Poly[hexa­aqua­octa-μ₃-hydroxido-tetra­kis(μ₃-methyl­enedisulfonato)-μ₆-oxido-hexa­ytterbium(III)]: the first lanthanide sulfonate containing a hexa­nuclear Ln–hydroxide/oxide cluster synthesized via `ligand-controlled acidolysis' of lanthanide oxide

The combination of redox and acid sites in lanthanide sulfonate leads to a potentially multifunctional catalyst for oxidation reactions. The title lanthanide sulfonate compound, [Yb₆(CH₂O₆S₂)₄O(OH)₈(H₂O)₆]_n, exhibits a novel one-dimensional columnar structure along the a direction. In the building unit of the columnar oligomer, a face-capped lanthanide octa­hedron, viz. [Ln₆(μ₆-O)(μ₃-OH)₈]⁸⁺, is found with an inter­stitial μ₆-oxide group lying on an inversion centre, reports of which are rare in the literature. Adjacent hexa­meric cations are connected via two pairs of O—S—O bridges, thus forming a neutral column. The three-dimensional network is stabilized by an intricate pattern of inter­columnar hydrogen bonds.

S1. Comment

Polynuclear metal–hydroxo/oxo complexes are of interest not only because of their promising application as advanced materials with noteworthy spectroscopic, magnetic and catalytic properties (Zheng, 2004), but also because of their potential biological relevance. It is known that Ln–hydroxo/oxo (Ln = lanthanide) clusters are capable of catalysing the hydrolytic cleavage of phosphate diester bonds (Straeter et al., 1996) and the robust bonds of nucleic acids (Oh et al., 1996).

Simple hydrolysis of lanthanide ions often leads to unpredictable, serendipitous and ill-defined lanthanide hydroxides and oxo/hydroxides as a result of the inherent properties of the lanthanide cations (Cotton, 1991). Because of the high charge and polarizing power of the lanthanide ions, there is a strong tendency for them to hydrolyse readily in aqueous solutions. Furthermore, trivalent rare earth ions show large and variable coordination numbers and geometries with small energy differences (Bünzli, 1997). Thus, it is generally difficult to control the oligomerization of rare earth centres. Chelating ligands such as amino acids, ketonates, carboxylates and alkoxides are introduced to control the hydrolysis of the lanthanide ions and selectively incorporate them into highly organized cluster architectures (Wang et al., 1999, 2001, 2002; Ma et al., 2000; Plakatouras et al., 1994; Chen et al., 1997; Evans et al., 1998; Anwander et al., 1997).

Due to the weak coordination strength of monosulfonate ions, the coordination chemistry of the sulfonate ion has been less well investigated in comparison with other organic acidato anions such as carbonates and phosphonates (Côté & Shimizu, 2003). However, by employing disulfonates, which can provide multiple potentially chelating coordination sites, stable architectures sustained by sulfonate–metal interactions can be obtained with various dimensionalities (Cai, 2004; Li et al., 2008; Mi et al., 2007; Videnova-Adrabinska, 2007). This integration into complexes of rare earth sulfonates could produce a multifunctional catalyst, especially for oxidation reactions, considering the strong catalytic activity of the rare earth elements and the relatively strong acid character of sulfonate groups (Snejko et al., 2002; Gándara et al., 2007). Nevertheless, to the best of our knowledge, sulfonate-supported lanthanide cluster architectures have rarely [not?] been reported previously. As an extension of these studies, we herein report the unique synthesis and structure of a hexanuclear Ln–hydroxo/oxo cluster supported by methylenedisulfonate, [Yb₆O(OH)₈(mds)₄(H₂O)₆]n [mds = CH₂(SO₃)₂], (I). As a relatively strong acid, sulfonates could accordingly react easily with metal oxides. Hence, instead of hydrolysis of the lanthanide ion with assistance of the ligand, hydrothermal reaction of mdsH₂ and Yb₂O₃ at a proper ratio results in acidolysis products, yielding colourless prism-like crystals of compound (I).

X-ray structure analysis reveals that (I) is composed of an unusual hexanuclear cation, [Yb₆(µ₆-O)(µ₃-OH)₈(H₂O)₆]⁸⁺, and methylenedisulfonate anions (Fig. 1). The hexameric cation is based on a slightly distorted Yb₆ octahedron, which is sustained by a µ₆-oxo ligand, O1, lying on an inversion centre. Each Yb₃ triangular face is further capped by a µ₃-hydroxo ligand. All bond lengths are comparable to those in {[(DMF)₁₆Yb₆(µ₆-O)(µ₃-OH)₈(µ-CN)Pd (µ-CN)(CN)₂]⁶⁺}_n [DMF = ?] with a similar hexa-metal core [Yb—O (interstitial O atom): 2.413 (1)–2.450 (1) Å; Yb—O (OH^- O atom): 2.270 (7)–2.405 (7) Å] (Liu, et al., 1998), which is a cyanide-bridged chain polymer. The Yb³⁺ cations in the asymmetric unit of (I) (Yb1, Yb2 and Yb3 in Fig. 1) are eight-coordinate. In addition to one interstitial and four hydroxyl O atoms, Yb1 and Yb2 are each chelated by an mds ligand using two sulfonate O atoms, and the remaining eighth coordination positions are occupied by a water O atom (O18) and a sulfonate O atom [O7ⁱⁱ, symmetry code (ii): 1+x, y, z], respectively. Yb3 is further surrounded by two coordinate water O atoms (O19 and O20) and one sulfonate O atom [O13^iv, symmetry code (iv): 2-x, 1-y, 1-z].

Adjacent hexameric cations are bridged via two pairs of O—S—O functionalities [functional groups?] (O6—S1—O7 and O12—S3—O13) from chelating methylenedisulfonates (mds^2-), thus generating a novel neutral one-dimensional columnar structure along the a direction (Fig. 2). Within the column, four intra-column hydrogen bonds are found: O4(H)···O14ⁱ, O5(H)···O12^iv, O19(H)···O10^vi and O20(H)···O17ⁱ [symmetry codes: (i) 1-x, 1-y, 1-z; (iv) 2-x, 1-y, 1-z; (vi) 1+x, y, z, see Table 2]. Each column has six equivalent neighbours. The three-dimensional network is stabilized by an intricate inter-column hydrogen-bond network [O2(H)···O16ⁱⁱ, O3(H)···O11ⁱⁱⁱ, O18(H)···O16ⁱⁱ, O8(H)···O14^v, O19(H)···O8^vii and O20(H)···O17^viii; symmetry codes: (ii) 1/2-x, 1/2+y, 3/2-z; (iii) 1-x, 1-y, 1-z; (v) -1/2+x, 3/2-y, 1/2+z; (vii) 1/2-x, -1/2+y, 3/2-z; (viii) x, -1+y, z, see Table 2].

In summary, compound (I) was directly synthesized via `ligand-controlled acidolysis' of lanthanide oxide and demonstrates a novel one-dimensional columnar structure. A face-capped octahedral [Ln₆(µ₆-O)(µ₃-OH)₈]⁸⁺ [unit?] with an interstitial µ₆-oxo group acts as a building block of the column. Thus, compound (I) is the first lanthanide sulfonate containing a hexanuclear Ln–hydroxo/oxo cluster. The chelating multidentate ligand, methylenedisulfonate, is crucial in the synthesis and formation of compound (I). Because methylenedisulfonic acid is a relatively strong acid, it is possible to synthesize the Ln–hydroxo/oxo cluster via acidolysis of lanthanide oxide. In addition, the chelation of methylenedisulfonate to the Yb cation stabilizes the hexamer cluster. The three-dimensional network is formed by bridged clusters via the coordination of unchelating sulfonate O to Yb cations of neighbouring clusters, and then by intercolumnar hydrogen bonds with sulfonate O atoms acting as acceptors. In this way, a high-dimensional architecture constructed from the Ln–hydroxo/oxo cluster unit is rationally synthesized via acidolysis of lanthanide oxide with the cooperation of other chelating multidentate sulfonate ligands. By the introduction of suitable guest moieties into the current system, these complexes of high-dimensional framework may potentially become competitive catalysts for oxidation reactions.

Related literature

For related literature, see: Anwander et al. (1997); Bünzli (1997); Côté & Shimizu (2003); Cai (2004); Chen et al. (1997); Cotton (1991); Evans et al. (1998); Gándara et al. (2007); Li et al. (2008); Liu et al. (1998); Ma et al. (2000); Mi et al. (2007); Oh et al. (1996); Plakatouras et al. (1994); Snejko et al. (2002); Straeter et al. (1996); Videnova-Adrabinska (2007); Wang et al. (1999, 2001, 2002); Zheng (2004).

S2. Experimental

Compound (I) was prepared by the hydrothermal reaction of a mixture of Yb₂O₃ (2 mmol, 0.78 g), mdsH₂ (3 mmol, 0.46 g) and 8.0 ml H₂O in a Teflon-lined stainless [steel?] autoclave (25 cm³), which was heated at 413 K for 48 h. Prism-like colourless crystals were collected. Yield: 16% based on Yb₂O₃. Analysis found: C 2.35, H 1.43%; calculated for C₄H₂₈O₃₉S₈Yb₆: C 2.41, H 1.41%.

S3. Refinement

All non-H atoms were located from the Fourier maps, and were refined anisotropically. H atoms of methylene groups were positioned geometrically and refined using a riding model. The H atoms attached to oxygen were located in the difference Fourier map and refined with the help of distance restraints on O—H bond lengths and restraining all H—O—H angles of water molecules to be similar. The isotropic vibration parameters of H atoms are related to the non-H atom to which they are bonded with U_iso = 1.2U_eq.

Computing details

Data collection: APEX2 (Bruker, 2004); cell refinement: SAINT (Bruker, 2004); data reduction: SAINT (Bruker, 2004); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008) and PLATON (Spek, 2003).

Figures

	Fig. 1. Building unit of compound (I) with the atomic labelling scheme (30% probability). All H atoms are omitted for clarity. Symmetry codes for the generated atoms are as follows: (ii) 1+x, y, z; (iii) 1-x, 1-y, 1-z; (iv) 2-x, 1-y, 1-z.
	Fig. 2. A chain consisting of bridged rare earth clusters in compound (I). The cluster consists of an octahedron, the six vertices of which represent Yb atoms. H atoms and coordinate O atoms except sulfonate ones are omitted for clarity. Symmetry codes: (i) -1+x, y, z; (ii) 1+x, y, z; (iii) 1-x, 1-y, 1-z; (iv) 2-x, 1-y, 1-z.

Poly[hexaaquaocta-µ₃-hydroxido-tetrakis(µ₃-methylenedisulfonato)-µ₆- oxido-hexaytterbium(III)]

Crystal data

[Yb6(CH2O6S2)4(OH)8O(H2O)6]	F(000) = 1824
Mr = 1994.98	Dx = 3.766 Mg m^−3
Monoclinic, P21/n	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: -P 2yn	Cell parameters from 9872 reflections
a = 8.7633 (2) Å	θ = 6.0–55.0°
b = 12.4480 (2) Å	µ = 16.39 mm^−1
c = 16.2201 (3) Å	T = 296 K
β = 96.158 (1)°	Prism-like, colorless
V = 1759.17 (6) Å^3	0.20 × 0.15 × 0.15 mm
Z = 2

Data collection

Bruker SMART APEXII diffractometer	3100 independent reflections
Radiation source: fine-focus sealed tube	2962 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.030
ω scans	θmax = 25.0°, θmin = 2.1°
Absorption correction: multi-scan (SADABS; Bruker, 2000)	h = −10→10
Tmin = 0.06, Tmax = 0.09	k = −14→14
14471 measured reflections	l = −19→19

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)] = 0.028	Hydrogen site location: inferred from neighbouring sites
wR(F^2) = 0.075	H atoms treated by a mixture of independent and constrained refinement
S = 1.06	w = 1/[σ^2(Fo^2) + (0.0556P)^2 + 2.8927P] where P = (Fo^2 + 2Fc^2)/3
3100 reflections	(Δ/σ)max = 0.001
289 parameters	Δρmax = 0.95 e Å^−3
13 restraints	Δρmin = −1.50 e Å^−3

Special details

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

Refinement. 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 > 2sigma(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
C1	0.0837 (8)	0.5310 (6)	0.7952 (4)	0.0175 (15)
H1A	−0.0044	0.5269	0.8266	0.021*
H1B	0.1687	0.5596	0.8319	0.021*
C2	0.9862 (7)	0.8662 (5)	0.5684 (4)	0.0135 (14)
H2A	1.0477	0.8354	0.6159	0.016*
H2B	1.0335	0.9336	0.5552	0.016*
O1	0.5000	0.5000	0.5000	0.0103 (13)
O2	0.6272 (5)	0.4765 (4)	0.6471 (3)	0.0117 (10)
H2	0.682 (7)	0.477 (6)	0.691 (2)	0.014*
O3	0.4627 (5)	0.6716 (4)	0.5809 (3)	0.0109 (9)
H3	0.459 (9)	0.727 (3)	0.608 (4)	0.013*
O4	0.3805 (5)	0.3425 (3)	0.5717 (3)	0.0126 (10)
H4	0.346 (8)	0.291 (4)	0.595 (4)	0.015*
O5	0.7871 (5)	0.4623 (3)	0.4980 (3)	0.0107 (9)
H5	0.869 (4)	0.436 (6)	0.489 (5)	0.013*
O6	0.1641 (6)	0.6128 (4)	0.6591 (3)	0.0192 (11)
O7	−0.1042 (6)	0.5872 (4)	0.6700 (3)	0.0244 (12)
O8	0.0338 (6)	0.7264 (4)	0.7490 (3)	0.0245 (12)
O9	0.2641 (7)	0.4113 (4)	0.7201 (4)	0.0330 (14)
O10	0.0035 (7)	0.3554 (5)	0.7150 (4)	0.0358 (13)
O11	0.1699 (7)	0.3443 (5)	0.8436 (4)	0.0356 (15)
O12	0.9286 (5)	0.6745 (4)	0.5083 (3)	0.0162 (10)
O13	1.1517 (6)	0.7666 (4)	0.4709 (3)	0.0220 (11)
O14	0.8958 (7)	0.8242 (4)	0.4125 (3)	0.0275 (13)
O15	0.7322 (6)	0.7877 (4)	0.6076 (3)	0.0210 (11)
O16	0.8219 (6)	0.9527 (4)	0.6727 (3)	0.0247 (12)
O17	0.7158 (6)	0.9511 (4)	0.5287 (3)	0.0249 (12)
O18	0.4633 (7)	0.5998 (4)	0.7527 (3)	0.0250 (12)
H18A	0.523 (8)	0.567 (6)	0.786 (4)	0.030*
H18B	0.443 (10)	0.661 (3)	0.766 (5)	0.030*
O19	0.7288 (6)	0.2612 (4)	0.6809 (3)	0.0210 (11)
H19A	0.805 (5)	0.297 (6)	0.696 (5)	0.025*
H19B	0.655 (5)	0.270 (6)	0.707 (4)	0.025*
O20	0.5586 (6)	0.1539 (4)	0.5441 (3)	0.0188 (11)
H20A	0.483 (5)	0.135 (6)	0.513 (4)	0.023*
H20B	0.633 (5)	0.114 (5)	0.544 (5)	0.023*
S1	0.04098 (19)	0.62200 (13)	0.71254 (10)	0.0126 (3)
S2	0.1317 (2)	0.39858 (14)	0.76587 (12)	0.0187 (4)
S3	0.98955 (19)	0.77673 (14)	0.48200 (10)	0.0137 (3)
S4	0.79995 (19)	0.89288 (13)	0.59619 (11)	0.0133 (3)
Yb1	0.37218 (3)	0.51501 (2)	0.625646 (17)	0.00951 (11)
Yb2	0.70535 (3)	0.61052 (2)	0.562251 (17)	0.00904 (11)
Yb3	0.63546 (3)	0.33629 (2)	0.554508 (16)	0.00927 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1	0.018 (3)	0.023 (4)	0.012 (3)	0.004 (3)	0.006 (3)	−0.002 (3)
C2	0.011 (3)	0.009 (3)	0.021 (4)	0.000 (3)	0.006 (3)	0.003 (3)
O1	0.014 (3)	0.006 (3)	0.011 (3)	0.001 (2)	0.001 (3)	−0.001 (3)
O2	0.012 (2)	0.014 (2)	0.009 (2)	−0.0012 (19)	−0.0006 (18)	0.0026 (19)
O3	0.011 (2)	0.009 (2)	0.013 (2)	0.0009 (18)	0.0048 (18)	−0.0032 (18)
O4	0.015 (2)	0.007 (2)	0.016 (2)	−0.0014 (18)	0.0041 (19)	0.0046 (19)
O5	0.009 (2)	0.009 (2)	0.015 (2)	0.0007 (18)	0.0050 (18)	−0.0003 (18)
O6	0.016 (3)	0.024 (3)	0.019 (3)	0.003 (2)	0.007 (2)	0.005 (2)
O7	0.017 (3)	0.032 (3)	0.022 (3)	−0.006 (2)	−0.008 (2)	0.011 (2)
O8	0.032 (3)	0.014 (3)	0.028 (3)	0.003 (2)	0.007 (2)	−0.005 (2)
O9	0.042 (3)	0.018 (3)	0.046 (4)	0.010 (2)	0.033 (3)	0.015 (2)
O10	0.038 (3)	0.027 (3)	0.041 (3)	−0.005 (2)	0.000 (3)	−0.007 (2)
O11	0.041 (4)	0.029 (3)	0.038 (3)	0.007 (3)	0.014 (3)	0.019 (3)
O12	0.011 (2)	0.015 (2)	0.024 (3)	0.0002 (19)	0.006 (2)	0.003 (2)
O13	0.016 (2)	0.018 (3)	0.035 (3)	0.003 (2)	0.013 (2)	0.002 (2)
O14	0.039 (3)	0.028 (3)	0.016 (3)	0.015 (2)	0.003 (2)	0.004 (2)
O15	0.017 (3)	0.017 (3)	0.030 (3)	−0.009 (2)	0.011 (2)	−0.008 (2)
O16	0.029 (3)	0.024 (3)	0.021 (3)	−0.007 (2)	0.003 (2)	−0.012 (2)
O17	0.028 (3)	0.023 (3)	0.023 (3)	0.014 (2)	0.000 (2)	−0.001 (2)
O18	0.032 (3)	0.024 (3)	0.017 (3)	0.010 (2)	−0.007 (2)	−0.012 (2)
O19	0.022 (3)	0.025 (3)	0.016 (3)	0.000 (2)	0.001 (2)	0.005 (2)
O20	0.018 (3)	0.010 (2)	0.028 (3)	−0.0004 (19)	0.000 (2)	−0.002 (2)
S1	0.0117 (8)	0.0146 (8)	0.0119 (8)	0.0026 (6)	0.0033 (6)	0.0008 (7)
S2	0.0219 (9)	0.0137 (8)	0.0222 (9)	−0.0010 (7)	0.0098 (7)	0.0040 (7)
S3	0.0117 (8)	0.0155 (8)	0.0149 (8)	0.0037 (6)	0.0051 (6)	0.0031 (7)
S4	0.0117 (8)	0.0120 (8)	0.0165 (8)	0.0011 (6)	0.0028 (6)	−0.0043 (6)
Yb1	0.00899 (17)	0.00976 (17)	0.01023 (17)	0.00016 (10)	0.00319 (11)	0.00017 (10)
Yb2	0.00804 (17)	0.00890 (17)	0.01025 (17)	−0.00008 (10)	0.00130 (11)	−0.00049 (10)
Yb3	0.00900 (17)	0.00893 (17)	0.01012 (17)	0.00048 (10)	0.00213 (12)	0.00071 (10)

Geometric parameters (Å, º)

C1—S1	1.765 (7)	O11—S2	1.437 (6)
C1—S2	1.779 (7)	O12—S3	1.461 (5)
C1—H1A	0.9700	O12—Yb2	2.366 (4)
C1—H1B	0.9700	O13—S3	1.457 (5)
C2—S4	1.771 (7)	O13—Yb3^iii	2.335 (5)
C2—S3	1.793 (7)	O14—S3	1.448 (5)
C2—H2A	0.9700	O15—S4	1.458 (5)
C2—H2B	0.9700	O15—Yb2	2.329 (5)
O1—Yb2^i	2.4001 (3)	O16—S4	1.443 (5)
O1—Yb2	2.4001 (3)	O17—S4	1.447 (5)
O1—Yb1^i	2.4357 (3)	O18—Yb1	2.375 (5)
O1—Yb1	2.4357 (3)	O18—H18A	0.82 (7)
O1—Yb3	2.4736 (3)	O18—H18B	0.82 (5)
O1—Yb3^i	2.4736 (3)	O19—Yb3	2.321 (5)
O2—Yb1	2.276 (4)	O19—H19A	0.82 (6)
O2—Yb3	2.309 (5)	O19—H19B	0.82 (5)
O2—Yb2	2.313 (4)	O20—Yb3	2.369 (5)
O2—H2	0.82 (4)	O20—H20A	0.82 (5)
O3—Yb1	2.254 (4)	O20—H20B	0.82 (5)
O3—Yb3^i	2.273 (4)	Yb1—O5^i	2.334 (5)
O3—Yb2	2.309 (4)	Yb1—Yb2	3.4116 (4)
O3—H3	0.82 (5)	Yb1—Yb2^i	3.4275 (4)
O4—Yb3	2.282 (5)	Yb1—Yb3^i	3.4536 (4)
O4—Yb2^i	2.297 (5)	Yb1—Yb3	3.4893 (4)
O4—Yb1	2.324 (4)	Yb2—O4^i	2.297 (5)
O4—H4	0.82 (6)	Yb2—O7^iv	2.301 (5)
O5—Yb2	2.272 (4)	Yb2—Yb3^i	3.4252 (4)
O5—Yb3	2.308 (4)	Yb2—Yb1^i	3.4275 (4)
O5—Yb1^i	2.334 (5)	Yb2—Yb3	3.4680 (4)
O5—H5	0.82 (4)	Yb2—H2	2.70 (6)
O6—S1	1.459 (5)	Yb3—O3^i	2.273 (4)
O6—Yb1	2.305 (5)	Yb3—O13^iii	2.335 (5)
O7—S1	1.448 (5)	Yb3—Yb2^i	3.4252 (4)
O7—Yb2^ii	2.301 (5)	Yb3—Yb1^i	3.4536 (4)
O8—S1	1.432 (5)	Yb3—H4	2.74 (6)
O9—S2	1.452 (5)	Yb3—H5	2.71 (6)
O9—Yb1	2.285 (5)	Yb3—H19A	2.65 (7)
O10—S2	1.426 (6)	Yb3—H19B	2.60 (7)
S1—C1—S2	115.4 (4)	O5—Yb2—O1	66.46 (11)
S1—C1—H1A	108.4	O4^i—Yb2—O1	66.01 (11)
S2—C1—H1A	108.4	O7^iv—Yb2—O1	134.17 (13)
S1—C1—H1B	108.4	O3—Yb2—O1	65.44 (11)
S2—C1—H1B	108.4	O2—Yb2—O1	65.20 (11)
H1A—C1—H1B	107.5	O15—Yb2—O1	136.17 (12)
S4—C2—S3	114.1 (4)	O12—Yb2—O1	130.52 (12)
S4—C2—H2A	108.7	O5—Yb2—Yb1	100.22 (11)
S3—C2—H2A	108.7	O4^i—Yb2—Yb1	99.77 (11)
S4—C2—H2B	108.7	O7^iv—Yb2—Yb1	107.54 (13)
S3—C2—H2B	108.7	O3—Yb2—Yb1	40.99 (11)
H2A—C2—H2B	107.6	O2—Yb2—Yb1	41.56 (11)
Yb2^i—O1—Yb2	180.000 (11)	O15—Yb2—Yb1	107.18 (12)
Yb2^i—O1—Yb1^i	89.734 (9)	O12—Yb2—Yb1	175.84 (12)
Yb2—O1—Yb1^i	90.266 (9)	O1—Yb2—Yb1	45.556 (6)
Yb2^i—O1—Yb1	90.266 (9)	O5—Yb2—Yb3^i	101.68 (11)
Yb2—O1—Yb1	89.734 (9)	O4^i—Yb2—Yb3^i	41.42 (11)
Yb1^i—O1—Yb1	180.0	O7^iv—Yb2—Yb3^i	164.24 (14)
Yb2^i—O1—Yb3	89.287 (9)	O3—Yb2—Yb3^i	41.24 (11)
Yb2—O1—Yb3	90.713 (9)	O2—Yb2—Yb3^i	99.93 (11)
Yb1^i—O1—Yb3	89.411 (9)	O15—Yb2—Yb3^i	92.52 (13)
Yb1—O1—Yb3	90.589 (9)	O12—Yb2—Yb3^i	115.90 (12)
Yb2^i—O1—Yb3^i	90.713 (9)	O1—Yb2—Yb3^i	46.231 (6)
Yb2—O1—Yb3^i	89.287 (9)	Yb1—Yb2—Yb3^i	60.683 (8)
Yb1^i—O1—Yb3^i	90.589 (9)	O5—Yb2—Yb1^i	42.62 (11)
Yb1—O1—Yb3^i	89.411 (9)	O4^i—Yb2—Yb1^i	42.42 (11)
Yb3—O1—Yb3^i	180.0	O7^iv—Yb2—Yb1^i	132.53 (15)
Yb1—O2—Yb3	99.12 (17)	O3—Yb2—Yb1^i	99.74 (11)
Yb1—O2—Yb2	96.05 (16)	O2—Yb2—Yb1^i	99.05 (11)
Yb3—O2—Yb2	97.25 (17)	O15—Yb2—Yb1^i	135.76 (13)
Yb1—O2—H2	127 (6)	O12—Yb2—Yb1^i	85.25 (12)
Yb3—O2—H2	121 (5)	O1—Yb2—Yb1^i	45.287 (6)
Yb2—O2—H2	110 (5)	Yb1—Yb2—Yb1^i	90.843 (9)
Yb1—O3—Yb3^i	99.44 (17)	Yb3^i—Yb2—Yb1^i	61.220 (8)
Yb1—O3—Yb2	96.80 (17)	O5—Yb2—Yb3	41.18 (11)
Yb3^i—O3—Yb2	96.75 (16)	O4^i—Yb2—Yb3	100.25 (11)
Yb1—O3—H3	122 (5)	O7^iv—Yb2—Yb3	90.80 (13)
Yb3^i—O3—H3	121 (5)	O3—Yb2—Yb3	99.63 (11)
Yb2—O3—H3	116 (5)	O2—Yb2—Yb3	41.33 (11)
Yb3—O4—Yb2^i	96.83 (17)	O15—Yb2—Yb3	162.75 (12)
Yb3—O4—Yb1	98.50 (17)	O12—Yb2—Yb3	117.90 (11)
Yb2^i—O4—Yb1	95.76 (16)	O1—Yb2—Yb3	45.497 (6)
Yb3—O4—H4	116 (6)	Yb1—Yb2—Yb3	60.948 (8)
Yb2^i—O4—H4	122 (5)	Yb3^i—Yb2—Yb3	91.728 (9)
Yb1—O4—H4	122 (5)	Yb1^i—Yb2—Yb3	60.110 (8)
Yb2—O5—Yb3	98.42 (16)	O5—Yb2—H2	84.8 (16)
Yb2—O5—Yb1^i	96.14 (16)	O4^i—Yb2—H2	147.8 (10)
Yb3—O5—Yb1^i	96.13 (16)	O7^iv—Yb2—H2	56.1 (11)
Yb2—O5—H5	138 (5)	O3—Yb2—H2	87.3 (16)
Yb3—O5—H5	110 (5)	O2—Yb2—H2	16.6 (10)
Yb1^i—O5—H5	110 (5)	O15—Yb2—H2	110.6 (13)
S1—O6—Yb1	146.6 (3)	O12—Yb2—H2	129.0 (13)
S1—O7—Yb2^ii	148.5 (3)	O1—Yb2—H2	81.7 (10)
S2—O9—Yb1	144.7 (3)	Yb1—Yb2—H2	54.0 (13)
S3—O12—Yb2	138.1 (3)	Yb3^i—Yb2—H2	114.4 (12)
S3—O13—Yb3^iii	151.3 (3)	Yb1^i—Yb2—H2	112.6 (12)
S4—O15—Yb2	147.0 (3)	Yb3—Yb2—H2	52.6 (13)
Yb1—O18—H18A	119 (5)	O3^i—Yb3—O4	81.10 (16)
Yb1—O18—H18B	125 (5)	O3^i—Yb3—O5	79.62 (16)
H18A—O18—H18B	115 (5)	O4—Yb3—O5	129.67 (15)
Yb3—O19—H19A	105 (6)	O3^i—Yb3—O2	128.77 (16)
Yb3—O19—H19B	101 (6)	O4—Yb3—O2	78.22 (16)
H19A—O19—H19B	116 (5)	O5—Yb3—O2	78.71 (16)
Yb3—O20—H20A	122 (6)	O3^i—Yb3—O19	153.76 (17)
Yb3—O20—H20B	112 (5)	O4—Yb3—O19	99.36 (17)
H20A—O20—H20B	114 (5)	O5—Yb3—O19	117.47 (17)
O8—S1—O7	113.2 (3)	O2—Yb3—O19	76.26 (17)
O8—S1—O6	112.6 (3)	O3^i—Yb3—O13^iii	91.87 (17)
O7—S1—O6	111.2 (3)	O4—Yb3—O13^iii	148.31 (16)
O8—S1—C1	106.5 (3)	O5—Yb3—O13^iii	78.34 (17)
O7—S1—C1	105.9 (3)	O2—Yb3—O13^iii	127.62 (17)
O6—S1—C1	106.9 (3)	O19—Yb3—O13^iii	73.87 (18)
O10—S2—O11	115.2 (4)	O3^i—Yb3—O20	79.31 (17)
O10—S2—O9	111.6 (4)	O4—Yb3—O20	76.48 (17)
O11—S2—O9	112.1 (4)	O5—Yb3—O20	142.60 (17)
O10—S2—C1	108.1 (4)	O2—Yb3—O20	137.92 (17)
O11—S2—C1	103.9 (3)	O19—Yb3—O20	75.37 (18)
O9—S2—C1	105.1 (3)	O13^iii—Yb3—O20	71.85 (18)
O14—S3—O13	114.7 (3)	O3^i—Yb3—O1	64.72 (11)
O14—S3—O12	112.8 (3)	O4—Yb3—O1	65.00 (11)
O13—S3—O12	110.6 (3)	O5—Yb3—O1	64.71 (11)
O14—S3—C2	107.4 (3)	O2—Yb3—O1	64.06 (11)
O13—S3—C2	104.4 (3)	O19—Yb3—O1	139.27 (13)
O12—S3—C2	106.0 (3)	O13^iii—Yb3—O1	138.64 (13)
O16—S4—O17	113.8 (3)	O20—Yb3—O1	129.95 (13)
O16—S4—O15	111.9 (3)	O3^i—Yb3—Yb2^i	42.02 (11)
O17—S4—O15	111.4 (3)	O4—Yb3—Yb2^i	41.75 (11)
O16—S4—C2	105.9 (3)	O5—Yb3—Yb2^i	98.86 (11)
O17—S4—C2	108.1 (3)	O2—Yb3—Yb2^i	97.32 (11)
O15—S4—C2	105.3 (3)	O19—Yb3—Yb2^i	140.36 (13)
O3—Yb1—O2	81.82 (16)	O13^iii—Yb3—Yb2^i	132.39 (13)
O3—Yb1—O9	152.86 (18)	O20—Yb3—Yb2^i	85.49 (13)
O2—Yb1—O9	104.43 (19)	O1—Yb3—Yb2^i	44.482 (6)
O3—Yb1—O6	86.20 (16)	O3^i—Yb3—Yb1^i	40.07 (11)
O2—Yb1—O6	149.77 (18)	O4—Yb3—Yb1^i	98.90 (11)
O9—Yb1—O6	75.23 (18)	O5—Yb3—Yb1^i	42.22 (11)
O3—Yb1—O4	130.68 (16)	O2—Yb3—Yb1^i	98.41 (11)
O2—Yb1—O4	78.04 (16)	O19—Yb3—Yb1^i	159.45 (13)
O9—Yb1—O4	76.28 (18)	O13^iii—Yb3—Yb1^i	95.06 (13)
O6—Yb1—O4	129.37 (17)	O20—Yb3—Yb1^i	118.28 (13)
O3—Yb1—O5^i	79.48 (16)	O1—Yb3—Yb1^i	44.848 (6)
O2—Yb1—O5^i	130.08 (16)	Yb2^i—Yb3—Yb1^i	59.465 (7)
O9—Yb1—O5^i	113.1 (2)	O3^i—Yb3—Yb2	97.15 (11)
O6—Yb1—O5^i	73.92 (16)	O4—Yb3—Yb2	97.69 (11)
O4—Yb1—O5^i	80.11 (16)	O5—Yb3—Yb2	40.40 (11)
O3—Yb1—O18	78.34 (18)	O2—Yb3—Yb2	41.42 (11)
O2—Yb1—O18	74.19 (18)	O19—Yb3—Yb2	108.69 (13)
O9—Yb1—O18	78.1 (2)	O13^iii—Yb3—Yb2	113.88 (12)
O6—Yb1—O18	76.26 (18)	O20—Yb3—Yb2	173.53 (13)
O4—Yb1—O18	135.73 (17)	O1—Yb3—Yb2	43.791 (6)
O5^i—Yb1—O18	143.69 (17)	Yb2^i—Yb3—Yb2	88.272 (9)
O3—Yb1—O1	65.64 (11)	Yb1^i—Yb3—Yb2	59.363 (8)
O2—Yb1—O1	65.15 (11)	O3^i—Yb3—Yb1	98.74 (11)
O9—Yb1—O1	141.14 (14)	O4—Yb3—Yb1	41.20 (11)
O6—Yb1—O1	133.14 (12)	O5—Yb3—Yb1	97.31 (11)
O4—Yb1—O1	65.03 (11)	O2—Yb3—Yb1	40.09 (11)
O5^i—Yb1—O1	64.95 (11)	O19—Yb3—Yb1	98.49 (13)
O18—Yb1—O1	128.15 (15)	O13^iii—Yb3—Yb1	167.66 (13)
O3—Yb1—Yb2	42.22 (11)	O20—Yb3—Yb1	116.19 (13)
O2—Yb1—Yb2	42.39 (11)	O1—Yb3—Yb1	44.268 (6)
O9—Yb1—Yb2	145.95 (16)	Yb2^i—Yb3—Yb1	59.422 (7)
O6—Yb1—Yb2	127.68 (12)	Yb1^i—Yb3—Yb1	89.115 (9)
O4—Yb1—Yb2	98.39 (11)	Yb2—Yb3—Yb1	58.728 (8)
O5^i—Yb1—Yb2	98.69 (11)	O3^i—Yb3—H4	87.6 (15)
O18—Yb1—Yb2	83.55 (15)	O4—Yb3—H4	15.6 (11)
O1—Yb1—Yb2	44.709 (6)	O5—Yb3—H4	145.2 (11)
O3—Yb1—Yb2^i	98.69 (11)	O2—Yb3—H4	84.7 (15)
O2—Yb1—Yb2^i	97.92 (12)	O19—Yb3—H4	87.3 (13)
O9—Yb1—Yb2^i	106.38 (16)	O13^iii—Yb3—H4	134.7 (12)
O6—Yb1—Yb2^i	111.32 (13)	O20—Yb3—H4	63.6 (13)
O4—Yb1—Yb2^i	41.82 (11)	O1—Yb3—H4	80.6 (11)
O5^i—Yb1—Yb2^i	41.23 (11)	Yb2^i—Yb3—H4	53.1 (13)
O18—Yb1—Yb2^i	171.83 (14)	Yb1^i—Yb3—H4	112.2 (13)
O1—Yb1—Yb2^i	44.448 (6)	Yb2—Yb3—H4	111.1 (13)
Yb2—Yb1—Yb2^i	89.157 (9)	Yb1—Yb3—H4	52.6 (13)
O3—Yb1—Yb3^i	40.49 (11)	O3^i—Yb3—H5	82.1 (16)
O2—Yb1—Yb3^i	99.91 (11)	O4—Yb3—H5	145.5 (11)
O9—Yb1—Yb3^i	153.93 (17)	O5—Yb3—H5	16.5 (10)
O6—Yb1—Yb3^i	88.40 (12)	O2—Yb3—H5	89.4 (14)
O4—Yb1—Yb3^i	100.09 (11)	O19—Yb3—H5	108.8 (14)
O5^i—Yb1—Yb3^i	41.64 (11)	O13^iii—Yb3—H5	61.9 (10)
O18—Yb1—Yb3^i	118.04 (14)	O20—Yb3—H5	129.1 (12)
O1—Yb1—Yb3^i	45.741 (6)	O1—Yb3—H5	80.6 (10)
Yb2—Yb1—Yb3^i	59.852 (8)	Yb2^i—Yb3—H5	110.2 (13)
Yb2^i—Yb1—Yb3^i	60.527 (8)	Yb1^i—Yb3—H5	50.8 (14)
O3—Yb1—Yb3	100.19 (11)	Yb2—Yb3—H5	55.0 (11)
O2—Yb1—Yb3	40.79 (11)	Yb1—Yb3—H5	113.2 (11)
O9—Yb1—Yb3	101.42 (13)	H4—Yb3—H5	161.0 (16)
O6—Yb1—Yb3	169.21 (13)	O3^i—Yb3—H19A	161.8 (16)
O4—Yb1—Yb3	40.30 (11)	O4—Yb3—H19A	111.5 (13)
O5^i—Yb1—Yb3	98.55 (11)	O5—Yb3—H19A	100.3 (10)
O18—Yb1—Yb3	113.40 (13)	O2—Yb3—H19A	68.3 (16)
O1—Yb1—Yb3	45.143 (6)	O19—Yb3—H19A	17.4 (10)
Yb2—Yb1—Yb3	60.324 (8)	O13^iii—Yb3—H19A	70.5 (16)
Yb2^i—Yb1—Yb3	59.357 (8)	O20—Yb3—H19A	90.7 (12)
Yb3^i—Yb1—Yb3	90.885 (9)	O1—Yb3—H19A	131.9 (15)
O5—Yb2—O4^i	81.99 (16)	Yb2^i—Yb3—H19A	153.1 (14)
O5—Yb2—O7^iv	90.41 (18)	Yb1^i—Yb3—H19A	142.5 (10)
O4^i—Yb2—O7^iv	152.56 (18)	Yb2—Yb3—H19A	94.1 (13)
O5—Yb2—O3	131.88 (16)	Yb1—Yb3—H19A	99.3 (16)
O4^i—Yb2—O3	80.04 (16)	H4—Yb3—H19A	101.6 (18)
O7^iv—Yb2—O3	123.03 (18)	H5—Yb3—H19A	92.9 (18)
O5—Yb2—O2	79.35 (16)	O3^i—Yb3—H19B	152.4 (15)
O4^i—Yb2—O2	131.21 (16)	O4—Yb3—H19B	82.0 (9)
O7^iv—Yb2—O2	72.17 (17)	O5—Yb3—H19B	127.7 (14)
O3—Yb2—O2	79.86 (16)	O2—Yb3—H19B	67.9 (16)
O5—Yb2—O15	152.60 (16)	O19—Yb3—H19B	18.0 (9)
O4^i—Yb2—O15	93.97 (17)	O13^iii—Yb3—H19B	91.2 (10)
O7^iv—Yb2—O15	80.76 (19)	O20—Yb3—H19B	75.7 (16)
O3—Yb2—O15	73.13 (16)	O1—Yb3—H19B	125.6 (13)
O2—Yb2—O15	121.42 (17)	Yb2^i—Yb3—H19B	123.6 (9)
O5—Yb2—O12	77.86 (16)	Yb1^i—Yb3—H19B	165.9 (16)
O4^i—Yb2—O12	76.36 (17)	Yb2—Yb3—H19B	106.6 (16)
O7^iv—Yb2—O12	76.27 (18)	Yb1—Yb3—H19B	82.3 (12)
O3—Yb2—O12	138.38 (16)	H4—Yb3—H19B	71.1 (17)
O2—Yb2—O12	140.58 (16)	H5—Yb3—H19B	123.0 (19)
O15—Yb2—O12	74.85 (16)	H19A—Yb3—H19B	30.6 (12)
Yb2^ii—O7—S1—O8	65.8 (7)	Yb2^i—Yb1—Yb2—O1	0.0
Yb2^ii—O7—S1—O6	−62.2 (8)	Yb3^i—Yb1—Yb2—O1	−55.911 (7)
Yb2^ii—O7—S1—C1	−178.0 (6)	Yb3—Yb1—Yb2—O1	54.669 (7)
Yb1—O6—S1—O8	129.9 (5)	O3—Yb1—Yb2—Yb3^i	−48.04 (17)
Yb1—O6—S1—O7	−101.8 (6)	O2—Yb1—Yb2—Yb3^i	158.65 (17)
Yb1—O6—S1—C1	13.3 (7)	O9—Yb1—Yb2—Yb3^i	174.7 (3)
S2—C1—S1—O8	−169.6 (4)	O6—Yb1—Yb2—Yb3^i	−60.70 (16)
S2—C1—S1—O7	69.7 (5)	O4—Yb1—Yb2—Yb3^i	96.84 (11)
S2—C1—S1—O6	−48.9 (5)	O5^i—Yb1—Yb2—Yb3^i	15.65 (11)
Yb1—O9—S2—O10	77.2 (7)	O18—Yb1—Yb2—Yb3^i	−127.78 (13)
Yb1—O9—S2—O11	−151.9 (6)	O1—Yb1—Yb2—Yb3^i	55.911 (7)
Yb1—O9—S2—C1	−39.7 (8)	Yb2^i—Yb1—Yb2—Yb3^i	55.911 (7)
S1—C1—S2—O10	−60.7 (5)	Yb3—Yb1—Yb2—Yb3^i	110.579 (8)
S1—C1—S2—O11	176.5 (4)	O3—Yb1—Yb2—Yb1^i	−103.95 (17)
S1—C1—S2—O9	58.6 (5)	O2—Yb1—Yb2—Yb1^i	102.74 (17)
Yb3^iii—O13—S3—O14	−105.6 (7)	O9—Yb1—Yb2—Yb1^i	118.8 (3)
Yb3^iii—O13—S3—O12	23.5 (8)	O6—Yb1—Yb2—Yb1^i	−116.61 (16)
Yb3^iii—O13—S3—C2	137.1 (7)	O4—Yb1—Yb2—Yb1^i	40.93 (11)
Yb2—O12—S3—O14	−62.4 (5)	O5^i—Yb1—Yb2—Yb1^i	−40.26 (11)
Yb2—O12—S3—O13	167.6 (4)	O18—Yb1—Yb2—Yb1^i	176.30 (13)
Yb2—O12—S3—C2	54.9 (5)	O1—Yb1—Yb2—Yb1^i	0.0
S4—C2—S3—O14	57.9 (5)	Yb2^i—Yb1—Yb2—Yb1^i	0.0
S4—C2—S3—O13	−179.8 (4)	Yb3^i—Yb1—Yb2—Yb1^i	−55.911 (7)
S4—C2—S3—O12	−62.9 (4)	Yb3—Yb1—Yb2—Yb1^i	54.669 (7)
Yb2—O15—S4—O16	−152.4 (5)	O3—Yb1—Yb2—Yb3	−158.62 (17)
Yb2—O15—S4—O17	79.0 (6)	O2—Yb1—Yb2—Yb3	48.07 (17)
Yb2—O15—S4—C2	−37.9 (7)	O9—Yb1—Yb2—Yb3	64.1 (3)
S3—C2—S4—O16	172.1 (4)	O6—Yb1—Yb2—Yb3	−171.28 (16)
S3—C2—S4—O17	−65.7 (4)	O4—Yb1—Yb2—Yb3	−13.74 (11)
S3—C2—S4—O15	53.4 (4)	O5^i—Yb1—Yb2—Yb3	−94.93 (11)
Yb3^i—O3—Yb1—O2	115.85 (18)	O18—Yb1—Yb2—Yb3	121.64 (13)
Yb2—O3—Yb1—O2	17.81 (16)	O1—Yb1—Yb2—Yb3	−54.669 (7)
Yb3^i—O3—Yb1—O9	−138.4 (4)	Yb2^i—Yb1—Yb2—Yb3	−54.669 (7)
Yb2—O3—Yb1—O9	123.6 (4)	Yb3^i—Yb1—Yb2—Yb3	−110.579 (8)
Yb3^i—O3—Yb1—O6	−91.98 (18)	Yb2^i—O4—Yb3—O3^i	−17.45 (16)
Yb2—O3—Yb1—O6	169.98 (18)	Yb1—O4—Yb3—O3^i	−114.35 (18)
Yb3^i—O3—Yb1—O4	49.4 (3)	Yb2^i—O4—Yb3—O5	51.0 (3)
Yb2—O3—Yb1—O4	−48.6 (3)	Yb1—O4—Yb3—O5	−45.9 (3)
Yb3^i—O3—Yb1—O5^i	−17.64 (16)	Yb2^i—O4—Yb3—O2	115.40 (17)
Yb2—O3—Yb1—O5^i	−115.68 (17)	Yb1—O4—Yb3—O2	18.51 (16)
Yb3^i—O3—Yb1—O18	−168.7 (2)	Yb2^i—O4—Yb3—O19	−170.87 (17)
Yb2—O3—Yb1—O18	93.25 (19)	Yb1—O4—Yb3—O19	92.23 (18)
Yb3^i—O3—Yb1—O1	49.49 (10)	Yb2^i—O4—Yb3—O13^iii	−96.5 (3)
Yb2—O3—Yb1—O1	−48.54 (10)	Yb1—O4—Yb3—O13^iii	166.6 (3)
Yb3^i—O3—Yb1—Yb2	98.04 (19)	Yb2^i—O4—Yb3—O20	−98.51 (19)
Yb3^i—O3—Yb1—Yb2^i	19.02 (15)	Yb1—O4—Yb3—O20	164.6 (2)
Yb2—O3—Yb1—Yb2^i	−79.01 (13)	Yb2^i—O4—Yb3—O1	48.72 (10)
Yb2—O3—Yb1—Yb3^i	−98.04 (19)	Yb1—O4—Yb3—O1	−48.18 (10)
Yb3^i—O3—Yb1—Yb3	79.26 (14)	Yb1—O4—Yb3—Yb2^i	−96.90 (18)
Yb2—O3—Yb1—Yb3	−18.78 (15)	Yb2^i—O4—Yb3—Yb1^i	18.59 (14)
Yb3—O2—Yb1—O3	−116.11 (18)	Yb1—O4—Yb3—Yb1^i	−78.31 (14)
Yb2—O2—Yb1—O3	−17.75 (16)	Yb2^i—O4—Yb3—Yb2	78.64 (13)
Yb3—O2—Yb1—O9	90.8 (2)	Yb1—O4—Yb3—Yb2	−18.26 (14)
Yb2—O2—Yb1—O9	−170.79 (19)	Yb2^i—O4—Yb3—Yb1	96.90 (18)
Yb3—O2—Yb1—O6	176.2 (2)	Yb2—O5—Yb3—O3^i	114.23 (18)
Yb2—O2—Yb1—O6	−85.4 (3)	Yb1^i—O5—Yb3—O3^i	17.07 (15)
Yb3—O2—Yb1—O4	18.60 (16)	Yb2—O5—Yb3—O4	45.1 (3)
Yb2—O2—Yb1—O4	116.96 (18)	Yb1^i—O5—Yb3—O4	−52.1 (2)
Yb3—O2—Yb1—O5^i	−47.3 (2)	Yb2—O5—Yb3—O2	−19.07 (16)
Yb2—O2—Yb1—O5^i	51.0 (2)	Yb1^i—O5—Yb3—O2	−116.23 (17)
Yb3—O2—Yb1—O18	163.8 (2)	Yb2—O5—Yb3—O19	−86.9 (2)
Yb2—O2—Yb1—O18	−97.9 (2)	Yb1^i—O5—Yb3—O19	175.90 (16)
Yb3—O2—Yb1—O1	−49.23 (11)	Yb2—O5—Yb3—O13^iii	−151.7 (2)
Yb2—O2—Yb1—O1	49.13 (10)	Yb1^i—O5—Yb3—O13^iii	111.18 (19)
Yb3—O2—Yb1—Yb2	−98.4 (2)	Yb2—O5—Yb3—O20	170.9 (2)
Yb3—O2—Yb1—Yb2^i	−18.41 (14)	Yb1^i—O5—Yb3—O20	73.7 (3)
Yb2—O2—Yb1—Yb2^i	79.96 (13)	Yb2—O5—Yb3—O1	47.42 (10)
Yb3—O2—Yb1—Yb3^i	−79.72 (13)	Yb1^i—O5—Yb3—O1	−49.75 (9)
Yb2—O2—Yb1—Yb3^i	18.64 (14)	Yb2—O5—Yb3—Yb2^i	76.69 (14)
Yb2—O2—Yb1—Yb3	98.4 (2)	Yb1^i—O5—Yb3—Yb2^i	−20.47 (14)
S2—O9—Yb1—O3	58.3 (10)	Yb2—O5—Yb3—Yb1^i	97.17 (18)
S2—O9—Yb1—O2	158.6 (7)	Yb1^i—O5—Yb3—Yb2	−97.17 (18)
S2—O9—Yb1—O6	9.9 (7)	Yb2—O5—Yb3—Yb1	16.63 (15)
S2—O9—Yb1—O4	−127.8 (7)	Yb1^i—O5—Yb3—Yb1	−80.53 (12)
S2—O9—Yb1—O5^i	−55.1 (7)	Yb1—O2—Yb3—O3^i	49.3 (2)
S2—O9—Yb1—O18	88.6 (7)	Yb2—O2—Yb3—O3^i	−48.0 (2)
S2—O9—Yb1—O1	−133.2 (6)	Yb1—O2—Yb3—O4	−18.94 (16)
S2—O9—Yb1—Yb2	147.5 (5)	Yb2—O2—Yb3—O4	−116.29 (18)
S2—O9—Yb1—Yb2^i	−98.4 (7)	Yb1—O2—Yb3—O5	116.01 (18)
S2—O9—Yb1—Yb3^i	−42.9 (9)	Yb2—O2—Yb3—O5	18.66 (15)
S2—O9—Yb1—Yb3	−159.6 (7)	Yb1—O2—Yb3—O19	−121.8 (2)
S1—O6—Yb1—O3	−152.5 (6)	Yb2—O2—Yb3—O19	140.9 (2)
S1—O6—Yb1—O2	−85.9 (7)	Yb1—O2—Yb3—O13^iii	−178.44 (16)
S1—O6—Yb1—O9	7.5 (6)	Yb2—O2—Yb3—O13^iii	84.2 (2)
S1—O6—Yb1—O4	65.2 (6)	Yb1—O2—Yb3—O20	−73.0 (3)
S1—O6—Yb1—O5^i	127.3 (6)	Yb2—O2—Yb3—O20	−170.33 (19)
S1—O6—Yb1—O18	−73.6 (6)	Yb1—O2—Yb3—O1	48.80 (10)
S1—O6—Yb1—O1	156.4 (5)	Yb2—O2—Yb3—O1	−48.55 (10)
S1—O6—Yb1—Yb2	−144.0 (5)	Yb1—O2—Yb3—Yb2^i	18.39 (14)
S1—O6—Yb1—Yb2^i	109.6 (6)	Yb2—O2—Yb3—Yb2^i	−78.96 (13)
S1—O6—Yb1—Yb3^i	167.0 (6)	Yb1—O2—Yb3—Yb1^i	78.47 (13)
S1—O6—Yb1—Yb3	80.7 (9)	Yb2—O2—Yb3—Yb1^i	−18.88 (14)
Yb3—O4—Yb1—O3	49.3 (3)	Yb1—O2—Yb3—Yb2	97.35 (19)
Yb2^i—O4—Yb1—O3	−48.6 (3)	Yb2—O2—Yb3—Yb1	−97.35 (19)
Yb3—O4—Yb1—O2	−18.80 (16)	Yb2^i—O1—Yb3—O3^i	46.23 (12)
Yb2^i—O4—Yb1—O2	−116.61 (18)	Yb2—O1—Yb3—O3^i	−133.77 (12)
Yb3—O4—Yb1—O9	−127.1 (2)	Yb1^i—O1—Yb3—O3^i	−43.51 (12)
Yb2^i—O4—Yb1—O9	135.1 (2)	Yb1—O1—Yb3—O3^i	136.49 (12)
Yb3—O4—Yb1—O6	175.58 (16)	Yb3^i—O1—Yb3—O3^i	169 (100)
Yb2^i—O4—Yb1—O6	77.8 (2)	Yb2^i—O1—Yb3—O4	−45.58 (13)
Yb3—O4—Yb1—O5^i	116.03 (17)	Yb2—O1—Yb3—O4	134.42 (13)
Yb2^i—O4—Yb1—O5^i	18.22 (15)	Yb1^i—O1—Yb3—O4	−135.32 (13)
Yb3—O4—Yb1—O18	−70.7 (3)	Yb1—O1—Yb3—O4	44.68 (13)
Yb2^i—O4—Yb1—O18	−168.6 (2)	Yb3^i—O1—Yb3—O4	77 (100)
Yb3—O4—Yb1—O1	49.16 (10)	Yb2^i—O1—Yb3—O5	136.40 (13)
Yb2^i—O4—Yb1—O1	−48.65 (10)	Yb2—O1—Yb3—O5	−43.60 (13)
Yb3—O4—Yb1—Yb2	18.61 (15)	Yb1^i—O1—Yb3—O5	46.66 (12)
Yb2^i—O4—Yb1—Yb2	−79.21 (13)	Yb1—O1—Yb3—O5	−133.34 (12)
Yb3—O4—Yb1—Yb2^i	97.82 (19)	Yb3^i—O1—Yb3—O5	−101 (100)
Yb3—O4—Yb1—Yb3^i	79.31 (14)	Yb2^i—O1—Yb3—O2	−134.23 (12)
Yb2^i—O4—Yb1—Yb3^i	−18.51 (14)	Yb2—O1—Yb3—O2	45.77 (12)
Yb2^i—O4—Yb1—Yb3	−97.82 (19)	Yb1^i—O1—Yb3—O2	136.03 (12)
Yb2^i—O1—Yb1—O3	−134.29 (13)	Yb1—O1—Yb3—O2	−43.97 (12)
Yb2—O1—Yb1—O3	45.71 (13)	Yb3^i—O1—Yb3—O2	−12 (100)
Yb1^i—O1—Yb1—O3	97 (100)	Yb2^i—O1—Yb3—O19	−120.1 (2)
Yb3—O1—Yb1—O3	136.42 (13)	Yb2—O1—Yb3—O19	59.9 (2)
Yb3^i—O1—Yb1—O3	−43.58 (13)	Yb1^i—O1—Yb3—O19	150.1 (2)
Yb2^i—O1—Yb1—O2	133.55 (12)	Yb1—O1—Yb3—O19	−29.9 (2)
Yb2—O1—Yb1—O2	−46.45 (12)	Yb3^i—O1—Yb3—O19	2 (100)
Yb1^i—O1—Yb1—O2	5 (100)	Yb2^i—O1—Yb3—O13^iii	107.4 (2)
Yb3—O1—Yb1—O2	44.26 (12)	Yb2—O1—Yb3—O13^iii	−72.6 (2)
Yb3^i—O1—Yb1—O2	−135.74 (12)	Yb1^i—O1—Yb3—O13^iii	17.7 (2)
Yb2^i—O1—Yb1—O9	51.4 (3)	Yb1—O1—Yb3—O13^iii	−162.3 (2)
Yb2—O1—Yb1—O9	−128.6 (3)	Yb3^i—O1—Yb3—O13^iii	−130 (100)
Yb1^i—O1—Yb1—O9	−77 (100)	Yb2^i—O1—Yb3—O20	−2.22 (17)
Yb3—O1—Yb1—O9	−37.9 (3)	Yb2—O1—Yb3—O20	177.78 (17)
Yb3^i—O1—Yb1—O9	142.1 (3)	Yb1^i—O1—Yb3—O20	−91.96 (17)
Yb2^i—O1—Yb1—O6	−75.88 (18)	Yb1—O1—Yb3—O20	88.04 (17)
Yb2—O1—Yb1—O6	104.12 (18)	Yb3^i—O1—Yb3—O20	120 (100)
Yb1^i—O1—Yb1—O6	155 (100)	Yb2—O1—Yb3—Yb2^i	180.0
Yb3—O1—Yb1—O6	−165.17 (18)	Yb1^i—O1—Yb3—Yb2^i	−89.742 (9)
Yb3^i—O1—Yb1—O6	14.83 (18)	Yb1—O1—Yb3—Yb2^i	90.258 (9)
Yb2^i—O1—Yb1—O4	45.63 (13)	Yb3^i—O1—Yb3—Yb2^i	122 (100)
Yb2—O1—Yb1—O4	−134.37 (13)	Yb2^i—O1—Yb3—Yb1^i	89.742 (9)
Yb1^i—O1—Yb1—O4	−83 (100)	Yb2—O1—Yb3—Yb1^i	−90.258 (9)
Yb3—O1—Yb1—O4	−43.66 (13)	Yb1—O1—Yb3—Yb1^i	180.0
Yb3^i—O1—Yb1—O4	136.34 (13)	Yb3^i—O1—Yb3—Yb1^i	−148 (100)
Yb2^i—O1—Yb1—O5^i	−44.85 (12)	Yb2^i—O1—Yb3—Yb2	180.0
Yb2—O1—Yb1—O5^i	135.15 (12)	Yb1^i—O1—Yb3—Yb2	90.258 (9)
Yb1^i—O1—Yb1—O5^i	−174 (100)	Yb1—O1—Yb3—Yb2	−89.742 (9)
Yb3—O1—Yb1—O5^i	−134.14 (12)	Yb3^i—O1—Yb3—Yb2	−58 (100)
Yb3^i—O1—Yb1—O5^i	45.86 (12)	Yb2^i—O1—Yb3—Yb1	−90.258 (9)
Yb2^i—O1—Yb1—O18	175.33 (17)	Yb2—O1—Yb3—Yb1	89.742 (9)
Yb2—O1—Yb1—O18	−4.67 (17)	Yb1^i—O1—Yb3—Yb1	180.0
Yb1^i—O1—Yb1—O18	47 (100)	Yb3^i—O1—Yb3—Yb1	32 (100)
Yb3—O1—Yb1—O18	86.04 (17)	O5—Yb2—Yb3—O3^i	−64.7 (2)
Yb3^i—O1—Yb1—O18	−93.96 (17)	O4^i—Yb2—Yb3—O3^i	0.36 (16)
Yb2^i—O1—Yb1—Yb2	180.0	O7^iv—Yb2—Yb3—O3^i	−154.40 (18)
Yb1^i—O1—Yb1—Yb2	51 (100)	O3—Yb2—Yb3—O3^i	81.87 (16)
Yb3—O1—Yb1—Yb2	90.710 (9)	O2—Yb2—Yb3—O3^i	144.3 (2)
Yb3^i—O1—Yb1—Yb2	−89.290 (9)	O15—Yb2—Yb3—O3^i	145.4 (4)
Yb2—O1—Yb1—Yb2^i	180.0	O12—Yb2—Yb3—O3^i	−79.54 (18)
Yb1^i—O1—Yb1—Yb2^i	−129 (100)	O1—Yb2—Yb3—O3^i	41.16 (11)
Yb3—O1—Yb1—Yb2^i	−89.290 (9)	Yb1—Yb2—Yb3—O3^i	95.91 (11)
Yb3^i—O1—Yb1—Yb2^i	90.710 (9)	Yb3^i—Yb2—Yb3—O3^i	41.16 (11)
Yb2^i—O1—Yb1—Yb3^i	−90.710 (9)	Yb1^i—Yb2—Yb3—O3^i	−13.89 (11)
Yb2—O1—Yb1—Yb3^i	89.290 (9)	O5—Yb2—Yb3—O4	−146.6 (2)
Yb1^i—O1—Yb1—Yb3^i	141 (100)	O4^i—Yb2—Yb3—O4	−81.58 (17)
Yb3—O1—Yb1—Yb3^i	180.0	O7^iv—Yb2—Yb3—O4	123.67 (18)
Yb2^i—O1—Yb1—Yb3	89.290 (9)	O3—Yb2—Yb3—O4	−0.07 (16)
Yb2—O1—Yb1—Yb3	−90.710 (9)	O2—Yb2—Yb3—O4	62.3 (2)
Yb1^i—O1—Yb1—Yb3	−39 (100)	O15—Yb2—Yb3—O4	63.4 (4)
Yb3^i—O1—Yb1—Yb3	180.0	O12—Yb2—Yb3—O4	−161.48 (18)
Yb3—O5—Yb2—O4^i	−115.71 (18)	O1—Yb2—Yb3—O4	−40.78 (12)
Yb1^i—O5—Yb2—O4^i	−18.56 (16)	Yb1—Yb2—Yb3—O4	13.97 (12)
Yb3—O5—Yb2—O7^iv	90.75 (18)	Yb3^i—Yb2—Yb3—O4	−40.78 (12)
Yb1^i—O5—Yb2—O7^iv	−172.10 (17)	Yb1^i—Yb2—Yb3—O4	−95.83 (12)
Yb3—O5—Yb2—O3	−46.9 (3)	O4^i—Yb2—Yb3—O5	65.0 (2)
Yb1^i—O5—Yb2—O3	50.3 (2)	O7^iv—Yb2—Yb3—O5	−89.7 (2)
Yb3—O5—Yb2—O2	18.99 (16)	O3—Yb2—Yb3—O5	146.6 (2)
Yb1^i—O5—Yb2—O2	116.14 (17)	O2—Yb2—Yb3—O5	−151.0 (2)
Yb3—O5—Yb2—O15	161.2 (3)	O15—Yb2—Yb3—O5	−149.9 (5)
Yb1^i—O5—Yb2—O15	−101.7 (4)	O12—Yb2—Yb3—O5	−14.8 (2)
Yb3—O5—Yb2—O12	166.60 (19)	O1—Yb2—Yb3—O5	105.85 (17)
Yb1^i—O5—Yb2—O12	−96.24 (17)	Yb1—Yb2—Yb3—O5	160.60 (17)
Yb3—O5—Yb2—O1	−48.45 (10)	Yb3^i—Yb2—Yb3—O5	105.85 (17)
Yb1^i—O5—Yb2—O1	48.71 (9)	Yb1^i—Yb2—Yb3—O5	50.80 (17)
Yb3—O5—Yb2—Yb1	−17.16 (15)	O5—Yb2—Yb3—O2	151.0 (2)
Yb1^i—O5—Yb2—Yb1	79.99 (12)	O4^i—Yb2—Yb3—O2	−143.9 (2)
Yb3—O5—Yb2—Yb3^i	−79.08 (14)	O7^iv—Yb2—Yb3—O2	61.3 (2)
Yb1^i—O5—Yb2—Yb3^i	18.08 (14)	O3—Yb2—Yb3—O2	−62.4 (2)
Yb3—O5—Yb2—Yb1^i	−97.15 (18)	O15—Yb2—Yb3—O2	1.1 (5)
Yb1^i—O5—Yb2—Yb3	97.15 (18)	O12—Yb2—Yb3—O2	136.2 (2)
Yb1—O3—Yb2—O5	48.0 (3)	O1—Yb2—Yb3—O2	−103.11 (17)
Yb3^i—O3—Yb2—O5	−52.4 (2)	Yb1—Yb2—Yb3—O2	−48.36 (17)
Yb1—O3—Yb2—O4^i	117.69 (18)	Yb3^i—Yb2—Yb3—O2	−103.11 (17)
Yb3^i—O3—Yb2—O4^i	17.29 (16)	Yb1^i—Yb2—Yb3—O2	−158.16 (17)
Yb1—O3—Yb2—O7^iv	−78.4 (2)	O5—Yb2—Yb3—O19	110.7 (2)
Yb3^i—O3—Yb2—O7^iv	−178.84 (17)	O4^i—Yb2—Yb3—O19	175.77 (18)
Yb1—O3—Yb2—O2	−17.62 (16)	O7^iv—Yb2—Yb3—O19	21.0 (2)
Yb3^i—O3—Yb2—O2	−118.01 (18)	O3—Yb2—Yb3—O19	−102.72 (18)
Yb1—O3—Yb2—O15	−145.0 (2)	O2—Yb2—Yb3—O19	−40.3 (2)
Yb3^i—O3—Yb2—O15	114.6 (2)	O15—Yb2—Yb3—O19	−39.2 (4)
Yb1—O3—Yb2—O12	173.76 (18)	O12—Yb2—Yb3—O19	95.87 (19)
Yb3^i—O3—Yb2—O12	73.4 (3)	O1—Yb2—Yb3—O19	−143.43 (14)
Yb1—O3—Yb2—O1	49.63 (10)	Yb1—Yb2—Yb3—O19	−88.68 (14)
Yb3^i—O3—Yb2—O1	−50.77 (10)	Yb3^i—Yb2—Yb3—O19	−143.43 (14)
Yb3^i—O3—Yb2—Yb1	−100.39 (19)	Yb1^i—Yb2—Yb3—O19	161.52 (14)
Yb1—O3—Yb2—Yb3^i	100.39 (19)	O5—Yb2—Yb3—O13^iii	30.6 (2)
Yb1—O3—Yb2—Yb1^i	79.93 (13)	O4^i—Yb2—Yb3—O13^iii	95.61 (19)
Yb3^i—O3—Yb2—Yb1^i	−20.46 (14)	O7^iv—Yb2—Yb3—O13^iii	−59.1 (2)
Yb1—O3—Yb2—Yb3	18.86 (15)	O3—Yb2—Yb3—O13^iii	177.12 (18)
Yb3^i—O3—Yb2—Yb3	−81.53 (13)	O2—Yb2—Yb3—O13^iii	−120.5 (2)
Yb1—O2—Yb2—O5	−118.95 (18)	O15—Yb2—Yb3—O13^iii	−119.4 (4)
Yb3—O2—Yb2—O5	−18.93 (16)	O12—Yb2—Yb3—O13^iii	15.7 (2)
Yb1—O2—Yb2—O4^i	−49.6 (3)	O1—Yb2—Yb3—O13^iii	136.41 (15)
Yb3—O2—Yb2—O4^i	50.4 (3)	Yb1—Yb2—Yb3—O13^iii	−168.84 (15)
Yb1—O2—Yb2—O7^iv	147.1 (2)	Yb3^i—Yb2—Yb3—O13^iii	136.41 (15)
Yb3—O2—Yb2—O7^iv	−112.8 (2)	Yb1^i—Yb2—Yb3—O13^iii	81.36 (15)
Yb1—O2—Yb2—O3	17.41 (16)	O5—Yb2—Yb3—O20	−121.1 (12)
Yb3—O2—Yb2—O3	117.43 (17)	O4^i—Yb2—Yb3—O20	−56.1 (12)
Yb1—O2—Yb2—O15	80.4 (2)	O7^iv—Yb2—Yb3—O20	149.2 (12)
Yb3—O2—Yb2—O15	−179.61 (16)	O3—Yb2—Yb3—O20	25.4 (12)
Yb1—O2—Yb2—O12	−174.50 (19)	O2—Yb2—Yb3—O20	87.8 (12)
Yb3—O2—Yb2—O12	−74.5 (3)	O15—Yb2—Yb3—O20	88.9 (12)
Yb1—O2—Yb2—O1	−50.10 (10)	O12—Yb2—Yb3—O20	−136.0 (12)
Yb3—O2—Yb2—O1	49.93 (10)	O1—Yb2—Yb3—O20	−15.3 (12)
Yb3—O2—Yb2—Yb1	100.02 (19)	Yb1—Yb2—Yb3—O20	39.5 (12)
Yb1—O2—Yb2—Yb3^i	−18.80 (15)	Yb3^i—Yb2—Yb3—O20	−15.3 (12)
Yb3—O2—Yb2—Yb3^i	81.22 (13)	Yb1^i—Yb2—Yb3—O20	−70.3 (12)
Yb1—O2—Yb2—Yb1^i	−80.96 (13)	O5—Yb2—Yb3—O1	−105.85 (17)
Yb3—O2—Yb2—Yb1^i	19.06 (14)	O4^i—Yb2—Yb3—O1	−40.80 (11)
Yb1—O2—Yb2—Yb3	−100.02 (19)	O7^iv—Yb2—Yb3—O1	164.45 (14)
S4—O15—Yb2—O5	25.1 (9)	O3—Yb2—Yb3—O1	40.71 (11)
S4—O15—Yb2—O4^i	−55.1 (6)	O2—Yb2—Yb3—O1	103.11 (16)
S4—O15—Yb2—O7^iv	97.8 (6)	O15—Yb2—Yb3—O1	104.2 (4)
S4—O15—Yb2—O3	−133.4 (6)	O12—Yb2—Yb3—O1	−120.70 (13)
S4—O15—Yb2—O2	160.2 (5)	Yb1—Yb2—Yb3—O1	54.751 (7)
S4—O15—Yb2—O12	19.6 (6)	Yb3^i—Yb2—Yb3—O1	0.0
S4—O15—Yb2—O1	−114.0 (5)	Yb1^i—Yb2—Yb3—O1	−55.047 (7)
S4—O15—Yb2—Yb1	−156.6 (6)	O5—Yb2—Yb3—Yb2^i	−105.85 (17)
S4—O15—Yb2—Yb3^i	−96.6 (6)	O4^i—Yb2—Yb3—Yb2^i	−40.80 (11)
S4—O15—Yb2—Yb1^i	−46.8 (7)	O7^iv—Yb2—Yb3—Yb2^i	164.45 (14)
S4—O15—Yb2—Yb3	159.3 (3)	O3—Yb2—Yb3—Yb2^i	40.71 (11)
S3—O12—Yb2—O5	153.9 (5)	O2—Yb2—Yb3—Yb2^i	103.11 (16)
S3—O12—Yb2—O4^i	69.3 (4)	O15—Yb2—Yb3—Yb2^i	104.2 (4)
S3—O12—Yb2—O7^iv	−112.7 (5)	O12—Yb2—Yb3—Yb2^i	−120.70 (13)
S3—O12—Yb2—O3	12.1 (6)	O1—Yb2—Yb3—Yb2^i	0.0
S3—O12—Yb2—O2	−150.1 (4)	Yb1—Yb2—Yb3—Yb2^i	54.751 (7)
S3—O12—Yb2—O15	−28.7 (4)	Yb3^i—Yb2—Yb3—Yb2^i	0.0
S3—O12—Yb2—O1	110.1 (4)	Yb1^i—Yb2—Yb3—Yb2^i	−55.047 (7)
S3—O12—Yb2—Yb1	91.0 (16)	O5—Yb2—Yb3—Yb1^i	−50.80 (17)
S3—O12—Yb2—Yb3^i	56.7 (5)	O4^i—Yb2—Yb3—Yb1^i	14.25 (11)
S3—O12—Yb2—Yb1^i	111.4 (4)	O7^iv—Yb2—Yb3—Yb1^i	−140.51 (14)
S3—O12—Yb2—Yb3	163.8 (4)	O3—Yb2—Yb3—Yb1^i	95.76 (11)
Yb2^i—O1—Yb2—O5	104 (81)	O2—Yb2—Yb3—Yb1^i	158.16 (16)
Yb1^i—O1—Yb2—O5	−45.72 (12)	O15—Yb2—Yb3—Yb1^i	159.3 (4)
Yb1—O1—Yb2—O5	134.28 (12)	O12—Yb2—Yb3—Yb1^i	−65.65 (13)
Yb3—O1—Yb2—O5	43.70 (12)	O1—Yb2—Yb3—Yb1^i	55.047 (7)
Yb3^i—O1—Yb2—O5	−136.30 (12)	Yb1—Yb2—Yb3—Yb1^i	109.799 (8)
Yb2^i—O1—Yb2—O4^i	−165 (81)	Yb3^i—Yb2—Yb3—Yb1^i	55.047 (7)
Yb1^i—O1—Yb2—O4^i	45.85 (12)	O5—Yb2—Yb3—Yb1	−160.60 (17)
Yb1—O1—Yb2—O4^i	−134.15 (12)	O4^i—Yb2—Yb3—Yb1	−95.55 (12)
Yb3—O1—Yb2—O4^i	135.27 (12)	O7^iv—Yb2—Yb3—Yb1	109.70 (14)
Yb3^i—O1—Yb2—O4^i	−44.73 (12)	O3—Yb2—Yb3—Yb1	−14.04 (11)
Yb2^i—O1—Yb2—O7^iv	38 (82)	O2—Yb2—Yb3—Yb1	48.36 (16)
Yb1^i—O1—Yb2—O7^iv	−111.4 (2)	O15—Yb2—Yb3—Yb1	49.5 (4)
Yb1—O1—Yb2—O7^iv	68.6 (2)	O12—Yb2—Yb3—Yb1	−175.45 (13)
Yb3—O1—Yb2—O7^iv	−21.9 (2)	O1—Yb2—Yb3—Yb1	−54.751 (7)
Yb3^i—O1—Yb2—O7^iv	158.1 (2)	Yb3^i—Yb2—Yb3—Yb1	−54.751 (7)
Yb2^i—O1—Yb2—O3	−75 (81)	Yb1^i—Yb2—Yb3—Yb1	−109.799 (8)
Yb1^i—O1—Yb2—O3	135.58 (12)	O3—Yb1—Yb3—O3^i	−78.68 (18)
Yb1—O1—Yb2—O3	−44.42 (12)	O2—Yb1—Yb3—O3^i	−143.2 (2)
Yb3—O1—Yb2—O3	−135.00 (12)	O9—Yb1—Yb3—O3^i	117.8 (2)
Yb3^i—O1—Yb2—O3	45.00 (12)	O6—Yb1—Yb3—O3^i	47.1 (6)
Yb2^i—O1—Yb2—O2	15 (81)	O4—Yb1—Yb3—O3^i	65.6 (2)
Yb1^i—O1—Yb2—O2	−134.53 (12)	O5^i—Yb1—Yb3—O3^i	2.07 (16)
Yb1—O1—Yb2—O2	45.47 (12)	O18—Yb1—Yb3—O3^i	−160.3 (2)
Yb3—O1—Yb2—O2	−45.12 (12)	O1—Yb1—Yb3—O3^i	−39.04 (11)
Yb3^i—O1—Yb2—O2	134.88 (12)	Yb2—Yb1—Yb3—O3^i	−93.10 (11)
Yb2^i—O1—Yb2—O15	−95 (81)	Yb2^i—Yb1—Yb3—O3^i	15.44 (11)
Yb1^i—O1—Yb2—O15	115.11 (18)	Yb3^i—Yb1—Yb3—O3^i	−39.04 (11)
Yb1—O1—Yb2—O15	−64.89 (18)	O3—Yb1—Yb3—O4	−144.3 (2)
Yb3—O1—Yb2—O15	−155.48 (18)	O2—Yb1—Yb3—O4	151.2 (2)
Yb3^i—O1—Yb2—O15	24.52 (18)	O9—Yb1—Yb3—O4	52.2 (2)
Yb2^i—O1—Yb2—O12	151 (81)	O6—Yb1—Yb3—O4	−18.5 (7)
Yb1^i—O1—Yb2—O12	1.90 (15)	O5^i—Yb1—Yb3—O4	−63.5 (2)
Yb1—O1—Yb2—O12	−178.10 (15)	O18—Yb1—Yb3—O4	134.1 (2)
Yb3—O1—Yb2—O12	91.32 (15)	O1—Yb1—Yb3—O4	−104.63 (17)
Yb3^i—O1—Yb2—O12	−88.68 (15)	Yb2—Yb1—Yb3—O4	−158.70 (17)
Yb2^i—O1—Yb2—Yb1	−30 (79)	Yb2^i—Yb1—Yb3—O4	−50.16 (17)
Yb1^i—O1—Yb2—Yb1	180.0	Yb3^i—Yb1—Yb3—O4	−104.63 (17)
Yb3—O1—Yb2—Yb1	−90.586 (9)	O3—Yb1—Yb3—O5	1.88 (16)
Yb3^i—O1—Yb2—Yb1	89.414 (9)	O2—Yb1—Yb3—O5	−62.7 (2)
Yb2^i—O1—Yb2—Yb3^i	−120 (79)	O9—Yb1—Yb3—O5	−161.6 (2)
Yb1^i—O1—Yb2—Yb3^i	90.586 (9)	O6—Yb1—Yb3—O5	127.6 (6)
Yb1—O1—Yb2—Yb3^i	−89.414 (9)	O4—Yb1—Yb3—O5	146.2 (2)
Yb3—O1—Yb2—Yb3^i	180.0	O5^i—Yb1—Yb3—O5	82.64 (16)
Yb2^i—O1—Yb2—Yb1^i	150 (79)	O18—Yb1—Yb3—O5	−79.7 (2)
Yb1—O1—Yb2—Yb1^i	180.0	O1—Yb1—Yb3—O5	41.53 (11)
Yb3—O1—Yb2—Yb1^i	89.414 (9)	Yb2—Yb1—Yb3—O5	−12.54 (11)
Yb3^i—O1—Yb2—Yb1^i	−90.586 (9)	Yb2^i—Yb1—Yb3—O5	96.00 (11)
Yb2^i—O1—Yb2—Yb3	60 (79)	Yb3^i—Yb1—Yb3—O5	41.52 (11)
Yb1^i—O1—Yb2—Yb3	−89.414 (9)	O3—Yb1—Yb3—O2	64.6 (2)
Yb1—O1—Yb2—Yb3	90.586 (9)	O9—Yb1—Yb3—O2	−98.9 (3)
Yb3^i—O1—Yb2—Yb3	180.0	O6—Yb1—Yb3—O2	−169.7 (7)
O3—Yb1—Yb2—O5	−145.8 (2)	O4—Yb1—Yb3—O2	−151.2 (2)
O2—Yb1—Yb2—O5	60.9 (2)	O5^i—Yb1—Yb3—O2	145.3 (2)
O9—Yb1—Yb2—O5	77.0 (3)	O18—Yb1—Yb3—O2	−17.0 (2)
O6—Yb1—Yb2—O5	−158.4 (2)	O1—Yb1—Yb3—O2	104.21 (17)
O4—Yb1—Yb2—O5	−0.90 (16)	Yb2—Yb1—Yb3—O2	50.15 (17)
O5^i—Yb1—Yb2—O5	−82.09 (17)	Yb2^i—Yb1—Yb3—O2	158.69 (17)
O18—Yb1—Yb2—O5	134.48 (18)	Yb3^i—Yb1—Yb3—O2	104.21 (17)
O1—Yb1—Yb2—O5	−41.83 (12)	O3—Yb1—Yb3—O19	121.18 (18)
Yb2^i—Yb1—Yb2—O5	−41.83 (12)	O2—Yb1—Yb3—O19	56.6 (2)
Yb3^i—Yb1—Yb2—O5	−97.74 (12)	O9—Yb1—Yb3—O19	−42.3 (2)
Yb3—Yb1—Yb2—O5	12.84 (12)	O6—Yb1—Yb3—O19	−113.1 (7)
O3—Yb1—Yb2—O4^i	−62.2 (2)	O4—Yb1—Yb3—O19	−94.5 (2)
O2—Yb1—Yb2—O4^i	144.4 (2)	O5^i—Yb1—Yb3—O19	−158.06 (17)
O9—Yb1—Yb2—O4^i	160.5 (3)	O18—Yb1—Yb3—O19	39.6 (2)
O6—Yb1—Yb2—O4^i	−74.91 (19)	O1—Yb1—Yb3—O19	160.83 (13)
O4—Yb1—Yb2—O4^i	82.63 (17)	Yb2—Yb1—Yb3—O19	106.76 (13)
O5^i—Yb1—Yb2—O4^i	1.44 (15)	Yb2^i—Yb1—Yb3—O19	−144.70 (13)
O18—Yb1—Yb2—O4^i	−142.00 (17)	Yb3^i—Yb1—Yb3—O19	160.83 (13)
O1—Yb1—Yb2—O4^i	41.70 (11)	O3—Yb1—Yb3—O13^iii	70.3 (6)
Yb2^i—Yb1—Yb2—O4^i	41.70 (11)	O2—Yb1—Yb3—O13^iii	5.8 (6)
Yb3^i—Yb1—Yb2—O4^i	−14.21 (11)	O9—Yb1—Yb3—O13^iii	−93.1 (6)
Yb3—Yb1—Yb2—O4^i	96.37 (11)	O6—Yb1—Yb3—O13^iii	−163.9 (8)
O3—Yb1—Yb2—O7^iv	120.5 (2)	O4—Yb1—Yb3—O13^iii	−145.4 (6)
O2—Yb1—Yb2—O7^iv	−32.8 (2)	O5^i—Yb1—Yb3—O13^iii	151.1 (6)
O9—Yb1—Yb2—O7^iv	−16.7 (3)	O18—Yb1—Yb3—O13^iii	−11.3 (6)
O6—Yb1—Yb2—O7^iv	107.9 (2)	O1—Yb1—Yb3—O13^iii	110.0 (6)
O4—Yb1—Yb2—O7^iv	−94.60 (19)	Yb2—Yb1—Yb3—O13^iii	55.9 (6)
O5^i—Yb1—Yb2—O7^iv	−175.79 (18)	Yb2^i—Yb1—Yb3—O13^iii	164.5 (6)
O18—Yb1—Yb2—O7^iv	40.8 (2)	Yb3^i—Yb1—Yb3—O13^iii	110.0 (6)
O1—Yb1—Yb2—O7^iv	−135.53 (15)	O3—Yb1—Yb3—O20	−161.01 (19)
Yb2^i—Yb1—Yb2—O7^iv	−135.53 (15)	O2—Yb1—Yb3—O20	134.4 (2)
Yb3^i—Yb1—Yb2—O7^iv	168.56 (15)	O9—Yb1—Yb3—O20	35.5 (2)
Yb3—Yb1—Yb2—O7^iv	−80.86 (15)	O6—Yb1—Yb3—O20	−35.3 (7)
O2—Yb1—Yb2—O3	−153.3 (2)	O4—Yb1—Yb3—O20	−16.7 (2)
O9—Yb1—Yb2—O3	−137.2 (3)	O5^i—Yb1—Yb3—O20	−80.25 (18)
O6—Yb1—Yb2—O3	−12.7 (2)	O18—Yb1—Yb3—O20	117.4 (2)
O4—Yb1—Yb2—O3	144.9 (2)	O1—Yb1—Yb3—O20	−121.36 (15)
O5^i—Yb1—Yb2—O3	63.7 (2)	Yb2—Yb1—Yb3—O20	−175.42 (15)
O18—Yb1—Yb2—O3	−79.7 (2)	Yb2^i—Yb1—Yb3—O20	−66.89 (15)
O1—Yb1—Yb2—O3	103.95 (17)	Yb3^i—Yb1—Yb3—O20	−121.36 (15)
Yb2^i—Yb1—Yb2—O3	103.95 (17)	O3—Yb1—Yb3—O1	−39.65 (12)
Yb3^i—Yb1—Yb2—O3	48.04 (17)	O2—Yb1—Yb3—O1	−104.21 (17)
Yb3—Yb1—Yb2—O3	158.62 (17)	O9—Yb1—Yb3—O1	156.87 (18)
O3—Yb1—Yb2—O2	153.3 (2)	O6—Yb1—Yb3—O1	86.1 (6)
O9—Yb1—Yb2—O2	16.1 (3)	O4—Yb1—Yb3—O1	104.63 (17)
O6—Yb1—Yb2—O2	140.7 (2)	O5^i—Yb1—Yb3—O1	41.11 (11)
O4—Yb1—Yb2—O2	−61.8 (2)	O18—Yb1—Yb3—O1	−121.26 (16)
O5^i—Yb1—Yb2—O2	−143.0 (2)	Yb2—Yb1—Yb3—O1	−54.062 (7)
O18—Yb1—Yb2—O2	73.6 (2)	Yb2^i—Yb1—Yb3—O1	54.473 (7)
O1—Yb1—Yb2—O2	−102.74 (17)	Yb3^i—Yb1—Yb3—O1	0.0
Yb2^i—Yb1—Yb2—O2	−102.74 (17)	O3—Yb1—Yb3—Yb2^i	−94.12 (12)
Yb3^i—Yb1—Yb2—O2	−158.65 (17)	O2—Yb1—Yb3—Yb2^i	−158.69 (17)
Yb3—Yb1—Yb2—O2	−48.07 (17)	O9—Yb1—Yb3—Yb2^i	102.40 (18)
O3—Yb1—Yb2—O15	35.0 (2)	O6—Yb1—Yb3—Yb2^i	31.6 (6)
O2—Yb1—Yb2—O15	−118.3 (2)	O4—Yb1—Yb3—Yb2^i	50.16 (17)
O9—Yb1—Yb2—O15	−102.2 (3)	O5^i—Yb1—Yb3—Yb2^i	−13.36 (11)
O6—Yb1—Yb2—O15	22.4 (2)	O18—Yb1—Yb3—Yb2^i	−175.73 (16)
O4—Yb1—Yb2—O15	179.90 (18)	O1—Yb1—Yb3—Yb2^i	−54.473 (7)
O5^i—Yb1—Yb2—O15	98.71 (18)	Yb2—Yb1—Yb3—Yb2^i	−108.535 (8)
O18—Yb1—Yb2—O15	−44.72 (19)	Yb3^i—Yb1—Yb3—Yb2^i	−54.473 (7)
O1—Yb1—Yb2—O15	138.98 (14)	O3—Yb1—Yb3—Yb1^i	−39.65 (12)
Yb2^i—Yb1—Yb2—O15	138.98 (14)	O2—Yb1—Yb3—Yb1^i	−104.21 (17)
Yb3^i—Yb1—Yb2—O15	83.07 (14)	O9—Yb1—Yb3—Yb1^i	156.87 (18)
Yb3—Yb1—Yb2—O15	−166.35 (14)	O6—Yb1—Yb3—Yb1^i	86.1 (6)
O3—Yb1—Yb2—O12	−83.6 (16)	O4—Yb1—Yb3—Yb1^i	104.63 (17)
O2—Yb1—Yb2—O12	123.1 (15)	O5^i—Yb1—Yb3—Yb1^i	41.11 (11)
O9—Yb1—Yb2—O12	139.1 (16)	O18—Yb1—Yb3—Yb1^i	−121.26 (16)
O6—Yb1—Yb2—O12	−96.3 (15)	O1—Yb1—Yb3—Yb1^i	0.0
O4—Yb1—Yb2—O12	61.3 (15)	Yb2—Yb1—Yb3—Yb1^i	−54.062 (7)
O5^i—Yb1—Yb2—O12	−19.9 (15)	Yb2^i—Yb1—Yb3—Yb1^i	54.473 (7)
O18—Yb1—Yb2—O12	−163.4 (15)	Yb3^i—Yb1—Yb3—Yb1^i	0.0
O1—Yb1—Yb2—O12	20.3 (15)	O3—Yb1—Yb3—Yb2	14.41 (12)
Yb2^i—Yb1—Yb2—O12	20.3 (15)	O2—Yb1—Yb3—Yb2	−50.15 (17)
Yb3^i—Yb1—Yb2—O12	−35.6 (15)	O9—Yb1—Yb3—Yb2	−149.07 (18)
Yb3—Yb1—Yb2—O12	75.0 (15)	O6—Yb1—Yb3—Yb2	140.1 (6)
O3—Yb1—Yb2—O1	−103.95 (17)	O4—Yb1—Yb3—Yb2	158.70 (17)
O2—Yb1—Yb2—O1	102.74 (17)	O5^i—Yb1—Yb3—Yb2	95.17 (11)
O9—Yb1—Yb2—O1	118.8 (3)	O18—Yb1—Yb3—Yb2	−67.20 (16)
O6—Yb1—Yb2—O1	−116.61 (16)	O1—Yb1—Yb3—Yb2	54.062 (7)
O4—Yb1—Yb2—O1	40.93 (11)	Yb2^i—Yb1—Yb3—Yb2	108.535 (8)
O5^i—Yb1—Yb2—O1	−40.26 (11)	Yb3^i—Yb1—Yb3—Yb2	54.062 (7)
O18—Yb1—Yb2—O1	176.30 (13)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O2—H2···O16^v	0.82 (4)	2.23 (5)	2.923 (7)	143 (7)
O3—H3···O11^vi	0.82 (5)	2.05 (4)	2.789 (7)	149 (7)
O4—H4···O14^i	0.82 (6)	2.55 (5)	3.220 (8)	140 (7)
O5—H5···O12^iii	0.82 (4)	2.24 (3)	3.029 (6)	162 (7)
O18—H18A···O16^v	0.82 (7)	2.03 (7)	2.805 (7)	157 (8)
O18—H18B···O14^vii	0.82 (5)	2.47 (8)	2.880 (7)	112 (7)
O19—H19A···O10^iv	0.82 (6)	1.88 (5)	2.682 (8)	166 (7)
O19—H19B···O8^viii	0.82 (5)	1.95 (3)	2.708 (7)	154 (7)
O20—H20A···O17^i	0.82 (5)	2.09 (3)	2.877 (7)	159 (8)
O20—H20B···O17^ix	0.82 (5)	2.18 (4)	2.900 (7)	148 (7)

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