Supra­molecular structure and second harmonic generation in strontium bis­(hydrogen L-malate) hexa­hydrate

The title compound, tetraaquabis(hydrogen L-malato)strontium(II) dihydrate, [Sr(C₄H₅O₅)₂(H₂O)₄]·2H₂O, is a new non-linear optical semi-organic material with a second harmonic generation efficiency approximately 3.5 times greater than that of potassium dihydrogen phosphate. The malate anions are inter­connected through directional O—H...O hydrogen bonding, in a head-to-tail arrangement, creating extended anionic chains along [001]. Neighbouring parallel chains are crosslinked by water mol­ecules, resulting in a three-dimensional architecture. The Sr²⁺ ion is coordinated by eight O atoms. This material is a new candidate for non-linear optical applications since the crystals are stable and easy to grow.

S1. Comment

Previous studies on organic and semi-organic crystals have shown that L-malic acid is a suitable anionic building block since it is a chiral dicarboxylic acid with two hydrogen-bond donors and five hydrogen-bond acceptors providing structural consistency and rigidity in crystalline solids. Hydrogen malate anions tend to create infinite chains through head-to-tail hydrogen-bond interactions and are able to generate supramolecular aggregates with unique chemical and physical properties (Aakeroy & Nieuwenhuyzen, 1996); an exception has, however, been found in L-histidinium hydrogen malate (de Matos Gomes et al., 2005). Moreover, its chirality ensures the absence of a center of symmetry, essential for optical nonlinear second harmonic generation. The synthesis and X-ray crystalline structure of some organic (Trivedi et al., 2003; Farrell et al., 2002; Aakeroy & Nieuwenhuyzen, 1996) and inorganic (Fleck et al., 2004) salts of L-malic acid have been previously reported but their physical properties have not been fully studied. Optical second harmonic generation has been reported in racemic potassium malate (Schuler et al., 1982), ammonium malate (Betzler et al., 1977), zinc malate 1,10-phenanthroline (He et al., 2004) and recently in caesium hydrogen malate (de Matos Gomes et al., 2005).

Strontium bis(hydrogen L-malate) hexahydrate, hereafter SrLM, is isostructural with its calcium analogue (Lenstra & Van Havere, 1980) having an orthorhombic unit cell and space group P2₁2₁2₁. The unit-cell volume of SrLM is only a few percent larger than that of the calcium compound. Although the ionic radius of an eight-coordinate Sr²⁺ ion is about 10% larger than Ca²⁺, steric effects due to the minimization of intermolecular repulsions should have a smoothing effect in the volume increase of the unit cell. The asymmetric unit cell contains two singly-ionized L-malate anions, one strontium(II) cation and six water molecules.

The conformation of the anions is staggered, as can be concluded from the Cn1—Cn2—Cn3—Cn4 (n = 1, 2) torsion angles, 179.1 (3) and 173.2 (3)°, respectively. Comparison of the C—O bond distances in the two carboxyl groups of each anion shows that only one of them is ionized, as usually found in the L-malic acid salts.

The cations are coordinated to eight O atoms forming irregular polyhedra; four of these O atoms belong to the anions, whereas the remaining four, O1–O4, belong to water molecules. The O atoms of the anions involved are O13 and O23 of the hydroxy groups and O12 and O22 of the ionized carboxylate groups. The coordination distances range from 2.541 (2) to 2.692 (3) Å. Nearest coordination polyhedra do not share any O atoms, the shortest distance between adjacent Sr²⁺ cations being 7.983 (2) Å. The bonding of nearest cations is established via hydrogen bonds between the coordination O atoms and non-coordinated water molecules, as well as carboxylate and carboxyl groups of the anions. Table 2 allows the comparison of their relative strengths. In fact, there are a large number of very strong hydrogen bonds, those between L-hydrogen malate anions connected in a head-to-tail arrangement being amongst the strongest.

The crystal packing can be described as malate anion chains running parallel to the [001] direction. Along these chains, the anions show a head-to-tail arrangement; the carboxyl group (COOH) of each anion is hydrogen bonded to the carboxylate group (COO^-) of the next anion in the chain, as shown in Fig. 2. There are four chains in the unit cell, two running up and two running down the b axis. Parallel chains along the [001] direction are cross-linked by water molecules via hydrogen bonds forming infinite layers of equivalent malate anions parallel to the bc plane. Consecutive layers along the a direction, generated by screw axis symmetry operations, are further linked via hydrogen bonds, giving rise to a three-dimensional packing network.

To investigate the linear and nonlinear optical properties of the title compound, the transmission curve of a 1 mm-thick SrLM plate was measured in the range 200–1200 nm using a Shimadzu spectrophotometer and showed a broad transparency, with a transmission greater than 80%. Preliminary measurements were undertaken to characterize the second-order nonlinear optical response of the SrLM crystals. Using crystals ranging in thickness from 1.4 to 2.0 mm, the second harmonic of a multi-mode Q-switched Nd:YAG laser was generated. The Nd:YAG laser emitted 8 ns pulses with roughly 5 mJ of energy that were weakly focused on to the crystal, which was oriented to provide a maximum second harmonic signal (angle phase-matched). Simultaneously, in order to account for the large shot-to-shot fluctuations due to the random correlation between modes, the signal generated by a 2 mm-thick z-cut quartz plate was monitored. Subsequently, using the same experimental setup, the signal generated by a reference KDP crystal orientated at its phase matching angle was also measured. Taking into account the difference in crystal thickness, SrLM crystals were 3.5 times more efficient than the KDP reference crystal. We plan to further characterize the second order nonlinear susceptibility using the Maker fringe technique in the near future.

The crystal stability and high optical second harmonic generation signal observed in SrLM make it a promising material for nonlinear optics.

S2. Experimental

An aqueous solution of analytical grade reagent, strontium hydroxide and L-malic acid (Aldrich) in a 1:2 molar ratio was stirred at 333 K for several hours and then allowed to cool to room temperature. Crystals were obtained after one week of evaporation of the solution and are stable in air. A suitable crystal was selected and checked by photographic methods before data collection.

S3. Refinement

All H atoms were located in a difference Fourier map; those bonded to C atoms and carboxyl O atoms where placed at idealized positions and refined as riding with C—H = 0.97 and 0.98 Å, and O—H = 0.82 Å [U_iso(H) = 1.2U_eq(C,O)]. The positions of the H atoms belonging to the water molecules were restrained so that the intramolecular O—H and H···H distances would be 0.96 Å and 1.52 Å within 0.01 Å, respectively, thus enforcing the known average geometry of water molecules [U_iso(H) = 1.5U_eq(O)]. Treatment of hydroxy groups? Examination of the crystal structure with PLATON (Spek, 2003) showed that there are no solvent-accessible voids in the crystal lattice.

Computing details

Data collection: CAD-4 Software (Enraf–Nonius, 1989); cell refinement: CAD-4 Software; data reduction: PLATON (Spek, 2003); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEPII (Johnson, 1976); software used to prepare material for publication: SHELXL97.

Figures

	Fig. 1. ORTEPII (Johnson, 1976) plot of the title compound. Displacement ellipsoids are drawn at the 50% probability level.
	Fig. 2. The packing, viewed along the a axis, showing the hydrogen-bonding network. All H atoms not involved in intermolecular hydorgen bonds have been omitted.

Strontium bis(hydrogen L-malate) hexahydrate

Crystal data

[Sr(C4H5O5)2(H2O)4]·2H2O	F(000) = 944
Mr = 461.88	Dx = 1.762 Mg m^−3
OrthorhombicP212121	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 25 reflections
a = 7.166 (3) Å	θ = 9.8–15.1°
b = 15.365 (5) Å	µ = 3.18 mm^−1
c = 15.818 (5) Å	T = 292 K
V = 1741.5 (10) Å^3	Block, clear colourless
Z = 4	0.2 × 0.2 × 0.1 mm

Data collection

Enraf–Nonius CAD-4 diffractometer	1970 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.011
Graphite monochromator	θmax = 27.5°, θmin = 2.6°
Profile data from ω–2θ scans	h = −5→9
Absorption correction: ψ scan (North et al., 1968)	k = −3→19
Tmin = 0.541, Tmax = 0.728	l = −3→20
2335 measured reflections	3 standard reflections every 180 min
2302 independent reflections	intensity decay: 10%

Refinement

Refinement on F^2	Hydrogen site location: inferred from neighbouring sites
Least-squares matrix: full	H atoms treated by a mixture of independent and constrained refinement
R[F^2 > 2σ(F^2)] = 0.021	w = 1/[σ^2(Fo^2) + (0.0361P)^2 + 0.288P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.055	(Δ/σ)max = 0.001
S = 1.00	Δρmax = 0.31 e Å^−3
2302 reflections	Δρmin = −0.31 e Å^−3
267 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
18 restraints	Extinction coefficient: 0.0064 (6)
Primary atom site location: structure-invariant direct methods	Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881
Secondary atom site location: difference Fourier map	Absolute structure parameter: −0.006 (7)

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
Sr1	0.17929 (4)	0.487504 (17)	0.454593 (18)	0.02066 (9)
O11	−0.0256 (4)	0.77582 (15)	0.47487 (14)	0.0355 (6)
O12	0.0653 (4)	0.64392 (14)	0.43311 (13)	0.0295 (6)
C11	0.0049 (5)	0.6965 (2)	0.48796 (19)	0.0225 (7)
C12	−0.0419 (5)	0.65847 (19)	0.57499 (19)	0.0229 (7)
H12	−0.1774	0.6503	0.5785	0.027*
O13	0.0453 (5)	0.57516 (15)	0.58076 (15)	0.0389 (7)
H13	0.0056	0.5494	0.6224	0.058*
C13	0.0190 (5)	0.7172 (2)	0.6478 (2)	0.0294 (8)
H13A	0.1529	0.7259	0.6447	0.035*
H13B	−0.0403	0.7736	0.6415	0.035*
C14	−0.0295 (5)	0.6806 (2)	0.73349 (19)	0.0233 (7)
O14	−0.1511 (4)	0.62665 (15)	0.74544 (14)	0.0300 (6)
O15	0.0743 (4)	0.71376 (17)	0.79374 (14)	0.0366 (6)
H15	0.0503	0.6895	0.8386	0.055*
O21	0.6964 (3)	0.30787 (14)	0.47166 (14)	0.0267 (5)
O22	0.4222 (3)	0.36626 (15)	0.43906 (13)	0.0266 (5)
C21	0.5545 (5)	0.35260 (19)	0.4888 (2)	0.0189 (6)
C22	0.5444 (5)	0.3901 (2)	0.57908 (19)	0.0210 (6)
H22	0.6608	0.4209	0.5919	0.025*
O23	0.3910 (3)	0.44895 (14)	0.58671 (14)	0.0255 (5)
H23	0.4267	0.4942	0.6089	0.038*
C23	0.5203 (5)	0.3142 (2)	0.6408 (2)	0.0256 (7)
H23A	0.4003	0.2868	0.6310	0.031*
H23B	0.6166	0.2712	0.6302	0.031*
C24	0.5318 (5)	0.3435 (2)	0.7318 (2)	0.0246 (7)
O24	0.6426 (4)	0.39851 (17)	0.75560 (14)	0.0362 (6)
O25	0.4156 (4)	0.30338 (17)	0.78112 (14)	0.0380 (7)
H25	0.4374	0.3164	0.8304	0.057*
O1	−0.1634 (4)	0.47945 (16)	0.38515 (15)	0.0360 (6)
H1A	−0.144 (6)	0.5219 (17)	0.3420 (16)	0.054*
H1B	−0.233 (5)	0.4338 (17)	0.359 (2)	0.054*
O2	0.0297 (3)	0.35725 (15)	0.53189 (18)	0.0308 (6)
H2A	0.107 (4)	0.3068 (15)	0.529 (3)	0.046*
H2B	−0.088 (3)	0.340 (2)	0.510 (2)	0.046*
O3	0.2257 (3)	0.48019 (19)	0.29551 (15)	0.0379 (6)
H3A	0.316 (4)	0.509 (2)	0.2618 (19)	0.057*
H3B	0.148 (5)	0.448 (2)	0.2576 (18)	0.057*
O4	0.4821 (4)	0.57286 (17)	0.43342 (19)	0.0399 (7)
H4A	0.492 (5)	0.6271 (15)	0.461 (3)	0.060*
H4B	0.603 (3)	0.549 (2)	0.430 (3)	0.060*
O5	0.4996 (4)	0.60119 (17)	0.66365 (17)	0.0361 (6)
H5A	0.623 (3)	0.603 (2)	0.685 (2)	0.054*
H5B	0.486 (5)	0.6515 (17)	0.629 (2)	0.054*
O6	−0.0003 (4)	0.44181 (16)	0.69520 (16)	0.0360 (6)
H6A	0.030 (5)	0.400 (2)	0.654 (2)	0.054*
H6B	−0.108 (4)	0.423 (2)	0.724 (2)	0.054*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sr1	0.02321 (13)	0.01952 (13)	0.01926 (12)	0.00273 (12)	−0.00014 (13)	−0.00002 (11)
O11	0.0607 (17)	0.0223 (11)	0.0235 (12)	0.0087 (12)	0.0028 (12)	0.0037 (9)
O12	0.0495 (16)	0.0232 (11)	0.0158 (11)	0.0062 (11)	0.0030 (11)	0.0000 (8)
C11	0.0287 (18)	0.0237 (16)	0.0150 (13)	0.0015 (14)	−0.0025 (14)	0.0022 (12)
C12	0.0296 (18)	0.0206 (15)	0.0184 (14)	0.0052 (14)	0.0059 (14)	0.0007 (11)
O13	0.072 (2)	0.0224 (11)	0.0228 (12)	0.0135 (13)	0.0118 (14)	0.0047 (9)
C13	0.045 (2)	0.0251 (16)	0.0185 (15)	−0.0018 (16)	0.0034 (16)	0.0019 (13)
C14	0.0327 (18)	0.0198 (15)	0.0175 (15)	0.0021 (14)	0.0000 (14)	0.0004 (12)
O14	0.0330 (15)	0.0327 (12)	0.0243 (11)	−0.0052 (11)	−0.0026 (11)	0.0045 (9)
O15	0.0510 (17)	0.0429 (15)	0.0159 (11)	−0.0151 (14)	−0.0049 (12)	0.0063 (10)
O21	0.0235 (11)	0.0276 (11)	0.0291 (12)	0.0042 (10)	0.0012 (11)	−0.0045 (9)
O22	0.0311 (13)	0.0328 (12)	0.0159 (11)	0.0070 (10)	−0.0020 (10)	−0.0034 (9)
C21	0.0218 (16)	0.0175 (14)	0.0173 (14)	−0.0039 (13)	0.0022 (13)	0.0025 (12)
C22	0.0223 (16)	0.0208 (15)	0.0200 (14)	0.0009 (13)	−0.0020 (13)	−0.0019 (12)
O23	0.0300 (12)	0.0240 (11)	0.0224 (11)	0.0068 (10)	−0.0060 (10)	−0.0065 (9)
C23	0.038 (2)	0.0221 (15)	0.0173 (14)	0.0000 (15)	−0.0035 (15)	−0.0007 (12)
C24	0.0290 (18)	0.0244 (16)	0.0205 (15)	0.0043 (15)	−0.0038 (14)	0.0004 (12)
O24	0.0346 (15)	0.0470 (15)	0.0269 (12)	−0.0112 (12)	0.0023 (11)	−0.0112 (11)
O25	0.0597 (18)	0.0377 (14)	0.0165 (11)	−0.0171 (14)	0.0025 (13)	−0.0024 (10)
O1	0.0364 (13)	0.0391 (13)	0.0326 (12)	−0.0111 (14)	−0.0041 (12)	0.0103 (11)
O2	0.0241 (12)	0.0252 (12)	0.0432 (16)	−0.0020 (10)	−0.0043 (12)	−0.0003 (11)
O3	0.0333 (15)	0.0573 (17)	0.0232 (11)	−0.0073 (14)	−0.0002 (10)	−0.0007 (12)
O4	0.0360 (15)	0.0302 (13)	0.0536 (18)	−0.0086 (12)	0.0060 (14)	−0.0080 (12)
O5	0.0359 (15)	0.0324 (13)	0.0398 (16)	−0.0083 (12)	−0.0062 (12)	0.0031 (11)
O6	0.0397 (16)	0.0365 (14)	0.0318 (13)	−0.0049 (13)	0.0064 (12)	−0.0035 (11)

Geometric parameters (Å, º)

Sr1—O3	2.541 (2)	C21—C22	1.541 (4)
Sr1—O4	2.557 (3)	C22—O23	1.428 (4)
Sr1—O12	2.561 (2)	C22—C23	1.530 (4)
Sr1—O22	2.561 (2)	C22—H22	0.9800
Sr1—O2	2.579 (3)	O23—H23	0.8200
Sr1—O1	2.693 (3)	C23—C24	1.511 (4)
Sr1—O13	2.592 (2)	C23—H23A	0.9700
Sr1—O23	2.650 (2)	C23—H23B	0.9700
O11—C11	1.256 (4)	C24—O24	1.219 (4)
O12—C11	1.262 (4)	C24—O25	1.297 (4)
C11—C12	1.532 (4)	O25—H25	0.8200
C12—O13	1.427 (4)	O1—H1A	0.95 (3)
C12—C13	1.527 (4)	O1—H1B	0.96 (3)
C12—H12	0.9800	O2—H2A	0.95 (3)
O13—H13	0.8200	O2—H2B	0.953 (10)
C13—C14	1.508 (4)	O3—H3A	0.95 (3)
C13—H13A	0.9700	O3—H3B	0.96 (3)
C13—H13B	0.9700	O4—H4A	0.94 (3)
C14—O14	1.217 (4)	O4—H4B	0.945 (10)
C14—O15	1.312 (4)	O5—H5A	0.949 (10)
O15—H15	0.8200	O5—H5B	0.95 (3)
O21—C21	1.257 (4)	O6—H6A	0.94 (3)
O22—C21	1.250 (4)	O6—H6B	0.94 (3)
O3—Sr1—O4	77.41 (8)	C21—O22—Sr1	125.25 (19)
O3—Sr1—O12	87.24 (8)	O22—C21—O21	124.7 (3)
O4—Sr1—O12	76.82 (9)	O22—C21—C22	119.0 (3)
O3—Sr1—O22	77.52 (8)	O21—C21—C22	116.3 (3)
O4—Sr1—O22	77.52 (9)	O23—C22—C23	110.0 (3)
O12—Sr1—O22	152.45 (9)	O23—C22—C21	110.6 (2)
O3—Sr1—O2	119.32 (9)	C23—C22—C21	108.1 (2)
O4—Sr1—O2	144.37 (9)	O23—C22—H22	109.4
O12—Sr1—O2	131.20 (8)	C23—C22—H22	109.4
O22—Sr1—O2	76.32 (8)	C21—C22—H22	109.4
O3—Sr1—O1	73.34 (8)	C22—O23—H23	109.5
O4—Sr1—O1	138.06 (8)	C24—C23—C22	112.0 (3)
O12—Sr1—O1	72.43 (8)	C24—C23—H23A	109.2
O22—Sr1—O1	123.16 (8)	C22—C23—H23A	109.2
O2—Sr1—O1	77.21 (8)	C24—C23—H23B	109.2
C11—O12—Sr1	128.22 (19)	C22—C23—H23B	109.2
O11—C11—O12	124.6 (3)	H23A—C23—H23B	107.9
O11—C11—C12	118.7 (3)	O24—C24—O25	124.2 (3)
O12—C11—C12	116.7 (3)	O24—C24—C23	122.4 (3)
O13—C12—C13	110.9 (3)	O25—C24—C23	113.4 (3)
O13—C12—C11	107.7 (3)	C24—O25—H25	109.5
C13—C12—C11	112.9 (3)	Sr1—O1—H1A	97 (3)
O13—C12—H12	108.4	Sr1—O1—H1B	133 (2)
C13—C12—H12	108.4	H1A—O1—H1B	106 (3)
C11—C12—H12	108.4	Sr1—O2—H2A	112 (2)
C12—O13—H13	109.5	Sr1—O2—H2B	114 (2)
C14—C13—C12	113.0 (3)	H2A—O2—H2B	106 (3)
C14—C13—H13A	109.0	Sr1—O3—H3A	129 (2)
C12—C13—H13A	109.0	Sr1—O3—H3B	125 (2)
C14—C13—H13B	109.0	H3A—O3—H3B	106.5 (15)
C12—C13—H13B	109.0	Sr1—O4—H4A	117 (2)
H13A—C13—H13B	107.8	Sr1—O4—H4B	126 (2)
O14—C14—O15	123.9 (3)	H4A—O4—H4B	107.7 (15)
O14—C14—C13	124.0 (3)	H5A—O5—H5B	105.8 (15)
O15—C14—C13	112.1 (3)	H6A—O6—H6B	108.1 (15)
C14—O15—H15	109.5
O3—Sr1—O12—C11	177.6 (3)	O3—Sr1—O22—C21	143.6 (3)
O4—Sr1—O12—C11	−104.7 (3)	O4—Sr1—O22—C21	63.9 (2)
O22—Sr1—O12—C11	−126.5 (3)	O12—Sr1—O22—C21	85.6 (3)
O2—Sr1—O12—C11	50.0 (3)	O2—Sr1—O22—C21	−91.7 (2)
O1—Sr1—O12—C11	104.2 (3)	O1—Sr1—O22—C21	−156.1 (2)
Sr1—O12—C11—O11	170.2 (3)	Sr1—O22—C21—O21	−162.3 (2)
Sr1—O12—C11—C12	−12.7 (4)	Sr1—O22—C21—C22	19.7 (4)
O11—C11—C12—O13	−166.2 (3)	O22—C21—C22—O23	−9.8 (4)
O12—C11—C12—O13	16.5 (4)	O21—C21—C22—O23	172.0 (3)
O11—C11—C12—C13	−43.4 (5)	O22—C21—C22—C23	110.7 (3)
O12—C11—C12—C13	139.3 (3)	O21—C21—C22—C23	−67.5 (4)
O13—C12—C13—C14	−59.9 (4)	O23—C22—C23—C24	−65.9 (4)
C11—C12—C13—C14	179.1 (3)	C21—C22—C23—C24	173.2 (3)
C12—C13—C14—O14	−21.8 (5)	C22—C23—C24—O24	−39.3 (5)
C12—C13—C14—O15	158.3 (3)	C22—C23—C24—O25	141.9 (3)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O13—H13···O6	0.82	2.01	2.753 (3)	150
O13—H13···O14	0.82	2.54	3.065 (3)	123
O15—H15···O22^i	0.82	1.82	2.607 (3)	162
O23—H23···O5	0.82	1.93	2.749 (3)	177
O25—H25···O12^i	0.82	1.74	2.541 (3)	167
O1—H1A···O24^ii	0.95 (3)	1.83 (3)	2.782 (3)	172 (4)
O1—H1B···O14^iii	0.96 (3)	2.19 (2)	3.051 (3)	150 (3)
O2—H2A···O21^iv	0.95 (3)	1.88 (2)	2.805 (3)	164 (3)
O2—H2B···O21^v	0.95 (1)	1.73 (1)	2.681 (3)	179 (4)
O3—H3A···O6^ii	0.95 (3)	1.85 (3)	2.797 (4)	176 (4)
O3—H3B···O5^ii	0.96 (3)	1.97 (3)	2.919 (4)	170 (3)
O4—H4A···O11^vi	0.94 (3)	1.81 (3)	2.741 (4)	169 (4)
O4—H4B···O1^vii	0.95 (1)	2.11 (2)	3.016 (4)	161 (4)
O5—H5A···O14^vii	0.95 (1)	1.91 (1)	2.845 (4)	167 (4)
O5—H5B···O11^vi	0.95 (3)	1.99 (2)	2.899 (3)	160 (4)
O6—H6A···O2	0.94 (3)	2.03 (2)	2.900 (4)	152 (4)
O6—H6B···O24^v	0.94 (3)	1.89 (2)	2.812 (4)	164 (4)

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