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

The crystal structure of dirubidium hydrogen citrate, 2Rb⁺·HC₆H₅O₇²⁻, 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 (O⋯O ∼ 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 six-coordinate, and share edges and corners to form layers in the ab plane. The inter­layer contacts are composed of the hydro­phobic methyl­ene groups.

1. 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. NaKHC₆H₅O₇, NaK₂C₆H₅O₇, Na₃C₆H₅O₇, NaH₂C₆H₅O₇, Na₂HC₆H₅O₇, and K₃C₆H₅O₇, have been published recently (Rammohan & Kaduk, 2016a,b,c,d,e; Rammohan et al., 2016), and two additional structures, i.e. KH₂C₆H₅O₇ and KH₂C₆H₅O₇(H₂O)₂, have been communicated (Kaduk & Stern, 2016a,b) to the Cambridge Structural Database (Groom et al., 2016).

2. 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 metal–oxygen bonding is ionic.

Figure 1 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.

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 refinement. The texture index was 1.078, indicating that preferred orientation was significant for this rotated flat plate specimen.

3. 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 hydrogen-acceptor bond is 0.161 e. By the correlation in Rammohan & Kaduk (2017), this hydrogen bond accounts for 21.9 kcal mol⁻¹ 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⁻¹ to the crystal energy.

Table 1
Hydrogen-bond geometry (Å, °) for the DFT-optimized structure of dirubidium hydrogen citrate

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O11—H21⋯O11	1.209	1.209	2.418	180.0
O17—H18⋯O15	0.979	1.992	2.611	119.0
O17—H18⋯O16	0.979	1.992	3.216	148.6

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

4. 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.

5. Synthesis and crystallization

H₃C₆H₅O₇(H₂O) (2.0768 g, 10.0 mmol) was dissolved in 10 ml deionized water. Rb₂CO₃ (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.

6. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2. Entering 22 peaks (after manually applying a constant 2θ 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, β = 93.93°, V = 478.33 ų, and Z = 2. Processing the pattern in DASH3.2 (David et al., 2006) suggested that the most probable space group was P2₁, 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.

Table 2
Experimental details

	Rietveld refinement	DFT optimization
Crystal data
Chemical formula	2Rb^+·HC6H5O7^2−	2Rb^+·HC6H5O7^2−
Mr	361.04	361.04
Crystal system, space group	Monoclinic, P21/m	Monoclinic, P21/m
Temperature (K)	300	300
a, b, c (Å)	5.97796 (17), 15.0960 (4), 5.32067 (19)	5.9780, 15.0961, 5.3207
β (°)	93.9341 (13)	93.9354
V (Å^3)	479.02 (4)	478.99
Z	2	2
Radiation type	Kα1, Kα2, λ = 1.540629, 1.544451 Å	–
Specimen shape, size (mm)	Flat sheet, 24 × 24	–
Data collection
Diffractometer	Bruker D2 Phaser	–
Specimen mounting	Normal sample holder	–
Data collection mode	Reflection	–
Data collection method	Step	–
θ values (°)	2θmin = 5.042 2θmax = 70.050 2θstep = 0.020	–
Refinement
R factors and goodness of fit	Rp = 0.021, Rwp = 0.028, Rexp = 0.015, R(F^2) = 0.0520, χ^2 = 3.312	–
No. of parameters	49	–
No. of restraints	15	–
H-atom treatment	Only H-atom displacement parameters refined	–
Computer programs: DIFFRAC.Measurement (Bruker, 2009), Endeavour (Putz et al., 1999), GSAS (Larson & Von Dreele, 2004), DIAMOND (Crystal Impact, 2015) and publCIF (Westrip, 2010).

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 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.

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 least-squares 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.

The structure was solved and initially refined in the space group P2₁. The ADDSYM module of PLATON (Spek, 2009) suggested the presence of an additional centre of symmetry, and that the space group was P2₁/m. Refinement in this space group yielded slightly better residuals (R_wp = 0.0277 and reduced χ² = 3.3236, compared to R_wp = 0.0282 and χ² = 3.454 for P2₁), and we believe that P2₁/m is the correct space group.

Stoichiometry requires one carb­oxy­lic acid proton per citrate. The space group P2₁ is consistent with ordered asymmetric hydrogen bonds, while P2₁/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 (P2₁) and symmetric (P2₁/m) hydrogen-bond models indicate that the symmetric model is 0.2 kcal mol⁻¹ 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 P2₁/m model with symmetric hydrogen bonds is the best model for this structure.

7. 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 k-points and the B3LYP functional, and took about 5 h. The U_iso from the Rietveld refinement were assigned to the optimized fractional coordinates.

Supporting information

Computing details

Data collection: DIFFRAC.Measurement (Bruker, 2009) for RAMM020C_publ. Program(s) used to solve structure: Endeavour (Putz et al., 1999) for RAMM020C_publ. Program(s) used to refine structure: GSAS for RAMM020C_publ. Molecular graphics: DIAMOND (Crystal Impact, 2015) for RAMM020C_publ. Software used to prepare material for publication: publCIF (Westrip, 2010) for RAMM020C_publ.

(RAMM020C_publ) Dirubidium hydrogen citrate

Crystal data

2Rb^+·HC6H5O7^2^−	V = 479.02 (4) Å^3
Mr = 361.04	Z = 2
Monoclinic, P21/m	Dx = 2.503 Mg m^−3
Hall symbol: -P 2yb	Kα1, Kα2 radiation, λ = 1.540629, 1.544451 Å
a = 5.97796 (17) Å	T = 300 K
b = 15.0960 (4) Å	white
c = 5.32067 (19) Å	flat_sheet, 24 × 24 mm
β = 93.9341 (13)°	Specimen preparation: Prepared at 333 K

Data collection

Bruker D2 Phaser diffractometer	Scan method: step
Specimen mounting: Normal sample holder	2θmin = 5.042°, 2θmax = 70.050°, 2θstep = 0.020°
Data collection mode: reflection

Refinement

Least-squares matrix: full	49 parameters
Rp = 0.021	15 restraints
Rwp = 0.028	Only H-atom displacement parameters refined
Rexp = 0.015	Weighting scheme based on measured s.u.'s
R(F^2) = 0.0520	(Δ/σ)max = 0.08
3217 data points	Background function: GSAS Background function number 1 with 4 terms. Shifted Chebyshev function of 1st kind 1: 3185.87 2: -310.317 3: -87.5319 4: 63.9418
Profile function: CW Profile function number 4 with 21 terms Pseudovoigt profile coefficients as parameterized in P. Thompson, D.E. Cox & J.B. Hastings (1987). J. Appl. Cryst.,20,79-83. Asymmetry correction of L.W. Finger, D.E. Cox & A. P. Jephcoat (1994). J. Appl. Cryst.,27,892-900. Microstrain broadening by P.W. Stephens, (1999). J. Appl. Cryst.,32,281-289. #1(GU) = 142.783 #2(GV) = 0.000 #3(GW) = 4.751 #4(GP) = 0.000 #5(LX) = 5.874 #6(ptec) = -0.71 #7(trns) = 1.83 #8(shft) = -25.7226 #9(sfec) = 0.00 #10(S/L) = 0.0441 #11(H/L) = 0.0005 #12(eta) = 0.0000 #13(S400 ) = 3.9E-02 #14(S040 ) = 8.9E-05 #15(S004 ) = 3.1E-01 #16(S220 ) = 9.7E-03 #17(S202 ) = -6.4E-02 #18(S022 ) = 5.7E-04 #19(S301 ) = -8.2E-03 #20(S103 ) = 2.5E-02 #21(S121 ) = -8.8E-03 Peak tails are ignored where the intensity is below 0.0100 times the peak Aniso. broadening axis 0.0 1.0 0.0

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

	x	y	z	Uiso*/Ueq
C1	0.2727 (12)	0.4151 (4)	0.5145 (14)	0.0556 (15)*
C2	0.3859 (11)	0.33308 (16)	0.4236 (14)	0.026 (4)*
C3	0.2821 (12)	0.25	0.5368 (15)	0.026 (4)*
C6	0.0268 (13)	0.25	0.463 (2)	0.0556 (15)*
H7	0.56395	0.33136	0.47541	0.018 (5)*
H8	0.35795	0.33169	0.21841	0.018 (5)*
O11	0.1036 (11)	0.4467 (5)	0.3841 (15)	0.0556 (15)*
O12	0.3502 (12)	0.4512 (5)	0.7178 (14)	0.0556 (15)*
O15	−0.0968 (16)	0.25	0.650 (2)	0.0556 (15)*
O16	−0.0415 (16)	0.25	0.232 (2)	0.0556 (15)*
O17	0.3416 (14)	0.25	0.7999 (15)	0.0556 (15)*
H18	0.17127	0.25	0.87091	0.068 (2)*
Rb19	−0.2264 (3)	0.10523 (10)	−0.0313 (3)	0.0590 (9)*
H21	0.0	0.0	0.5	0.07*

Geometric parameters (Å, º)

C1—C2	1.5070 (17)	O12—Rb19^iv	2.907 (7)
C1—O11	1.278 (5)	O15—C6	1.281 (5)
C1—O12	1.270 (5)	O15—Rb19^v	2.903 (7)
C2—C1	1.5070 (17)	O15—Rb19^vi	2.903 (7)
C2—C3	1.5400 (17)	O16—C6	1.267 (5)
C2—H7	1.081 (7)	O16—Rb19	2.784 (7)
C2—H8	1.093 (7)	O16—Rb19^i	2.784 (7)
C3—C2	1.5400 (17)	O17—C3	1.420 (5)
C3—C2^i	1.5400 (17)	O17—H18	1.110 (8)
C3—C6	1.5499 (18)	O17—Rb19^vii	3.454 (7)
C3—O17	1.420 (5)	O17—Rb19^iv	3.455 (7)
C6—C3	1.5499 (18)	H18—O17	1.110 (8)
C6—O15	1.281 (5)	Rb19—O11^viii	3.159 (7)
C6—O16	1.267 (5)	Rb19—O11^i	2.965 (7)
H7—C2	1.081 (7)	Rb19—O12^ix	2.984 (6)
H8—C2	1.093 (8)	Rb19—O12^x	2.907 (7)
O11—C1	1.278 (5)	Rb19—O15^xi	2.903 (7)
O11—Rb19^ii	3.159 (7)	Rb19—O16	2.784 (7)
O11—Rb19^i	2.965 (7)	Rb19—O17^xii	3.454 (7)
O11—H21^iii	1.209 (6)	H21—O11^ix	1.209 (6)
O12—C1	1.270 (5)	H21—O11^i	1.209 (6)
O12—Rb19^iii	2.984 (6)
C2—C1—O11	119.2 (4)	C6—O15—Rb19^v	130.21 (19)
C2—C1—O12	118.7 (4)	C6—O15—Rb19^xv	130.21 (19)
O11—C1—O12	122.1 (4)	Rb19^v—O15—Rb19^xv	97.7 (3)
C1—C2—C3	110.0 (4)	C6—O16—Rb19	125.3 (2)
C1—C2—H7	113.2 (4)	C6—O16—Rb19^xiii	125.3 (2)
C1—C2—H8	17.29 (4)	Rb19—O16—Rb19^xiii	103.5 (4)
C3—C2—H7	107.3 (5)	C3—O17—H18	99.3 (7)
C3—C2—H8	109.7 (5)	O11^viii—Rb19—O11^xiii	94.2 (2)
H7—C2—H8	109.5 (5)	O11^viii—Rb19—O12^ix	79.54 (16)
C2—C3—C2^xiii	109.1 (4)	O11^viii—Rb19—O12^xvi	74.7 (2)
C2—C3—C6	108.5 (4)	O11^viii—Rb19—O15^xi	98.11 (18)
C2—C3—O17	107.8 (4)	O11^viii—Rb19—O16	142.5 (2)
C2^xiii—C3—C6	108.5 (4)	O11^xiii—Rb19—O12^ix	63.59 (19)
C2^xiii—C3—O17	107.8 (4)	O11^xiii—Rb19—O12^xvi	141.13 (14)
C6—C3—O17	115.2 (7)	O11^xiii—Rb19—O15^xi	116.3 (2)
C3—C6—O15	114.4 (9)	O11^xiii—Rb19—O16	67.2 (2)
C3—C6—O16	119.5 (9)	O12^ix—Rb19—O12^xvi	77.7 (2)
O15—C6—O16	126.1 (9)	O12^ix—Rb19—O15^xi	177.6 (2)
C1—O11—Rb19^ii	113.5 (7)	O12^ix—Rb19—O16	115.8 (3)
C1—O11—Rb19^xiii	140.0 (4)	O12^xvi—Rb19—O15^xi	102.2 (2)
Rb19^ii—O11—Rb19^xiii	85.8 (2)	O12^xvi—Rb19—O16	139.9 (2)
C1—O12—Rb19^iii	136.0 (4)	O15^xi—Rb19—O16	65.8 (2)
C1—O12—Rb19^xiv	121.4 (4)	O11^ix—H21—O11^xiii	180.0
Rb19^iii—O12—Rb19^xiv	102.3 (2)

Symmetry codes: (i) x, −y+1/2, z; (ii) −x, y+1/2, −z; (iii) −x, y+1/2, −z+1; (iv) x+1, −y+1/2, z+1; (v) x, y, z+1; (vi) x, −y+1/2, z+1; (vii) x+1, y, z+1; (viii) −x, y−1/2, −z; (ix) −x, y−1/2, −z+1; (x) x−1, −y+1/2, z−1; (xi) x, y, z−1; (xii) x−1, y, z−1; (xiii) x, −y+3/2, z; (xiv) x+1, −y+3/2, z+1; (xv) x, −y+3/2, z+1; (xvi) x−1, −y+3/2, z−1.

(ramm020c_DFT)

Crystal data

C6H6O7Rb2	c = 5.3207 Å
Mr = 361.04	β = 93.9354°
Monoclinic, P21/m	V = 478.99 Å^3
Hall symbol: -P 2yb	Z = 2
a = 5.9780 Å	T = 300 K
b = 15.0961 Å

Data collection

h = →	l = →
k = →

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

	x	y	z	Uiso*/Ueq
C1	0.28187	0.41704	0.52143	0.05270*
C2	0.38508	0.33363	0.42243	0.01400*
C3	0.27797	0.25000	0.53116	0.01400*
C6	0.02276	0.25000	0.45797	0.05270*
H7	0.56395	0.33136	0.47541	0.01820*
H8	0.35795	0.33169	0.21841	0.01820*
O11	0.10613	0.44671	0.38734	0.05270*
O12	0.35379	0.45283	0.72015	0.05270*
O15	−0.10430	0.25000	0.63801	0.05270*
O16	−0.03680	0.25000	0.22772	0.05270*
O17	0.31806	0.25000	0.79999	0.05270*
H18	0.17127	0.25000	0.87091	0.06840*
Rb19	−0.22414	0.10319	−0.03836	0.05980*
H21	0.00000	0.00000	0.50000	0.07000*

Bond lengths (Å)

C1—C2	1.513	Rb19—O11^ii	2.997
C1—O11	1.308	Rb19—O16	2.820
C1—O12	1.238	Rb19—O12^viii	2.966
C2—C3	1.546	C3—C2^ii	1.546
C2—H7	1.087	C3—C6	1.548
C2—H8	1.087	C3—O17	1.434
O11—Rb19^i	3.115	C6—O15	1.263
O11—Rb19^ii	2.997	C6—O16	1.252
O11—H21^iii	1.209	O15—Rb19^ix	2.926
O12—Rb19^iv	2.879	O15—Rb19^x	2.926
O12—Rb19^iii	2.966	O16—Rb19^ii	2.820
Rb19—O12^v	2.879	O17—H18	0.979
Rb19—O15^vi	2.926	H21—O11^ii	1.209
Rb19—O11^vii	3.115	H21—O11^viii	1.209

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

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O11—H21···O11	1.209	1.209	2.418	180.0
O17—H18···O15	0.979	1.992	2.611	119.0
O17—H18···O16	0.979	1.992	3.216	148.6