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1. Chemical context

A systematic study of the crystal structures of Group 1 (alkali metal) citrate salts has been reported in Rammohan & Kaduk (2018). This paper represents the extension of the study to Group 2 (alkaline earth) citrates. The only magnesium citrate previously reported is Mg₃(C₆H₅O₇)₂(H₂O)₁₀, more properly formulated as [Mg(H₂O)₆][Mg(C₆H₅O₇)(H₂O)]₂(H₂O)₂ (MGCITD; Johnson, 1965). I now describe the syntheses and crystal structures of magnesium hydrogen citrate dihydrate, Mg(HC₆H₅O₇)(H₂O)₂ (I) and bis­(di­hydro­gen­citrato)magnesium, Mg(H₂C₆H₅O₇)₂ (II). Attempts to prepare Be(H₂C₆H₅O₇)₂, BeHC₆H₅O₇, and Be₃(C₆H₅O₇)₂ by HCl-catalyzed reaction of Be metal with a citric acid solution have so far yielded only amorphous products (see Fig. S1 in thesupporting information).

2. Structural commentary

Thecrystal structure of (I) was solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional techniques. (Fig. 1) The root-mean-square Cartesian displacement of the non-hydrogen citrate atoms in the Rietveld refined and DFT-optimized structures is 0.062 Å (Fig. 2) The absolute difference in the position of the Mg cation in the unit cell is 0.055 Å. The excellent agreement between the structures is evidence that the experimental structure is correct (van de Streek & Neumann, 2014): the rest of the discussion will emphasize the DFT-optimized structure. All of the citrate bond distances, bond angles, and torsion angles fall within the normal ranges indicated by aMercury Mogul geometry check (Macraeet al., 2020). The citrate anion occurs in thetrans, trans-conformation (about C2—C3 and C3—C4, respectively), which is one of the two low-energy conformations of an isolated citrate anion (Rammohan & Kaduk, 2018). The central carboxyl­ate group and the hydroxyl group exhibit a significant twist [O17—C3—C6—O15 = −15.6°] from the normal planar arrangement.

Figure 1 The expanded asymmetric unit of (I) with the atom numbering and 50% probability spheroids. Symmetry-generated atoms [Mg19(x,y,z − 1) and O13(x,y,z + 1)] are linked by dashed bonds.

Figure 2 Comparison of the refined and optimized structures of (I). The refined structure is in red, and the DFT-optimized structure is in blue.

The Mg cation in (I) is six-coordinate (octa­hedral); the ligands are three carboxyl­ate oxygen atoms, the citrate hydroxyl group, and twocis water mol­ecules. The Mulliken overlap populations indicate that the Mg—O bonds have significant covalent character. The Mg bond-valence sum is 2.22. The citrate anion triply chelates to the Mg cation through the terminal carboxyl­ate O14, the central carboxyl­ate O15, and the hydroxyl group O17 oxygen atoms.

The Bravais–Friedel–Donnay–Harker (Bravais, 1866; Friedel, 1907; Donnay & Harker, 1937) method suggests that we might expect platy morphology for magnesium hydrogen citrate dihydrate, with {200} as the major faces. A 4th order spherical harmonic model was included in the refinement. The texture index was 1.000 (0), indicating that preferred orientation was not significant in this rotated capillary specimen.

The crystal structure of (II) was solved and refined in the same way (Fig. 3) The root-mean-square Cartesian displacement of the non-hydrogen citrate atoms in the Rietveld refined and DFT-optimized structures is 0.043 Å (Fig. 4). The excellent agreement between the structures is evidence that the experimental structure is correct (van de Streek & Neumann, 2014) and this discussion will emphasize the DFT-optimized structure. All of the citrate bond distances, bond angles, and torsion angles fall within the normal ranges indicated by aMercury Mogul geometry check (Macraeet al., 2020). The citrate anion occurs in thetrans, gauche-conformation (about C2—C3 and C3—C4, respectively), which is one of the two low-energy conformations of an isolated citrate anion (Rammohan & Kaduk, 2018). The central carboxyl­ate group and the hydroxyl group exhibit a significant twist [O17—C3—C6—O16 = 10.6°] from the normal planar arrangement.

Figure 3 The asymmetric unit of (II) with the atom numbering and 50% probability spheroids.

Figure 4 Comparison of the refined and optimized structures of (II). The refined structure is in red, and the DFT-optimized structure is in blue.

The magnesium cation in (II) is six-coordinate (octa­hedral) and resides on a twofold axis; the ligands are twocis hydroxyl groups and 4 central carboxyl­ate groups O16. Ionizing the central carboxyl­ate group of citric acid first is the normal pattern (Rammohan & Kaduk, 2018). The Mulliken overlap populations indicate that the Mg—O bonds have significant covalent character and the Mg bond-valence sum is 2.12. The citrate anion doubly chelates to the Mg cation through the hydroxyl group O17 and the central carboxyl­ate group O16.

The Bravais–Friedel–Donnay–Harker method suggests that we might expect elongated morphology for crystals of (II), with [001] as the long axis. A 2nd order spherical harmonic model was included in the refinement. The texture index was 1.004 (0), indicating that preferred orientation was not significant in this rotated capillary specimen.

The root-mean-square Cartesian displacement of the non-hydrogen atoms in the reported and DFT-optimized structures of magnesium citrate deca­hydrate (MGCITD), [Mg(H₂O)₆][Mg(C₆H₅O₇)(H₂O)]₂(H₂O)₂ are 0.016 Å for thehexaaqua cation and 0.030 Å for the citrate complex, confirming the excellent quality of the Johnson (1965) single-crystal structure. The citrate anion occurs in thetrans, trans conformation. In Group 1 citrates, thetrans, gauche conformation is more common for salts of the smaller alkali metals, and thetrans, trans conformation is prevalent for the larger cations. Already with three Mg citrates, we see that the structures are more complicated. The torsion angle between the hydroxyl group and the central carboxyl­ate is only −4.8°. The citrate triply chelates to a Mg through the hydroxyl group, the central carboxyl­ate group, and one of the terminal carboxyl­ate groups.

3. Supra­molecular features

The MgO₆ coordination polyhedra in (I) are isolated (Fig. 5). The crystal structure is characterized by layers parallel to thebc-plane. The un-ionized carb­oxy­lic acid O12—H26 forms a strong charge-assisted hydrogen bond to the central carboxyl­ate group O16. The hydroxyl group O17—H18 also acts as a donor to O16. All four protons of the water mol­ecules act as donors in O—H⋯O hydrogen bonds. Three of them involve ionized carboxyl­ate groups, and the fourth is to the other water mol­ecule. (Table 1).

Table 1 Hydrogen-bond geometry (Å, °) for (I) (DFT) D—H⋯A D—H H⋯A D⋯A D—H⋯A O12—H26⋯O16i 1.00 1.64 2.614 161 O17—H18⋯O16ii 1.00 1.69 2.682 176 O20—H22⋯O21iii 0.98 1.82 2.795 171 O20—H23⋯O13iii 0.98 1.89 2.844 166 O21—H24⋯O15ii 1.00 1.69 2.666 166 O21—H25⋯O14iv 0.99 1.81 2.792 174 Symmetry codes: (i); (ii)x,y-1,z; (iii); (iv).

Figure 5 The crystal structure of (I), viewed down theb axis.

The MgO₆ octa­hedra in (II) share edges to form chains propagating along thec-axis direction (Fig. 6). The two un-ionized terminal carb­oxy­lic acid groups form centrosymmetricR₂²(8) loops, which link the citrate anions into chains along thec-axis direction. The hydroxyl group O17 forms an inter­molecular hydrogen bond to the central carboxyl­ate O15. The energies of the O—H⋯O hydrogen bonds were calculated using the correlation of Rammohan & Kaduk (2018). Weak C—H⋯O hydrogen bonds are also present (Table 2).

Table 2 Hydrogen-bond geometry (Å, °) for (II) (DFT) D—H⋯A D—H H⋯A D⋯A D—H⋯A O11—H21⋯O12i 1.02 1.55 2.567 179 O14—H20⋯O13ii 1.01 1.64 2.640 176 O17—H18⋯O15iii 0.99 1.72 2.708 174 C4—H9⋯O13iv 1.10 2.57 3.580 152 C4—H10⋯O15v 1.09 2.47 3.522 161 Symmetry codes: (i)-x, -y+1, -z; (ii); (iii)x,y,z+1; (iv); (v).

Figure 6 The crystal structure of (II), viewed down thec axis.

In magnesium citrate deca­hydrate (MGCITD), [Mg(H₂O)₆][Mg(C₆H₅O₇)(H₂O)]₂(H₂O)₂, the MgO₆ octa­hedra are isolated (Fig. 7). All of the H atoms of the water mol­ecules act as donors in O—H⋯O hydrogen bonds. The hydroxyl group forms bifurcated hydrogen bonds: one intra­molecular to the terminal carboxyl­ate O24 and the other inter­molecular to the terminal carboxyl­ate O28.

Figure 7 The crystal structure of [Mg(H2O)6][Mg(C6H5O7)(H2O)]2(H2O)2, (MGCITD) viewed down theb axis.

4. Database survey

Details of the comprehensive literature search for citrate structures are presented in Rammohan & Kaduk (2018). A search of the Cambridge Structural Database (Groomet al., 2016) using a citrate fragment and Mg, C, H, and O only yielded Mg₃(C₆H₅O₇)₂(H₂O)₁₀ (MGCITD; Johnson, 1965). Reduced-cell searches using the unit cells of both compounds of this study yielded no citrate structures. A search of the Powder Diffraction File (Gates-Rector & Blanton, 2019) yielded entry 02-063-3628 calculated from MGCITD, as well as the experimental entry 00-001-0186 (Hanawaltet al., 1938) for the same compound.

5. Synthesis and crystallization

To prepare (I), magnesium hydrogen citrate dihydrate was synthesized by dissolving 2.0798 g (10.0 mmol) of H₃C₆H₅O₇(H₂O) in 10 ml of water, and adding 0.8427 g (10.0 mmol) of `MgCO₃' to the clear solution [the magnesium carbonate reagent was actually Mg₅(CO₃)₄(OH)₂]. After slow fizzing, a clear colorless solution was obtained. This solution was dried in a 333 K oven to yield (I) as a white solid.

Compound (II) was obtained from the scale [94.5 (1) wt% magnesian calcite Ca_0.84Mg_0.16CO₃, 5.3 (4) wt% brucite Mg(OH)₂, and 0.2 (1) wt% vaterite polymorph of CaCO₃] in a Megahome water still. The still was cleaned by filling the tank with tap water (from Lake Michigan), adding several tablespoons of citric acid monohydrate, and boiling for ∼2 h. The pale-yellow solution was deca­nted into a plastic pail, and allowed to evaporate at ambient conditions. Over five months, several white solids (calcium citrates, which will be discussed in another paper) crystallized, and were isolated. After five months, a clear yellow syrup remained. This was dried at 423 K to yield (II) as a white powder.

6. Refinement

Crystal data, data collection and structurerefinement details for (I) are summarized in Table 3. A laboratory powder pattern, measured using CuKα radiation, was indexed usingDICVOL (Louër & Boultif, 2007) as incorporated intoFOX (Favre-Nicolin & Černý, 2002) on a primitive ortho­rhom­bic cell witha = 26.9042 (24),b = 5.9323 (4),c = 6.1649 (5) Å,V = 985.27 (17) ų, andZ = 4. Attempts to solve the structure with multiple programs using the laboratory data were unsuccessful. The powder pattern measured at 11-BM using a wavelength of 0.413070 Å was indexed on a primitive ortho­rhom­bic cell withDICVOL as incorporated intoFOX:a = 26.91159 (14),b = 5.92442 (2),c = 6.15170 (2) Å,V = 980.800 (7) ų, andZ = 4. TheSpace Group Explorer suggestedPna2₁, which was confirmed by successful solution and refinement of the structure. The structure was solved using Monte Carlo-simulated annealing techniques as implemented inFOX. The scatterers were a citrate anion, a Mg atom, and two O atoms (water mol­ecules). In the best solution, one of the water mol­ecules was too close to a carboxyl­ate oxygen atom, and was discarded. The Mg coordination was 5/6 of an octa­hedron, so the second water mol­ecule was placed manually usingMaterials Studio (Dassault Systems, 2019).

Table 3 Experimental details   (I) (II) Crystal data Chemical formula Mg2+·C6H6O72−·2H2O Mg(H2C6H5O7)2 Mr 250.44 380.13 Crystal system, space group Orthorhombic,Pna21 Monoclinic,C2/c Temperature (K) 295 295 a,b,c (Å) 26.91181 (13), 5.924517 (17), 6.151787 (18) 23.26381 (16), 10.97790 (4), 5.924466 (18) α,β,γ (°) 90, 90, 90 90, 82.5511 (3), 90 V (Å3) 980.84 (1) 1500.267 (6) Z 4 4 Radiation type Synchrotron,λ = 0.41307 Å Synchrotron,λ = 0.41307 Å Specimen shape, size (mm) Cylinder, 3.0 × 1.5 Cylinder, 3.0 × 1.5   Data collection Diffractometer APS 11-BM 11-BM APS Specimen mounting Kapton capillary Kapton capillary Data collection mode Transmission Transmission Data collection method Step Step θ values (°) 2θmin = 0.500 2θmax = 49.991 2θstep = 0.001 2θmin = 0.500 2θmax = 49.991 2θstep = 0.001   Refinement R factors and goodness of fit Rp = 0.086,Rwp = 0.110,Rexp = 0.060,χ2 = 3.486 Rp = 0.098,Rwp = 0.120,Rexp = 0.083,χ2 = 2.16 No. of parameters 76 60 No. of restraints 29 – Computer programs:FOX (Favre-Nicolin & Černý, 2002),GSAS-II (Toby & Von Dreele, 2013),Mercury (Macraeet al., 2020),DIAMOND (Crystal Impact, 2015),publCIF (Westrip, 2010).

The structure of (I) was refined by theRietveld method usingGSAS-II (Toby & Von Dreele, 2013) (Fig. 8). The initial refinement clarified the presence of extra peaks, which were identified as citric acid (02-061-2110; CITRAC10), which was added as a second phase; its concentration refined to 12.2 wt%. A few very weak peaks indicate the presence of an unidentified impurity. Analysis of potential hydrogen bonding usingMercury (Macraeet al., 2020) made it possible to determine approximate positions for the hydroxyl hydrogen atom H18 and the four water mol­ecule hydrogen atoms. The C1—O12 bond was longer than the other carboxyl­ate distances, and the O12⋯O16ⁱ distance was 2.62 Å, making it clear that H26, the proton of the un-ionized carboxyl group, was located on O12. All heavy-atom bond distances and angles of the citrate anion were restrained: C1—C2 = C4—C5 = 1.51 (3), C2—C3 = C3—C4 = 1.54 (3), C3—C6 = 1.55 (3), C3—O17 = 1.42 (3), C1—O11 = 1.22 (3), C1—O12 = 1.32 (3), and the C—O of the ionized carboxyl­ate groups = 1.27 (3) Å, C1—C2—C3 = C3—C4—C5 = 115 (3), the angles around C3 = 109.5 (3), the O—C—C angles of the carboxyl­ate groups = 115 (3), and the O—C—O angles of the carboxyl­ate groups = 130 (3)°. The restraints contributed 1.5% to the finalχ². The hydrogen atoms were included in fixed positions, which were re-calculated during the course of the refinement usingMaterials Studio. TheU_iso values of C2, C3, and C4 were constrained to be equal, and those of H7, H8, H9, and H10 were constrained to be 1.3× that of these carbon atoms. TheU_iso values of C1, C5, C6, and the oxygen atoms were constrained to be equal, and that of H18 was constrained to be 1.3× this value. TheU_iso values of the O atoms of the water mol­ecules were constrained to be equal, and theU_iso values of their H atoms to be 1.3× this value. The background was described by a four-term shifted Chebyshev polynomial, with a peak at 10.84° to describe the scattering from the Kapton capillary and any amorphous component.

Figure 8 Rietveld plot for (I). The blue crosses represent the observed data points, and the green line is the calculated pattern. The cyan curve is the normalized error plot. The vertical scale has been multiplied by a factor of 5× for 2θ > 10.0°, and by a factor of 20× for 2θ > 15.0°. The row of blue tick marks indicates the calculated reflection positions, and the red tick marks indicate the peak positions for the citric acid impurity. The red line is the background curve.

A density functional geometry optimization for (I) (fixed experimental unit cell) was carried out usingCRYSTAL09 (Dovesiet al., 2005). The basis sets for the H, C, N, and O atoms were those of Gattiet al. (1994), and the basis set for Mg was that of McCarthy & Harrison (1994). The calculation used 8k-points and the B3LYP functional, and took around four days on a 2.4 GHz PC.

Crystal data, data collection and structure refinement details for (II) are summarized in Table 3. It proved difficult to index the laboratory pattern, though the correct cell was included in hits found byDICVOL06 (Louër & Boultif, 2007). The synchrotron pattern was indexed on a primitive monoclinic unit cell withN-TREOR (Altomareet al., 2013):a = 23.24984 (8),b = 10.97779 (3),c = 5.92449 (1) Å,β = 979.1860 (2)°,V = 1500.241 (8) ų, andZ = 4. Thesystematic absences unambiguously determined thespace group asP2₁/c The structure was solved bydirect methods usingEXPO2009 (Altomareet al., 2013), assuming that it was a Ca salt. During the refinement, the electron density at the metal site and the metal–oxygen bond distances made it clear that it was a Mg salt rather than a Ca compound.

The structure was refined by the Rietveld method usingGSAS-II (Toby & Von Dreele, 2013) (Fig. 9). Analysis of the refined structure usingPLATON (Spek, 2020) and the Find Symmetry module ofMaterials Studio (Dassault Systems, 2019) suggested the presence of extra symmetry, and that the true space group wasC2/c (transformation matrix 1 0 1 / 0 0 / 0 0). The structure was re-refined in this space group, using the strategy described above for (I). The position of the peak in the background was 5.37°.

Figure 9 Rietveld plot for (II). The blue crosses represent the observed data points, and the green line is the calculated pattern. The cyan curve is the normalized error plot. The vertical scale has been multiplied by a factor of 2× for 2θ > 3.0°, by a factor of 10× for 2θ > 12.0°, and by a factor of 40× for 2θ > 17.0°. The row of blue tick marks indicates the calculated reflection positions. The red line is the background curve.

A density functional geometry optimization for (II) (fixed experimental unit cell) was carried out usingCRYSTAL17 (Dovesiet al., 2018). The basis sets for the H, C, N, and O atoms were those of Gattiet al. (1994), and the basis set for Mg was that of Peintingeret al. (2013). The calculation used 8k-points and the B3LYP functional, and took ∼15 h on a 3.54 GHz PC.

A density functional geometry optimization (fixed experimental unit cell) of the structure of magnesium citrate deca­hydrate (MGCITD) was carried out usingCRYSTAL09 (Dovesiet al., 2005). The basis sets for the H, C, N, and O atoms were those of Gattiet al. (1994), and the basis set for Mg was that of McCarthy & Harrison (1994). The calculation used 8k-points and the B3LYP functional, and took 11 days on a 2.4 GHz PC.

Supporting information

Acknowledgements

Use of the Advanced Photon Source at Argonne National Laboratory was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02–06CH11357. I thank Lynn Ribaud and Saul Lapidus for their assistance in the data collection.

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