Sodium rubidium hydrogen citrate, NaRbHC6H5O7, and sodium caesium hydrogen citrate, NaCsHC6H5O7: crystal structures and DFT comparisons

The crystal structures of sodium rubidium hydrogen citrate and sodium caesium hydrogen citrate have been solved and refined using laboratory X-ray powder diffraction data, and optimized using density functional techniques. In NaRbHC6H5O7, the Na and Rb cation coordination spheres form triple chains along the a-axis direction, and chains of very strong O—H—O hydrogen bonds run along [111], while in NaCsHC6H5O7 the Na and Cs coordination polyhedra form layers parallel to (101), and there are chains of very short and strong hydrogen bonds along [100].

The crystal structure of sodium rubidium hydrogen citrate, NaRbHC 6 H 5 O 7 or [NaRb(C 6 H 6 O 7 )] n , has been solved and refined using laboratory powder X-ray diffraction data, and optimized using density functional techniques. This compound is isostructural to NaKHC 6 H 5 O 7 . The Na atom is six-coordinate, with a bond-valence sum of 1.16. The Rb atom is eight-coordinate, with a bondvalence sum of 1.17. The distorted [NaO 6 ] octahedra share edges to form chains along the a-axis direction. The irregular [RbO 8 ] coordination polyhedra share edges with the [NaO 6 ] octahedra on either side of the chain, and share corners with other Rb atoms, resulting in triple chains along the a-axis direction. The most prominent feature of the structure is the chain along [111] of very short, very strong hydrogen bonds; the OÁ Á ÁO distances are 2.426 and 2.398 Å . The Mulliken overlap populations in these hydrogen bonds are 0.140 and 0.143 electrons, which correspond to hydrogen-bond energies of about 20.3 kcal mol À1 . The crystal structure of sodium caesium hydrogen citrate, NaCsHC 6 H 5 O 7 or [NaCs(C 6 H 6 O 7 )] n , has also been solved and refined using laboratory powder X-ray diffraction data, and optimized using density functional techniques. The Na atom is six-coordinate, with a bond-valence sum of 1.15. The Cs atom is eight-coordinate, with a bond-valence sum of 0.97. The distorted trigonal-prismatic [NaO 6 ] coordination polyhedra share edges to form zigzag chains along the b-axis direction. The irregular [CsO 8 ] coordination polyhedra share edges with the [NaO 6 ] polyhedra to form layers parallel to the (101) plane, unlike the isolated chains in NaKHC 6 H 5 O 7 and NaRbHC 6 H 5 O 7 . A prominent feature of the structure is the chain along [100] of very short, very strong O-HÁ Á ÁO hydrogen bonds; the refined OÁ Á ÁO distances are 2.398 and 2.159 Å , and the optimized distances are 2.398 and 2.347 Å . The Mulliken overlap populations in these hydrogen bonds are 0.143 and 0.133 electrons, which correspond to hydrogen-bond energies about 20.3 kcal mol À1 .

Chemical context
A systematic study of the crystal structures of Group 1 (alkali metal) citrate salts has been reported in Rammohan & Kaduk (2018). The study was extended to lithium metal hydrogen citrates in Cigler & Kaduk (2018). The two title compounds (Figs. 1 and 2) are a further extension to citrates that contain more than one alkali metal cation.

Structural commentary
Sodium rubidium hydrogen citrate is isostructural to NaKHC 6 H 5 O 7 (Rammohan & Kaduk, 2016). Sodium caesium hydrogen citrate has a related but different structure. The root-mean-square deviations of the non-hydrogen atoms in the refined and optimized structures are 0.116 and 0.105 Å for NaRbHC 6 H 5 O 7 and NaCsHC 6 H 5 O 7 , respectively. Comparisons of the refined and optimized structures are given in Figs. 3 and 4. The excellent agreement between the structures is strong evidence that the experimental structures are correct (van de Streek & Neumann, 2014). This discussion uses the DFT-optimized structures. All of the citrate bond distances, bond angles, and torsion angles fall within the normal ranges indicated by a Mercury Mogul Geometry Check (Macrae et al., 2008). The citrate anion in both structures occurs in the trans,trans-conformation (about C2-C3 and C3-C4), which is one of the two low-energy conformations of an isolated citrate (Rammohan & Kaduk, 2018). The central carboxylate group and the hydroxy group occur in the normal planar arrangement.
In the Rb compound, the citrate chelates to Na19 through the terminal carboxylate oxygen O11 and the central carboxylate oxygen O16. The Na + cation is six-coordinate, with a bond-valence sum of 1.16. The Rb + cation is eightcoordinate, with a bond-valence sum of 1.17. Both cations are thus slightly crowded.
In the Cs compound, the citrate triply chelates to Na20 through the terminal carboxylate oxygen O12, the central carboxylate oxygen O15, and the hydroxyl oxygen O17. The Na + cation is six-coordinate, with a bond-valence sum of 1.15. The Cs + cation is eight-coordinate, with a bond-valence sum of 0.97. The Rb-O and Cs-O bonds are ionic, but the Na-O bonds have slight covalent character, according to the Mulliken overlap populations.
The Bravais-Friedel-Donnay-Harker (Bravais, 1866;Friedel, 1907;Donnay & Harker, 1937) method suggests that we might expect a platy morphology for NaRbHC 6 H 5 O 7 , with {001} as the principal faces, and an elongated morphology for NaCsHC 6 H 5 O 7 , with {010} as the long axis. Fourth-order spherical harmonic preferred orientation models were included in the refinements; the texture indices were 1.050 and 1.011, indicating that preferred orientation was slight for the rotated flat-plate specimen of NaRbHC 6 H 5 O 7 , but not significant in this rotated capillary specimen of NaCsHC 6 H 5 O 7 . Examination of the products under an optical microscope indicated that the morphologies were not especially anisotropic.

Supramolecular features
In the crystal structure of NaRbHC 6 H 5 O 7 (Fig. 5) The asymmetric unit of NaCsHC 6 H 5 O 7 , with the atom numbering and 50% probability spheroids.

Figure 3
Comparison of the refined and optimized structures of sodium rubidium hydrogen citrate. The refined structure is in red, and the DFT-optimized structure is in blue.

Figure 4
Comparison of the refined and optimized structures of sodium caesium hydrogen citrate. The refined structure is in red, and the DFT-optimized structure is in blue.

Figure 1
The asymmetric unit of NaRbHC 6 H 5 O 7 , with the atom numbering and 50% probability spheroids. edges with the [NaO 6 ] octahedra on either side of the chain, resulting in triple chains along the a-axis direction. The most prominent feature of the structure is the chain along [111] of very short, very strong O-HÁ Á ÁO hydrogen bonds (Table 1); the refined OÁ Á ÁO distances are 2.180 (9) and 2.234 (20) Å , and the optimized distances are 2.426 and 2.398 Å . The Mulliken overlap populations in these hydrogen bonds are 0.140 and 0.143 electrons, which correspond to hydrogen-bond energies about 20.6 kcal mol À1 , according to the correlation in Rammohan & Kaduk (2018). H18 forms bifurcated hydrogen bonds: one is intramolecular to O15, and the other is intermolecular to O11.

Figure 5
Crystal structure of NaRbHC 6 H 5 O 7 , viewed down the a axis.

Figure 6
Crystal structure of NaCsHC 6 H 5 O 7 , viewed down the b axis.
the pattern was indexed using Jade9.  (Rammohan & Kaduk, 2016). After manually locating the peaks in the pattern of NaCsHC 6 H 5 O 7 , the pattern was indexed on a C-centered monoclinic cell using Jade9.8 (MDI, 2017). A reduced-cell search in the CSD yielded no hits. The cell was converted to Icentered, to yield a angle closer to 90 .

Synthesis and crystallization
Stoichiometric quantities of Na 2 CO 3 and Rb 2 CO 3 were added to a solution of 10.0 mmol citric acid monohydrate in 10 mL water. After the fizzing subsided, the clear solution was dried in an oven at 403 K to yield the white solid NaRbHC 6 H 5 O 7 .
2.0236 g (10.0 mmol) of H 3 C 6 H 5 O 7 (H 2 O) were dissolved in 10 mL of deionized water. 0.5318 g of Na 2 CO 3 (1.0 mmol Na, Sigma-Aldrich) and 1.6911 g of Cs 2 CO 3 (10.0 mmol of Ca, Sigma-Aldrich) were added to the citric acid solution slowly with stirring. The resulting clear colorless solution was evaporated to dryness in a 403 K oven to yield NaCsHC 6 H 5 O 7 .

Refinement
The initial structural model for NaRbHC 6 H 5 O 7 was taken from Rammohan & Kaduk (2016), replacing the K by Rb and changing the lattice parameters to the observed values. Pseudovoigt profile coefficients were as parameterized in Thompson et al. (1987) and the asymmetry correction of Finger et al. (1994) was applied as well as the microstrain broadening description by Stephens (1999). The hydrogen atoms were included in fixed positions, which were re-calculated during the course of the refinement. Crystal data, data collection and structure refinement ( Fig. 7) details are summarized in Table 3. The U iso of C2, C3, and C4 were constrained to be equal, and those of H7, H8, H9, and H10 were constrained to be 1.3 Â that of these carbon atoms. The U iso of C1, C5, C6, and the oxygen atoms were constrained to be equal, and that of H18 was constrained to be 1.3 Â this value. The U iso of H21 and H22 were fixed.
Analysis of the systematic absences in the pattern of NaCsHC 6 H 5 O 7 suggested the space groups I2, Im, or I2/m. The volume of the unit cell corresponded to Z = 4. Space group I2 was selected, and confirmed by successful solution and refinement of the structure. The structure was solved with FOX (Favre-Nicolin & Č erný, 2002). The maximum sin / used for structure solution was 0.55 Å , and a citrate, Cs, Na, and O (water molecule) were used as fragments. The solution with the lowest cost factor has the Cs, Na, and O on top of each other, but the Cs was eight-coordinate and all six carboxylate oxygen atoms were coordinated to the Cs atom. The structure was examined for voids using Materials Studio (Dassault Systemes, 2017). One void at approximately 0.375,0.600,0.379 had acceptable coordination to O atoms, and was assigned as Na20. Another void was assigned as O21, but this moved too close to the citrate anion on refinement and was discarded. Active hydrogen atoms were placed by analysis of hydrogenbonding interactions. The refinement strategy (Fig. 8) was similar to that used for the Rb compound. Cs19 was refined anisotropically.
Density functional geometry optimizations (fixed experimental unit cells) were carried out using CRYSTAL14 Rietveld plot for NaCsHC 6 H 5 O 7 . The red crosses represent the observed data points, and the green line is the calculated pattern. The magenta curve is the difference pattern, plotted at the same scale as the other patterns. The vertical scale has been multiplied by a factor of 10 for 2 > 28.8 . The row of black tick marks indicates the reflection positions for this phase.

Figure 7
Rietveld plot for NaRbHC 6 H 5 O 7 . The red crosses represent the observed data points, and the green line is the calculated pattern. The magenta curve is the difference pattern, plotted at the same scale as the other patterns. The vertical scale has been multiplied by a factor of 10 for 2 > 46.0 . The row of black tick marks indicates the reflection positions for this phase.