Crystal structure or chemical composition of salt–sugar-based metal–organic frameworks: what are the nonlinear optical properties due to?

In the last few decades optical imaging techniques based on nonlinear optical properties have been of interest for biosensing applications. This work focuses on two isostructural and isomorphous sugar-derived metal–organic frameworks (MOFs) with second-harmonic generation (SHG) properties, in order to investigate their possible application as biosensors in view of their high biocompatibility. Combining 2-de­oxy-D-galactose with the metal halogenides CaX₂ (X = Br, I), two new isomorphous MOFs of formula [Ca(C₆H₁₂O₅)₂]X₂ were obtained and characterized through single-crystal X-ray diffraction. The first-order static hyperpolarizability and second-order susceptibility were estimated by in vacuo and in-crystal density functional theory calculations, and compared with the experimental SHG response of powdered samples. The parameters influencing the SHG response of these compounds were investigated by comparison with similar previously analysed MOFs, to understand how to design more efficient materials to be used as nanoprobes by exploiting crystal engineering techniques.

1. Introduction

In the last few decades optical imaging techniques based on the nonlinear optical (NLO) properties, and in particular the second-harmonic generation (SHG), of materials have been of interest for biosensing applications (Boyd, 2003), i.e. these materials can be used in biological systems for the selective detection of biostructures. The advantage of SHG-based nanoprobes is that in principle they do not bleach or blink, and the second-harmonic signal does not saturate with increasing illumination intensity (Campagnola & Loew, 2003; Dempsey et al., 2012; Huang et al., 2006; Jin, 2012; Liu et al., 2017; McKinlay et al., 2010; Pantazis et al., 2010; Park, 2009). SHG nanoprobes are often composed of inorganic compounds or metals that cannot be considered as biocompatible materials (Holzinger et al., 2014). For many years, our research has been focused on sugar-derived metal–organic frameworks (MOFs) with SHG properties and their potential application as biosensors in view of their high biocompatibility. Our main interest is related to the parameters influencing the SHG response of this type of compound, and to be able to design more efficient materials by exploiting crystal engineering techniques.

It is well known that a lack of inversion symmetry in a crystal structure is necessary to generate an SHG response. We thus focused our attention towards sugar-based MOFs that are intrinsically not centrosymmetric. Our previous work on this subject was aimed at investigating the influence of composition on the SHG response, analysing four iso­morphous MOFs based on β-D-fructose and alkali earth halogenides, MX₂ (M = Ca, Sr; X = Cl, Br) (Marabello et al., 2017). We showed that the cation did not play a significant role, while a heavier anion was responsible for a high first-order static hyperpolarizability (β) and second-order susceptibility [χ⁽²⁾]. We also analysed similar MOFs with similar composition (fructose, Sr and I) but different structures and stoichiometries (Marabello et al., 2015, 2019b). In all these cases, we observed that different arrangements of the same building blocks in the crystal structure play a fundamental role in determining the SHG efficiency, and, furthermore, some peculiar combinations of symmetry elements can cancel the SHG response even in an acentric structure.

The aim of the present work is to analyse the role of the sugar in determining the SHG properties in this type of MOF. In the past, by screening experimentally the SHG efficiencies of about 150 powdered saccharides, Bourhill et al. (1993) observed that a higher SHG signal was produced by those saccharides that crystallize in space groups with lower symmetry. Among them, 2-de­oxy-D-galactose (DGal) showed the most promising SHG response. Thus, we oriented our synthesis towards MOFs containing this saccharide, along with alkali earth halogenides, hoping that it would impart high SHG efficiency to the crystals.

DGal is a de­oxy hexose sugar known to interfere with the glycoprotein metabolism in the influenza virus (Klenk et al.,1972) and rat liver (Keppler et al., 1970). It crystallizes in the polar space group P2₁, with all the molecular units adopting the β-2-de­oxy-D-galactopyran­ose ring form (Puliti et al., 1984) (see scheme).

By combining 2-de­oxy-D-galactose with the halogenides CaX₂ (X = Br, I), we obtained two new isomorphous MOFs of formula [Ca(C₆H₁₂O₅)₂]X₂, named CaDGalBr and CaDGalI, respectively, for which the SHG is expected to be higher than that of fructose-based MOFs, if the contribution of the sugar is what causes the SHG efficiency. In order to understand this perspective, the two compounds were characterized by single-crystal X-ray diffraction. The first-order static hyperpolarizability and second-order susceptibility were estimated by in vacuo and in-crystal density functional theory (DFT) calculations, and compared with experimental SHG values obtained for powdered samples.

2. Experimental

2.1. Synthesis of [Ca(C₆H₁₂O₅)₂]Br₂ (CaDGalBr)

Calcium bromide and 2-de­oxy-D-galactose in stoichiometric ratios of 2:1 (0.200:0.075 g), 1:1 (0.100:0.075 g) and 1:2 (0.050:0.075 g) were dissolved in ethanol (1 g). The solvents were evaporated slowly at room temperature and after a few days colourless crystalline powders were formed. The powders were washed with a few drops of ethanol and dried in an oven at 323 K.

2.2. Synthesis of [Ca(C₆H₁₂O₅)₂]I₂ (CaDGalI)

Calcium iodide and 2-de­oxy-D-galactose in stoichiometric ratios of 2:1 (0.180:0.050 g), 1:1 (0.090:0.050 g) and 1:2 (0.045:0.050 g) were dissolved in ethanol (1 ml). The solutions were heated up to 353 K for 30 min, cooled to room temperature and the solvent was evaporated for two days in an oven at 323 K to give colourless crystalline powders. The powders were washed with a few drops of ethanol and dried in an oven at 323 K.

2.3. Single-crystal X-ray diffraction (XRD)

X-ray diffraction data for CaDGalBr and CaDGalI were collected at room temperature using an Oxford Diffraction Gemini R Ultra diffractometer. Data were collected with mirror-monochromated Cu Kα radiation (1.5418 Å). The CrysAlisPro (Agilent, 2014) package was used for data collection and integration, SHELXT (Sheldrick, 2015a) for resolution, SHELXL (Sheldrick, 2015b) for refinement and OLEX2 (Dolomanov et al., 2009) for graphics.

Crystal data for CaDGalBr (M_w = 564.24): monoclinic, space group P2₁, Z = 2. Cell parameters are reported in Table 1. Reflections collected 5021, of which 2698 unique (R_int = 0.0374). R₁ = 0.0350, wR₂ = 0.0764 (all data).

Table 1
Cell parameters for the DGal ligand and the compounds CaDGalBr and CaDGalI

	DGal†	CaDGalBr	CaDGalI
Crystal system	Monoclinic	Monoclinic	Monoclinic
Space group	P21	P21	P21
a (Å)	9.811 (1)	7.5022 (4)	7.6384 (2)
b (Å)	6.953 (1)	14.2259 (6)	14.4621 (4)
c (Å)	5.315 (1)	10.4520 (6)	10.7490 (3)
β (°)	91.58 (2)	109.931 (6)	109.233 (4)
Volume (Å^3)	362.43 (9)	1048.7 (1)	1121.14 (6)

†Literature data from CSD refcode DACHIY (Puliti et al., 1984).

Crystal data for CaDGalI (M_w = 658.22): monoclinic, space group P2₁, Z = 2. Cell parameters are reported in Table 1. Reflections collected 11 076, of which 3737 unique (R_int = 0.0434). R₁ = 0.0316, wR₂ = 0.0792 (all data).

All atoms except H atoms were refined with anisotropic displacement parameters. Due to the low number of reflections collected, even if the H-atom peaks were observed in the difference Fourier maps, the H atoms were calculated and refined as riding with U_iso = 1.2 or 1.5 times U_eq of the connected carbon or oxygen atom. The interested reader can find further details of crystal data, data collection, least-squares refinements and bond lengths in the supporting information (Tables S1 and S2) and CIF files (CCDC 2058083 and 2058084).

2.4. Computational methods

2.4.1. In vacuo calculations

The calculations were performed with the GAUSSIAN09 and GAUSSIAN16 set of programs (Frisch et al., 2009, 2016). All the structures in this work were optimized by gradient-based techniques (Schlegel & Daudel, 1981; Schlegel, 1982a,b; Schlegel et al., 1984) with no symmetry constraints at the density functional theory (DFT) B3LYP level of theory (Becke, 1988, 1993), in conjunction with the 6-31G(d) basis set, for the C, H, O, Ca and Br atoms (Hehre et al., 1986). For iodine the LANL2DZ basis was used (Wadt & Hay, 1985). All critical points were characterized as energy minima by calculating their analytical frequencies. The total dipole moment, polarizability and first-order hyperpolarizability were calculated at the same level of theory. Molecular volumes were computed by averaging ten different volume calculations on the optimized geometries at the B3LYP level of theory with the options scf = tight, volume = tight and iop(6/45 = 500,6/46 = 1) (Parsons & Ninham, 2009).

2.4.2. Bulk calculations

DFT quantum simulations in the solid state were performed with the linear combination of Gaussian-type function (LCGTF) approach as implemented in the CRYSTAL14 package (Dovesi et al., 2014a). According to the results of our former study (Marabello et al., 2019b), the hybrid PBE0 hamiltonian (Adamo & Barone, 1999) was selected throughout. C, H and O atoms were modelled with a 6-31G* split-valence basis set optimized for molecular crystals (Spackman & Mitchell, 2001). A Doll–Stoll large-core pseudopotential was applied to the bromide and iodide species (Doll & Stoll, 1998), while Ca²⁺ ions were described by a Kaupp small-core pseudopotential (Kaupp et al., 1991; Kulkarni et al., 2010). All the simulations relied on X-ray derived structures, with atomic coordinates having been fully relaxed at fixed experimental unit-cell parameters. Coupled perturbed (CP) Kohn–Sham calculations were then used to estimate the first- and second-order polarizabilities (Ferrero et al., 2008a,b,c). The same quantum simulations were also carried out on crystalline sucrose (Gražulis et al., 2009; Russo et al., 2013) and 2-de­oxy-β-galactose (Puliti et al., 1984), taken as references for estimating the relative SHG response of CaDGalBr and CaDGalI. The interested reader can find full technical details of the computational procedure in Section S2 of the supporting information.

2.5. SHG measurements

The SHG efficiency of the powdered compounds was measured by the method of Kurtz & Perry (1968). Samples were ground in an agate mortar (grain sizes below 100 µm) and heated in an oven at 323 K to avoid the absorption of humidity, before being sealed into capillaries.

The non-resonant 1064 nm wavelength of a Nd:YAG pulsed laser beam was directed onto capillaries containing the samples. The scattered radiation was collected by an elliptical mirror, filtered to select only the second-order contribution at 532 nm (I^2ω), and re-collected with a Hamamatsu R 5108 photomultiplier tube. The SHG efficiency was evaluated by taking as reference the SHG signal of ground sucrose powders (I^2ω/I^2ω_sucrose).

3. Results and discussion

3.1. Synthesis and crystal structures

Both compounds were synthesized through a simple procedure, as were the analogous compounds of our previous studies, by dissolution of the reagents in ethanol and subsequent evaporation of the solvent. For each compound, three solutions with salt:sugar stoichiometric ratios of 2:1, 1:1 and 1:2 were prepared and after few days a white crystalline precipitate was observed. The only difference between the syntheses of the two compounds was that in the case of CaDGalI the solutions were heated up to 353 K for 30 min and maintained at 323 K during evaporation, to avoid the formation of the I₃⁻ ion. The dried powders are slightly hygroscopic in humid air and stable below 353 K; above this temperature they degrade to a dark-brown amorphous powder.

Crystals suitable for X-ray structure determination were obtained for both compounds from the solutions with a stoichiometric ratio of 1:1. To avoid the absorption of water by the mounted crystals they were covered with a paraffin oil for the X-ray measurements.

The two compounds are almost perfectly isostructural (root-mean-square deviation or r.m.s.d. = 0.163 Å) and do not exhibit any disorder. As expected, the I-containing crystal has a slightly larger (by 6.9%) cell volume, but the large iodine ions do not imply any significant change in the packing motifs (Table 1). Thus, any difference in the optical behaviour is expected to be due to the different chemical nature of the polarizable halogen atoms.

The asymmetric unit of both compounds consists of one Ca²⁺ ion, two X⁻ anions, two sugar molecules and two water molecules coordinated to the metal atom (Fig. 1). One sugar molecule adopts the α-D-pyran­ose form, the other the β-D-furan­ose form. It is worth noting that at equilibrium in aqueous solution the two cyclic forms coexist, with a pre­dominance of the six-membered one (∼5:1) (Angyal & Pickles, 1972). Our conditions clearly shift the equilibrium toward a 1:1 ratio of pyran­ose:furan­ose forms for both compounds. This is likely to be due to a metal-mediated template effect, as β-2-de­oxy-D-galactofuran­ose is a more effective chelating agent. Each furan­ose ring can bind two Ca²⁺ ions by exploiting at the same time the exocyclic hydroxyl groups on the anomeric side, and the aliphatic ones on the opposite side, forming extended Ca–furan­ose chains that run along the a axis (Fig. 2). Thus, the structures are classified as 1D-MOFs. Each Ca²⁺ ion is also chelated by a pyran­ose ring that does not bridge to any other cation. Pyran­ose rings are too large to fill the space around the cations effectively, and in fact they are arranged orthogonally with respect to the metal–organic chains, along the b direction (Fig. 2, and Fig. S7 in the supporting information). In the end, the coexistence of smaller and larger rings in this structure allows an efficient occupation of space, in agreement with Kitaigorodskii's principle of close packing (Kitaigorodskii, 1961).

Figure 1 The asymmetric unit of both compounds (X = Br, I). Displacement ellipsoids are drawn at the 50% probability level and H atoms are shown as small spheres of arbitrary radii. Dotted lines indicate O⋯X hydrogen bonds.

Figure 2 Chains of metals and sugar molecules developed in the [100] direction.

One-dimensional chains were also observed in some of analogue MOF structures containing fructose and alkali earth halogenides (Marabello et al., 2017, 2019b). In these cases, two metal cations were bridged by two fructose mol­ecules, while in the present compounds and in [Sr(fructose)(H₂O)₃I]I (Marabello et al., 2019b) only one sugar molecule bridges two metal cations.

In the present compounds, the Ca–furan­ose parallel chains are reciprocally connected in the crystal through strong hydrogen bonds involving the halogen anion, the water molecules and the free OH groups of the pyran­ose sugar molecules (Fig. 3, and Table S3 and Fig. S1).

Figure 3 Two adjacent chains connected through several hydrogen bonds, shown as dotted lines. Atom labelling is as reported in Fig. S1 of the supporting information).

3.2. Computational results

For experimental applications, the MOFs have to be reduced to particles of a few tens of nanometres, which can be obtained by vigorously grinding the crystals. In fact, in our previous work (Marabello et al., 2019a) on analogous structures (two MOFs composed of Sr²⁺, fructose and Cl⁻/I⁻) we demonstrated the inverse proportionality between the size of the ground particles and the grinding energy of a planetary mill (grinding time and number of revolutions per minute).

Therefore, it is important to ascertain the SHG behaviour of small fragments of the compounds analysed, by considering the structural distortion that the surface forces can induce at the nanoscale level.

3.2.1. In vacuo computational results

To this end, two different small fragments of the crystal were selected (Figs. 4 and 5) and the relevant geometries were recomputed by optimizing the atomic coordinates derived from the X-ray structures.

Figure 4 Fragment1 of the crystal structure of CaDGgalX (X = Br,I), optimized at the B3LYP level of theory. Dotted lines indicate hydrogen bonds.

Figure 5 Fragment2 of the crystal structure of CaDGgalX (X = Br, I), optimized at the B3LYP level of theory. Dotted lines indicate hydrogen bonds.

The composition of the fragments does not reflect their stoichiometry, but an excess of sugar molecules was added at the boundary of the structure to attain full coordination of the metal. Fragment1 in Fig. 4 is selected by cutting the crystal along the 1D Ca–furan­ose chain and is composed of three calcium ions, eight 2-D-galactose molecules, six anions (Br⁻ or I⁻) and six water molecules, while Fragment2 in Fig. 5 is obtained by cutting the crystal along two parallel Ca–furan­ose chains, connected through several hydrogen bonds, and is composed of three calcium ions, seven 2-D-galactose mol­ecules, six anions (Br⁻ or I⁻) and six water molecules. Since sucrose is the usual reference compound for SHG measurements, the same types of calculation were carried out on a model of bulk sucrose, composed of four sucrose units. The atomic coordinates of sucrose were obtained from the Cambridge Structural Database (CSD; Russo et al., 2013). All geometries were re-optimized at the B3LYP level of theory to obtain the corresponding minima.

Tables 2 and 3 show the most relevant geometric parameters compared with the corresponding X-ray data for the two fragments.

Table 2
Relevant distances (Å) around the metal atom in Fragment1 from X-ray data and B3LYP/6-31G(d) calculations

	CaDGalBr		CaDGalI
	XRD	B3LYP	XRD	B3LYP
Ca1—O1W	2.444 (7)	2.458	2.447 (8)	3.152
Ca1—O2B	2.491 (6)	2.520	2.478 (6)	2.534
Ca1—O2W	2.409 (7)	2.550	2.388 (7)	2.507
Ca1—O3A	2.471 (6)	2.586	2.468 (6)	2.556
Ca1—O3B	2.391 (6)	2.528	2.429 (6)	2.617
Ca1—O4A	2.466 (6)	2.548	2.471 (5)	2.541
Ca1—O4B1	2.414 (6)	2.474	2.415 (6)	2.460
Ca1—O5B1	2.504 (6)	3.100	2.500 (7)	2.554
Ca^2+⋯Ca^2+ (average)	9.665	8.048	11.162	8.767
Ca^2+⋯X^− (average)	5.207	4.568	5.805	5.133

Table 3
Relevant distances (Å) around the metal atom in Fragment2 from X-ray data and B3LYP/6-31G(d) calculations

	CaDGalBr		CaDGalI
	XRD	B3LYP	XRD	B3LYP
Ca1—O1W	2.444 (7)	2.511	2.447 (8)	2.516
Ca1—O2B	2.491 (6)	2.627	2.478 (6)	2.618
Ca1—O2W	2.409 (7)	2.487	2.388 (7)	2.499
Ca1—O3A	2.471 (6)	2.601	2.468 (6)	2.680
Ca1—O3B	2.391 (6)	2.486	2.429 (6)	2.472
Ca1—O4A	2.466 (6)	2.594	2.471 (5)	2.596
Ca1—O4B1	2.414 (6)	2.493	2.415 (6)	2.497
Ca1—O5B1	2.504 (6)	2.710	2.500 (7)	2.687
Ca^2+⋯Ca^2+ (average)	7.503	6.492	7.638	6.417
Ca^2+⋯X^− (average)	4.968	4.370	5.508	4.363

As expected, the optimized structural parameters show deviations from the corresponding X-ray data, probably due to the small size of the computed fragments, which involve a certain degree of asymmetry with respect to the crystal. The most relevant differences between the X-ray data and the theoretical calculations are found in the bonds between Ca²⁺ and the coordinated O atoms and range from 0.01 Å to a maximum of 0.59 Å in the CaDGalBr Fragment1. In Fragment2, the bond differences are smaller and range from 0.07 Å to a maximum of 0.20 Å. The same trend is observed in the CaDGalI complex, where the differences range from 0.04 to 0.69 Å in Fragment1 and decrease in Fragment2, ranging from 0.05 to 0.21 Å. Greater differences are observed in the distances between the Ca²⁺ ions and between Ca cations and X anions: the differences in the Ca²⁺⋯Ca²⁺ distances range from a minimum of 1.0 Å to 2.4 Å and in the Ca²⁺⋯X⁻ distances from 0.6 to 1.1 Å. The differences between the experimental and theoretical calculation results are probably caused by the difficulty that DFT with double-ζ basis sets has to describe the non-covalently bound entities.

Table S4 collects the results of natural bond orbital (NBO) calculations: the natural atomic charges on Ca, Br and I and the group charges of the galactose and water molecules are reported. No significant differences were observed between the complexes or between the different fragments.

Table 4 shows the computed values of the dipole moment μ, the mean polarizability α, the first static hyperpolarizability β_tot and the second-order susceptibility χ⁽²⁾ for the two compounds and the two different fragments. The ratio between the second-order susceptibility of the compounds to that of sucrose is also reported, in order to compare the computational results with the experimental second harmonic measurements.

Table 4
In vacuo computed dipole moments μ (Debye), mean polarizabilities 〈α〉 (a.u.), first-order static hyperpolarizabilities β_tot (10⁻³⁰ cm⁵ esu⁻¹), second-order susceptibilities χ⁽²⁾ (pm V⁻¹), second-order susceptibility ratios, E_HOMO, E_LUMO and ΔE (a.u.) with respect to sucrose values

	Fragment1		Fragment2
	CaDGalBr	CaDGalI	CaDGalBr	CaDGalI	DGal
μ	24.93	26.43	21.57	19.41	26.13
〈α〉	868.442	880.400	782.787	807.653	681.773
βtot	9.4	14.9	7.8	14.3	7.4
χ^(2)	1.55	2.28	1.42	2.35	1.55
χ^(2)/χ^(2)sucrose	0.85	1.25	0.78	1.29	0.85
EHOMO	−0.20328	−0.19556	−0.22553	−0.20715	−0.19248
ELUMO	−0.02593	−0.03832	−0.03929	−0.02404	−0.15356
ΔE	0.17735	0.15724	0.18624	0.18311	0.03892

The total dipole moments μ and the mean polarizabilities α in a Cartesian frame are defined as:

The total intrinsic hyperpolarizability β_tot is defined as:

where = , = and = .

The relationship between the macroscopic second-order susceptibility, the quantity that correlates to the second-harmonic intensity, and the microscopic total hyperpolarizability is given by equation (4),

where N is the number of particles per unit volume and F is the local field factor. F depends upon the crystal symmetry. It is related to the crystal's refractive index, and it can vary if different compounds are considered. Values between 1 and 2 are generally reported (Choudhury & Chitra, 2011) and in particular for saccharides this value is close to 1.0. Furthermore, since the compounds studied have the same structure, we expect their refractive indices to be equal. Thus, since our interest is focused on the trend of χ⁽²⁾ values, we assumed F = 1.

In Table 4, we observe that for both fragments the values of the total intrinsic hyperpolarizability are very different for the two complexes, i.e. the value of β_tot for the iodine complex is twice the value of the bromine complex. For Fragment1 this trend correlates with the substantial decrease in the frontier orbitals gap of the iodine complex. The same trend is not observed for Fragment2.

The calculated static susceptibility χ⁽²⁾ values are similar for the two fragments of the same complex, underlying that the geometry of the fragments does not affect this result, while a difference is observed by comparing the χ⁽²⁾ values of the Br⁻ versus I⁻ complexes. The complexes containing the larger and more polarizable I⁻ anions show a higher value of χ⁽²⁾, confirming the trend already observed in our previous work.

3.2.2. Bulk computational results

Bulk coupled perturbed Kohn–Sham (CPKS) DFT simulations (Section 2.4, and Section S2.1 in the supporting information) included the coupling of an external electric field with the crystal field, allowing us to extract from the Bloch-consistent periodic wavefunction information on optical axes, dielectric tensors and first- and second-order polarizabilities. This approach bears several advantages against the more classical sum-over-state (SOS) method under Unsöld's approximations (Unsöld, 1927). One of these advantages is that CPKS simulations allow the wavefunction to relax self-consistently under a perturbing electric field. Moreover, the Born–von Karman boundary conditions account for the periodicity of the crystal structure. The DFT-optimized crystal structures are fully consistent with the experimental X-ray ones (Figs. S4–S5): the r.m.s.d.s on the coordinates of C, O, Ca²⁺ and halogen atoms within the whole unit cell do not exceed 0.12/0.28 Å in the compounds CaDGalBr/CaDGalI. As expected, the largest deviations affect H atoms, and particularly the relative orientation of Ca-coordinated water molecules [Figs. S4(a)–S4(b) and S5(a)–S5(b)]. However, the main structural and coordination features discussed above are fully preserved.

Since CaDGalBr and CaDGalI are almost perfectly isostructural, any difference in their optical behaviour is expected to be due to the different chemical nature of the polarizable halogen atoms. Indeed, NLO properties in these structures cannot be rationalized in terms of simple geometric/charge-transfer models, like in push–pull systems (Beverina et al., 2011). The nonlinear response is mostly due to the large polarizability of the halogen (Marabello et al., 2017). Therefore, no significant bond-length alternation (BLA) effects are detectable in the sugar. Moreover, all the NLO measurements were carried out on micrometre-to-millimetre sized grains. Thus, the average crystallite dimensions are larger than the coherence length, making the second-harmonic efficiencies independent, on average, of the particle size (Marabello et al., 2019b; Bourhill et al., 1993). Under these conditions, the second-order intensity is proportional to the square averaged 〈(ijk)²〉 second-order polarizability tensor elements, which can be estimated from DFT bulk calculations.

Table 5 displays the predicted first- and second-order responses of CaDGalBr and CaDGalI, in comparison with sucrose (Bourhill et al., 1993) and DGal sugars. According to the procedure developed by Marabello et al. (2019b), a weighted average of second-order matrix elements was carried out based on P2₁-compatible symmetry multiplicities (three for xxy and yyz, six for xyz and one for yyy). All averages were computed from the squared d_ijk elements in MKS units, and the corresponding ratios with respect to sucrose, 〈d_ijk²〉_sucrose, were evaluated (Table 6).

Table 5
DFT-derived first-order electric susceptibilities [χ⁽¹⁾, dimensionless], diagonalized dielectric tensor elements (ɛ, dimensionless†) and second-order electric susceptibilities [χ⁽²⁾, atomic units‡] for bulk CaDGalBr, CaDGalI, sucrose and 2-de­oxy-β-D-galactose (DGal), all in space group P2₁

	CaDGalBr	CaDGalI	Sucrose§	DGal
χxx^(1)	1.0553	1.0263	1.1622	1.1580
χxz^(1)	0.01	0.0306	−0.0435	−0.0563
χyy^(1)	1.0901	1.1064	1.2136	1.2302
χzz^(1)	1.0078	1.0893	1.1750	1.1576
ɛ11	2.0573	2.0138	2.1247	2.2141
ɛ22	2.0901	2.1064	2.2136	2.2302
ɛ33	2.0057	2.1017	2.2125	2.1015
χxxy^(2)	−0.0664	0.2583	0.1447	−0.1493
χxyz^(2)	0.1552	0.1050	−0.0013	−0.1954
χyyy^(2)	0.2424	0.3996	0.2885	−0.4466
χyzz^(2)	0.2434	0.6075	0.2048	−0.0472

†Diagonal elements of the dielectric tensor, ɛ, in the principal axes system.
‡Second-order susceptibilities can be expressed in other conventions through the usual conversion factors. Frequent alternative expressions of the second-order tensor components as β_ijk or d_ijk quantities (always in atomic units) are β_ijk = (Vχ_ijk)/2π, V being the unit-cell volume in cubic bohr, and d_ijk = χ_ijk/2. Conversion to the MKS system in terms of reciprocal electric field units can be accomplished according to d_ijk(MKS) = d_ijk(a.u.)/0.514220632 pm V⁻¹. See also https://physics.nist.gov/cuu/Constants/index.html.
§DFT estimates for sucrose at the same level of theory employed in this work have been taken from Marabello et al. (2019b).

Table 6
Ratio between the average second-order susceptibilities of the two fragments with respect to the sucrose values obtained from in vacuo calculations, ratio between the average second-order squared susceptibility tensor elements with respect to crystalline sucrose as estimated through bulk calculations, and ratio between the second-harmonic signal at 532 nm produced by powdered samples and that of standard sucrose under the same experimental conditions, for compounds CaDGalBr, CaDGalI and 2-de­oxy-β-D-galactose

		CaDGalBr	CaDGalI	DGal
In vacuo (DFT:B3LYP)	χ^(2)/χ^(2)sucrose	0.82	1.27	0.85
Bulk (DFT:PBE0)	〈dijk^2〉/〈dijk^2〉sucrose	1.50	5.60	1.80
SHG measurements	I^2ω/I^2ωsucrose	0.64	0.78	1.20

3.3. SHG results and comparison with theoretical calculations

The SHG values of the two compounds obtained from Kurtz–Perry measurements on ground powders of sizes below 100 µm and from theoretical calculations performed both in vacuo and in bulk are reported in Table 6. A qualitative agreement is observed among the B3LYP and bulk DFT predictions and the experimental outcomes.

The experimental SHG efficiency of DGal previously reported by Bourhill et al. (1993) equals 3.9 times that of sucrose. The orders of magnitude of the experimental values obtained using our modified Kurtz–Perry setup agree with those of Bourhill et al. (1993), except that the measured efficiency of DGal is only slightly higher than that of sucrose.

By comparing the results in Table 6 it turns out that, for both the calculations (in vacuo and in bulk) and the experimental measurements, the SHG response of the two compounds is approximately the same as DGal itself. For the bulk calculations, it is noticeable that there is a slightly higher difference between the values of the two MOFs with respect to the experimental measurements. This, however, is to be expected, considering that experiments are carried out in conditions of non-ideality, while DFT calculations refer instead to static (no thermal motion) geometries at 0 K in the limit of static (no time-dependency) high-frequency (only electronic contributions) dielectric susceptibilities. Moreover, the experiments were carried out on powdered samples, to be confronted with the infinite perfect lattices of our CPKS model. Therefore, bulk simulations lack thermal motion, dispersive behaviour of refractive indices at finite wavelengths and possible iso-orientations of crystallites, and the observed discrepancies are probably imputable to the intrinsic limits of the computational approaches. The take-home message from Table 6 is that there is a general qualitative agreement between experiment and theory, as the predicted and observed susceptibilities are roughly of the same order of magnitude.

A closer comparison of the theoretical results alone (first two rows of Table 6) shows that the three systems follow the same trend, irrespective of the length scale, as both molecular clusters and bulk simulations rank the second-order susceptibilities in the following order: CaDGalBr < DGal < CaDGalI. However, in bulk systems the expected response is from ∼2 to ∼4 times higher. There is a 1:1 correspondence among the X-ray observed crystal structures and the model we employed to perform bulk calculations (see Section 3.2 above). Therefore, the enhancement of the predicted NLO response of the bulk calculations with respect to the isolated clusters is entirely ascribable to crystal field effects.

Different from our previous findings for fructose-containing derivatives, the involvement of DGal in a MOF structure has no significant influence on the NLO response. However, in this case we are in a different crystallographic situation: fructose crystallizes in a more symmetric structure with respect to its calcium MOFs (orthorhombic versus monoclinic) while the DGal sugar crystallizes in the same monoclinic space group (P2₁) as CaDGalX MOFs. This observation confirms the assertion that the SHG response is principally influenced by the symmetries in the structure: the lower the symmetries the higher the SHG efficiency. As the three materials share the same crystal symmetry and have similar packing features, it should be expected that they produce similar NLO outcomes. From a structural viewpoint, the average ratios (〈B/A〉) of imaginary and real contributions to the structure-factor amplitudes of DFT-predicted nonextinct reflections within sinθ/λ = 0.55 Å⁻¹ are identical [DGal 3.7 (8), CaDGalBr 3.8 (5) and CaDGalI 3.7 (5)]. Thus, symmetry breaking is not the main trigger of the NLO response. This is consistent with our Kurtz–Perry measurements, even though the bulk DFT simulations predict that, under ideal conditions, the iodine chromophore should perform better than the bromine one (Table 6). Any difference in the performance of these isomorphous crystal architectures should be ascribed to electronic reasons. However, further studies are needed to shed light on how electronic and chemical degrees of freedom are related to the crystal symmetry.

As mentioned above, we expected that substituting fructose with DGal would impart a higher SHG efficiency to the M(sugar)X MOFs. Instead, the two DGal MOFs analysed in this work do not show the expected enhancement of SHG efficiency with respect to the analogous fructose-based ones studied in our previous work. Thus, the nature of the sugar can influence the SHG behaviour of the compounds only because it entails a change in the crystal structure.

The SHG measurements and the theoretical calculations agree on the fact that the SHG efficiency of CaDGalI is greater than that of CaDGalBr. Since the two compounds are isostructural and isomorphous, this behaviour is necessarily imputable to the larger polarizability of iodine ions and was observed in all the isostructural and isomorphous compounds previously analysed. It is noteworthy that in the bulk calculations the difference in the responses of the two MOFs is greater than for the other two methods. This behaviour might be traced back to cooperativity effects, that is, to the symmetry-constrained alignment of polar molecules in the bulk crystal. It is known, for example, that an external electric field can partially align polar mol­ecules, eliciting a temperature-dependent contribution to SHG even in an otherwise isotropic achiral liquid (Wagnière & Woźniak, 2017).

4. Conclusions

In this work we analysed the SHG efficiency of two iso­structural and isomorphous DGal-derived MOFs with respect to the sugar itself and similar fructose-derived MOFs analysed previously. Based on the results, we can conclude that the nature of the sugar present in this kind of MOF does not significantly affect the SHG response: the most important role of the sugar is to cause the absence of an inversion centre and to determine a change in the structural arrangements. Instead, the lower symmetry in the structure seems to have a fundamental role in the SHG efficiency, and likewise the presence of the more polarizable iodide ion. Furthermore, the bulk calculations suggest that, in principle, large bulk crystals should show a higher SHG response than isolated molecular clusters or nanoparticles.

In conclusion, even though the compounds analysed show an SHG efficiency comparable with that of sucrose and can thus be usefully applied as bio-sensors, the results of this work suggest that we can try to improve the SHG efficiency by suitably modulating the symmetry of the crystal structure and the chemical composition, i.e. less symmetric structures with more polarizable anions.

5. Related literature

For further literature related to the supporting information, see Dovesi et al. (2014b), Broyden (1965), Johnson (1988), Lacivita et al. (2016, 2012), Cremer & Pople (1975) and Boeyens (1978).

Supporting information

Computing details

For both structures, data collection: CrysAlis PRO 1.171.40.67a (Rigaku OD, 2019); cell refinement: CrysAlis PRO 1.171.40.67a (Rigaku OD, 2019); data reduction: CrysAlis PRO 1.171.40.67a (Rigaku OD, 2019). Program(s) used to solve structure: SHELXT 2018/2 (Sheldrick, 2018) for CaDgalBr_new; SHELXT (Sheldrick, 2015) for CaDgalI_new. For both structures, program(s) used to refine structure: SHELXL 2018/3 (Sheldrick, 2015); molecular graphics: Olex2 1.3 (Dolomanov et al., 2009); software used to prepare material for publication: Olex2 1.3 (Dolomanov et al., 2009).

(CaDgalBr_new)

Crystal data

2(Br)·C12H28CaO12	F(000) = 572
Mr = 564.24	Dx = 1.787 Mg m^−3
Monoclinic, P21	Cu Kα radiation, λ = 1.54184 Å
a = 7.5022 (4) Å	Cell parameters from 1992 reflections
b = 14.2259 (6) Å	θ = 6.3–61.2°
c = 10.4517 (6) Å	µ = 7.56 mm^−1
β = 109.931 (6)°	T = 293 K
V = 1048.65 (10) Å^3	Prism, colourless
Z = 2	0.29 × 0.13 × 0.03 mm

Data collection

Xcalibur, Ruby, Gemini ultra diffractometer	2698 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance Ultra (Cu) X-ray Source	2457 reflections with I > 2σ(I)
Mirror monochromator	Rint = 0.037
Detector resolution: 10.2890 pixels mm^-1	θmax = 58.9°, θmin = 4.5°
ω scans	h = −8→7
Absorption correction: gaussian CrysAlisPro 1.171.40.67a (Rigaku Oxford Diffraction, 2019) Numerical absorption correction based on gaussian integration over a multifaceted crystal model Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	k = −15→15
Tmin = 0.401, Tmax = 0.821	l = −10→11
5021 measured reflections

Refinement

Refinement on F^2	Hydrogen site location: mixed
Least-squares matrix: full	H atoms treated by a mixture of independent and constrained refinement
R[F^2 > 2σ(F^2)] = 0.035	w = 1/[σ^2(Fo^2) + (0.0283P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.076	(Δ/σ)max < 0.001
S = 1.06	Δρmax = 0.33 e Å^−3
2698 reflections	Δρmin = −0.28 e Å^−3
254 parameters	Absolute structure: Flack x determined using 913 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
17 restraints	Absolute structure parameter: −0.017 (18)
Primary atom site location: dual

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Br1	0.08595 (14)	0.60627 (6)	−0.25434 (11)	0.0491 (3)
Br2	0.26873 (13)	0.76332 (6)	0.21969 (10)	0.0446 (3)
Ca1	−0.0094 (2)	0.47533 (12)	0.24570 (17)	0.0295 (4)
O1A	−0.2737 (7)	0.7597 (4)	−0.0393 (5)	0.0348 (13)
O1B	0.5553 (9)	0.5454 (4)	0.4345 (8)	0.0527 (19)
O1W	0.1692 (10)	0.5385 (5)	0.1085 (7)	0.060 (2)
H1WA	0.218542	0.590179	0.143907	0.091*
H1WB	0.147642	0.519359	0.027507	0.091*
O2A	−0.3014 (10)	0.7083 (4)	−0.2522 (6)	0.0398 (15)
H2A	−0.222549	0.667693	−0.249486	0.060*
O2B	0.2390 (8)	0.5790 (4)	0.4003 (6)	0.0353 (15)
H2B	0.237120	0.634442	0.378623	0.053*
O2W	−0.0282 (10)	0.3608 (5)	0.0719 (7)	0.056 (2)
H2WA	−0.124616	0.344816	0.004567	0.084*
H2WB	0.062534	0.352956	0.041607	0.084*
O3A	−0.3436 (8)	0.4961 (4)	0.0986 (6)	0.0334 (14)
H3A	−0.425207	0.457116	0.061224	0.050*
O3B	0.2582 (7)	0.3777 (4)	0.3566 (6)	0.0353 (15)
H3B	0.257091	0.324448	0.326328	0.053*
O4A	−0.1141 (8)	0.6403 (4)	0.2036 (6)	0.0344 (14)
H4A	−0.052 (4)	0.687 (2)	0.191 (8)	0.052*
O4B	0.9020 (8)	0.4867 (4)	0.4466 (6)	0.0376 (15)
H4B	0.947372	0.522104	0.511437	0.056*
O5A	−0.3264 (11)	0.9233 (4)	0.0973 (7)	0.0526 (19)
H5A	−0.269972	0.967210	0.144735	0.079*
O5B	0.8274 (9)	0.3343 (4)	0.2976 (7)	0.0412 (15)
H5B	0.865045	0.285280	0.274152	0.062*
C1A	−0.3701 (13)	0.6947 (6)	−0.1446 (9)	0.033 (2)
H1A	−0.506415	0.707970	−0.176141	0.040*
C1B	0.4197 (12)	0.5568 (6)	0.4978 (10)	0.037 (2)
H1B	0.459506	0.606075	0.567265	0.044*
C2A	−0.3357 (12)	0.5955 (6)	−0.0889 (9)	0.034 (2)
H2AA	−0.201932	0.580527	−0.063192	0.041*
H2AB	−0.405945	0.551420	−0.158604	0.041*
C2B	0.4076 (14)	0.4643 (6)	0.5622 (9)	0.038 (2)
H2BA	0.284317	0.455770	0.571589	0.046*
H2BB	0.505222	0.458615	0.651016	0.046*
C3A	−0.3984 (12)	0.5863 (6)	0.0347 (9)	0.033 (2)
H3AA	−0.536821	0.591619	0.004613	0.040*
C3B	0.4383 (12)	0.3947 (6)	0.4623 (9)	0.031 (2)
H3BA	0.494800	0.336118	0.507568	0.038*
C4A	−0.3134 (12)	0.6604 (6)	0.1399 (9)	0.030 (2)
H4AA	−0.374925	0.658155	0.208861	0.036*
C4B	0.5744 (12)	0.4474 (6)	0.4069 (10)	0.033 (2)
H4BA	0.538854	0.437142	0.308655	0.040*
C5A	−0.3478 (11)	0.7578 (6)	0.0709 (8)	0.0307 (19)
H5AA	−0.484932	0.768445	0.033006	0.037*
C5B	0.7811 (12)	0.4194 (6)	0.4788 (10)	0.035 (2)
H5BA	0.808108	0.418841	0.577367	0.042*
C6A	−0.2607 (13)	0.8369 (6)	0.1662 (10)	0.037 (2)
H6AA	−0.296768	0.832539	0.246736	0.045*
H6AB	−0.123558	0.833576	0.194267	0.045*
C6B	0.8325 (14)	0.3256 (7)	0.4350 (10)	0.042 (3)
H6BA	0.958332	0.307147	0.493574	0.064*
H6BB	0.743032	0.278057	0.441099	0.064*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Br1	0.0512 (7)	0.0381 (6)	0.0543 (7)	0.0051 (5)	0.0133 (5)	0.0007 (5)
Br2	0.0403 (6)	0.0458 (6)	0.0454 (6)	−0.0039 (5)	0.0114 (5)	0.0058 (5)
Ca1	0.0275 (9)	0.0289 (9)	0.0313 (10)	0.0012 (8)	0.0088 (8)	−0.0014 (8)
O1A	0.037 (3)	0.029 (3)	0.036 (3)	0.003 (3)	0.010 (3)	−0.001 (3)
O1B	0.048 (4)	0.030 (4)	0.089 (6)	0.004 (3)	0.035 (4)	0.010 (4)
O1W	0.071 (5)	0.070 (5)	0.054 (5)	−0.017 (4)	0.038 (4)	−0.020 (4)
O2A	0.056 (5)	0.035 (4)	0.032 (4)	0.003 (3)	0.019 (3)	0.004 (3)
O2B	0.037 (3)	0.028 (4)	0.036 (4)	0.004 (3)	0.005 (3)	0.000 (3)
O2W	0.045 (4)	0.065 (5)	0.049 (5)	0.005 (4)	0.005 (3)	−0.029 (4)
O3A	0.032 (3)	0.024 (3)	0.038 (4)	−0.003 (3)	0.004 (3)	0.008 (3)
O3B	0.028 (3)	0.027 (3)	0.045 (4)	−0.003 (3)	0.005 (3)	−0.007 (3)
O4A	0.027 (3)	0.025 (3)	0.046 (4)	0.001 (2)	0.006 (3)	0.002 (3)
O4B	0.037 (4)	0.041 (4)	0.037 (4)	−0.012 (3)	0.016 (3)	−0.012 (3)
O5A	0.067 (5)	0.023 (3)	0.051 (5)	0.008 (3)	−0.002 (4)	−0.001 (3)
O5B	0.050 (4)	0.031 (3)	0.049 (4)	−0.001 (3)	0.025 (3)	0.001 (3)
C1A	0.032 (5)	0.033 (5)	0.030 (5)	−0.003 (4)	0.005 (4)	−0.003 (4)
C1B	0.032 (5)	0.031 (5)	0.038 (6)	0.002 (4)	0.000 (5)	−0.004 (4)
C2A	0.038 (5)	0.029 (5)	0.030 (5)	−0.004 (4)	0.004 (4)	−0.004 (4)
C2B	0.039 (6)	0.041 (6)	0.032 (6)	0.003 (4)	0.007 (4)	−0.002 (4)
C3A	0.029 (5)	0.036 (6)	0.029 (5)	−0.003 (4)	0.005 (4)	0.001 (4)
C3B	0.029 (5)	0.027 (5)	0.037 (5)	0.004 (4)	0.011 (4)	0.000 (4)
C4A	0.031 (5)	0.026 (5)	0.029 (5)	0.002 (4)	0.005 (4)	−0.002 (4)
C4B	0.034 (5)	0.033 (5)	0.036 (6)	0.001 (4)	0.016 (4)	0.001 (4)
C5A	0.030 (5)	0.025 (4)	0.035 (5)	0.003 (4)	0.009 (4)	−0.003 (4)
C5B	0.026 (5)	0.048 (6)	0.034 (6)	−0.007 (4)	0.015 (4)	0.005 (5)
C6A	0.041 (6)	0.031 (5)	0.037 (6)	0.005 (4)	0.009 (4)	0.001 (4)
C6B	0.040 (6)	0.034 (6)	0.056 (7)	0.011 (4)	0.019 (5)	0.011 (5)

Geometric parameters (Å, º)

Ca1—O1W	2.444 (7)	O5A—C6A	1.425 (10)
Ca1—O2B	2.491 (6)	O5B—H5B	0.8200
Ca1—O2W	2.409 (7)	O5B—C6B	1.429 (11)
Ca1—O3A	2.471 (6)	C1A—H1A	0.9800
Ca1—O3B	2.391 (6)	C1A—C2A	1.515 (12)
Ca1—O4A	2.466 (6)	C1B—H1B	0.9800
Ca1—O4B^i	2.414 (6)	C1B—C2B	1.494 (13)
Ca1—O5B^i	2.504 (6)	C2A—H2AA	0.9700
O1A—C1A	1.430 (10)	C2A—H2AB	0.9700
O1A—C5A	1.440 (9)	C2A—C3A	1.523 (12)
O1B—C1B	1.399 (11)	C2B—H2BA	0.9700
O1B—C4B	1.440 (10)	C2B—H2BB	0.9700
O1W—H1WA	0.8497	C2B—C3B	1.514 (12)
O1W—H1WB	0.8500	C3A—H3AA	0.9800
O2A—H2A	0.8200	C3A—C4A	1.499 (11)
O2A—C1A	1.401 (10)	C3B—H3BA	0.9800
O2B—H2B	0.8200	C3B—C4B	1.531 (12)
O2B—C1B	1.426 (10)	C4A—H4AA	0.9800
O2W—H2WA	0.8500	C4A—C5A	1.543 (12)
O2W—H2WB	0.8502	C4B—H4BA	0.9800
O3A—H3A	0.8200	C4B—C5B	1.528 (13)
O3A—C3A	1.441 (9)	C5A—H5AA	0.9800
O3B—H3B	0.8200	C5A—C6A	1.497 (12)
O3B—C3B	1.444 (10)	C5B—H5BA	0.9800
O4A—H4A	0.853 (13)	C5B—C6B	1.502 (13)
O4A—C4A	1.443 (10)	C6A—H6AA	0.9700
O4B—H4B	0.8200	C6A—H6AB	0.9700
O4B—C5B	1.436 (10)	C6B—H6BA	0.9700
O5A—H5A	0.8200	C6B—H6BB	0.9700
O1W—Ca1—O2B	74.0 (2)	O1B—C1B—C2B	106.1 (7)
O1W—Ca1—O3A	103.5 (2)	O2B—C1B—H1B	110.3
O1W—Ca1—O4A	75.6 (2)	O2B—C1B—C2B	109.1 (7)
O1W—Ca1—O5B^i	145.9 (2)	C2B—C1B—H1B	110.3
O2B—Ca1—O5B^i	130.3 (2)	C1A—C2A—H2AA	109.6
O2W—Ca1—O1W	73.1 (3)	C1A—C2A—H2AB	109.6
O2W—Ca1—O2B	136.7 (2)	C1A—C2A—C3A	110.1 (7)
O2W—Ca1—O3A	80.0 (2)	H2AA—C2A—H2AB	108.1
O2W—Ca1—O4A	125.2 (2)	C3A—C2A—H2AA	109.6
O2W—Ca1—O4B^i	137.6 (3)	C3A—C2A—H2AB	109.6
O2W—Ca1—O5B^i	73.4 (2)	C1B—C2B—H2BA	111.2
O3A—Ca1—O2B	135.1 (2)	C1B—C2B—H2BB	111.2
O3A—Ca1—O5B^i	76.3 (2)	C1B—C2B—C3B	102.6 (7)
O3B—Ca1—O1W	87.7 (2)	H2BA—C2B—H2BB	109.2
O3B—Ca1—O2B	73.15 (18)	C3B—C2B—H2BA	111.2
O3B—Ca1—O2W	78.2 (2)	C3B—C2B—H2BB	111.2
O3B—Ca1—O3A	151.3 (2)	O3A—C3A—C2A	110.3 (7)
O3B—Ca1—O4A	143.40 (19)	O3A—C3A—H3AA	108.7
O3B—Ca1—O4B^i	93.0 (2)	O3A—C3A—C4A	107.7 (7)
O3B—Ca1—O5B^i	79.7 (2)	C2A—C3A—H3AA	108.7
O4A—Ca1—O2B	71.03 (18)	C4A—C3A—C2A	112.6 (7)
O4A—Ca1—O3A	65.25 (19)	C4A—C3A—H3AA	108.7
O4A—Ca1—O5B^i	130.7 (2)	O3B—C3B—C2B	108.3 (7)
O4B^i—Ca1—O1W	148.7 (2)	O3B—C3B—H3BA	111.4
O4B^i—Ca1—O2B	76.3 (2)	O3B—C3B—C4B	111.3 (7)
O4B^i—Ca1—O3A	90.7 (2)	C2B—C3B—H3BA	111.4
O4B^i—Ca1—O4A	85.8 (2)	C2B—C3B—C4B	102.6 (7)
O4B^i—Ca1—O5B^i	64.2 (2)	C4B—C3B—H3BA	111.4
C1A—O1A—C5A	111.8 (6)	O4A—C4A—C3A	108.3 (7)
C1B—O1B—C4B	110.2 (7)	O4A—C4A—H4AA	109.1
Ca1—O1W—H1WA	107.9	O4A—C4A—C5A	112.1 (7)
Ca1—O1W—H1WB	120.7	C3A—C4A—H4AA	109.1
H1WA—O1W—H1WB	128.1	C3A—C4A—C5A	109.1 (7)
C1A—O2A—H2A	109.5	C5A—C4A—H4AA	109.1
Ca1—O2B—H2B	116.9	O1B—C4B—C3B	105.9 (7)
C1B—O2B—Ca1	130.6 (5)	O1B—C4B—H4BA	110.1
C1B—O2B—H2B	109.5	O1B—C4B—C5B	108.0 (7)
Ca1—O2W—H2WA	128.3	C3B—C4B—H4BA	110.1
Ca1—O2W—H2WB	121.4	C5B—C4B—C3B	112.4 (7)
H2WA—O2W—H2WB	102.7	C5B—C4B—H4BA	110.1
Ca1—O3A—H3A	130.5	O1A—C5A—C4A	110.0 (7)
C3A—O3A—Ca1	117.6 (4)	O1A—C5A—H5AA	108.2
C3A—O3A—H3A	109.5	O1A—C5A—C6A	108.6 (7)
Ca1—O3B—H3B	116.9	C4A—C5A—H5AA	108.2
C3B—O3B—Ca1	133.3 (5)	C6A—C5A—C4A	113.5 (7)
C3B—O3B—H3B	109.5	C6A—C5A—H5AA	108.2
Ca1—O4A—H4A	128 (3)	O4B—C5B—C4B	109.1 (7)
C4A—O4A—Ca1	119.2 (4)	O4B—C5B—H5BA	109.3
C4A—O4A—H4A	108 (2)	O4B—C5B—C6B	105.8 (7)
Ca1^ii—O4B—H4B	126.9	C4B—C5B—H5BA	109.3
C5B—O4B—Ca1^ii	122.9 (5)	C6B—C5B—C4B	113.9 (8)
C5B—O4B—H4B	109.5	C6B—C5B—H5BA	109.3
C6A—O5A—H5A	109.5	O5A—C6A—C5A	108.3 (7)
Ca1^ii—O5B—H5B	111.9	O5A—C6A—H6AA	110.0
C6B—O5B—Ca1^ii	116.1 (5)	O5A—C6A—H6AB	110.0
C6B—O5B—H5B	109.5	C5A—C6A—H6AA	110.0
O1A—C1A—H1A	109.3	C5A—C6A—H6AB	110.0
O1A—C1A—C2A	109.3 (7)	H6AA—C6A—H6AB	108.4
O2A—C1A—O1A	107.5 (7)	O5B—C6B—C5B	107.9 (7)
O2A—C1A—H1A	109.3	O5B—C6B—H6BA	110.1
O2A—C1A—C2A	112.1 (7)	O5B—C6B—H6BB	110.1
C2A—C1A—H1A	109.3	C5B—C6B—H6BA	110.1
O1B—C1B—O2B	110.8 (8)	C5B—C6B—H6BB	110.1
O1B—C1B—H1B	110.3	H6BA—C6B—H6BB	108.4
Ca1—O2B—C1B—O1B	81.7 (8)	O4B—C5B—C6B—O5B	−51.1 (9)
Ca1—O2B—C1B—C2B	−34.8 (10)	C1A—O1A—C5A—C4A	63.6 (8)
Ca1—O3A—C3A—C2A	78.6 (7)	C1A—O1A—C5A—C6A	−171.7 (7)
Ca1—O3A—C3A—C4A	−44.6 (8)	C1A—C2A—C3A—O3A	−172.5 (6)
Ca1—O3B—C3B—C2B	35.6 (10)	C1A—C2A—C3A—C4A	−52.2 (9)
Ca1—O3B—C3B—C4B	−76.4 (9)	C1B—O1B—C4B—C3B	−1.2 (10)
Ca1—O4A—C4A—C3A	−37.1 (8)	C1B—O1B—C4B—C5B	−121.8 (8)
Ca1—O4A—C4A—C5A	−157.4 (5)	C1B—C2B—C3B—O3B	−85.0 (8)
Ca1^ii—O4B—C5B—C4B	−86.1 (8)	C1B—C2B—C3B—C4B	32.8 (8)
Ca1^ii—O4B—C5B—C6B	36.8 (9)	C2A—C3A—C4A—O4A	−71.1 (9)
Ca1^ii—O5B—C6B—C5B	46.8 (8)	C2A—C3A—C4A—C5A	51.1 (9)
O1A—C1A—C2A—C3A	56.4 (9)	C2B—C3B—C4B—O1B	−20.3 (9)
O1A—C5A—C6A—O5A	66.5 (9)	C2B—C3B—C4B—C5B	97.4 (8)
O1B—C1B—C2B—C3B	−34.9 (9)	C3A—C4A—C5A—O1A	−55.6 (9)
O1B—C4B—C5B—O4B	−49.4 (9)	C3A—C4A—C5A—C6A	−177.4 (7)
O1B—C4B—C5B—C6B	−167.3 (8)	C3B—C4B—C5B—O4B	−165.9 (7)
O2A—C1A—C2A—C3A	175.6 (7)	C3B—C4B—C5B—C6B	76.2 (10)
O2B—C1B—C2B—C3B	84.5 (8)	C4A—C5A—C6A—O5A	−170.9 (7)
O3A—C3A—C4A—O4A	50.7 (8)	C4B—O1B—C1B—O2B	−95.5 (8)
O3A—C3A—C4A—C5A	172.9 (6)	C4B—O1B—C1B—C2B	22.8 (10)
O3B—C3B—C4B—O1B	95.4 (8)	C4B—C5B—C6B—O5B	68.7 (9)
O3B—C3B—C4B—C5B	−146.9 (7)	C5A—O1A—C1A—O2A	174.3 (6)
O4A—C4A—C5A—O1A	64.3 (8)	C5A—O1A—C1A—C2A	−63.8 (9)
O4A—C4A—C5A—C6A	−57.5 (9)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1W—H1WA···Br2	0.85	2.58	3.398 (7)	163
O1W—H1WB···O5A^iii	0.85	2.56	3.229 (10)	136
O2A—H2A···Br1	0.82	2.49	3.255 (6)	156
O2B—H2B···Br2	0.82	2.54	3.283 (6)	152
O2W—H2WA···Br2^iii	0.85	2.51	3.273 (6)	151
O2W—H2WB···O1A^iii	0.85	2.07	2.800 (9)	143
O3A—H3A···O5A^iv	0.82	2.08	2.818 (8)	149
O3B—H3B···O2A^iii	0.82	1.90	2.710 (8)	168
O4B—H4B···Br1^v	0.82	2.60	3.410 (6)	169
O5A—H5A···Br1^vi	0.82	2.46	3.272 (7)	171
O5B—H5B···Br1^vii	0.82	2.59	3.368 (6)	159
C1B—H1B···O2A^v	0.98	2.57	3.481 (12)	156
C4B—H4BA···O3A^ii	0.98	2.76	3.549 (11)	138

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

(CaDgalI_new)

Crystal data

2(I)·C12H28CaO12	F(000) = 644
Mr = 658.22	Dx = 1.950 Mg m^−3
Monoclinic, P21	Cu Kα radiation, λ = 1.54184 Å
a = 7.6384 (3) Å	Cell parameters from 6384 reflections
b = 14.4621 (4) Å	θ = 4.3–66.9°
c = 10.7490 (3) Å	µ = 24.52 mm^−1
β = 109.233 (4)°	T = 293 K
V = 1121.14 (6) Å^3	Prism, colourless
Z = 2	0.25 × 0.11 × 0.08 mm

Data collection

Xcalibur, AtlasS2, Gemini ultra diffractometer	3737 independent reflections
Radiation source: fine-focus sealed X-ray tube, Enhance Ultra (Cu) X-ray Source	3590 reflections with I > 2σ(I)
Mirror monochromator	Rint = 0.043
Detector resolution: 5.1990 pixels mm^-1	θmax = 66.9°, θmin = 4.4°
ω scans	h = −8→7
Absorption correction: gaussian CrysAlisPro 1.171.40.67a (Rigaku Oxford Diffraction, 2019) Numerical absorption correction based on gaussian integration over a multifaceted crystal model Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	k = −17→17
Tmin = 0.091, Tmax = 0.337	l = −11→12
11076 measured reflections

Refinement

Refinement on F^2	Hydrogen site location: mixed
Least-squares matrix: full	H atoms treated by a mixture of independent and constrained refinement
R[F^2 > 2σ(F^2)] = 0.032	w = 1/[σ^2(Fo^2) + (0.0436P)^2 + 0.4062P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.079	(Δ/σ)max < 0.001
S = 1.04	Δρmax = 0.50 e Å^−3
3737 reflections	Δρmin = −0.79 e Å^−3
257 parameters	Absolute structure: Flack x determined using 1525 quotients [(I+)-(I-)]/[(I+)+(I-)] (Parsons, Flack and Wagner, Acta Cryst. B69 (2013) 249-259).
1 restraint	Absolute structure parameter: −0.016 (9)
Primary atom site location: dual

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.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
I1	0.77763 (8)	0.68054 (4)	0.72648 (5)	0.04633 (18)
I2	0.58728 (8)	0.50584 (4)	0.23699 (5)	0.04716 (18)
Ca1	0.4867 (2)	0.38036 (10)	0.73658 (14)	0.0311 (3)
O1A	0.2193 (8)	0.6599 (3)	0.4514 (5)	0.0358 (12)
O1B	1.0320 (11)	0.4528 (5)	0.9154 (9)	0.0591 (19)
O1W	0.6723 (12)	0.4393 (6)	0.6068 (8)	0.066 (2)
H1WA	0.697158	0.496717	0.613025	0.13 (8)*
H1WB	0.694508	0.424477	0.536915	0.15 (9)*
O2A	0.1838 (10)	0.6122 (4)	0.2418 (6)	0.0455 (15)
H2A	0.281822	0.585125	0.252069	0.05 (3)*
O2B	0.7224 (8)	0.4818 (4)	0.8893 (6)	0.0401 (14)
H2B	0.726877	0.528782	0.847808	0.060*
O2W	0.4827 (11)	0.2625 (6)	0.5801 (7)	0.061 (2)
H2WA	0.592408	0.242960	0.593747	0.092*
H2WB	0.417308	0.293010	0.513317	0.092*
O3A	0.1660 (8)	0.3996 (4)	0.5857 (5)	0.0365 (13)
H3A	0.096832	0.358615	0.544315	0.055*
O3B	0.7534 (8)	0.2843 (4)	0.8472 (6)	0.0386 (13)
H3B	0.754027	0.230980	0.821540	0.058*
O4A	0.3817 (8)	0.5419 (4)	0.6864 (6)	0.0392 (13)
H4A	0.442011	0.578222	0.658197	0.059*
O4B	1.3771 (8)	0.3993 (4)	0.9217 (6)	0.0400 (13)
H4B	1.418771	0.436388	0.981894	0.09 (5)*
O5A	0.1637 (11)	0.8193 (4)	0.5844 (7)	0.058 (2)
H5A	0.211256	0.863097	0.632060	0.087*
O5B	1.3210 (10)	0.2450 (4)	0.7903 (6)	0.0451 (15)
H5B	1.357937	0.195792	0.770187	0.05 (3)*
C1A	0.1259 (12)	0.5958 (6)	0.3493 (8)	0.0355 (18)
H1A	−0.007597	0.607937	0.322820	0.043*
C1B	0.9022 (13)	0.4623 (7)	0.9802 (9)	0.045 (2)
H1B	0.940528	0.511109	1.046979	0.054*
C2A	0.1614 (13)	0.4979 (6)	0.4029 (8)	0.0392 (19)
H2AA	0.091758	0.454717	0.335684	0.047*
H2AB	0.292045	0.483476	0.424612	0.047*
C2B	0.8957 (14)	0.3708 (7)	1.0442 (8)	0.045 (2)
H2BA	0.776650	0.360892	1.056105	0.054*
H2BB	0.993300	0.365769	1.128783	0.054*
C3A	0.1051 (12)	0.4867 (5)	0.5241 (8)	0.0354 (18)
H3AA	−0.030342	0.489968	0.498335	0.042*
C3B	0.9256 (11)	0.3041 (6)	0.9455 (8)	0.0345 (17)
H3BA	0.983189	0.247014	0.989407	0.041*
C4A	0.1888 (11)	0.5607 (5)	0.6264 (8)	0.0330 (16)
H4AA	0.129042	0.557778	0.694253	0.040*
C4B	1.0590 (12)	0.3560 (6)	0.8900 (8)	0.0366 (18)
H4BA	1.025144	0.345162	0.795023	0.044*
C5A	0.1494 (12)	0.6552 (5)	0.5597 (8)	0.0315 (17)
H5AA	0.014659	0.663560	0.524854	0.038*
C5B	1.2621 (12)	0.3332 (6)	0.9581 (8)	0.0385 (19)
H5BA	1.289182	0.335456	1.053719	0.046*
C6A	0.2306 (13)	0.7348 (6)	0.6518 (9)	0.042 (2)
H6AA	0.194131	0.730199	0.729869	0.050*
H6AB	0.364875	0.733032	0.678869	0.050*
C6B	1.3158 (14)	0.2391 (7)	0.9206 (10)	0.045 (2)
H6BA	1.436383	0.221190	0.980649	0.055*
H6BB	1.225736	0.193112	0.925312	0.055*

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
I1	0.0391 (3)	0.0538 (3)	0.0426 (3)	−0.0058 (3)	0.0088 (2)	0.0033 (2)
I2	0.0460 (3)	0.0423 (3)	0.0498 (3)	0.0033 (2)	0.0112 (2)	0.0001 (2)
Ca1	0.0279 (8)	0.0340 (7)	0.0301 (7)	0.0029 (6)	0.0079 (6)	−0.0010 (6)
O1A	0.037 (3)	0.031 (3)	0.040 (3)	−0.006 (2)	0.015 (2)	−0.001 (2)
O1B	0.046 (4)	0.041 (4)	0.098 (6)	0.004 (3)	0.036 (4)	0.005 (3)
O1W	0.069 (5)	0.082 (6)	0.061 (4)	−0.006 (4)	0.041 (4)	−0.008 (4)
O2A	0.053 (4)	0.045 (3)	0.040 (3)	0.002 (3)	0.017 (3)	0.009 (3)
O2B	0.035 (3)	0.041 (3)	0.041 (3)	0.003 (2)	0.008 (2)	0.002 (2)
O2W	0.047 (4)	0.080 (5)	0.049 (4)	0.019 (4)	0.004 (3)	−0.023 (4)
O3A	0.034 (3)	0.031 (3)	0.039 (3)	−0.002 (2)	0.005 (2)	0.005 (2)
O3B	0.028 (3)	0.039 (3)	0.044 (3)	0.002 (2)	0.006 (2)	−0.005 (2)
O4A	0.034 (3)	0.031 (3)	0.044 (3)	−0.002 (2)	0.001 (3)	0.004 (2)
O4B	0.035 (3)	0.047 (3)	0.042 (3)	−0.010 (3)	0.018 (3)	−0.008 (3)
O5A	0.060 (5)	0.029 (3)	0.064 (4)	0.007 (3)	−0.007 (3)	−0.006 (3)
O5B	0.054 (4)	0.036 (3)	0.051 (4)	0.002 (3)	0.024 (3)	−0.003 (3)
C1A	0.032 (4)	0.036 (4)	0.037 (4)	−0.005 (3)	0.008 (3)	0.000 (3)
C1B	0.042 (5)	0.044 (4)	0.044 (5)	0.003 (4)	0.007 (4)	−0.008 (4)
C2A	0.048 (5)	0.034 (4)	0.033 (4)	−0.009 (4)	0.009 (3)	−0.002 (3)
C2B	0.046 (5)	0.054 (5)	0.032 (4)	0.010 (4)	0.009 (4)	0.002 (4)
C3A	0.032 (4)	0.033 (4)	0.037 (4)	0.000 (3)	0.007 (3)	0.003 (3)
C3B	0.029 (4)	0.042 (4)	0.030 (4)	0.004 (3)	0.007 (3)	0.003 (3)
C4A	0.029 (4)	0.034 (4)	0.037 (4)	0.001 (3)	0.012 (3)	0.003 (3)
C4B	0.032 (4)	0.039 (4)	0.040 (4)	0.001 (3)	0.014 (3)	0.000 (3)
C5A	0.029 (4)	0.031 (4)	0.035 (4)	0.002 (3)	0.011 (3)	0.000 (3)
C5B	0.031 (5)	0.054 (5)	0.031 (4)	−0.006 (4)	0.011 (3)	0.002 (3)
C6A	0.039 (5)	0.037 (4)	0.042 (5)	0.003 (4)	0.003 (4)	−0.007 (3)
C6B	0.046 (6)	0.050 (5)	0.049 (5)	0.008 (4)	0.026 (4)	0.010 (4)

Geometric parameters (Å, º)

Ca1—O1W	2.447 (8)	O5A—H5A	0.8200
Ca1—O2B	2.478 (6)	O5A—C6A	1.427 (11)
Ca1—O2W	2.388 (7)	O5B—H5B	0.8200
Ca1—H2WA	2.7884	O5B—C6B	1.416 (11)
Ca1—H2WB	2.6073	C1A—H1A	0.9800
Ca1—O3A	2.468 (6)	C1A—C2A	1.520 (11)
Ca1—O3B	2.429 (6)	C1B—H1B	0.9800
Ca1—O4A	2.471 (5)	C1B—C2B	1.500 (14)
Ca1—O4B^i	2.415 (6)	C2A—H2AA	0.9700
Ca1—O5B^i	2.500 (7)	C2A—H2AB	0.9700
O1A—C1A	1.434 (10)	C2A—C3A	1.509 (13)
O1A—C5A	1.433 (10)	C2B—H2BA	0.9700
O1B—C1B	1.394 (13)	C2B—H2BB	0.9700
O1B—C4B	1.453 (11)	C2B—C3B	1.506 (12)
O1W—H1WA	0.8502	C3A—H3AA	0.9800
O1W—H1WB	0.8500	C3A—C4A	1.516 (11)
O2A—H2A	0.8200	C3B—H3BA	0.9800
O2A—C1A	1.387 (11)	C3B—C4B	1.536 (12)
O2B—H2B	0.8200	C4A—H4AA	0.9800
O2B—C1B	1.427 (11)	C4A—C5A	1.527 (11)
O2W—H2WA	0.8499	C4B—H4BA	0.9800
O2W—H2WB	0.8500	C4B—C5B	1.518 (12)
O3A—H3A	0.8200	C5A—H5AA	0.9800
O3A—C3A	1.429 (9)	C5A—C6A	1.511 (11)
O3B—H3B	0.8200	C5B—H5BA	0.9800
O3B—C3B	1.418 (10)	C5B—C6B	1.514 (14)
O4A—H4A	0.8200	C6A—H6AA	0.9700
O4A—C4A	1.427 (10)	C6A—H6AB	0.9700
O4B—H4B	0.8200	C6B—H6BA	0.9700
O4B—C5B	1.437 (11)	C6B—H6BB	0.9700
O1W—Ca1—O2B	75.0 (3)	O1A—C1A—H1A	108.3
O1W—Ca1—H2WA	66.8	O1A—C1A—C2A	109.3 (6)
O1W—Ca1—H2WB	67.9	O2A—C1A—O1A	108.2 (7)
O1W—Ca1—O3A	102.8 (3)	O2A—C1A—H1A	108.3
O1W—Ca1—O4A	75.7 (3)	O2A—C1A—C2A	114.2 (7)
O1W—Ca1—O5B^i	146.8 (3)	C2A—C1A—H1A	108.3
O2B—Ca1—H2WA	120.5	O1B—C1B—O2B	111.1 (8)
O2B—Ca1—H2WB	141.2	O1B—C1B—H1B	110.3
O2B—Ca1—O5B^i	128.5 (2)	O1B—C1B—C2B	106.2 (8)
O2W—Ca1—O1W	73.8 (3)	O2B—C1B—H1B	110.3
O2W—Ca1—O2B	136.6 (3)	O2B—C1B—C2B	108.6 (8)
O2W—Ca1—H2WA	16.7	C2B—C1B—H1B	110.3
O2W—Ca1—H2WB	18.9	C1A—C2A—H2AA	109.4
O2W—Ca1—O3A	80.7 (2)	C1A—C2A—H2AB	109.4
O2W—Ca1—O3B	75.6 (2)	H2AA—C2A—H2AB	108.0
O2W—Ca1—O4A	126.4 (3)	C3A—C2A—C1A	111.2 (7)
O2W—Ca1—O4B^i	137.2 (3)	C3A—C2A—H2AA	109.4
O2W—Ca1—O5B^i	73.4 (3)	C3A—C2A—H2AB	109.4
H2WA—Ca1—H2WB	32.4	C1B—C2B—H2BA	111.4
O3A—Ca1—O2B	135.7 (2)	C1B—C2B—H2BB	111.4
O3A—Ca1—H2WA	97.1	C1B—C2B—C3B	101.9 (7)
O3A—Ca1—H2WB	66.0	H2BA—C2B—H2BB	109.2
O3A—Ca1—O4A	64.51 (19)	C3B—C2B—H2BA	111.4
O3A—Ca1—O5B^i	76.8 (2)	C3B—C2B—H2BB	111.4
O3B—Ca1—O1W	85.9 (3)	O3A—C3A—C2A	110.6 (7)
O3B—Ca1—O2B	72.8 (2)	O3A—C3A—H3AA	109.0
O3B—Ca1—H2WA	60.9	O3A—C3A—C4A	107.0 (6)
O3B—Ca1—H2WB	93.3	C2A—C3A—H3AA	109.0
O3B—Ca1—O3A	151.3 (2)	C2A—C3A—C4A	112.3 (7)
O3B—Ca1—O4A	143.8 (2)	C4A—C3A—H3AA	109.0
O3B—Ca1—O5B^i	81.1 (2)	O3B—C3B—C2B	109.6 (7)
O4A—Ca1—O2B	72.42 (19)	O3B—C3B—H3BA	110.4
O4A—Ca1—H2WA	133.3	O3B—C3B—C4B	112.3 (6)
O4A—Ca1—H2WB	107.7	C2B—C3B—H3BA	110.4
O4A—Ca1—O5B^i	129.7 (2)	C2B—C3B—C4B	103.5 (7)
O4B^i—Ca1—O1W	148.6 (3)	C4B—C3B—H3BA	110.4
O4B^i—Ca1—O2B	76.1 (2)	O4A—C4A—C3A	108.6 (7)
O4B^i—Ca1—H2WA	140.9	O4A—C4A—H4AA	108.7
O4B^i—Ca1—H2WB	142.4	O4A—C4A—C5A	113.4 (7)
O4B^i—Ca1—O3A	89.5 (2)	C3A—C4A—H4AA	108.7
O4B^i—Ca1—O3B	97.1 (2)	C3A—C4A—C5A	108.7 (6)
O4B^i—Ca1—O4A	84.1 (2)	C5A—C4A—H4AA	108.7
O4B^i—Ca1—O5B^i	63.8 (2)	O1B—C4B—C3B	104.2 (7)
O5B^i—Ca1—H2WA	80.2	O1B—C4B—H4BA	110.2
O5B^i—Ca1—H2WB	82.4	O1B—C4B—C5B	107.7 (7)
C5A—O1A—C1A	111.5 (6)	C3B—C4B—H4BA	110.2
C1B—O1B—C4B	110.9 (7)	C5B—C4B—C3B	114.2 (7)
Ca1—O1W—H1WA	116.9	C5B—C4B—H4BA	110.2
Ca1—O1W—H1WB	137.6	O1A—C5A—C4A	110.8 (6)
H1WA—O1W—H1WB	102.2	O1A—C5A—H5AA	108.0
C1A—O2A—H2A	109.5	O1A—C5A—C6A	108.3 (7)
Ca1—O2B—H2B	106.3	C4A—C5A—H5AA	108.0
C1B—O2B—Ca1	131.5 (5)	C6A—C5A—C4A	113.5 (7)
C1B—O2B—H2B	109.5	C6A—C5A—H5AA	108.0
Ca1—O2W—H2WA	109.4	O4B—C5B—C4B	110.1 (7)
Ca1—O2W—H2WB	95.3	O4B—C5B—H5BA	109.1
H2WA—O2W—H2WB	126.2	O4B—C5B—C6B	106.4 (7)
Ca1—O3A—H3A	126.7	C4B—C5B—H5BA	109.1
C3A—O3A—Ca1	120.3 (5)	C6B—C5B—C4B	113.0 (7)
C3A—O3A—H3A	109.5	C6B—C5B—H5BA	109.1
Ca1—O3B—H3B	118.1	O5A—C6A—C5A	108.6 (7)
C3B—O3B—Ca1	132.2 (5)	O5A—C6A—H6AA	110.0
C3B—O3B—H3B	109.5	O5A—C6A—H6AB	110.0
Ca1—O4A—H4A	120.4	C5A—C6A—H6AA	110.0
C4A—O4A—Ca1	119.5 (4)	C5A—C6A—H6AB	110.0
C4A—O4A—H4A	109.5	H6AA—C6A—H6AB	108.3
Ca1^ii—O4B—H4B	125.1	O5B—C6B—C5B	107.9 (7)
C5B—O4B—Ca1^ii	123.9 (5)	O5B—C6B—H6BA	110.1
C5B—O4B—H4B	109.5	O5B—C6B—H6BB	110.1
C6A—O5A—H5A	109.5	C5B—C6B—H6BA	110.1
Ca1^ii—O5B—H5B	111.9	C5B—C6B—H6BB	110.1
C6B—O5B—Ca1^ii	117.2 (6)	H6BA—C6B—H6BB	108.4
C6B—O5B—H5B	109.5
Ca1—O2B—C1B—O1B	77.9 (9)	O4B—C5B—C6B—O5B	−47.7 (9)
Ca1—O2B—C1B—C2B	−38.5 (10)	C1A—O1A—C5A—C4A	64.3 (8)
Ca1—O3A—C3A—C2A	82.8 (7)	C1A—O1A—C5A—C6A	−170.6 (6)
Ca1—O3A—C3A—C4A	−39.8 (8)	C1A—C2A—C3A—O3A	−170.7 (7)
Ca1—O3B—C3B—C2B	38.7 (10)	C1A—C2A—C3A—C4A	−51.3 (9)
Ca1—O3B—C3B—C4B	−75.8 (9)	C1B—O1B—C4B—C3B	1.0 (10)
Ca1—O4A—C4A—C3A	−39.6 (8)	C1B—O1B—C4B—C5B	−120.7 (8)
Ca1—O4A—C4A—C5A	−160.5 (5)	C1B—C2B—C3B—O3B	−85.6 (8)
Ca1^ii—O4B—C5B—C4B	−90.9 (8)	C1B—C2B—C3B—C4B	34.5 (8)
Ca1^ii—O4B—C5B—C6B	31.8 (8)	C2A—C3A—C4A—O4A	−73.0 (8)
Ca1^ii—O5B—C6B—C5B	46.6 (9)	C2A—C3A—C4A—C5A	50.8 (9)
O1A—C1A—C2A—C3A	55.4 (9)	C2B—C3B—C4B—O1B	−22.6 (8)
O1A—C5A—C6A—O5A	64.6 (9)	C2B—C3B—C4B—C5B	94.6 (8)
O1B—C1B—C2B—C3B	−34.9 (9)	C3A—C4A—C5A—O1A	−56.5 (9)
O1B—C4B—C5B—O4B	−51.5 (9)	C3A—C4A—C5A—C6A	−178.6 (7)
O1B—C4B—C5B—C6B	−170.3 (7)	C3B—C4B—C5B—O4B	−166.7 (6)
O2A—C1A—C2A—C3A	176.7 (7)	C3B—C4B—C5B—C6B	74.5 (9)
O2B—C1B—C2B—C3B	84.6 (8)	C4A—C5A—C6A—O5A	−171.9 (8)
O3A—C3A—C4A—O4A	48.5 (9)	C4B—O1B—C1B—O2B	−96.4 (9)
O3A—C3A—C4A—C5A	172.3 (7)	C4B—O1B—C1B—C2B	21.4 (10)
O3B—C3B—C4B—O1B	95.5 (8)	C4B—C5B—C6B—O5B	73.2 (10)
O3B—C3B—C4B—C5B	−147.2 (7)	C5A—O1A—C1A—O2A	172.6 (6)
O4A—C4A—C5A—O1A	64.3 (8)	C5A—O1A—C1A—C2A	−62.5 (9)
O4A—C4A—C5A—C6A	−57.8 (10)

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O1W—H1WA···I1	0.85	2.90	3.714 (9)	160
O1W—H1WB···I2	0.85	3.27	3.930 (8)	136
O1W—H1WB···O5A^iii	0.85	2.47	3.240 (12)	151
O2A—H2A···I2	0.82	2.65	3.460 (7)	169
O2B—H2B···I1	0.82	2.65	3.463 (6)	174
O2W—H2WA···O1A^iii	0.85	2.05	2.829 (9)	152
O2W—H2WA···O2A^iii	0.85	2.76	3.416 (10)	135
O3A—H3A···O5A^iv	0.82	2.09	2.828 (9)	149
O3B—H3B···O2A^iii	0.82	1.96	2.764 (8)	166
O4A—H4A···I1	0.82	2.84	3.535 (6)	144
O4B—H4B···I2^v	0.82	2.80	3.585 (6)	160
O5A—H5A···I2^vi	0.82	2.68	3.489 (7)	169
O5B—H5B···I2^vii	0.82	2.78	3.560 (6)	159
C1B—H1B···O2A^v	0.98	2.72	3.640 (11)	156
C2B—H2BA···O4B^i	0.97	2.97	3.763 (12)	140
C2B—H2BB···I1^viii	0.97	3.30	3.977 (9)	129
C3A—H3AA···O1W^i	0.98	2.97	3.759 (12)	139
C3B—H3BA···I1^viii	0.98	3.15	3.937 (8)	139
C4B—H4BA···O3A^ii	0.98	2.90	3.678 (11)	137
C6A—H6AA···I1^i	0.97	3.25	3.881 (10)	124

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