Chiral, Racemic, and Meso-Lithium Tartrate Framework Polymorphs: A

Article pubs.acs.org/crystal

Chiral, Racemic, and Meso-Lithium Tartrate Framework Polymorphs: A Detailed Structural Analysis Hamish H.-M. Yeung,† Monica Kosa,‡ Michele Parrinello,§ and Anthony K. Cheetham*,† †

Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, U.K., CB2 3QZ Department of Chemistry, Bar Ilan University, Faculty of Exact Sciences, Ramat Gan IL-52900, Israel § Department of Chemistry and Applied Biosciences, ETH Zurich, USI-Campus, Via G. Buffi 13, 6900 Lugano, Switzerland ‡

S Supporting Information *

ABSTRACT: Following our previous report of five anhydrous lithium tartrates 1−5 (tart = C4H4O62−), we have synthesized and solved the single crystal structures of four new I1O2 inorganic−organic frameworks, all with the same chemical formula, Li2(tart). Reactions between lithium acetate and the meso, chiral, and racemic isomers of tartaric acid in water:ethanol mixtures have yielded two new polymorphs of Li2(meso-tart) in space groups P21/c 6 and Cc 7, racemic Li2(D,L-tart) in P21/c 8, and chiral Li2(L-tart) in C2 9. Hydrogen bond graph set analysis was adapted for use with framework materials and employed here to examine the motifs displayed by the eight anhydrous dilithium tartrates 2−9. A variety of hydrogen-bonding patterns and dimensionalities are observed in this system, and the relative hydrogen bond strengths are found to correlate well with O−H stretching frequency shifts in the FTIR spectra. The relative formation energies of the framework isomers have been calculated by DFT methods, using schemes that include dispersion correction, zero-point vibrational energy, and thermal vibrations at room temperature. Although the energy ordering depends slightly on the scheme used, it is generally found to relate to the differences in crystallographic density and hydrogen bond strength rather than other structural features.

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amorphous.6 This leads us to believe that nonporous inorganic−organic framework materials may offer key advantages for such applications, including superior stability and longevity compared to conventional liquid phase or amorphous electrolytes, and will be free of complications arising due to residual solvent within porous frameworks. We are therefore exploring the large diversity of nonporous lithium−organic frameworks and investigating these materials in order to understand and improve their lithium mobility for use as rechargeable battery electrolytes. The lithium tartrates described in this manuscript do not exhibit the unusual redox behavior that is seen in the aromatic dicarboxylates reported by Tarascon and co-workers5a but adopt a very interesting range of structures. Tartaric acid has three isomers, L-, D- and meso-tartaric acid (Scheme 1), which crystallize both separately and as a racemate of the L- and D-enantiomers, D,L-tartaric acid. Chiral inorganic− organic frameworks involving tartaric acid and other ligands are of great interest for enantiomorphic separations and catalysis, magnetic, optical, and dielectric properties.2a,e,7 Before our recent publication,8 the Cambridge Structural Database contained just three lithium tartrates,9 but the diversity shown by other systems, such as magnesium7e and other

INTRODUCTION Inorganic−organic frameworks are highly regarded as potential new materials for diverse applications in energy storage, smart devices, and other technologies.1 They are composed of metal centers connected by organic ligands in an infinite, regular fashion, and form 1-, 2-, or 3-dimensional (1D, 2D, and 3D, respectively) structures. While porous inorganic−organic frameworks, also known as metal−organic frameworks (MOFs) or porous coordination polymers (PCPs), have gained considerable attention for their gas storage and molecular separation capabilities,2 nonporous frameworks are increasingly being investigated for magnetic, optical, and electrical properties.3 We are interested in lithium-rich frameworks due to their potential to combine the properties of the lightest metallic element, high electropositivity, high charge density, and large standard electrode potential, with systematic and tunable architectures derived from the multitudes of possible organic linkers. Gas uptake in porous frameworks has been shown to be increased by lithium insertion, and exposed lithium sites can lead to enhanced heats of adsorption;4 furthermore, lithium may contribute to a higher gravimetric capacity than may be expected with other, heavier metals. Inorganic−organic frameworks are also being investigated for redox behavior and ionic conductivity for fuel cell and battery technologies.5 Contrary to previous understanding, materials such as poly(ethylene oxide)6:LiXF6 (X = P, As, or Sb) have been shown to have higher ionic conductivity in the crystalline state than when © 2013 American Chemical Society

Received: May 14, 2013 Revised: June 17, 2013 Published: June 17, 2013 3705

dx.doi.org/10.1021/cg400741b | Cryst. Growth Des. 2013, 13, 3705−3715

Crystal Growth & Design

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Scheme 1. Configurations of L-, D-, and Meso-Tartaric Acida

been carried out. In this work, we propose a slight modification to the graph set theory developed by Etter, Bernstein, and others,15 which allows an extension of such widely used analysis of hydrogen bonding in molecular crystals to hydrogen bonding in framework materials. Upon examining dilithium tartrates 2− 9, we find several different motifs and hydrogen bond network dimensionalities from zero-dimensional (0D) to 2D. Furthermore, there is a good agreement between the relative hydrogen bond strengths and the FTIR spectral shifts in the O−H region.

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a

EXPERIMENTAL METHODS

Synthesis. All reagents, lithium acetate dihydrate (98%, Fisher Scientific U.K.), D,L-tartaric acid (99.5%, Fisher Scientific U.K.), Ltartaric acid (>99%, Fisher Scientific U.K.), and meso-tartaric acid monohydrate (≥97%, Sigma-Aldrich) and solvents, ethanol (reagent grade, Fisher Scientific U.K.) and in-house deionized water, were used as received under aerobic conditions. Reactions were carried out in 4 and 12 mL borosilicate glass vials with PTFE-lined caps (Fisher Scientific U.K.) and 23 mL PTFE-lined stainless steel autoclaves obtained from Parr Instrument Company.16 [Li2(meso-C4H4O6)] 6. A solution of lithium acetate dihydrate (2 mmol) in water:ethanol (1:2, 5 mL) was layered under a solution of meso-tartaric acid monohydrate (1 mmol) in water:ethanol (1:2, 5 mL) in a 23 mL PTFE-lined stainless steel autoclave, which was heated at 125 °C. After three days, the autoclave was cooled to 25 °C and the product, colorless crystals of 6 (124 mg, 76%), was filtered, washed (water:ethanol 1:2), and dried in air. Another bulk sample used for further analysis was synthesized at 100 °C. Elemental analysis found C, 29.65% and H, 2.47% (calculated for C4H4Li2O6: C, 29.67% and H, 2.49%). [Li2(meso-C4H4O6)] 7. A solution of lithium acetate dihydrate (2 mmol) in water:ethanol (1:2, 5 mL) was layered under a solution of meso-tartaric acid monohydrate (1 mmol) in water:ethanol (1:2, 5 mL) in a 12 mL borosilicate vial, which was heated to 60 °C. After three days, it was cooled to 25 °C, and the contents, colorless crystals of 8 (96 mg, 59%), were filtered, washed (water:ethanol 1:2), and dried in air. Another bulk sample used for further analysis was synthesized at room temperature using a water:ethanol ratio for the acid solution of 1:4, and dryed in air at 60 °C. Elemental analysis found C, 29.43% and H, 2.51% (calculated for C4H4Li2O6: C, 29.67% and H, 2.49%). [Li2(D,L-C4H4O6)] 8. A solution of lithium acetate dihydrate (2 mmol) in water:ethanol (1:4, 5 mL) was layered under a solution of D,L-tartaric acid (1 mmol) in water:ethanol (1:9, 5 mL) in a 12 mL borosilicate vial, which was left to stand at 25 °C. After six days, the vial contained colorless plates suitable for single crystal X-ray diffraction studies. A bulk sample used for further analysis was synthesized as follows: a solution of lithium acetate dihydrate (2 mmol) in water:ethanol (1:2, 5 mL) was layered under a solution of D,L-tartaric acid (1 mmol) in water:ethanol (1:4, 5 mL) in a 23 mL PTFE-lined stainless steel autoclave, which was heated at 100 °C. After three days, the autoclave was cooled to 25 °C and the product, colorless crystals of 8 (30 mg, 18%), was filtered, washed (water:ethanol 1:4), and dried in air. Elemental analysis found C, 29.45% and H, 2.39% (calculated: C, 29.67% and H, 2.49%). [Li2(L-C4H4O6)] 9. A solution of lithium acetate dihydrate (2 mmol) in water:ethanol (1:2, 5 mL) was layered under a solution of L-tartaric acid (1 mmol) in water:ethanol (1:4, 5 mL) in a 23 mL PTFE-lined stainless steel autoclave, which was heated at 125 °C. After three days, the autoclave was cooled to 25 °C and colorless crystals were handpicked from the reaction product for single crystal X-ray diffraction studies. A purer sample of 9 (containing ∼20% 2 by PXRD) for further analyses was obtained as follows: lithium acetate dihydrate (2 mmol), L-tartaric acid (1 mmol), water (3 mL), and ethanol (7 mL) were placed in a 23 mL PTFE-lined stainless steel autoclave, which was heated at 150 °C. After 7 days, the autoclave was cooled to 25 °C and the product, colorless rods (93 mg, 57%), was filtered, washed in solvent, and dried at 60 °C overnight. A phase-pure sample could not be obtained for elemental analysis.

C is shown as grey spheres, H as white, and O as red.

alkaline earth metal tartrates,7f hinted at the possibility that others might exist. Our preliminary investigations into lithium tartrates yielded the anhydrous crystalline phases 1−5, for which initial energy calculations were undertaken.8 The lithium hydrogen tartrate, 1, was found to have a much higher formation energy than the dilithium tartrates, 2−5, due to having fewer Li atoms per ligand moiety. The range of energies in the framework isomers, 2−5, was found to increase when vibrational contributions within the harmonic approximation at ambient temperature were included, indicating the importance of full energetic analysis for framework materials. The data also revealed interesting energy landscapes and complex phase behavior, the former of which is the subject of this article and the latter of which will be published in a forthcoming paper.10 In this work, we describe and compare four new anhydrous forms of dilithium tartrate, 6−9, whose structures were solved by single crystal X-ray diffraction methods. Like 2−5, they are 3D nonporous frameworks with I1O2 connectivity, as defined by Cheetham et al.3a Despite the topological similarities between 2−9, several subtle differences in the framework architectures arise from the ligand isomers used, their conformations, binding modes to Li, hydrogen bonding, and the relative orientations of inorganic and organic units. Such variety in these compounds, all with identical elemental composition, Li2(C4H4O6), and similar ligand (C−H, C−C, C−O, and O−H) and framework (Li−O) bonding, provide an opportunity to examine structure-energy relationships of inorganic−organic frameworks in more detail. We have therefore calculated the energies of 2−9, using DFT methods with dispersion corrections, including electronic, zero point vibrational, and thermal vibrational contributions, and we have analyzed the correlations between the energy and different structural parameters. We find that the relative energies are primarily affected by density-related dispersion effects and interligand hydrogen bonding. Hydrogen bonding is known to be important in directing the structures and host−guest behavior of inorganic−organic frameworks11 and it can also be responsible for physical properties such as catalysis,12 mechanical strength,13 and ferroelectricity.3c,f Indeed, the first reported ferroelectric material was an alkali metal tartrate framework, KNa(LC4H4O4)·4H2O, otherwise known as Rochelle Salt, whose dielectric properties are a result of switchable hydrogen bond orientation.14 However, no systematic structural analysis of hydrogen bonding in inorganic−organic frameworks has yet 3706



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Table 1. Summary of Crystal Data for Lithium Tartrates 6−9 crystal size (mm) crystal system space group T (K) a (Å) b (Å) c (Å) α (°) β (°) γ (°) V (Å3) asymmetrical unit Z dcalc (g cm−3) μ (mm−1) reflections collected unique reflections observed data [I > 2σ(I)] parameters Rint R1 wR2 [I > 2σ(I)] R1 (all data) wR2 (all data) GOF

Li2(meso-tart) (6)

Li2(meso-tart) (7)

Li2(D,L-tart) (8)

Li2(L-tart) (9)

0.4 × 0.2 × 0.03 monoclinic P21/c 120(2) 6.4777(5) 5.0082(4) 8.9897(8) 90 95.679(8) 90 290.21(4) C2H2LiO3 2 1.853 0.171 1215 669 538 58 0.0296 0.0459 0.1149 0.0612 0.1320 1.041

0.15 × 0.15 × 0.02 monoclinic Cc 120(2) 9.6880(5) 5.3821(2) 11.4090(6) 90 93.959(5) 90 593.47(5) C4H4Li2O6 4 1.813 0.167 2956 1344 1240 115 0.0269 0.0343 0.0749 0.0386 0.0778 1.061

0.5 × 0.4 × 0.4 monoclinic P21/c 120(2) 12.0809(15) 4.9703(6) 9.4471(11) 90 91.241(11) 90 567.12(12) C4H4Li2O6 4 1.897 0.175 1885 1885 1478 116 0.0 (merged data) 0.0495 0.1238 0.0617 0.1288 0.976

0.8 × 0.3 × 0.2 monoclinic C2 120(2) 15.153(6) 5.0136(8) 10.376(4) 90 131.89(6) 90 586.8(3) C4H4Li2O6 4 1.833 0.169 1316 1092 1074 115 0.0077 0.0221 0.0578 0.0225 0.0581 1.045

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Crystal Structure Determinations. The relevant details of structure determinations are presented in the Supporting Information. Crystal structure determinations by X-ray diffraction were performed on an Oxford Diffraction Gemini E Ultra diffractometer equipped with dual source Cu radiation (λ = 1.54184 Å, operating at 40 kV and 40 mA with confocal mirrors to increase flux) and Mo radiation (λ = 0.7107 Å, operating at 50 kV and 40 mA). Data were collected at 120 K using ω scans, and the mean detector area resolution was 10.4 pixels mm−1. Data collection, cell determination and refinement, intensity integration, and face indexation were performed using CrysAlisPro.17 Structures were solved by direct methods, and full matrix least-squares refinements against |F2| were carried out using the SHELXTL-PLUS package of programs18 within the WinGX interface.19 All nonhydrogen atoms were refined anisotropically; hydrogen atoms were then inserted using a riding model and refined with isotropic displacement parameters constrained to 1.2 and 1.5 times those of their adjacent carbon (nonmethyl) and oxygen and methyl carbon atoms, respectively. Visualization of structures was carried out using the Diamond20 and Mercury21 programs. Powder X-ray Diffraction. Data were collected on a Bruker D8 theta/theta (fixed sample) diffractometer with a LynxEye positionsensitive detector, in Bragg−Brentano parafocusing geometry, reflection mode using Cu Kα radiation (λ = 1.5418 Å). Scans were taken over an angular range of 5°−60° (2θ) with a step size of 0.01°. Analysis of the data was carried out using the X’Pert HighScore Plus program.22 Thermal Behavior. Thermogravimetric analysis was performed using a TA Instruments Q500 TGA instrument with 9−13 mg samples in an air flow of 60 mL min−1 at a heating rate of 10 °C min−1 from room temperature to 700 °C. Infrared Spectroscopy. Fourier-transform infrared spectroscopy was carried out using a Bruker Tensor 27 infrared spectrometer with a diamond-attenuated total reflectance (ATR) attachment in absorbance mode. Multiple spectra were recorded in the range of 4000−500 cm−1 and subsequently averaged. Elemental Analysis. CHN analysis was performed on samples of mass 2−5 mg by the Microanalysis Service at the University of Cambridge Chemical Laboratory.

THEORETICAL CALCULATIONS The formation energies involving electronic energy only, ΔEelec, of 1−5 were calculated using the CP2K code23 in our previous article and the methods described in detail therein.8 ΔEelec of the newly reported dilithium tartrates, 6−9, and the formation energies including dispersion correction, ΔEelec (PBE + D2), of all dilithium tartrates, 2−9, were also calculated using the CP2K code. In addition, the formation energies of 2−9 have been calculated using the PAW augmented pseudopotentials24 and an explicit k-point sampling scheme, as implemented in the VASP code.25 The formation energies of 2−9 involving the electronic energy, ΔEelec, zero-point vibrational energy, ZPVE, and vibrational contributions at 298.15 K, ΔEvib298.15, were calculated using the PBE functional,26 alone and with local dispersion corrections,27 D2 and D3.28 The computed relative energies were converted to units of kJ mol−1 of formula unit (i.e., Li2C4H4O6).

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RESULTS AND DISCUSSION The crystal structures of phases 1−5 were described previously.8 The crystal structures of four new anhydrous lithium tartrates, 6−9, were solved by single-crystal X-ray diffraction methods. A summary of the crystal data for the new phases can be found in Table 1 and the Ortep extended asymmetric units shown in Figures S10−S14 of the Supporting Information. Structure of Li 2 (meso-C 4 H 4 O 6 ) in P2 1 /c 6. The asymmetric unit of 6 consists of one lithium atom and half of a tartaric acid ligand, which is completed by equivalent atoms generated by inversion symmetry (Figure S11 of the Supporting Information). Each lithium atom is coordinated by four oxygen atoms in a tetrahedral manner. The tartrate carboxylate groups each bond to three lithium atoms, and the tartrate hydroxyl oxygen atoms bond to one lithium atom each. 3707



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oxygen atoms. The tartaric acid torsion angle is unusually small [62.0(2)°], resulting in gauche carboxylate groups. The resulting structure is again chains of corner-sharing LiO4 tetrahedra, connected by tartaric acid ligands to form a 3D, I1O2 framework (Figure 2). The chains of tetrahedra are

Li−O bond distances are in the range of 1.908(4)− 1.958(4) Å, a smaller distribution than other similar structures. Bond angles within the tetrahedron vary a little more, from 101.8(2)° to 118.9(2)°. By symmetry, the carbon skeleton of the tartaric acid moiety has a torsion angle of 180°. The ligand may be classed as μ8, κ6; that is, it binds to eight different lithium atoms through all six oxygen atoms. The resulting arrangement is chains of corner-sharing distorted LiO4 tetrahedra bridged via the carboxylate groups of the tartaric acid ligands, which are arranged in a herringbone array to form a 2D sheet, as in phases 2, 5, and 8 (Figure 1a). The apical positions on the tetrahedra

Figure 1. Structure of Li2(meso-C4H4O6) 6 (a) viewed down [1 0 1̅ ], showing chains of LiO4 tetrahedra bridged by a 2D herringbone array of tartaric acid ligands and (b) viewed down the chains of cornersharing LiO4 tetrahedra with sheets horizontal. C, H, and O atoms and LiO4 tetrahedra are colored gray, white, red, and green, respectively.

Figure 2. Structure of Li2(meso-C4H4O6) 7 (a) viewed down [1 1 0], showing chains of LiO4 tetrahedra bridged by tartaric acid ligands (chains on the right side run into the picture) and (b) viewed down the c axis, showing the relative orientations of the inorganic chains (shaded darker in the layer below). C, H, and O atoms and LiO4 tetrahedra are colored gray, white, red, and green, respectively.

are occupied by hydroxyl oxygen atoms of the ligands in sheets above and below, which link the sheets to form a 3D, I1O2 framework, as defined by Cheetham et al. (Figure 1b).3a Structure of Li2(meso-C4H4O6) in Cc 7. The asymmetric unit of 7 consists of one complete tartaric acid ligand and two crystallographically independent lithium atoms (Figure S12 of the Supporting Information). In a similar manner to 3 and 4,8 each tartaric acid ligand coordinates to six lithium atoms in a μ6, κ6 fashion. At each end of the ligand, separate lithium atoms are coordinated by each of the carboxylate oxygen atoms in a monodentate fashion and another is chelated by neighboring hydroxyl and carboxylate oxygen atoms. The lithium environments are distorted tetrahedra, with Li−O distances in the range of 1.911(4)−2.014(4) Å and bond angles from 82.10(2)° to 126.5(2)°. The two smallest angles involve the chelating

arranged in layers in the ab-plane, in which the chains are parallel. However, unlike all the other dilithium tartrates, the chains in adjacent layers run in different directions, making an angle of approximately 58°. Structure of Li2(D,L-C4H4O6) in P21/c 8. The asymmetric unit of 8 consists of one complete tartaric acid ligand and two lithium atoms (Figure S13 of the Supporting Information). The lithium atoms are coordinated by four oxygen atoms in a distorted tetrahedron, with bond distances 1.908(4)−2.001(4) Å and bond angles from 99.9(2)° to 124.6(2)°. The ligand has a near-linear torsion angle of 172.7(2)° and, as in phase 6, it coordinates to eight lithium atoms in a μ8, κ6 fashion. The resulting structure is an I1O2, 3D framework comprised of chains of corner-sharing LiO4 tetrahedra connected by tartaric acid ligands in 2D herringbone arrays and capped by the 3708



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hydroxyl groups of ligands above and below (Figure 3). The presence of a glide plane results in both L- and D-tartaric acid

Figure 4. Structure of Li2(L-C4H4O6) 9: (a) one layer, viewed down the a axis, showing chains of LiO4 tetrahedra bridged by a 2D array of tartaric acid ligands and (b) viewed down the chains of corner-sharing LiO4 tetrahedra with sheets horizontal. C, H, and O atoms and LiO4 tetrahedra are colored gray, white, red, and green, respectively.

Figure 3. Structure of Li2(D,L-C4H4O6) 8 (a) viewed down [1 0 1̅ ], showing chains of LiO4 tetrahedra bridged by a 2D herringbone array of tartaric acid ligands and (b) viewed down the chains of cornersharing LiO4 tetrahedra with sheets horizontal. C, H, and O atoms and LiO4 tetrahedra are colored gray, white, red, and green, respectively.

along the a axis, the hydroxyl groups in adjacent arrays point in opposite directions. In a similar manner to 2, 5, 6, and 8, the hydroxyl oxygen atoms link the sheets by filling the apical positions on the LiO4 tetrahedra, giving rise to a 3D, I1O2 framework (Figure 4b). Structural Comparison of Dilithium Tartrates 2−9. The calculated relative enthalpies (298.15 K) of the anhydrous dilithium tartrates 2−9 range from 5.18 kJ mol−1 to −18.01 kJ mol−1 at the PBE + D3 level of theory (see later section and Table S2 in the Supporting Information). These eight framework isomers are all I1O2 frameworks with the same elemental formula, Li2(C4H4O6), and the same number of covalent (C−C, C−H, C−O, O−H) and coordination (Li−O) bonds per formula unit. The variation in energy between frameworks must therefore arise from other factors, such as distortion in the lithium coordination sphere and ligand conformation, or noncovalent interactions such as hydrogen bonding and dispersion forces, which are weaker than the bonds that give rise to extended framework connectivity but are nonetheless important in directing the structures and properties of such materials.3c,f,11−14 Indeed, hydrogen bonding and density are expected to have significant effects on the relative energies of 2−9, as predicted by the infrared and density rules for polymorphs in general.29 These experimentally determined structural variations are summarized in Table 2. Use of chiral, racemic, and meso-tartrate ligands results in framework isomers with different space groups. Densities vary by up to 10% due to the packing of the inorganic LiO4 units

enantiomers being present in the structure in equal proportions, therefore the overall structure is achiral. Structure of Li2(L-C4H4O6) in C2 9. The asymmetric unit of 9 consists of two halves of tartaric acid ligands and two crystallographically independent lithium atoms (Figure S14 of the Supporting Information). Two crystallographically distinct tartaric acid moieties are completed by symmetric generations of the corresponding atoms. In a similar manner to 2, 5, 6, and 8, each ligand coordinates to eight lithium atoms in a μ8, κ6 fashion: at each end of the ligand, one carboxylate oxygen atom and the hydroxyl oxygen atom coordinate to one lithium atom each, and the other carboxylate oxygen atom bridges between two crystallographically identical lithium atoms. Li−O bond distances are 1.887(3)−1.986(3) Å. Each lithium atom is coordinated by four oxygen atoms in a distorted tetrahedron [bond angles from 101.76(13)° to 122.43(13)°]. In contrast to 2, 5, 6, and 8, the tartaric acid moieties have an almost eclipsed conformation, with torsion angles of 138.6(2)° and 140.6(2)°. The overall structure of 9 consists of corner-sharing LiO4 tetrahedra in 1D chains, bridged by chiral tartaric acid moieties in a 2D array (Figure 4a). There are two crystallographically distinct arrays, each containing a single ligand and lithium atom. The structure of each array is almost identical, with hydrogen bonding occurring within sheets between neighboring hydroxyl groups and carboxylate oxygen atoms. Notably, when viewed 3709



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Table 2. Summary of Structural Variation in the Dilithium Tartrates 2−9 2

3

4

5

6

7

8

9

ligand isomer

L-

L-

meso-

D, L -

meso-

meso-

D, L -

L-

space group density (g cm−3) average Li−O bond valence suma LiO4 tetrahedral distortion, δtet (°)b average C4 torsion angle (°) H-bond strength, δOH (cm−1)c

P212121 1.77 1.1 6.65 177 141.5

C2221 1.76 1.13 12.62 151 301

P21/c 1.72 1.15 13.34 180 n/a

C2/c 1.82 1.12 4.93 174 98

P21/c 1.85 1.13 5.01 180 289

Cc 1.81 1.06 14.86 62 389

P21/c 1.90 1.1 6.64 173 131

C2 1.83 1.14 5.92 139 221.5

a

This is as defined by Brese et al.30 bThis is as defined by Harding.31 cDefined here as the shift in the O−H stretching frequency in the FTIR spectrum, relative to the least-shifted peak in 8. Peak assignments and shift values for individual hydroxyl groups are shown in Table S1 of the Supporting Information. A bulk product of 4 could not be obtained for FTIR analysis.

Figure 5. Hydrogen bonding motifs in anhydrous dilithium tartrates. Clockwise, from top left: (a) 2, (b) 5, (c) 8, (d) 9, (e) 7, (f) 4, and (g) 3. Center: (h) 6. Crystallographically distinct hydrogen bonds in a given structure are shown with different colored dashed lines and labels corresponding to those in Table S1 of the Supporting Information.

Hydrogen bonding in the anhydrous dilithium tartrates 2−9. Examination of the crystal structures of 2−9 reveals, in addition to the variation in framework bonding, a wide range of hydrogen-bonding motifs between hydroxyl groups and carboxylate oxygen atoms (Figure 5). In the fields of organic molecules, polymorphs, and cocrystals, graph set theory developed by Etter, Bernstein, and others has been widely used to describe hydrogen-bonding motifs and patterns between discrete molecules.15 However, an extended inorganic−organic array can be thought of as one single molecule: the ligand units are linked to each other through coordination bonding with the metal centers, and so all hydrogen bonds between ligands are essentially intramolecular and would be denoted “S” (i.e., self-hydrogen bonding) with conventional graph set theory.34 In the analysis of inorganic− organic framework structures, we propose to ignore the coordination bonding to metal centers and use the organic ligands and guest molecules as the individual units to be linked by hydrogen bonds, rather than each molecule. This has the advantage of considering hydrogen bonding as separate from the bonding of the main framework architecture, and so their

and the organic ligands, which results in changes in the Li bond valence sum,30 tetrahedral angle distortion, δtet,31 and ligand C4 torsion angle. The range of bond valence sums, 1.06−1.15, is as expected for monovalent Li32 and reflects the variation in the Li−O bond length. O−Li−O angles also vary considerably, resulting in two groups, according to the binding mode to lithium: structures with δtet ≈ 5° exhibit monodentate binding, while those with δtet ≈ 13° exhibit chelation modes. Most structures have a trans ligand conformation, which reduces the intramolecular steric clash and ionic repulsion between carboxylate groups. However, the L-tartrates 3 and 9 have C4 torsion angles approaching unfavorable eclipsing conformations, while meso-tartrate 7 has a gauche conformation. It is notable that the ligand moieties in the structures of lithium tartrates 1−9 and reported hydrated phases generally retain the conformation found in the crystal structures of the parent acid (i.e., trans-C4 backbone for L- and D,L-tartaric acids and gaucheC4 for meso-tartaric acid).33 Only with higher synthesis temperatures, resulting in 4, or strong thermodynamic driving forces (6 and 9), are different conformations obtained. 3710



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Table 3. Summary of Hydrogen Bonding in 2−9

a

distinct OH groups

interligand H-bonds per ligand

intraligand H-bonds per ligand

H-bond dimensionality

H-bond unitary CAGS notation

higher order CAGS notation

2a

4

2

0.5

1

C(5)C(5)C(6)C(6)S(5)

3 4 5 6 7 8a

1 1 2 1 2 2

2 0 2 2 2 2

0 2 0 0 0 1

1 0 1 1 2 2

C(5)[R22(12)] S(6) C(5)C(6) C(5)[R22(12)] C(5)C(5) C(5)C(5)S(5)

9

2

2

0

1

C(5)[R22(12)], C(5)[R22(12)]

N2:R12(7), R12(7), C21(7); N3: R22(7) − N2:R12(7) R12(7) − N2:C22(12), C22(12), R44(24) N2:C22(12), C22(12), R44(24), C21(4) −

Phases 2 and 8 contain bifurcated hydrogen bonds, which are included in both interligand and intraligand counts.

chains in the b direction; combined, they result in a sevenmembered ring with CAGS notation R12(7). There are three distinct hydrogen bonds in the structure of 8 (Figure 5e), the strongest likely to be between the hydroxyl oxygen O6 and neighboring carboxylate oxygen O4 [D−A distance 2.696(2) Å, D−H···A angle 170(3)°]. The hydroxyl group O3/H4 participates in a bifurcated hydrogen bond, donating to both O1 and O2 in inter- and intraligand fashion, respectively. The interligand hydrogen bonds result in chains, which run perpendicular to each other, giving rise to a 2D network and the unitary CAGS notation C(5)C(5)S(5). Notably, the different hydrogen bond motifs also combine to give binary graph sets R44(24) and C21(4). Hydrogen Bond Strength and FTIR Spectral Shift. The relative strengths of hydrogen bonds in 2−9 can be indirectly observed in the shifts of O−H stretching frequencies in the compounds’ FTIR spectra shown in Table 2. Hydrogen bonding causes a weakening of the donor O−H σ bond, which increases with the strength of the hydrogen bond (i.e., the linearity and proximity of the O−H···O interaction, corresponding to the top left corner of Figure 6).8,35 This effect can clearly be seen in the infrared spectra of the dilithium tartrates, where the stretching frequencies for hydroxyl groups participating in hydrogen bonding are shifted to lower wavenumbers (Figure 7). Most notably, the O−H stretching

relative contributions to the energy of each structure can be separated. We call this modification of the original methodology coordination-adapted graph set (CAGS) analysis. By way of example, any hydrogen bonding motif with CAGS notation “S” in an inorganic−organic framework must be between functional groups on the same ligand moiety (i.e., it is an intraligand hydrogen bond), such as is found in lithium tartrate 4. Table 3 contains a summary of the hydrogen bonding in anhydrous lithium tartrates, including types of hydrogen bond, hydrogen bond dimensionality, and graph sets. In addition, geometric parameters and FTIR assignments of all hydrogen bonds in 2−9 are shown in Table S1 of the Supporting Information. CAGS Analysis of Dilithium L-Tartrates 2, 3, and 9. The structure of 2 contains five different hydrogen bonds, four of which occur between crystallographically identical ligands in the a direction and one of which is intraligand (Figure 5a). The interligand hydrogen bonds give rise to unitary CAGS notation C(5) and C(6); when combined, they form rings involving a single carboxylate acceptor [binary graph set R12(7)]. In contrast, there is just one crystallographically independent hydrogen bond in 3, between hydroxyl group O2/H2O and carboxylate oxygen O1B (Figure 5g). Combined along the a axis, they result in a chain of rings, with the CAGS notation C(5)[R22(12)]. Graph set analysis of the hydrogen-bonding network in 9 confirms two distinct hydrogen bonds (Figure 5d), which form chains of rings running along the b axis (N1: C(5)[R22(12)]C(5)[R22(12)]). CAGS Analysis of Dilithium Meso-Tartrates 4, 6, and 7. There is one hydrogen bond in the structure of 4, which occurs between the carboxylate oxygen O1B and the hydroxyl group in the β-position of the same ligand, O2/O2O (Figure 5f). They form intraligand six-membered rings, giving rise to the CAGS notation S(6). Each hydroxyl group in 6 forms a hydrogen bond with a carboxylate oxygen of a nearby ligand within the same 2D herringbone array (Figure 5h). The presence of a crystallographic center of symmetry gives rise to chains of rings along the b axis, resulting in the unitary CAGS notation C(5)[R22(12)]. Each hydroxyl group in 7 forms a hydrogen bond with a carboxylate oxygen atom from a ligand nearby (Figure 5e), resulting in the unitary CAGS notation C(5)C(5) and a binary graph set that includes C22(12) chains and an infinite range of rings in 2D, of which R44(24) has the lowest degree. CAGS Analysis of Dilithium D,L-Tartrates 5 and 8. There are two distinct hydrogen bonds in 5, both of which involve carboxylate oxygen O5 as the interligand acceptor (Figure 5b). The separate hydrogen bonds give rise to C(5) and C(6)

Figure 6. Plot of hydrogen bond angle vs hydrogen-acceptor distance for dilithium tartrates 2−9. Red circles, squares, and diamonds show values for dilithium L-tartrates 2, 3, and 9, respectively. Open blue circles, diamonds, and squares represent dilithium meso-tartrates 4, 6, and 7, respectively, and green multiplication and plus signs represent dilithium D,L-tartrates 5 and 8, respectively. 3711



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values (see Tables S3 and S4 of the Supporting Information), leading to overestimations in the total cell volume (e.g., from 2.0% for structure 5 to 8.3% for structure 8). Inclusion of dispersion, either at the PBE + D2 or PBE + D3 levels, brings the lattice parameters into much closer agreement with experimentally determined values. Due to topological differences and structural anisotropy in 2−9, the effect of considering dispersion forces is to reduce the cell parameters within each structure differentially. We observe that the most prominent contractions arising from the inclusion of dispersion corrections occur in directions between chains of inorganic Li−O connectivity, while the least contraction is seen in directions parallel to the inorganic chains (see Table S4 of the Supporting Information). We note here that inclusion of dispersion correction also has a notable effect on the calculated elastic properties of these materials; our investigations in this area will be published in the near future.37 Structure−Energy Correlations. As described earlier, the framework bonding is very similar in isomers 2−9; therefore, we expect that the spread of relative energies is a result of more subtle structural features, such as those shown in Table 2. In order to determine which of those features, if any, were significant, we have examined their correlations with the calculated energies Δ(Eelec + ZPVE + Evib298.15). We found that only density and hydrogen bond strength (via the average O− H stretching frequency shift in the FTIR spectra, δOH) correlated well with energy, while lithium bond valence sum, LiO4 tetrahedral angle distortion, δtet, and ligand C4 torsion angle showed no such trends (see Figure S3 of the Supporting Information). Figure 8 shows the correlation between Δ(Eelec +

Figure 7. Fourier-transform infrared spectra of dilithium L-tartrates 2, 3, and 5−9 in the region corresponding to stretching modes of bonds to hydrogen, showing perturbations in the O−H stretching frequency due to hydrogen bonding.

frequencies of 3, 6, and 7 are shifted to the lowest frequencies due to their short, linear hydrogen bonds. In contrast, 2, 5, and 8 have some O−H stretching frequencies that are relatively unperturbed by hydrogen bonding. Phase 9 exhibits two overlapping sharp peaks, which have intermediate shifts, due to its two well-defined and similar hydrogen bond environments. Structure Calculations of Dilithium Tartrates 2−9. In general, there is good agreement between the formation energies obtained with the CP2K and VASP codes, which use different pseudopotentials and valence electron description approaches (see Table S2 and Figure S1 of the Supporting Information). Therefore, for simplicity, only the data obtained with the VASP code is discussed in the main text. In general, the additions of zero-point vibrational energy, ZPVE, and thermal vibrational contributions at 298.15 K, Evib298.15, change the relative framework energies by less than 10 kJ mol−1. While in most cases, the resultant ordering of energies is unchanged, in some cases the thermodynamic preference for one phase over another is reversed, meaning that the accuracy of the calculation model is critical. Inclusion of the dispersion corrections D2 and D3 results in a dramatic change in the ordering of the frameworks’ energies. Striking offsets from the inclusion of dispersion corrections have also been reported in other recent studies.36 In the subsequent discussion of structure−energy relationships, we therefore use the most detailed, accurate calculation scheme [i.e., Δ(Eelec + ZPVE + Evib298.15)], using the PBE functional with D3 dispersion correction (Table 4). We also note that the there is a good agreement in the relative position of the computed O−H stretching modes within structures 2−9, although there are more pronounced differences between the absolute computed and measured values of vibrational modes (see Figure S2 of the Supporting Information). At the PBE level, the cell parameters of all structures are overestimated compared to the experimentally determined

Figure 8. Correlation between the calculated relative energies (PBE + D3), including electronic energy, zero-point vibrational energy, and vibrational contributions at room temperature, Δ(Eelec +ZPVE + Evib298.15), and the average hydrogen bond strength, δOH, of anhydrous dilithium tartrates 2−9.

ZPVE + Evib298.15) and δOH for framework isomers 2, 3, and 5− 9. The outlying values are for 2 and 3, which have a higher

Table 4. Calculated Relative Energies in kJ mol−1 of Dilithium Tartrates 2−9, Including Electronic Energy, Eelec, Zero-Point Vibrational Energy, ZPVE, and Vibrational Contributions at 298.15 K, Evib298.15, at the PBE + D3 Level of Theory Using the VASP Code dilithium tartrate phase ligand isomer Δ(Eelec + ZPVE + Evib298.15)a a

3

4

L-

2

L-

1.95

0

meso5.18

5 D,L-

−4.76

6

7

meso−18.01

meso−10.42

8

9

D,L-

L-

−4.40

−6.62

Relative to 3, see Table S2 of the Supporting Information for details. 3712



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rather than the exact framework architecture. There is no discernible correlation between enthalpy and decomposition temperature in this system.

energy than expected from just hydrogen-bonding effects, and 6, whose energy is lower. These discrepancies may be explained by the additional contribution from dispersion interactions associated with increased density: 6 has a higher density than the average for 2−9, while those of 2 and 3 are lower. The effect of density is even more clearly seen in Figure 9. The overall correlation is better, and the outlying values in this

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CONCLUSIONS In summary, we have discovered four new anhydrous forms of dilithium tartrate in addition to the four anhydrous structures we reported previously8 and the hydrated structures reported by others.9 The dilithium tartrates 2−9 are all nonporous frameworks with I1O2 connectivity and identical covalent and coordination bonding. Such a large number of inorganic− organic framework isomers with the same chemical formula is unprecedented, and this family offers a unique opportunity to study the structure−energy relationships of such materials in detail, without the complexity imposed by the presence of solvent molecules. The detailed analysis of the framework isomer structures reveals variations in several features, which relate to their formation behavior and relative energies. In particular, increases in both crystallographic density and hydrogen bond strength are found to give rise to lower energy structures. Furthermore, we have examined the hydrogen bonding of 2−9, using a coordination-adapted graph set, CAGS, analysis similar to that developed by Bernstein and Etter15 but here adapted to enable comparison of ligand−ligand interactions in framework materials. In the dilithium tartrates, we have found several different hydrogen-bonding motifs and dimensionalities. Reassuringly, the O−H stretching frequency peak shifts in the infrared spectra of 2−9 correlate well with the strength of hydrogen bonding expected from their crystal structures. We propose that such detailed examination of hydrogen bonding in inorganic−organic frameworks offers a useful tool in structure analysis, energetics, and resultant properties, such as ferroelectricity and framework−guest interactions, of these materials. Given the wide interest in inorganic−organic frameworks and the increasing number of computational manuscripts, the observation that the energetics of framework isomers, on the kJ mol−1 scale, is described in a similar manner when using different electronic structure codes (e.g., VASP, CP2K) is important. Our findings also suggest that inclusion of dispersion corrections is essential for the adequate description of the cell parameters and bonding of framework structures, as is the consideration of ZPVE and thermal contributions. The great diversity of nonporous chiral, racemic, and mesolithium tartrates we have found suggests a need for classification of such structures. In accordance with the classification of framework isomers proposed by Makal et al.,38 the anhydrous lithium tartrates, which have the same elemental composition, Li2C4H4O6, are “ligand-originated isomers” if they contain different ligand isomers. Those which contain the same ligand are “ligand conformational isomers” but, in our case, can be considered polymorphs, as there are no other components that contribute to the crystal structure. Hydrated structures, which have altogether different chemical formulas, may be thought of as pseudopolymorphs of the anhydrous lithium tartrates. We are currently investigating the phase behavior of the lithium tartrates, which upon initial investigation is explained well by the relative energies coupled to kinetic factors (e.g., conformational changes, solubility, and temperature). We are also examining the effect of framework architecture on their dielectric and mechanical properties, using impedance spectroscopy and nanoindentation and computational methods, respectively.

Figure 9. Correlation between the calculated relative energies (PBE + D3), including electronic energy, zero-point vibrational energy, and vibrational contributions at room temperature, Δ(Eelec +ZPVE + Evib298.15), and the crystallographic density of anhydrous dilithium tartrates 2−9.

case are explained well by the additional effect of hydrogen bonding: 2, 4, and 8 exhibit relatively weak hydrogen bonds and so their energies are higher than if density was the only significant factor. On the other hand, strong hydrogen bonding in 6 and 7 lowers their energies even further than the effect of density alone. Energy−Synthesis Correlations. It is interesting to note the difference between the synthesis conditions of the framework isomers reported previously, 2−5, and those reported in this article for the first time, 6−9. The former structures were synthesized in anhydrous solvents under solvothermal conditions.8 The latter structures, which generally have lower energies, were synthesized from mixed water:ethanol solutions under a range of conditions, from room temperature to 150 °C. This suggests that the presence of water might assist the formation of thermodynamic products, and its absence may lead to metastable, higher-energy phases. In this regard, choice of solvent may be more important than temperature, although we believe that entropic and kinetic effects play crucial roles in the phase behavior of this system. For example, although the energy of chiral Li2(L-tart) 9 is approximately 2 kJ mol−1 lower than either racemic Li2(D,L-tart) phases, 5 and 8, no conglomerate of L- and D- phases is observed. This may be due to the high-activation energy barrier for the formation of the eclipsed tartrate ligand in 9. Thermal Behavior. Pure samples of 6−8 (Li2C4H4O6 FW 162 g mol−1) were stable up to 275 °C, after which they decomposed, losing around 50% mass (see Figures S8−S10 of the Supporting Information). The FTIR spectra of the resulting solids were consistent with lithium carbonate (Li2CO3, FW 74 g mol−1, 46%). All anhydrous dilithium tartrates measured previously show similar behavior, leading us to conclude that it is the bulk structural similarities (e.g., 3D, I1O2 connectivity) and constituent building blocks that affect their thermal stability 3713



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ASSOCIATED CONTENT

S Supporting Information *

Crystallographic information files for 6−9; individual hydrogen bond geometrical parameters and FTIR assignments for 2−9; calculated energies at PBE, PBE + D2, and PBE + D3 levels of theory using the CP2K and VASP codes, including electronic energy, Eelec, zero-point vibrational energy, ZPVE, and vibrational contributions at 298.15 K, Evib298.15; calculated cell volumes, cell parameters, and deviations from experimental values of 2−9; a comparison between the calculated normalmode frequencies and experimental FTIR spectra of 2, 3, and 5−9 in the X−H stretching region; ORTEP-extended asymmetric units, PXRD and TGA, of 6−9. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +44 (0)1223 767061. Fax: +44 1223 334567. Web: http://www.fihm.msm.cam.ac.uk/. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the EPSRC and ERC for funding (H. H.-M. Y.) and the European Research Council for Advanced Investigator Awards (A.K.C. and M.P.). M.K. acknowledges the Israeli Ministry of Absorption for generous financial support. We thank Joshua Furman for the initial investigation of the structure of 6.

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REFERENCES

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Chiral, Racemic, and Meso-Lithium Tartrate Framework Polymorphs: A

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