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

The crystal structure of trirubidium citrate, 3Rb⁺·C₆H₅O₇³⁻, has been solved and refined using laboratory X-ray powder diffraction data, and optimized using density functional techniques. The two independent Rb⁺ cations are seven- and eight-coordinate, with bond-valence sums of 0.99 and 0.92 valence units. The coordination polyhedra share edges and corners to form a three-dimensional framework. The only hydrogen bond is an intra­molecular one between the hy­droxy group and the central carboxyl­ate, with graph set S(5). The hydro­phobic methyl­ene groups lie in pockets in the framework.

1. Chemical context

In the course of a systematic study of the crystal structures of Group 1 (alkali metal) citrate salts to understand the anion's conformational flexibility, ionization, coordination tendencies, and hydrogen bonding, we have determined several new crystal structures. Most of the new structures were solved using X-ray powder diffraction data (laboratory and/or synchrotron), but single crystals were used where available. The general trends and conclusions about the sixteen new compounds and twelve previously characterized structures are being reported separately (Rammohan & Kaduk, 2017a). Eight of the new structures – NaKHC₆H₅O₇, NaK₂C₆H₅O₇, Na₃C₆H₅O₇, NaH₂C₆H₅O₇, Na₂HC₆H₅O₇, K₃C₆H₅O₇, Rb₂HC₆H₅O₇, and Rb₃C₆H₅O₇(H₂O) – have been published recently (Rammohan & Kaduk, 2016a,b,c,d,e, 2017b,c; Rammohan et al., 2016), and two additional structures – KH₂C₆H₅O₇ and KH₂C₆H₅O₇(H₂O)₂ – have been communicated to the CSD (Kaduk & Stern, 2016a,b).

2. Structural commentary

The asymmetric unit of the title compound is shown in Fig. 1. The root-mean-square deviation of the non-hydrogen atoms in the Rietveld-refined and DFT-optimized structures is 0.052 Å (Fig. 2). The largest difference is 0.086 Å, at C1. The excellent 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 C3—C2—C1 angle of 116.5° is flagged as unusual [Z-score = 2.3; average = 112.7 (16)°]. The C2—C3—C2 angle of 106.0° is also flagged as unusual [Z-score = 2.5; average = 109.6 (14)°]. This hygroscopic compound was measured in situ, so perhaps slightly unusual geometry could be expected.

Figure 1 The asymmetric unit of trirubidium citrate, showing the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 2 Comparison of the refined and optimized structures of trirubidium citrate. The refined structure is in red, and the DFT-optimized structure is in blue.

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 a mirror plane. The terminal carboxyl­ate O11 atom and the central carboxyl­ate O15 atom chelate to Rb19, O11 and the central carboxyl­ate O16 atom chelate to a second Rb19, and the terminal carboxyl­ate O12 atom and the O17 hy­droxy group chelate to a third Rb19. The terminal O11–C1–C12 carboxyl­ate group acts as a bidentate ligand to Rb20. The Mulliken overlap populations and atomic charges indicate that the metal-oxygen bonding is ionic.

The Bravais–Friedel–Donnay–Harker (Bravais, 1866; Friedel, 1907; Donnay & Harker, 1937) morphology suggests that we might expect blocky morphology for trirubidium citrate, with {011} as the principal faces. A 4th-order spherical harmonic texture model was included in the refinement. The texture index was 1.001, indicating that preferred orientation was not significant for this rotated flat-plate specimen.

3. Supra­molecular features

The two independent Rb⁺ cations, Rb19 and Rb20, are seven- and eight-coordinate, with bond-valence sums of 0.99 and 0.92 valence units, respectively. The coordination polyhedra share edges and corners to form a three-dimensional network (Fig. 3). The only hydrogen bond is an intra­molecular one (Table 1) between the hy­droxy group and the central carboxyl­ate, with graph set S(5). The Mulliken overlap population indicates, by the correlation in Rammohan & Kaduk (2017a), that this hydrogen bond contributes 12.6 kcal mol⁻¹ to the crystal energy.

Table 1
Hydrogen-bond geometry (Å, °) for ramm077c_DFT

D—H⋯A	D—H	H⋯A	D⋯A	D—H⋯A
O17—H18⋯O16	0.981	1.862	2.572	126.7

Figure 3 Crystal structure of trirubidium citrate, viewed down the b axis.

4. Database survey

Details of the comprehensive literature search for citrate structures are presented in Rammohan & Kaduk (2017a). A reduced cell search of the cell of trirubidium citrate monohydrate in the Cambridge Structural Database (Groom et al., 2016) (increasing the default tolerance from 1.5 to 2.0%) yielded 221 hits, but combining the cell search with the elements C, H, O, and Rb only yielded no hits.

5. Synthesis and crystallization

A portion of Rb₃(C₆H₅O₇)(H₂O)₁ (Rammohan & Kaduk, 2017c) was heated at 14 K min⁻¹ to 463 K and held at that temperature for 10 min. The white solid was immediately transferred to a glass vial to cool.

6. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2. Diffraction data are displayed in Fig. 4. The white solid was ground in a mortar and pestle, blended with NIST 640b Si inter­nal standard in order to verify the calibrated goniometer zero error, packed into a standard Bruker D2 sample cell and protected from the atmosphere by an 8 µm thick Kapton window attached to the cell with Vaseline. The powder pattern indicated that the sample was still hydrated, so the blend was re-heated at 17 K min⁻¹ to 483 (10) K and held for 10 min. Re-measuring the powder pattern indicated that a new phase had formed.

Table 2
Experimental details

Crystal data
Chemical formula	3Rb^+·C6H5O7^3−
Mr	445.50
Crystal system, space group	Orthorhombic, Pnma
Temperature (K)	300
a, b, c (Å)	7.9096 (2), 10.7733 (3), 12.6986 (3)
V (Å^3)	1082.08 (7)
Z	4
Radiation type	Kα1, Kα2, λ = 1.540593, 1.544451 Å
Specimen shape, size (mm)	Flat sheet, 24 × 24
Data collection
Diffractometer	Bruker D2 Phaser
Specimen mounting	Standard PMMA holder with Kapton window
Data collection mode	Reflection
Scan method	Step
2θ values (°)	2θmin = 5.00 2θmax = 100.01 2θstep = 0.020
Refinement
R factors and goodness of fit	Rp = 0.020, Rwp = 0.025, Rexp = 0.023, R(F^2) = 0.048, χ^2 = 1.232
No. of parameters	57
No. of restraints	13
The same symmetry and lattice parameters were used for the DFT calculation. Computer programs: DIFFRAC.Measurement (Bruker, 2009), GSAS (Larson & Von Dreele, 2004), DIAMOND (Crystal Impact, 2015) and publCIF (Westrip, 2010).

Figure 4 Rietveld plot for the refinement of trirubidium 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 red tick marks indicate the positions of the peaks of the Si inter­nal standard.

The pattern was indexed using DICVOL06 (Louër & Boultif, 2007) on a primitive ortho­rhom­bic cell having a = 7.904, b = 12.701, c = 10.773 Å, and V = 1081.8 ų. These lattice parameters are 2.6, 1.8, and 3.3% larger than those of K₃C₆H₅O₇ (Rammohan & Kaduk, 2016e), and the volume is 7.9% larger. The compound was assumed to be isostructural to the K analogue (space group Pna2₁), and the coordinates of tripotassium citrate were used as the initial model for the Rietveld 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 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 hydrogen atoms were included at fixed positions, which were recalculated during the course of the refinement using Materials Studio (Dassault Systèmes, 2014). The U_iso value of the C atom in the central part of the citrate anion, and the C and O atoms on the exterior, were constrained to be equal, and the U_iso valuess of the hydrogen atoms were constrained to be 1.3 times those of the atoms to which they are attached.

The structure refined satisfactorily (R_wp = 0.0301 and reduced χ² = 1.828 for 69 variables) in space group Pna2₁ (the space group of the K analogue), but both the ADDSYM module of PLATON (Spek, 2009) and the Find Symmetry module of Materials Studio (Dassault Systèmes, 2014) suggested the presence of an additional centre of symmetry, and that the space group was Pnma (with a transformation of axes). The tolerance on the search was 0.12 Å. Because lower residuals were obtained with fewer parameters, we believe that Pnma is the correct space group.

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 seven h. The U_iso values from the Rietveld refinement were assigned to the optimized fractional coordinates.

Supporting information

Computing details

Data collection: DIFFRAC.Measurement (Bruker, 2009) for RAMM077C_phase_1. Molecular graphics: DIAMOND (Crystal Impact, 2015) for RAMM077C_phase_1. Software used to prepare material for publication: publCIF (Westrip, 2010) for RAMM077C_phase_1.

(RAMM077C_phase_1) Trirubidium citrate

Crystal data

3Rb^+·C6H5O7^3^−	c = 12.6986 (3) Å
Mr = 445.50	V = 1082.08 (7) Å^3
Orthorhombic, Pnma	Z = 4
Hall symbol: -P 2ac 2n	Dx = 2.735 Mg m^−3
a = 7.9096 (2) Å	T = 300 K
b = 10.7733 (3) Å

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

	x	y	z	Uiso*/Ueq
C1	0.8481 (8)	0.5192 (4)	0.1236 (8)	0.0129 (18)*
C2	0.9284 (10)	0.6373 (4)	0.0836 (8)	0.028 (5)*
C3	0.8129 (13)	0.75	0.1037 (8)	0.028 (5)*
C6	0.6630 (17)	0.75	0.0251 (11)	0.0129 (18)*
H7	1.03549	0.6517	0.12302	0.036 (6)*
H8	0.9452	0.62963	−0.00257	0.036 (6)*
O11	0.6988 (9)	0.4914 (7)	0.0961 (6)	0.0129 (18)*
O12	0.9397 (9)	0.4386 (5)	0.1695 (6)	0.0129 (18)*
O15	0.6865 (17)	0.75	−0.0763 (10)	0.0129 (18)*
O16	0.5218 (18)	0.75	0.0658 (10)	0.0129 (18)*
O17	0.7506 (12)	0.75	0.2090 (9)	0.0129 (18)*
H18	0.61955	0.75	0.19313	0.017 (2)*
Rb19	0.3442 (2)	0.97103 (16)	0.12323 (13)	0.0255 (6)*
Rb20	0.1377 (4)	0.25	0.29027 (16)	0.0255 (6)*

Geometric parameters (Å, º)

C1—C2	1.5102 (11)	O15—Rb20^viii	3.074 (13)
C1—O11	1.267 (3)	O15—Rb20^ix	3.053 (14)
C1—O12	1.272 (3)	O16—C6	1.231 (19)
C2—C1	1.5102 (11)	O16—Rb19	2.859 (8)
C2—C3	1.5410 (11)	O16—Rb19^i	2.859 (8)
C2—H7	0.996 (9)	O16—Rb20^viii	3.719 (13)
C2—H8	1.105 (10)	O17—C3	1.425 (3)
C3—C2	1.5410 (11)	O17—H18	1.056 (9)
C3—C2^i	1.5410 (11)	O17—Rb19^ii	3.280 (8)
C3—C6	1.5502 (11)	O17—Rb19^x	3.280 (8)
C3—O17	1.425 (3)	H18—O17	1.056 (9)
C6—C3	1.5502 (11)	Rb19—O11^i	2.855 (7)
C6—O15	1.300 (16)	Rb19—O11^xi	3.766 (7)
C6—O16	1.231 (19)	Rb19—O11^xii	2.815 (8)
H7—C2	0.996 (9)	Rb19—O12^xiii	3.395 (7)
H8—C2	1.105 (10)	Rb19—O12^xi	2.906 (7)
O11—C1	1.267 (3)	Rb19—O15^vii	3.074 (3)
O11—Rb19^i	2.855 (7)	Rb19—O16	2.859 (8)
O11—Rb19^ii	3.766 (7)	Rb19—O17^xi	3.280 (8)
O11—Rb19^iii	2.815 (8)	Rb20—O11^xiv	3.013 (7)
O11—Rb20^iv	3.013 (7)	Rb20—O11^xv	3.013 (7)
O12—C1	1.272 (3)	Rb20—O12^xvi	2.989 (6)
O12—Rb19^v	3.395 (7)	Rb20—O12^xvii	2.989 (6)
O12—Rb19^ii	2.906 (7)	Rb20—O12^xiv	3.178 (7)
O12—Rb20^vi	2.989 (6)	Rb20—O12^xv	3.178 (7)
O12—Rb20^iv	3.178 (7)	Rb20—O15^xviii	3.074 (13)
O15—C6	1.300 (16)	Rb20—O15^ix	3.053 (14)
O15—Rb19^vii	3.074 (3)	Rb20—O16^xviii	3.719 (13)
O15—Rb19^iii	3.074 (3)
C2—C1—O11	119.9 (3)	Rb19^xix—O17—Rb19^xxi	93.1 (3)
C2—C1—O12	119.3 (3)	O11^i—Rb19—O11^xxii	89.3 (2)
C2—C1—Rb19^xix	108.2 (5)	O11^i—Rb19—O12^xiii	155.0 (2)
O11—C1—O12	119.7 (3)	O11^i—Rb19—O12^xxiii	78.8 (2)
C1—C2—C3	111.0 (3)	O11^i—Rb19—O15^vii	85.2 (3)
C1—C2—H7	108.7 (5)	O11^i—Rb19—O16	66.7 (3)
C1—C2—H8	108.7 (7)	O11^i—Rb19—O17^xxiii	113.8 (3)
C3—C2—H7	107.3 (6)	O11^xxii—Rb19—O12^xiii	92.01 (17)
C3—C2—H8	107.1 (5)	O11^xxii—Rb19—O12^xxiii	154.38 (18)
H7—C2—H8	114.0 (8)	O11^xxii—Rb19—O15^vii	73.9 (3)
C2—C3—C2^i	104.0 (6)	O11^xxii—Rb19—O16	82.6 (3)
C2—C3—C6	110.3 (3)	O11^xxii—Rb19—O17^xxiii	132.2 (2)
C2—C3—O17	111.2 (3)	O12^xiii—Rb19—O12^xxiii	89.55 (15)
C2^i—C3—C6	110.3 (3)	O12^xiii—Rb19—O15^vii	71.3 (3)
C2^i—C3—O17	111.2 (3)	O12^xiii—Rb19—O16	138.2 (3)
C6—C3—O17	109.9 (3)	O12^xiii—Rb19—O17^xxiii	83.3 (2)
C3—C6—O15	121.9 (10)	O12^xxiii—Rb19—O15^vii	82.5 (3)
C3—C6—O16	115.1 (10)	O12^xxiii—Rb19—O16	112.5 (3)
O15—C6—O16	123.0 (11)	O12^xxiii—Rb19—O17^xxiii	73.4 (2)
C1—O11—Rb19^i	148.1 (7)	O15^vii—Rb19—O16	143.5 (3)
C1—O11—Rb19^xii	113.8 (6)	O15^vii—Rb19—O17^xxiii	144.9 (3)
C1—O11—Rb20^xx	102.8 (3)	O16—Rb19—O17^xxiii	70.9 (3)
Rb19^i—O11—Rb19^xii	90.7 (2)	O11^xxiv—Rb20—O11^xxv	119.3 (3)
Rb19^i—O11—Rb20^xx	84.7 (2)	O11^xxiv—Rb20—O12^xvi	156.4 (3)
Rb19^xii—O11—Rb20^xx	112.8 (3)	O11^xxiv—Rb20—O12^xvii	75.1 (2)
C1—O12—Rb19^v	105.2 (4)	O11^xxiv—Rb20—O12^xxiv	41.44 (11)
C1—O12—Rb19^xix	92.2 (6)	O11^xxiv—Rb20—O12^xxv	110.8 (2)
C1—O12—Rb20^vi	175.9 (6)	O11^xxiv—Rb20—O15^xviii	82.52 (19)
C1—O12—Rb20^xx	94.7 (3)	O11^xxiv—Rb20—O15^ix	110.68 (17)
Rb19^v—O12—Rb19^xix	107.8 (2)	O11^xxv—Rb20—O12^xvi	75.1 (2)
Rb19^v—O12—Rb20^vi	77.87 (16)	O11^xxv—Rb20—O12^xvii	156.4 (3)
Rb19^v—O12—Rb20^xx	156.85 (19)	O11^xxv—Rb20—O12^xxiv	110.8 (2)
Rb19^xix—O12—Rb20^vi	84.22 (19)	O11^xxv—Rb20—O12^xxv	41.44 (11)
Rb19^xix—O12—Rb20^xx	82.72 (18)	O11^xxv—Rb20—O15^xviii	82.52 (19)
Rb20^vi—O12—Rb20^xx	82.91 (15)	O11^xxv—Rb20—O15^ix	110.68 (17)
C6—O15—Rb19^vii	100.4 (3)	O12^xvi—Rb20—O12^xvii	85.7 (3)
C6—O15—Rb19^xii	100.4 (3)	O12^xvi—Rb20—O12^xxiv	155.67 (15)
C6—O15—Rb20^viii	115.2 (9)	O12^xvi—Rb20—O12^xxv	92.37 (19)
C6—O15—Rb20^ix	161.1 (10)	O12^xvi—Rb20—O15^xviii	81.1 (2)
Rb19^vii—O15—Rb19^xii	155.8 (5)	O12^xvi—Rb20—O15^ix	77.4 (2)
Rb19^vii—O15—Rb20^viii	80.0 (2)	O12^xvii—Rb20—O12^xxiv	92.37 (19)
Rb19^vii—O15—Rb20^ix	82.1 (3)	O12^xvii—Rb20—O12^xxv	155.67 (15)
Rb19^xii—O15—Rb20^viii	80.0 (2)	O12^xvii—Rb20—O15^xviii	81.1 (2)
Rb19^xii—O15—Rb20^ix	82.1 (3)	O12^xvii—Rb20—O15^ix	77.4 (2)
Rb20^viii—O15—Rb20^ix	83.6 (3)	O12^xxiv—Rb20—O12^xxv	79.5 (2)
C6—O16—Rb19	123.6 (2)	O12^xxiv—Rb20—O15^xviii	122.6 (2)
C6—O16—Rb19^i	123.6 (2)	O12^xxiv—Rb20—O15^ix	78.5 (2)
Rb19—O16—Rb19^i	112.8 (5)	O12^xxv—Rb20—O15^xviii	122.6 (2)
C3—O17—H18	99.2 (8)	O12^xxv—Rb20—O15^ix	78.5 (2)
C3—O17—Rb19^xix	122.1 (3)	O15^xviii—Rb20—O15^ix	150.6 (4)
C3—O17—Rb19^xxi	122.1 (3)

Symmetry codes: (i) x, −y+3/2, z; (ii) x+1/2, −y+3/2, −z+1/2; (iii) −x+1, y−1/2, −z; (iv) x+1/2, −y+1/2, −z+1/2; (v) x+1, −y+3/2, z; (vi) x+1, y, z; (vii) −x+1, −y+2, −z; (viii) −x+1/2, y+1/2, z−1/2; (ix) −x+1, −y+1, −z; (x) x+1/2, y, −z+1/2; (xi) x−1/2, −y+3/2, −z+1/2; (xii) −x+1, y+1/2, −z; (xiii) x−1, −y+3/2, z; (xiv) x−1/2, −y+1/2, −z+1/2; (xv) x−1/2, y, −z+1/2; (xvi) x−1, y, z; (xvii) x−1, −y+1/2, z; (xviii) −x+1/2, y−1/2, z+1/2; (xix) x+3/2, −y+5/2, −z+3/2; (xx) x+3/2, −y+3/2, −z+3/2; (xxi) x+3/2, y, −z+3/2; (xxii) −x+1, y+3/2, −z; (xxiii) x+1/2, −y+5/2, −z+3/2; (xxiv) x+1/2, −y+3/2, −z+3/2; (xxv) x+1/2, y, −z+3/2.

(RAMM077C_phase_2)

Crystal data

Si	V = 160.20 Å^3
Mr = 28.09	Z = 8
Cubic, Fd3m	Dx = 2.329 Mg m^−3
Hall symbol: -F 4vw 2vw	T = 300 K
a = 5.43105 Å

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

	x	y	z	Uiso*/Ueq
Si1	0.125	0.125	0.125	0.01*

Geometric parameters (Å, º)

Si1—Si1^i	2.3517	Si1—Si1^iii	2.3517
Si1—Si1^ii	2.3517	Si1—Si1^iv	2.3517
Si1^i—Si1—Si1^ii	109.4712	Si1^ii—Si1—Si1^iii	109.4712
Si1^i—Si1—Si1^iii	109.4712	Si1^ii—Si1—Si1^iv	109.4712
Si1^i—Si1—Si1^iv	109.4712	Si1^iii—Si1—Si1^iv	109.4712

Symmetry codes: (i) x+1/4, y+1/4, −z; (ii) −z, x+1/4, y+1/4; (iii) y+1/4, −z, x+1/4; (iv) −x, −y, −z.

(ramm077c_DFT)

Crystal data

C6H5O7Rb3	b = 10.7733 Å
Mr = 445.50	c = 12.6986 Å
Orthorhombic, Pnma	V = 1082.08 Å^3
a = 7.9096 Å	Z = 4

Data collection

h = →	l = →
k = →

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

	x	y	z	Uiso*/Ueq
C1	0.85652	0.51237	0.11762	0.01290*
C2	0.92710	0.63666	0.08156	0.02780*
H7	1.04404	0.65330	0.12425	0.03610*
H8	0.95879	0.63156	−0.00199	0.03610*
O11	0.70573	0.48606	0.09469	0.01290*
O12	0.95620	0.44175	0.16822	0.01290*
Rb19	0.34329	0.97183	0.12807	0.02550*
C3	0.81408	0.75000	0.09868	0.02780*
C6	0.65846	0.75000	0.02369	0.01290*
O15	0.68502	0.75000	−0.07431	0.01290*
O16	0.51559	0.75000	0.06782	0.01290*
O17	0.75259	0.75000	0.20645	0.01290*
H18	0.62975	0.75000	0.19609	0.01680*
Rb20	0.14960	0.25000	0.29368	0.02550*

Bond lengths (Å)

C1—C2	1.521	C3—C2^i	1.529
C1—O11	1.260	C3—C6	1.556
C1—O12	1.270	C3—O17	1.452
C2—C3	1.529	C6—O15	1.262
C2—H7	1.087	C6—O16	1.261
C2—H8	1.092	O17—H18	0.981

Symmetry code: (i) x, −y+3/2, z.

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O17—H18···O16	0.981	1.862	2.572	126.7