Was Bijvoet right? Sodium rubidium (+)-tartrate tetra­hydrate revisited

The first determination of the absolute configuration of an organic compound was published in 1951 on sodium rubidium (+)-tartrate tetra­hydrate, Na⁺·Rb⁺·C₄H₄O₆^2-·4H₂O, but the atomic coordinates are not available in the public literature. This structure has therefore been redetermined using current equipment. The most up-to-date techniques for the determination of the absolute configuration have been applied and the question posed in the title can be answered with an unequivocal `yes'.

S1. Comment

In their seminal experiment on sodium rubidium tartrate, (I), the group of Bijvoet (Peerdeman et al., 1951; Bijvoet et al., 1951) performed the first determination of the absolute configuration of an organic compound. This experiment changed the history of organic chemistry, because the stereochemistry could now be determined by experiment. It also started a new era in X-ray crystallography, because molecular properties could now be related to the absolute configuration.

The Bijvoet experiment to determine the absolute configuration of the organic tartrate molecule made use of the resonant scattering effect, which had been discovered a few years before with the inorganic compound ZnS (Coster et al., 1930). By chosing a wavelength close to the K-absorption edge, the equivalence of reflection intensities due to Friedel's law is broken and a difference of intensities occurs. Nowadays, these differences are often called `Bijvoet differences'. By comparing 15 of these differences from the diffraction experiment with the differences calculated from the structural model, Bijvoet et al. (1951) could confirm that the arbitrary Fischer nomenclature and absolute structure assignment for the organic stereochemistry was actually correct.

The experimental X-ray data used by Bijvoet et al. (1951) were measured with monochromated Zr radiation and obtained from a first layer (001) Weissenberg diagram. The structural model and atomic coordinates were taken from a Cu experiment by Beevers & Hughes (1941). These atomic coordinates, which are also given in the PhD thesis of Peerdeman (1955), are not available in the Cambridge Structural Database (Allen, 2002). Interestingly, newer X-ray crystal structure determinations of (I) are also absent from this database. We therefore decided to redetermine the crystal structure with modern equipment and experimental conditions, and to apply current methods and algorithms for the absolute structure determination.

The crystal structure of (I) is isomorphous with the corresponding sodium potassium tartrate (Rochelle salt or Seignette's salt) and sodium ammonium tatrate (ammonium Rochelle salt). The crystal structures of these salts have been described before (Brożek & Stadnicka, 1994; Brożek et al., 1994; Suzuki, Muta et al., 1996; Suzuki, Kabasawa et al., 1996; Solans et al., 1997). The rubidium ions are located on two independent special positions on twofold rotation axes (Wyckoff positions a and b) and the sodium ions are on general positions. Therefore, the overall composition in the asymmetric unit is one tartrate anion, one sodium ion, two half rubidium ions and four water molecules (Fig. 1).

The crystal structure consists of alternating layers of metal coordination polyhedra and hydrogen-bonded tartrate–water networks, which are both parallel to the crystallographic ac plane (Fig. 2). Atom Rb1 has a very large variation in Rb—O distances. It is thus difficult to define its first coordination sphere. We assume for atom Rb1 a sixfold coordination with a severely distorted octahedral geometry, but it should be noted that the Rb—O distances of 3.4088 (18) and 3.5925 (15) Å, which we consider to be in the second coordination sphere, are also quite short. For atom Rb2, the range of Rb—O distances is more narrow and we consider this ion as eight-coordinated with a bicapped trigonal–prismatic geometry. Atom Na1 has a distorted octahedral geometry.

The tartrate molecule has no molecular symmetry. The O1—C1—C2—C3 and O4—C4—C3—C2 torsion angles, which should be equal in the case of twofold symmetry, differ by 10.4 (2)°. Both carboxylate groups are deprotonated, while the hydroxy groups are still protonated. Atoms O2 of a carboxylate group and O6 of a hydroxy group are not directly coordinated to an alkali metal ion, but there is no difference in C—O distances compared with the corresponding coordinated atoms. The uncoordinated atom O6 is an acceptor of two hydrogen bonds, in contrast to the coordinated atom O5, which does not accept hydrogen bonds. The hydrogen bonds between the tartrate ions and the water molecules, with the exception of water molecule O8, form a complicated two-dimensional network, which is located between the layers of coordination polyhedra. The coordination polyhedra are linked in the b direction via the hydrogen -onded network, and vice versa. Water molecule O8 is an exception, because it does not belong to the two-dimensional hydrogen-bonded network but is coordinated to three alkali metal ions and is a linker between the water/tartrate layers. Atom O8 does not accept hydrogen bonds but is a donor of two. The geometry of the hydrogen bonds (Table 2) corresponds well with the published data (Solans et al., 1997). Atoms C2 and C3 both have the R configuration, which is established from the enantiopure starting material and by the absolute structure determination in the X-ray diffraction experiment (see below).

In the original Bijvoet experiment Zr radiation with a wavelength of 0.788 Å was used because it is close to the K-absorption limit of rubidium (0.814 Å; Peerdeman, 1955). This led to values of -3.1 and 3.2 for f' and f'', respectively. With the software SCATFAC (Laugier & Bochu, 2002) using the method of Waasmaier & Kirfel (1995), newer values for f' and f'' are calculated as -2.523 and 3.535, respectively, and the latest edition of the International Tables for Crystallography (Deslattes et al., 2004) gives a theoretical value of 0.815270 (12) Å for the K-absorption edge of Rb. In the present diffraction experiment of (I), we used Mo radiation with a wavelength of 0.71073 Å, which is more readily available but is slightly further away from the rubidium K-absorption edge. Therefore the magnitudes of f' and f'' are somewhat smaller, at -0.953 and 2.928, respectively.

In a careful analysis of absolute structure determinations by Flack & Shmueli (2007), it has been shown that not only the strongest resonant scatterers but all atoms in the unit cell must be taken into account. That publication introduces a parameter, Friedif, in order to make an a priori estimation of the Bijvoet differences on the basis of the composition of the crystal. For (I), we calculate Friedif as 1302 × 10^-4 and 1096 × 10^-4 for Zr and Mo radiation. A search for additional symmetry using the ADDSYM routine of PLATON (Spek, 2003) shows that the Rb and Na atoms have a centrosymmetric substructure [100% fit to space group Pmmn after an origin shift of (1/4, 1/4, 0)]. This centrosymmetric substructure can be taken into account in the calculation of Friedif (Flack & Shmueli, 2007), which is then 1216 × 10^-4 and 1024 × 10^-4 for Zr and Mo radiation.

The Bijvoet differences for the 15 reflections reported in the original papers (see above) were recalculated with the present Mo radiation data of (I). Despite the different wavelength in the present experiment, all signs of Δ_obs comply with the corresponding Δ_calc values (Table 3). The magnitudes of Δ_obs and Δ_calc are also very similar, but the magnitudes are less important for the absolute structure determination. By using the same methology and the same 15 reflections as in the 50-year old experiment we could confirm the absolute configuration of (I).

As introduced by Flack (1983), every noncentrosymmetric crystal structure can be refined as an inversion twin. The observed intensities I then have contributions from both individuals, I(h,k,l,x) = (1 - x)|F(h,k,l)|² + x|F(¯h,¯k,¯l)|², and the Flack parameter x can be refined in the least-squares refinement together with other structural parameters, such as, for example, atomic coordinates and displacement parameters. The standard uncertainty u obtained from this refinement is a measure of the inversion-distinguishing power (Flack & Bernardinelli, 2000). To avoid an underestimation of u, we included TWIN/BASF cards into the instruction file. The refined value of x for (I) is -0.007 (6), confirming the enantiopurity of the crystal and the correct absolute structure. The standard uncertainty (<0.04) is small enough to characterize the inversion-distinguishing power as strong.

Hooft et al. (2008) introduced a method that can be considered as a further development of the original Bijvoet idea. Here, only a small subset of 15 reflections is used, and the Bijvoet differences are calculated for all Bijvoet pairs present. By the application of Bayesian statistics, it is possible to extract valuable information from these differences, even in the case of weak anomalous scattering power. With this method, a value of y can be derived from a probability distribution of differences (Δ_obs - Δ_calc)/σ_Δ; y has a physical range between 0.0 and 1.0, and its behaviour is thus comparable to that of the Flack x parameter. Because y is calculated from the F²_obs/F²_calc listing, y is not part of the least-squares refinement and is thus not affected by correlations with the atomic parameters. For (I), we determine y = -0.011 (4), again confirming the enantiopurity and correctness of the absolute configuration. The completeness of Friedel pairs is 99.9%. A plot of 934 Bijvoet pairs with significant Bijvoet differences is shown in Fig. 3. Besides the confirmation of the absolute structure, this plot shows that the largest Bijvoet differences are for the reflections ¯-132 and 221, which both have the correct sign. They do not belong to the selection of 15 reflections in the original Bijvoet experiment.

The program DIRDIF2008 (Beurskens et al., 2008) calculates a Bijvoet coefficient B for the 100 strongest Bijvoet pairs. Thereby B is a weighted average of the signs of the Bijvoet differences. The expected range of B is between -1.0 for the wrong and +1.0 for the correct assignment of the absolute configuration. For the calculation of B we used an atomic model with isotropic displacement parameters and without the contribution of H atoms. For (I), a value of 1.000 is obtained for B, which is another confirmation of the correct absolute configuration.

Related literature

For related literature, see: Allen (2002); Beevers & Hughes (1941); Beurskens et al. (2008); Bijvoet et al. (1951); Brozek & Stadnicka (1994a); Brozek et al. (1994b); Coster et al. (1930); Deslattes et al. (2004); Flack (1983); Flack & Bernardinelli (2000); Flack & Shmueli (2007); Hooft et al. (2008); Laugier & Bochu (2002); Peerdeman (1955); Peerdeman et al. (1951); Solans et al. (1997); Spek (2003); Suzuki et al. (1996a, 1996b); Waasmaier & Kirfel (1995).

S2. Experimental

A solution of (+)-tartaric acid (BDH Chemicals Ltd, Poole, England) in water was heated to 333 K, and an aqueous solution of equimolar amounts of sodium carbonate and rubidium carbonate was added dropwise. At first, rubidium hydrogen tartrate precipitated. Addition of the carbonate solution was continued until the evolution of CO₂ stopped and the initial precipitate had completely redissolved. This solution was then left at room temperature until a white solid formed. Crystals suitable for single-crystal X-ray diffraction were obtained by recrystallization from a minimum amount of water.

S3. Refinement

All H atoms were located in difference Fourier maps. H atoms bonded to C atoms were kept fixed on their located positions with U_iso = 0.05, and with C—H distances of 0.94 and 0.99 Å. H atoms bonded to O atoms were refined freely with isotropic displacement parameters, giving a range of O—H distances of 0.72 (3)–0.93 (4) Å. TWIN/BASF instructions were included in the refinement for the determination of the Flack (1983) parameter.

Computing details

Data collection: COLLECT (Nonius, 1999); cell refinement: PEAKREF (Schreurs, 2008); data reduction: EVAL15 (Xian et al., 2006); program(s) used to solve structure: initial coordinates taken from the literature (Peerdeman, 1955); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008); molecular graphics: PLATON (Spek, 2003) and DRAWxtl (Finger et al., 2007); software used to prepare material for publication: SHELXL97 (Sheldrick, 2008).

Figures

	Fig. 1. : Displacement ellipsoid plot and atomic numbering schemes of (I). Ellipsoids are drawn at the 50% probability level. H atoms are drawn as spheres with arbitrary radii.
	Fig. 2. : The packing of (I) in the unit cell, viewed along the crystallographic c axis. Coordination polyhedra of Rb are drawn in green and of Na in yellow.
	Fig. 3. : A scatter plot of Bijvoet differences, prepared using the program PLATON (Spek, 2003). Shown are 934 pairs where Δobs > 0.25σ(Δobs). 842 reflections confirming the absolute structure are drawn in black. 92 reflections with the wrong sign are drawn in red.

Rubidium sodium (+)-(2R,3R)-tartrate tetrahydrate

Crystal data

Na^+·Rb^+·C4H4O6^2^−·4H2O	F(000) = 656
Mr = 328.60	Dx = 2.036 Mg m^−3
Orthorhombic, P21212	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2 2ab	Cell parameters from 2726 reflections
a = 11.9764 (4) Å	θ = 2.2–27.5°
b = 14.3836 (3) Å	µ = 4.70 mm^−1
c = 6.22447 (16) Å	T = 150 K
V = 1072.25 (5) Å^3	Irregular plate, colourless
Z = 4	0.39 × 0.19 × 0.03 mm

Data collection

Nonius KappaCCD diffractometer	2477 independent reflections
Radiation source: rotating anode	2305 reflections with I > 2σ(I)
Graphite monochromator	Rint = 0.034
ϕ and ω scans	θmax = 27.5°, θmin = 2.2°
Absorption correction: multi-scan (SADABS; Sheldrick, 2002)	h = −15→15
Tmin = 0.161, Tmax = 0.862	k = −18→18
15473 measured reflections	l = −8→8

Refinement

Refinement on F^2	Secondary atom site location: difference Fourier map
Least-squares matrix: full	Hydrogen site location: difference Fourier map
R[F^2 > 2σ(F^2)] = 0.019	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.041	w = 1/[σ^2(Fo^2) + (0.0151P)^2 + 0.5434P] where P = (Fo^2 + 2Fc^2)/3
S = 1.04	(Δ/σ)max = 0.001
2477 reflections	Δρmax = 0.28 e Å^−3
187 parameters	Δρmin = −0.28 e Å^−3
0 restraints	Absolute structure: Flack (1983), 1023 Bijvoet pairs
Primary atom site location: structure-invariant direct methods	Absolute structure parameter: −0.007 (6)

Special details

Experimental. The X-ray intensities of (I) were obtained with an exposure time of 25 s per frame and rotation angles of 1° (364 ϕ and 394 ω scans).

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
O1	0.62309 (12)	0.61037 (9)	0.3530 (2)	0.0132 (3)
O2	0.71219 (13)	0.70248 (10)	0.1174 (2)	0.0161 (3)
O3	0.73257 (13)	0.90587 (10)	0.8184 (2)	0.0195 (3)
O4	0.55442 (12)	0.85880 (10)	0.8419 (2)	0.0178 (3)
O5	0.67086 (13)	0.85670 (10)	0.3246 (3)	0.0142 (3)
H5	0.697 (2)	0.8382 (19)	0.216 (5)	0.030 (8)*
O6	0.79937 (13)	0.74861 (11)	0.6323 (3)	0.0143 (3)
H6	0.827 (2)	0.791 (2)	0.601 (5)	0.024 (9)*
C1	0.65767 (17)	0.68816 (14)	0.2855 (3)	0.0112 (4)
C2	0.63068 (17)	0.77359 (13)	0.4235 (3)	0.0109 (4)
H2	0.5478	0.7751	0.4281	0.050*
C3	0.68253 (17)	0.76371 (13)	0.6467 (3)	0.0116 (4)
H3	0.6458	0.7140	0.7148	0.050*
C4	0.65413 (18)	0.85017 (14)	0.7817 (3)	0.0144 (4)
Na1	0.73182 (6)	0.49322 (7)	0.51534 (12)	0.01375 (16)
O7	0.89274 (14)	0.58484 (11)	0.4701 (3)	0.0182 (3)
H7A	0.931 (2)	0.5952 (18)	0.364 (5)	0.022 (7)*
H7B	0.868 (3)	0.636 (2)	0.520 (6)	0.063 (12)*
O8	0.25734 (14)	0.45859 (13)	−0.1204 (3)	0.0196 (3)
H8A	0.241 (2)	0.503 (3)	−0.016 (5)	0.045 (8)*
H8B	0.260 (2)	0.411 (2)	−0.057 (5)	0.033 (9)*
O9	0.55972 (16)	0.30150 (14)	−0.0430 (3)	0.0264 (4)
H9A	0.528 (3)	0.244 (2)	−0.076 (5)	0.062 (11)*
H9B	0.614 (3)	0.284 (2)	0.008 (5)	0.036 (9)*
O10	0.57615 (14)	0.39448 (12)	0.5686 (3)	0.0221 (4)
H10A	0.505 (3)	0.3934 (19)	0.515 (4)	0.040 (8)*
H10B	0.573 (2)	0.364 (2)	0.668 (5)	0.035 (9)*
Rb1	0.5000	0.5000	0.03657 (4)	0.02204 (7)
Rb2	0.5000	1.0000	0.15972 (4)	0.01560 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.0151 (7)	0.0105 (7)	0.0141 (7)	−0.0005 (6)	−0.0021 (6)	−0.0006 (6)
O2	0.0212 (8)	0.0156 (7)	0.0116 (7)	0.0012 (6)	0.0033 (6)	−0.0013 (6)
O3	0.0276 (9)	0.0154 (7)	0.0157 (8)	−0.0048 (6)	0.0004 (7)	−0.0039 (6)
O4	0.0183 (8)	0.0209 (8)	0.0143 (7)	0.0049 (6)	0.0005 (6)	−0.0036 (7)
O5	0.0229 (8)	0.0094 (7)	0.0101 (7)	0.0000 (6)	0.0003 (7)	0.0008 (6)
O6	0.0145 (8)	0.0125 (8)	0.0160 (8)	0.0018 (6)	−0.0014 (7)	0.0007 (6)
C1	0.0110 (10)	0.0123 (10)	0.0103 (10)	0.0015 (8)	−0.0033 (8)	0.0000 (8)
C2	0.0128 (10)	0.0081 (9)	0.0117 (10)	0.0001 (8)	−0.0004 (8)	−0.0008 (8)
C3	0.0148 (10)	0.0098 (9)	0.0100 (9)	0.0002 (7)	0.0002 (8)	0.0014 (8)
C4	0.0227 (11)	0.0128 (10)	0.0079 (9)	0.0034 (9)	−0.0021 (9)	0.0012 (8)
Na1	0.0149 (4)	0.0119 (4)	0.0145 (3)	−0.0002 (4)	−0.0005 (3)	0.0012 (4)
O7	0.0170 (8)	0.0173 (9)	0.0204 (9)	0.0004 (6)	0.0046 (7)	0.0022 (7)
O8	0.0327 (10)	0.0132 (8)	0.0130 (8)	0.0021 (7)	−0.0010 (7)	−0.0003 (7)
O9	0.0200 (9)	0.0304 (10)	0.0289 (10)	0.0000 (8)	−0.0071 (8)	0.0043 (8)
O10	0.0145 (8)	0.0251 (9)	0.0267 (9)	−0.0049 (7)	−0.0027 (7)	0.0055 (8)
Rb1	0.02587 (15)	0.02194 (14)	0.01832 (13)	−0.01043 (17)	0.000	0.000
Rb2	0.01649 (12)	0.01638 (12)	0.01392 (11)	0.00254 (15)	0.000	0.000

Geometric parameters (Å, º)

O1—Rb1	2.9279 (14)	C2—C3	1.529 (3)
O8—Rb1	3.1235 (17)	C2—H2	0.9932
O9—Rb1	2.9848 (19)	C3—C4	1.539 (3)
O4—Rb2^i	2.9090 (15)	C3—H3	0.9403
O5—Rb2	3.0804 (15)	Na1—Rb2^ii	3.7969 (7)
O7—Rb2^ii	2.9067 (16)	Na1—Rb1	4.0741 (8)
O8—Rb2^iii	3.1485 (17)	Na1—Rb1^i	4.2713 (8)
Na1—O1	2.3571 (16)	O7—H7A	0.82 (3)
Na1—O3^iv	2.4646 (17)	O7—H7B	0.86 (4)
Na1—O5^iv	2.4914 (18)	O8—Na1^vii	2.3742 (18)
Na1—O7	2.3517 (18)	O8—H8A	0.93 (4)
Na1—O8^v	2.3742 (18)	O8—H8B	0.79 (3)
Na1—O10	2.3670 (19)	O9—H9A	0.93 (3)
O1—C1	1.265 (2)	O9—H9B	0.76 (3)
O2—C1	1.250 (3)	O10—Rb1^i	3.4089 (19)
O3—C4	1.256 (3)	O10—H10A	0.91 (3)
O3—Na1^vi	2.4646 (17)	O10—H10B	0.76 (3)
O3—Rb1^ii	3.5926 (15)	Rb1—O10^viii	3.4089 (19)
O4—C4	1.258 (3)	Rb1—O3^iv	3.5926 (16)
O5—C2	1.428 (2)	Rb2—O7^vi	2.9067 (17)
O5—Na1^vi	2.4914 (18)	Rb2—O4^viii	2.9090 (15)
O5—H5	0.79 (3)	Rb2—O5^ix	3.0804 (15)
O6—C3	1.419 (3)	Rb2—O8^x	3.1485 (17)
O6—H6	0.72 (3)	Rb2—Na1^vi	3.7969 (8)
C1—C2	1.534 (3)
C1—O1—Na1	126.44 (13)	Na1—O10—Rb1^i	93.63 (6)
C1—O1—Rb1	114.90 (13)	Na1—O10—H10A	133.9 (17)
Na1—O1—Rb1	100.31 (5)	Rb1^i—O10—H10A	94.0 (17)
C4—O3—Na1^vi	107.56 (13)	Na1—O10—H10B	120 (2)
C4—O3—Rb1^ii	162.40 (13)	Rb1^i—O10—H10B	64 (2)
Na1^vi—O3—Rb1^ii	82.27 (5)	H10A—O10—H10B	104 (3)
C4—O4—Rb2^i	118.96 (13)	O1—Rb1—O1^xi	95.45 (6)
C2—O5—Na1^vi	130.17 (12)	O1—Rb1—O9	120.64 (5)
C2—O5—Rb2	118.67 (11)	O1^xi—Rb1—O9	73.36 (5)
Na1^vi—O5—Rb2	85.22 (5)	O9—Rb1—O9^xi	160.89 (7)
C2—O5—H5	103 (2)	O1—Rb1—O8	141.48 (4)
Na1^vi—O5—H5	115 (2)	O1^xi—Rb1—O8	68.81 (4)
Rb2—O5—H5	102 (2)	O9—Rb1—O8	89.35 (5)
C3—O6—H6	109 (2)	O9^xi—Rb1—O8	84.70 (5)
O2—C1—O1	126.49 (19)	O8—Rb1—O8^xi	143.53 (6)
O2—C1—C2	116.53 (18)	O1—Rb1—O10^viii	132.96 (4)
O1—C1—C2	116.99 (18)	O1^xi—Rb1—O10^viii	117.91 (4)
O5—C2—C3	109.43 (16)	O9—Rb1—O10^viii	50.82 (5)
O5—C2—C1	111.00 (16)	O9^xi—Rb1—O10^viii	110.38 (5)
C3—C2—C1	110.42 (16)	O8—Rb1—O10^viii	84.07 (4)
O5—C2—H2	109.3	O8^xi—Rb1—O10^viii	64.44 (4)
C3—C2—H2	112.4	O1^xi—Rb1—O10^vii	132.96 (4)
C1—C2—H2	104.1	O8—Rb1—O10^vii	64.44 (4)
O6—C3—C2	110.93 (17)	O10^viii—Rb1—O10^vii	62.59 (6)
O6—C3—C4	112.10 (17)	O1—Rb1—O3^iv	65.57 (4)
C2—C3—C4	109.36 (16)	O1^xi—Rb1—O3^iv	94.33 (4)
O6—C3—H3	111.9	O9—Rb1—O3^iv	57.83 (5)
C2—C3—H3	106.9	O9^xi—Rb1—O3^iv	128.01 (5)
C4—C3—H3	105.4	O8—Rb1—O3^iv	146.75 (4)
O3—C4—O4	126.40 (19)	O8^xi—Rb1—O3^iv	47.24 (4)
O3—C4—C3	116.71 (18)	O10^viii—Rb1—O3^iv	78.96 (4)
O4—C4—C3	116.89 (18)	O10^vii—Rb1—O3^iv	128.40 (4)
O7—Na1—O1	90.04 (6)	O1—Rb1—O3^xii	94.33 (4)
O7—Na1—O10	176.86 (8)	O1^xi—Rb1—O3^xii	65.57 (4)
O1—Na1—O10	93.09 (6)	O9—Rb1—O3^xii	128.01 (4)
O7—Na1—O8^v	84.60 (6)	O9^xi—Rb1—O3^xii	57.83 (5)
O1—Na1—O8^v	103.35 (7)	O8—Rb1—O3^xii	47.24 (4)
O10—Na1—O8^v	94.85 (7)	O8^xi—Rb1—O3^xii	146.75 (4)
O7—Na1—O3^iv	92.46 (6)	O10^viii—Rb1—O3^xii	128.40 (4)
O1—Na1—O3^iv	95.66 (6)	O10^vii—Rb1—O3^xii	78.96 (4)
O10—Na1—O3^iv	87.05 (7)	O3^iv—Rb1—O3^xii	150.88 (5)
O8^v—Na1—O3^iv	160.75 (7)	O7^vi—Rb2—O7^xii	75.12 (7)
O7—Na1—O5^iv	96.10 (6)	O7^vi—Rb2—O4^viii	137.15 (4)
O1—Na1—O5^iv	173.37 (6)	O7^xii—Rb2—O4^viii	110.18 (5)
O10—Na1—O5^iv	80.77 (6)	O7^vi—Rb2—O4^xiii	110.18 (5)
O8^v—Na1—O5^iv	79.79 (6)	O7^xii—Rb2—O4^xiii	137.15 (4)
O3^iv—Na1—O5^iv	81.62 (6)	O4^viii—Rb2—O4^xiii	94.32 (6)
O7—Na1—Rb2^ii	49.92 (4)	O7^vi—Rb2—O5	73.93 (4)
O1—Na1—Rb2^ii	132.63 (5)	O7^xii—Rb2—O5	75.44 (4)
O10—Na1—Rb2^ii	127.38 (6)	O4^viii—Rb2—O5	67.08 (4)
O8^v—Na1—Rb2^ii	55.78 (4)	O4^xiii—Rb2—O5	147.41 (4)
O3^iv—Na1—Rb2^ii	108.40 (5)	O7^vi—Rb2—O5^ix	75.44 (4)
O5^iv—Na1—Rb2^ii	53.95 (4)	O7^xii—Rb2—O5^ix	73.93 (4)
C4^iv—Na1—Rb2^ii	87.82 (4)	O4^viii—Rb2—O5^ix	147.41 (4)
O7—Na1—Rb1	117.22 (5)	O4^xiii—Rb2—O5^ix	67.08 (4)
O1—Na1—Rb1	45.00 (4)	O5—Rb2—O5^ix	141.08 (6)
O10—Na1—Rb1	65.17 (5)	O7^vi—Rb2—O8^x	125.00 (5)
O8^v—Na1—Rb1	136.78 (5)	O7^xii—Rb2—O8^x	63.23 (4)
O3^iv—Na1—Rb1	60.90 (4)	O4^viii—Rb2—O8^x	91.97 (4)
O5^iv—Na1—Rb1	129.06 (5)	O4^xiii—Rb2—O8^x	81.95 (4)
C4^iv—Na1—Rb1	83.07 (4)	O5—Rb2—O8^x	123.34 (4)
Rb2^ii—Na1—Rb1	164.90 (2)	O5^ix—Rb2—O8^x	60.15 (4)
O7—Na1—Rb1^i	127.65 (5)	O7^vi—Rb2—O8^xiv	63.23 (4)
O1—Na1—Rb1^i	87.15 (4)	O7^xii—Rb2—O8^xiv	125.00 (5)
O10—Na1—Rb1^i	52.80 (5)	O4^viii—Rb2—O8^xiv	81.95 (4)
O8^v—Na1—Rb1^i	45.86 (4)	O4^xiii—Rb2—O8^xiv	91.97 (4)
O3^iv—Na1—Rb1^i	139.84 (5)	O5—Rb2—O8^xiv	60.15 (4)
O5^iv—Na1—Rb1^i	91.05 (4)	O5^ix—Rb2—O8^xiv	123.34 (4)
C4^iv—Na1—Rb1^i	139.31 (5)	O8^x—Rb2—O8^xiv	171.09 (6)
Rb2^ii—Na1—Rb1^i	98.316 (16)	O7^vi—Rb2—Na1^vi	38.25 (3)
Rb1—Na1—Rb1^i	96.438 (16)	O7^xii—Rb2—Na1^vi	86.61 (4)
Na1—O7—Rb2^ii	91.83 (6)	O4^viii—Rb2—Na1^vi	98.90 (3)
Na1—O7—H7A	131.2 (19)	O4^xiii—Rb2—Na1^vi	124.73 (3)
Rb2^ii—O7—H7A	117.9 (19)	O5—Rb2—Na1^vi	40.83 (3)
Na1—O7—H7B	99 (2)	O5^ix—Rb2—Na1^vi	113.68 (3)
Rb2^ii—O7—H7B	103 (2)	O8^x—Rb2—Na1^vi	149.83 (3)
H7A—O7—H7B	110 (3)	O8^xiv—Rb2—Na1^vi	38.57 (3)
Na1^vii—O8—Rb1	101.08 (6)	C4^viii—Rb2—Na1^vi	84.34 (4)
Na1^vii—O8—Rb2^iii	85.65 (5)	C4^xiii—Rb2—Na1^vi	141.14 (4)
Rb1—O8—Rb2^iii	154.03 (6)	O7^vi—Rb2—Na1^xii	86.61 (4)
Na1^vii—O8—H8A	118 (2)	O7^xii—Rb2—Na1^xii	38.25 (3)
Rb1—O8—H8A	81.2 (17)	O4^viii—Rb2—Na1^xii	124.73 (3)
Rb2^iii—O8—H8A	73.7 (17)	O4^xiii—Rb2—Na1^xii	98.90 (3)
Na1^vii—O8—H8B	137 (2)	O5—Rb2—Na1^xii	113.68 (3)
Rb1—O8—H8B	89 (2)	O5^ix—Rb2—Na1^xii	40.83 (3)
Rb2^iii—O8—H8B	104 (2)	O8^x—Rb2—Na1^xii	38.57 (3)
H8A—O8—H8B	105 (3)	O8^xiv—Rb2—Na1^xii	149.83 (3)
Rb1—O9—H9A	142 (2)	C4^viii—Rb2—Na1^xii	141.14 (4)
Rb1—O9—H9B	117 (2)	C4^xiii—Rb2—Na1^xii	84.34 (4)
H9A—O9—H9B	98 (3)	Na1^vi—Rb2—Na1^xii	115.62 (2)
Na1—O1—C1—O2	75.2 (3)	Na1—O1—Rb1—O3^iv	−27.35 (4)
Rb1—O1—C1—O2	−50.8 (2)	C1—O1—Rb1—O3^xii	−90.65 (13)
Na1—O1—C1—C2	−104.51 (18)	Na1—O1—Rb1—O3^xii	130.77 (5)
Rb1—O1—C1—C2	129.48 (15)	Na1^vii—O8—Rb1—O1	120.05 (7)
Na1^vi—O5—C2—C3	−15.3 (2)	Rb2^iii—O8—Rb1—O1	17.02 (18)
Rb2—O5—C2—C3	−125.06 (13)	Na1^vii—O8—Rb1—O1^xi	−168.81 (7)
Na1^vi—O5—C2—C1	−137.47 (14)	Rb2^iii—O8—Rb1—O1^xi	88.15 (14)
Rb2—O5—C2—C1	112.81 (15)	Na1^vii—O8—Rb1—O9	−96.43 (7)
O2—C1—C2—O5	2.4 (2)	Rb2^iii—O8—Rb1—O9	160.53 (14)
O1—C1—C2—O5	−177.82 (16)	Na1^vii—O8—Rb1—O9^xi	65.39 (7)
O2—C1—C2—C3	−119.11 (19)	Rb2^iii—O8—Rb1—O9^xi	−37.65 (14)
O1—C1—C2—C3	60.6 (2)	Na1^vii—O8—Rb1—O8^xi	−16.28 (5)
O5—C2—C3—O6	−66.6 (2)	Rb2^iii—O8—Rb1—O8^xi	−119.31 (14)
C1—C2—C3—O6	55.9 (2)	Na1^vii—O8—Rb1—O10^viii	−45.78 (6)
O5—C2—C3—C4	57.6 (2)	Rb2^iii—O8—Rb1—O10^viii	−148.82 (14)
C1—C2—C3—C4	−179.95 (17)	Na1^vii—O8—Rb1—O10^vii	16.61 (6)
Na1^vi—O3—C4—O4	−104.0 (2)	Rb2^iii—O8—Rb1—O10^vii	−86.43 (14)
Rb1^ii—O3—C4—O4	133.9 (4)	Na1^vii—O8—Rb1—O3^iv	−105.14 (8)
Na1^vi—O3—C4—C3	74.88 (18)	Rb2^iii—O8—Rb1—O3^iv	151.82 (11)
Rb1^ii—O3—C4—C3	−47.2 (5)	Na1^vii—O8—Rb1—O3^xii	115.42 (8)
Rb2^i—O4—C4—O3	−12.1 (3)	Rb2^iii—O8—Rb1—O3^xii	12.38 (11)
Rb2^i—O4—C4—C3	168.99 (12)	O2—C1—Rb1—O1	141.4 (2)
O6—C3—C4—O3	15.4 (3)	C2—C1—Rb1—O1	−85.2 (2)
C2—C3—C4—O3	−108.0 (2)	O2—C1—Rb1—O1^xi	166.84 (11)
O6—C3—C4—O4	−165.54 (18)	O1—C1—Rb1—O1^xi	25.41 (16)
C2—C3—C4—O4	71.0 (2)	C2—C1—Rb1—O1^xi	−59.80 (19)
C1—O1—Na1—O7	−1.52 (17)	O2—C1—Rb1—O9	80.00 (13)
Rb1—O1—Na1—O7	130.26 (6)	O1—C1—Rb1—O9	−61.42 (15)
C1—O1—Na1—O10	178.67 (17)	C2—C1—Rb1—O9	−146.63 (17)
Rb1—O1—Na1—O10	−49.55 (7)	O2—C1—Rb1—O9^xi	−79.77 (12)
C1—O1—Na1—O8^v	82.94 (17)	O1—C1—Rb1—O9^xi	138.81 (15)
Rb1—O1—Na1—O8^v	−145.28 (5)	C2—C1—Rb1—O9^xi	53.60 (18)
C1—O1—Na1—O3^iv	−93.99 (17)	O2—C1—Rb1—O8	−110.36 (12)
Rb1—O1—Na1—O3^iv	37.78 (6)	O1—C1—Rb1—O8	108.21 (13)
C1—O1—Na1—Rb2^ii	27.50 (19)	C2—C1—Rb1—O8	23.0 (2)
Rb1—O1—Na1—Rb2^ii	159.28 (3)	O2—C1—Rb1—O8^xi	29.10 (11)
C1—O1—Na1—Rb1	−131.77 (18)	O1—C1—Rb1—O8^xi	−112.33 (14)
C1—O1—Na1—Rb1^i	126.19 (16)	C2—C1—Rb1—O8^xi	162.5 (2)
Rb1—O1—Na1—Rb1^i	−102.04 (4)	O2—C1—Rb1—O10^viii	15.23 (14)
O1—Na1—O7—Rb2^ii	152.20 (5)	O1—C1—Rb1—O10^viii	−126.20 (13)
O8^v—Na1—O7—Rb2^ii	48.79 (6)	C2—C1—Rb1—O10^viii	148.59 (17)
O3^iv—Na1—O7—Rb2^ii	−112.13 (5)	O2—C1—Rb1—O10^vii	−48.30 (12)
O5^iv—Na1—O7—Rb2^ii	−30.30 (6)	O1—C1—Rb1—O10^vii	170.27 (13)
C4^iv—Na1—O7—Rb2^ii	−90.08 (6)	C2—C1—Rb1—O10^vii	85.06 (18)
Rb1—Na1—O7—Rb2^ii	−170.44 (3)	O2—C1—Rb1—O3^iv	79.01 (12)
Rb1^i—Na1—O7—Rb2^ii	65.77 (7)	O1—C1—Rb1—O3^iv	−62.42 (13)
O1—Na1—O10—Rb1^i	−84.06 (6)	C2—C1—Rb1—O3^iv	−147.63 (19)
O8^v—Na1—O10—Rb1^i	19.63 (6)	O2—C1—Rb1—O3^xii	−127.82 (11)
O3^iv—Na1—O10—Rb1^i	−179.58 (5)	O1—C1—Rb1—O3^xii	90.75 (13)
O5^iv—Na1—O10—Rb1^i	98.44 (5)	C2—C1—Rb1—O3^xii	5.54 (18)
C4^iv—Na1—O10—Rb1^i	158.10 (5)	C2—O5—Rb2—O7^vi	110.23 (13)
Rb2^ii—Na1—O10—Rb1^i	69.42 (7)	Na1^vi—O5—Rb2—O7^vi	−23.56 (5)
Rb1—Na1—O10—Rb1^i	−120.42 (5)	C2—O5—Rb2—O7^xii	31.85 (13)
C1—O1—Rb1—O1^xi	−156.47 (14)	Na1^vi—O5—Rb2—O7^xii	−101.95 (5)
Na1—O1—Rb1—O1^xi	64.94 (4)	C2—O5—Rb2—O4^viii	−87.94 (13)
C1—O1—Rb1—O9	129.66 (13)	Na1^vi—O5—Rb2—O4^viii	138.26 (6)
Na1—O1—Rb1—O9	−8.93 (8)	C2—O5—Rb2—O4^xiii	−147.30 (12)
C1—O1—Rb1—O9^xi	−36.09 (13)	Na1^vi—O5—Rb2—O4^xiii	78.91 (8)
Na1—O1—Rb1—O9^xi	−174.67 (7)	C2—O5—Rb2—O5^ix	70.87 (13)
C1—O1—Rb1—O8	−94.06 (14)	Na1^vi—O5—Rb2—O5^ix	−62.92 (4)
Na1—O1—Rb1—O8	127.36 (6)	C2—O5—Rb2—O8^x	−11.44 (15)
C1—O1—Rb1—O8^xi	59.83 (13)	Na1^vi—O5—Rb2—O8^x	−145.23 (5)
Na1—O1—Rb1—O8^xi	−78.76 (6)	C2—O5—Rb2—O8^xiv	178.19 (14)
C1—O1—Rb1—O10^viii	66.52 (14)	Na1^vi—O5—Rb2—O8^xiv	44.40 (5)
Na1—O1—Rb1—O10^viii	−72.07 (7)	C2—O5—Rb2—Na1^vi	133.79 (15)
C1—O1—Rb1—O10^vii	−10.86 (14)	C2—O5—Rb2—Na1^xii	31.40 (14)
Na1—O1—Rb1—O10^vii	−149.44 (5)	Na1^vi—O5—Rb2—Na1^xii	−102.40 (5)
C1—O1—Rb1—O3^iv	111.24 (13)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O5—H5···O2	0.79 (3)	2.05 (3)	2.613 (2)	128 (3)
O6—H6···O10^vi	0.72 (3)	2.16 (3)	2.861 (3)	164 (3)
O7—H7A···O4^ii	0.82 (3)	2.07 (3)	2.860 (2)	164 (3)
O7—H7B···O6	0.86 (4)	1.94 (4)	2.796 (2)	176 (3)
O8—H8A···O3^xii	0.93 (4)	1.80 (4)	2.725 (2)	171 (3)
O8—H8B···O2^xi	0.79 (3)	1.99 (3)	2.774 (2)	171 (3)
O9—H9A···O4^vii	0.93 (3)	1.85 (3)	2.774 (2)	171 (3)
O9—H9B···O2^xv	0.76 (3)	2.52 (3)	3.115 (2)	136 (3)
O9—H9B···O6^iv	0.76 (3)	2.52 (3)	3.156 (2)	142 (3)
O10—H10A···O1^xi	0.91 (3)	1.84 (3)	2.739 (2)	168 (2)
O10—H10B···O9^i	0.76 (3)	2.02 (3)	2.770 (3)	170 (3)

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