Structures of dipotassium rubidium citrate monohydrate, K2RbC6H5O7(H2O), and potassium dirubidium citrate monohydrate, KRb2C6H5O7(H2O), from laboratory X-ray powder diffraction data and DFT calculations

The crystal structures of the isostructural mixed-cation compounds dipotassium rubidium citrate monohydrate and potassium dirubidium citrate monohydrate have been solved and refined using laboratory X-ray powder diffraction data and optimized using density functional techniques.


Structural commentary
The crystal structures of dipotassium rubidium citrate monohydrate K 2 RbC 6 H 5 O 7 (H 2 O), (I), and potassium dirubidium citrate monohydrate KRb 2 C 6 H 5 O 7 (H 2 O), (II), have been solved and refined using laboratory X-ray powder diffraction data, and optimized using density functional techniques. The two compounds are isostructural (Fig. 1). The powder patterns (Fig. 2) and the unit cells show that these compounds are isostructural to K 3 C 6 H 5 O 7 (H 2 O) and Rb 3 C 6 H 5 O 7 (H 2 O). In each compound, the K and Rb cations are disordered over the three cation sites: in (I), the K/Rb site occupancies are 0.93/ 0.07, 0.64/0.36, and 0.53/0.47 for the K19/Rb20, K21/Rb22 and K23/Rb24 sites, respectively and in (II) the refined K/Rb occupancies are 0.62/0.38, 0.39/0.61 and 0.36/0.64 for the same metal sites. The refined site occupancies correlate well to the bond-valence sums calculated for K and Rb at each cation site ( Fig. 3). DFT calculations on ordered cation systems show that in (I) occupation of site 19 by Rb is disfavored by 0.19 kcal mol À1 , while in (II) occupation of this site by K is favored by 0.28 kcal mol À1 . These trends are consistent with the refined occupancies, but the energy differences are within the expected errors for such calculations.
For (I), the root-mean-square Cartesian displacement of the non-H atoms of the citrate anion in the disordered refined structure and the ordered DFT-optimized structures is 0.114, 0.080, and 0.079 Å for Rb at site 19, 20, and 21 (Fig. 4) Overlay of the crystal structures of (I) and (II), viewed approximately down the a-axis direction.

Figure 3
Correlations between the refined K and Rb site occupancies in (K,Rb) 3 C 6 H 5 O 7 (H 2 O) and the bond valence sums for each cation at each of the three potential sites.

Figure 4
Comparison of the refined asymmetric unit of (I) (red) and the DFToptimized structures with Rb at site 19 (blue), site 20 (green), and site 21 (purple). 0.085 (29) Å , and the average absolute difference in the position of the water oxygen atom is 0.26 (11) Å . For (II), the similar r.m.s. citrate-atom displacements are 0.077, 0.104, and 0.101 Å (Fig. 5). The average absolute difference in the cation positions is 0.084 (54) Å , and the average absolute difference in the position of the water molecule oxygen atom is 0.28 (14) Å . The good agreement between the disordered refined structures and the ordered DFT-optimized structures provides confidence that the experimental structures are correct (van de Streek & Neumann, 2014).

Supramolecular features
The MO 6 and MO 7 coordination polyhedra in both structures share edges to form a three-dimensional framework (Fig. 6). The hydrophobic methylene group sides of the citrate anions occupy channels in the framework. The hydrogen bonds in the six ordered systems used for the DFT calculations differ slightly but the general pattern is similar: Tables 1-3 list the geometrical data for (I) with the Rb atom placed at the M19, M21 and M23 sites, respectively and the K atoms occupying the other two sites. Tables 4-6 present data for (II) with the K atom occupying the M19, M21 and M23 sites, respectively and the Rb atoms occupying the other two sites. The water molecule O25/H26/H27 forms strong charge-assisted hydrogen bonds to the central carboxylate oxygen atom O15 and the terminal carboxylate O13. The energies of the O-HÁ Á ÁO hydrogen bonds were calculated using the correlation of Rammohan & Kaduk (2018). The hydroxyl group O17 forms an intramolecular hydrogen bond to the central carboxylate O16. In some of the ordered models, the hydroxyl group also Symmetry codes: (i) Àx þ 1; Ày; Àz; (ii) Àx þ 1 2 ; y þ 1 2 ; Àz þ 1 2 .

Figure 5
Comparison of the refined asymmetric unit of (II) (red) and the DFToptimized structures with K at site 19 (blue), site 20 (green), and site 21 (purple).
forms an intermolecular hydrogen bond to the terminal carboxylate O13.

Database survey
Details of the comprehensive literature search for citrate structures are presented in Rammohan & Kaduk (2018

Synthesis and crystallization
Dipotassium rubidium citrate monohydrate, (I), was synthesized by adding stoichiometric quantities of 1.382 g K 2 CO 3 (Sigma-Aldrich) and 1.154 g Rb 2 CO 3 (Sigma-Aldrich) to a solution of 2.03 g citric acid monohydrate (10.0 mmol, Sigma-Aldrich) in 10 ml of water. After the fizzing subsided, the clear solution was dried in a 403 K oven to yield a white solid. Potassium dirubidium citrate monohydrate, (II), was synthesized in the same way starting from 0.691 g of K 2 CO 3 and 2.309 g of Rb 2 CO 3 .

Refinement
Crystal data, data collection and structure refinement details for (I) are summarized in Table 7 ( Fig. 7). To minimize Rb fluorescence, the pulse height discriminator lower level of the X'Celerator detector was raised from the default 39.0% to 51.0%. The structure was solved with FOX (Favre-Nicolin & Č erný, 2002), using 2 K atoms, 1 Rb atom and a citrate anion as fragments. A Le Bail fit yielded R wp = 3.73%. Initial refinement did not include the water molecule, and yielded an acceptable fit (R wp = 4.8%), but the U iso values of the C atoms in the central part of the molecule were relatively large ($0.10 Å 2 ). The bond-valence sums of the cations were, however, far too low, showing that the water molecule was indeed present. It was inserted in the position from the known monohydrate structures. 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 3Â for 2 > 26.0 . The row of blue tick marks indicates the calculated reflection positions. The red line is the background curve. Table 4 Hydrogen-bond geometry (Å , ) for (II) M19. Symmetry codes: (i) Àx þ 1; Ày; Àz; (ii) Àx þ 1 2 ; y þ 1 2 ; Àz þ 1 2 . Table 5 Hydrogen-bond geometry (Å , ) for (II) M20. Symmetry code: (i) Àx þ 1 2 ; y þ 1 2 ; Àz þ 1 2 . Table 6 Hydrogen-bond geometry (Å , ) for (II) M21.   (3) . Each of the three cation sites was modeled as a mixture of K and Rb; the sums of the site occupancies were constrained to be unity, but the total K and Rb contents were not constrained/ restrained, to provide an internal consistency check. The U iso of the atoms in the central and outer portions of the citrate anion were constrained to be equal, and the U iso of the hydrogen atoms were constrained to be 1.3Â those of the atoms to which they are attached. The U iso of the cations were constrained to be equal. A capillary absorption model (fixed .R = 0.84, calculated using the tool on the 11-BM web site) was included into the refinement. A Chebyschev polynomial function with four coefficients, along with a peak at 13.11 to model the scattering of the glass capillary, was used to model the background.
Because DFT techniques cannot accommodate disordered systems, three density functional geometry optimizations (with Rb at each of the three cations sites, and K at the other two) were carried out using CRYSTAL14 (Dovesi et al., 2014). The basis sets for the H, C, N, and O atoms were those of Gatti et al. (1994), and the basis sets for K and Rb were those of Peintinger et al. (2013). The calculations were run on eight 2.1 GHz Xeon cores (each with 6 Gb RAM) of a 304-core Dell Linux cluster at IIT, using 8 k-points and the B3LYP functional.
Crystal data, data collection and structure refinement details for (II) are summarized in Table 7 (Fig. 8). The same solution and refinement strategy as for (I) was followed. Three density functional geometry optimizations (with K at each of the three cations sites, and Rb at the other two) were carried out using CRYSTAL17 (Dovesi et al., 2018) with atom basis sets and computer hardware as described in the previous paragraph.