Crystal structure of dirubidium hydrogen citrate from laboratory X-ray powder diffraction data and DFT comparison

The crystal structure of dirubidium hydrogen citrate has been solved and refined using laboratory X-ray powder diffraction data, and optimized using density functional techniques.

The crystal structure of dirubidium hydrogen citrate, 2Rb + ÁHC 6 H 5 O 7 2À , has been solved and refined using laboratory X-ray powder diffraction data, and optimized using density functional techniques. The un-ionized carboxylic acid group forms helical chains of very strong hydrogen bonds (OÁ Á ÁO $ 2.42 Å ) along the b axis. The hydroxy group participates in a chain of intra-and intermolecular hydrogen bonds along the c axis. These hydrogen bonds result in corrugated hydrogen-bonded layers in the bc plane. The Rb + cations are sixcoordinate, and share edges and corners to form layers in the ab plane. The interlayer contacts are composed of the hydrophobic methylene groups.

Chemical context
In the course of a systematic study of the crystal structures of Group 1 (alkali metal) citrate salts to understand the conformational flexibility, ionization, coordination tendencies, and hydrogen bonding of the anion, we have determined several new crystal structures. Most of the new structures were solved using powder diffraction data (laboratory and/or synchrotron), but single crystals were used where available. The general trends and conclusions about the 16 new compounds and 12 previously characterized structures are being reported separately (Rammohan & Kaduk, 2017). Six of the new structures, i.e. NaKHC 6 H 5 O 7 , NaK 2 C 6 H 5 O 7 , Na 3 C 6 H 5 O 7 , NaH 2 C 6 H 5 O 7 , Na 2 HC 6 H 5 O 7 , and K 3 C 6 H 5 O 7 , have been published recently (Rammohan & Kaduk, 2016a,b,c,d,e;Rammohan et al., 2016), and two additional structures, i.e. KH 2 C 6 H 5 O 7 and KH 2 C 6 H 5 O 7 (H 2 O) 2 , have been communicated (Kaduk & Stern, 2016a,b) to the Cambridge Structural Database (Groom et al., 2016). ISSN 2056-9890

Structural commentary
The asymmetric unit of the title compound is shown in Fig. 1. The r.m.s. deviation of the non-H atoms in the Rietveld refined and DFT-optimized structures is 0.052 Å (Fig. 2), and the maximum deviation is 0.083 Å , at atom C1. The good agreement between the two structures is strong evidence that the experimental structure is correct (van de Streek & Neumann, 2014). This discussion uses the DFT-optimized structure. Most of the bond lengths, bond angles, and torsion angles fall within the normal ranges indicated by a Mercury Mogul Geometry Check (Macrae et al., 2008). The C1-C2-C3 angle of 111.1 is flagged as unusual [Z-score = 2.7; average = 114.3 (11) ]. The Z-score is the result of the low standard uncertainty on the average; the absolute difference of 3.2 is well within the expected range of such angles. The citrate anion occurs in the trans,trans-conformation, which is one of the two low-energy conformations of an isolated citrate. The central carboxylate group and the hydroxy group lie on the mirror plane. The central carboxylate O15 atom and the terminal carboxylic acid O11 atom chelate to Rb19, and the central carboxylate O16 atom and the terminal carboxylic acid O11 atom chelate to another Rb19. The Mulliken overlap populations and atomic charges indicate that the metaloxygen bonding is ionic.
The Bravais-Friedel-Donnay-Harker (Bravais, 1866;Friedel, 1907;Donnay & Harker, 1937) morphology suggests that we might expect a platy morphology for dirubidium hydrogen citrate, with {020} as the principal faces. A 4th order spherical harmonic texture model was included in the refine-ment. The texture index was 1.078, indicating that preferred orientation was significant for this rotated flat plate specimen.

Supramolecular features
The Rb cation is six-coordinate (bond-valence sum = 0.96). The coordination polyhedra share corners and edges to form layers in the ab plane (Fig. 3). The un-ionized terminal carboxylic acid forms a very strong symmetric hydrogen bond ( Table 1). The Mulliken overlap population in the hydrogenacceptor bond is 0.161 e. By the correlation in Rammohan & Kaduk (2017), this hydrogen bond accounts for 21.9 kcal mol À1 of crystal energy. The hydroxy group participates in two hydrogen bonds to ionized central carboxylate groups; one is intramolecular with graph-set motif S(5), and the other is intermolecular. These hydrogen bonds contribute 9.3 and 8.6 kcal mol À1 to the crystal energy.

Database survey
Details of the comprehensive literature search for citrate structures are presented in Rammohan & Kaduk (2017). A reduced cell search of the cell of dirubidium hydrogen citrate in the Cambridge Structural Database (Groom et al., 2016) (increasing the default tolerance from 1.5 to 2.0%) yielded 12 hits, but limiting the chemistry to C, H, Rb, and O only resulted in no hits. The powder pattern is now contained in the the Powder Diffraction File (ICDD, 2016) as entry 00-063-1541. The asymmetric unit of the title compound, showing the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 2
Comparison of the refined and optimized structures of dirubidium hydrogen citrate. The refined structure is in red and the DFT-optimized structure is in blue. Table 1 Hydrogen-bond geometry (Å , ) for the DFT-optimized structure of dirubidium hydrogen citrate.

Figure 3
The crystal structure of dirubidium hydrogen citrate, viewed down the a axis.

Synthesis and crystallization
H 3 C 6 H 5 O 7 (H 2 O) (2.0768 g, 10.0 mmol) was dissolved in 10 ml deionized water. Rb 2 CO 3 (10.0 mmol, 2.3170 g, Sigma-Aldrich) was added to the citric acid solution slowly with stirring. The resulting clear colorless solution was evaporated to dryness in an oven at 333 K.

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 2. Entering 22 peaks (after manually applying a constant 2 shift to approximate specimen displacement effects) into ITO/CRYSFIRE (Visser, 1969;Shirley, 2002) yielded a primitive monoclinic cell having a = 5.978, b = 15.096, c = 5.320 Å , = 93.93 , V = 478.33 Å 3 , and Z = 2. Processing the pattern in DASH3.2 (David et al., 2006) suggested that the most probable space group was P2 1 , but no acceptable solution was found. A peak list was created from the results of a Le Bail fit using the REFLIST option in GSAS, and imported into Endeavour1.7b (Putz et al., 1999). Using a citrate, two Rb atoms, and the O atom of a water molecule as fragments yielded a successful structure solution. In the initial refinements, the water molecule moved very close to one of the Rb atoms, and so was removed from the refinement. Pseudo-Voigt profile coefficients were as parameterized in Thompson et al. (1987) with profile coefficients for Simpson's rule integration of the pseudo-Voigt function according to Howard (1982). The asymmetry correction of Finger et al. (1994) was applied, and microstrain broadening by Stephens (1999). The structure was refined by the Rietveld (Fig. 4) method using GSAS/EXPGUI (Larson & Von Dreele, 2004;Toby, 2001). All C-C and C-O bond lengths were restrained, as were all bond angles. The H atoms were included at fixed positions, which were recalculated during the course of the refinement using Materials Studio (Dassault

Figure 4
Rietveld plot for the refinement of dirubidium hydrogen citrate. The vertical scale is not the raw counts but the counts multiplied by the leastsquares weights. This plot emphasizes the fit of the weaker peaks. 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 row of black tick marks indicates the reflection positions. Systemes, 2014). The U iso of the atoms in the central and outer portions of the citrate were constrained to be equal, and the U iso of the H atoms were constrained to be 1.3 times those of the atoms to which they are attached. The structure was solved and initially refined in the space group P2 1 . The ADDSYM module of PLATON (Spek, 2009) suggested the presence of an additional centre of symmetry, and that the space group was P2 1 /m. Refinement in this space group yielded slightly better residuals (R wp = 0.0277 and reduced 2 = 3.3236, compared to R wp = 0.0282 and 2 = 3.454 for P2 1 ), and we believe that P2 1 /m is the correct space group.
Stoichiometry requires one carboxylic acid proton per citrate. The space group P2 1 is consistent with ordered asymmetric hydrogen bonds, while P2 1 /m is consistent with both disordered asymmetric hydrogen bonds or symmetric hydrogen bonds. Crystallographically, it would be difficult to distinguish these two possibilities, especially using X-ray powder diffraction data. DFT calculations on the asymmetric (P2 1 ) and symmetric (P2 1 /m) hydrogen-bond models indicate that the symmetric model is 0.2 kcal mol À1 lower in energy. This difference is within the expected error range of such calculations. Since the crystallography strongly indicates the higher symmetry, we believe that the P2 1 /m model with symmetric hydrogen bonds is the best model for this structure.

DFT calculations
After the Rietveld refinement, a density functional geometry optimization (fixed experimental unit cell) was carried out using CRYSTAL14 (Dovesi et al., 2014). The basis sets for the C, H, and O atoms were those of Peintinger et al. (2012), and the basis set for Rb was that of Schoenes et al. (2008). The calculation was run on eight 2.1 GHz Xeon cores (each with 6 Gb RAM) of a 304-core Dell Linux cluster at IIT, used 8 kpoints and the B3LYP functional, and took about 5 h. The U iso from the Rietveld refinement were assigned to the optimized fractional coordinates.