmax = 6.92 e Å^−3
137 parameters	Δρmin = −2.66 e Å^−3

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	Occ. (<1)
W1	0.536013 (18)	0.07203 (4)	0.79253 (8)	0.02227 (13)
W2	0.40948 (4)	0.20474 (2)	0.30982 (9)	0.02713 (14)
W3	0.27020 (4)	0.135100 (18)	0.72991 (8)	0.02414 (13)
Rb1	0.58080 (5)	0.41920 (5)	0.2646 (2)	0.0334 (4)
Rb2	0.33394 (8)	0.33394 (8)	0.0000	0.0289 (4)
Rb3	0.51037 (11)	0.25519 (5)	0.7690 (2)	0.0328 (4)
Rb4	0.33234 (9)	0.33234 (9)	0.5000	0.0311 (4)
Rb5	0.09113 (6)	0.18226 (12)	0.7345 (2)	0.0399 (4)
F1	0.5654 (4)	0.0013 (5)	0.7307 (12)	0.059 (2)
F2	0.6267 (4)	0.1221 (5)	0.9270 (12)	0.048 (2)
F3	0.5000	0.0000	1.0000	0.060 (6)
F4	0.3416 (5)	0.1058 (4)	0.2394 (10)	0.044 (2)
F5	0.4535 (4)	0.1626 (4)	0.4460 (10)	0.0373 (18)
F6	0.3258 (7)	0.1629 (3)	0.5042 (14)	0.042 (3)
F7	0.2333 (11)	0.0411 (7)	0.666 (3)	0.301 (8)
F8	0.3462 (8)	0.1152 (11)	0.791 (2)	0.155 (7)
O1	0.5692 (5)	0.1385 (10)	0.633 (2)	0.067 (4)
O2	0.4804 (9)	0.2402 (4)	0.1534 (17)	0.042 (3)
O3	0.2182 (12)	0.1091 (6)	0.923 (3)	0.106 (10)
F9	0.0000	0.0000	0.761 (6)	0.055 (13)	0.50
F10	0.6667	0.3333	0.261 (4)	0.027 (7)*	0.50
F11	0.6667	0.3333	−0.013 (4)	0.022 (6)*	0.50

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
W1	0.02068 (17)	0.0277 (3)	0.0208 (3)	0.01386 (13)	0.00049 (11)	0.0010 (2)
W2	0.0414 (3)	0.02434 (18)	0.0214 (3)	0.02068 (17)	−0.0056 (3)	−0.00282 (14)
W3	0.0264 (3)	0.02446 (19)	0.0222 (3)	0.01321 (13)	0.0059 (2)	0.00296 (11)
Rb1	0.0322 (4)	0.0322 (4)	0.0251 (7)	0.0080 (5)	0.0010 (3)	−0.0010 (3)
Rb2	0.0367 (4)	0.0367 (4)	0.0133 (6)	0.0183 (5)	−0.0019 (3)	0.0019 (3)
Rb3	0.0440 (9)	0.0275 (5)	0.0324 (8)	0.0220 (4)	−0.0032 (7)	−0.0016 (4)
Rb4	0.0420 (4)	0.0420 (4)	0.0147 (6)	0.0249 (5)	0.0044 (3)	−0.0044 (3)
Rb5	0.0411 (6)	0.0473 (10)	0.0333 (9)	0.0236 (5)	−0.0056 (4)	−0.0113 (8)
F1	0.064 (3)	0.087 (4)	0.052 (5)	0.058 (3)	−0.012 (4)	−0.034 (4)
F2	0.027 (3)	0.063 (5)	0.046 (5)	0.016 (3)	0.002 (3)	−0.006 (4)
F3	0.052 (8)	0.017 (7)	0.099 (17)	0.008 (4)	0.003 (5)	0.006 (9)
F4	0.069 (4)	0.027 (3)	0.038 (4)	0.026 (3)	−0.014 (4)	−0.006 (3)
F5	0.047 (3)	0.039 (3)	0.033 (4)	0.026 (3)	−0.014 (3)	−0.002 (3)
F6	0.040 (6)	0.046 (5)	0.037 (6)	0.020 (3)	−0.004 (5)	−0.002 (3)
F7	0.347 (14)	0.023 (5)	0.387 (17)	−0.015 (8)	0.324 (12)	−0.029 (8)
F8	0.067 (7)	0.221 (14)	0.135 (11)	0.040 (8)	−0.014 (8)	0.105 (10)
O1	0.068 (7)	0.080 (9)	0.058 (8)	0.040 (5)	0.031 (4)	0.062 (7)
O2	0.062 (9)	0.043 (5)	0.027 (6)	0.031 (5)	−0.004 (6)	−0.002 (3)
O3	0.051 (11)	0.18 (2)	0.040 (10)	0.025 (6)	−0.003 (9)	−0.001 (5)
F9	0.054 (15)	0.054 (15)	0.06 (3)	0.027 (8)	0.000	0.000

Geometric parameters (Å, º)

W1—O1	1.736 (14)	Rb4—F5^x	2.981 (7)
W1—F1^i	1.863 (10)	Rb4—F5^v	2.981 (7)
W1—F1	1.863 (10)	Rb4—F8^x	3.22 (2)
W1—F2	1.923 (8)	Rb4—F8^v	3.22 (2)
W1—F2^i	1.923 (8)	Rb5—F7^xiii	2.823 (13)
W1—F3	2.0976 (6)	Rb5—F7^v	2.823 (13)
W1—Rb2^ii	3.9487 (15)	Rb5—O3^xiv	2.85 (2)
W1—Rb2^iii	3.9487 (15)	Rb5—F4^x	3.080 (9)
W1—Rb3^iv	3.9780 (6)	Rb5—F4^xv	3.080 (9)
W1—Rb3	3.9780 (6)	Rb5—F6^x	3.163 (12)
W2—O2	1.771 (15)	Rb5—F9	3.187 (4)
W2—F4	1.855 (7)	F1—F3	2.540 (9)
W2—F4^v	1.855 (7)	F1—F1^i	2.607 (17)
W2—F5	1.863 (8)	F1—F2	2.639 (13)
W2—F5^v	1.863 (8)	F1—O1	2.838 (17)
W2—F6	2.147 (12)	F2—F3	2.576 (8)
W2—Rb4^ii	3.9228 (5)	F2—F2^i	2.644 (18)
W2—Rb4	3.9227 (5)	F2—O1	2.738 (17)
W2—Rb1^iv	3.9750 (7)	F3—F1^xvi	2.540 (9)
W2—Rb1	3.9750 (7)	F3—F1^xvii	2.540 (9)
W3—F7	1.731 (12)	F3—F1^i	2.540 (9)
W3—F7^v	1.731 (12)	F3—F2^xvii	2.576 (8)
W3—O3	1.80 (2)	F3—F2^xvi	2.576 (8)
W3—F8	1.834 (18)	F3—F2^i	2.576 (8)
W3—F8^v	1.834 (18)	F4—F6	2.527 (13)
W3—F6	2.068 (12)	F4—F5	2.570 (11)
W3—Rb4^ii	3.9806 (13)	F4—F4^v	2.620 (16)
W3—Rb4	3.9806 (13)	F4—O2	2.840 (15)
W3—Rb5^ii	4.060 (2)	F4—F7^xviii	3.08 (2)
Rb1—F5^vi	2.965 (9)	F4—F1^xix	3.503 (13)
Rb1—F5^v	2.965 (9)	F5—F5^v	2.582 (16)
Rb1—F10	2.9962 (19)	F5—F6	2.618 (13)
Rb1—O1^vi	3.009 (16)	F5—O2	2.738 (14)
Rb1—F2^vii	3.113 (10)	F5—O1	3.017 (11)
Rb1—F2^viii	3.113 (10)	F5—F8	3.368 (19)
Rb1—F1^ix	3.127 (9)	F6—F4^v	2.527 (13)
Rb1—F1^x	3.127 (8)	F6—F7^v	2.578 (17)
Rb1—O2	3.257 (9)	F6—F7	2.578 (17)
Rb1—O2^vi	3.257 (9)	F6—F5^v	2.618 (13)
Rb2—F8^viii	2.779 (18)	F6—F8^v	2.626 (19)
Rb2—F8^x	2.779 (18)	F6—F8	2.626 (19)
Rb2—F4^xi	2.827 (8)	F7—F8	2.24 (3)
Rb2—F4^v	2.827 (8)	F7—O3	2.59 (2)
Rb2—F1^ix	2.987 (10)	F7—F7^v	3.04 (3)
Rb2—F1^vii	2.987 (10)	F7—F7^xviii	3.05 (4)
Rb2—F2^ix	2.997 (11)	F7—F4^xviii	3.08 (2)
Rb2—F2^vii	2.997 (11)	F7—F8^v	3.48 (2)
Rb3—F2^vi	2.848 (8)	F8—F8^v	2.33 (4)
Rb3—F2^i	2.848 (8)	F8—O3	2.73 (3)
Rb3—F5	3.080 (8)	O1—F2^i	2.738 (17)
Rb3—F5^v	3.080 (8)	O1—F1^i	2.838 (17)
Rb3—F8	3.098 (14)	O1—F5^i	3.017 (11)
Rb3—F8^v	3.098 (14)	O2—F5^v	2.738 (14)
Rb3—O2^xii	3.156 (14)	O2—F4^v	2.840 (15)
Rb3—F11^xii	3.248 (19)	O2—F2^xx	3.135 (12)
Rb3—O1	3.307 (13)	O2—F2^vii	3.135 (12)
Rb3—O1^vi	3.307 (13)	O3—F7^v	2.59 (2)
Rb4—F1^vi	2.791 (9)	O3—F8^v	2.73 (3)
Rb4—F1^ix	2.791 (9)	F10—Rb1^vi	2.9962 (19)
Rb4—F7^x	2.852 (19)	F10—Rb1^iv	2.9962 (19)
Rb4—F7^v	2.852 (19)	F11—Rb3^xxi	3.248 (18)
Rb4—F4^v	2.938 (8)	F11—Rb3^xxii	3.248 (18)
Rb4—F4^x	2.938 (8)	F11—Rb3^vii	3.248 (18)
O1—W1—F1^i	104.0 (5)	F5—W2—F5^v	87.8 (5)
O1—W1—F1	104.0 (5)	O2—W2—F6	178.5 (6)
F1^i—W1—F1	88.8 (5)	F4—W2—F6	77.9 (3)
O1—W1—F2	96.8 (5)	F4^v—W2—F6	77.9 (3)
F1^i—W1—F2	159.1 (4)	F5—W2—F6	81.2 (3)
F1—W1—F2	88.4 (4)	F5^v—W2—F6	81.2 (3)
O1—W1—F2^i	96.8 (5)	F7—W3—F7^v	123.1 (18)
F1^i—W1—F2^i	88.4 (4)	F7—W3—O3	94.0 (7)
F1—W1—F2^i	159.1 (4)	F7^v—W3—O3	94.0 (7)
F2—W1—F2^i	86.9 (6)	F7—W3—F8	77.9 (10)
O1—W1—F3	174.9 (6)	F7^v—W3—F8	155.3 (9)
F1^i—W1—F3	79.5 (3)	O3—W3—F8	97.4 (7)
F1—W1—F3	79.5 (3)	F7—W3—F8^v	155.3 (9)
F2—W1—F3	79.6 (3)	F7^v—W3—F8^v	77.9 (10)
F2^i—W1—F3	79.6 (3)	O3—W3—F8^v	97.4 (7)
O2—W2—F4	103.1 (4)	F8—W3—F8^v	78.9 (12)
O2—W2—F4^v	103.1 (4)	F7—W3—F6	85.0 (6)
F4—W2—F4^v	89.8 (6)	F7^v—W3—F6	85.0 (6)
O2—W2—F5	97.8 (4)	O3—W3—F6	177.8 (8)
F4—W2—F5	87.4 (3)	F8—W3—F6	84.3 (6)
F4^v—W2—F5	159.0 (4)	F8^v—W3—F6	84.3 (6)
O2—W2—F5^v	97.8 (4)	W1^xvii—F3—W1	180.0
F4—W2—F5^v	159.0 (4)	W3—F6—W2	165.1 (6)
F4^v—W2—F5^v	87.4 (3)

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