Structural Diversity and Energetics in Anhydrous Lithium Tartrates

Nov 24, 2010 - University of Nevada, Las Vegas, 4505 South Maryland Parkway, Box 454003, Las Vegas,. Nevada 89154-4003, United States. Received ...
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DOI: 10.1021/cg101170k

Structural Diversity and Energetics in Anhydrous Lithium Tartrates: Experimental and Computational Studies of Novel Chiral Polymorphs and Their Racemic and Meso Analogues

2011, Vol. 11 221–230

Hamish H.-M. Yeung,† Monica Kosa,‡ Michele Parrinello,‡ Paul M. Forster,§ and Anthony K. Cheetham*,† †

Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, U.K., CB2 3QZ, ‡Department of Chemistry and Applied Biosciences, ETH Zurich, USI-Campus, Via G. Buffi 13, 6900 Lugano, Switzerland, and §Department of Chemistry, University of Nevada, Las Vegas, 4505 South Maryland Parkway, Box 454003, Las Vegas, Nevada 89154-4003, United States Received September 3, 2010; Revised Manuscript Received October 21, 2010

ABSTRACT: Five novel anhydrous inorganic-organic frameworks based on crystalline modifications of lithium tartrate (tart2-= C4H4O62-) have been synthesized by solvothermal means and investigated by single crystal X-ray and computational methods. Reactions between lithium acetate dihydrate and L-tartaric acid yielded three chiral compounds, LiH(L-tart) in space group P21 (1), Li2(L-tart), P212121 (2), and Li2(L-tart), C2221 (3), a polymorph of 2. Two achiral compounds, Li2(meso-tart), P21/c (4) and Li2(D,L-tart), C2/c (5), were obtained from the reaction of lithium acetate dihydrate with meso-tartaric acid and D,L-tartaric acid, respectively. The singly deprotonated tartrate 1 contains isolated LiO4 tetrahedra, while the tetrahedra in the doubly deprotonated tartrates 2-5 share corners to form parallel chains. The tartaric acid ligands employ a variety of binding modes to connect the inorganic moieties, resulting in nonporous three-dimensional frameworks in all cases. The relative formation energies of structures 2-5 were calculated using density functional theory (DFT) methods and are found to be within the narrow range of ca. 5 kJ mol-1 when electronic energies only are considered. However, when the contributions of zero point vibrational energy (ZPVE) and thermal vibrational energy are considered, the relative energy range increases to ca. 15 kJ mol-1. Analysis of the vibrational modes shows that the non-negligible difference in ZPVE arises from degrees of freedom associated with the heavy backbone atoms rather than, for example, O-H modes.

*To whom correspondence should be addressed. E-mail: [email protected]. Telephone: þ44 (0)1223 767061. Fax: þ44 1223 334567. Web: http://www.msm. cam.ac.uk/fihm/.

for such applications. These should offer superior stability and longevity compared to conventional liquid phase or amorphous electrolytes. Tartaric acid exists as three isomers, L-, D-, and meso-tartaric acid, due to the occurrence of two chiral centers in the carbon chain (see Scheme 1). A racemate of the L- and D- enantiomers crystallizes as a fourth polymorph, D,L-tartaric acid. Inorganicorganic frameworks that contain tartaric acid6 or other chiral ligands7 are known to exhibit a wide variety of porous and nonporous structures and as a result can be suitable for enantiomorphic separations and catalysis as well as optical and dielectric applications. Inspection of the Cambridge Structural Database8 yields three previously reported structures of lithium tartrates, all of which contain waters of hydration.9 We expect that such compounds would be unsuitable for applications such as energy storage, as previous studies have shown that increasing hydration correlates with decreasing thermal stability.10 Computational tools can provide valuable information about the energetic contribution of different building blocks to the relative stabilities of frameworks. However, computational studies on relative stabilities of hybrid frameworks are very limited.6g,11 For example, Bailey et al. have demonstrated that relative stabilities of layered racemic and chiral phases of zinc cyclohexane trans-1,2-dicarboxylate frameworks can be rationalized in terms of the differences in the internal intralayer energies of the component single layers and the nonbonded, interlayer interactions.11c Assessment of the energetic contribution of more fine structural elements such as the conformation of organic ligand linkers has proven to be more

r 2010 American Chemical Society

Published on Web 11/24/2010

Introduction Inorganic-organic framework materials are currently under intense investigation due to their wide-ranging chemical and structural diversity and their many technologically relevant potential applications. Properties of hybrid frameworks span phenomena such as magnetism, electronics, optics, gas storage, catalysis, and molecular separations.1 Discovery and investigation of lithium-containing inorganic-organic frameworks2 is important for two main reasons. First, porous inorganicorganic frameworks have shown potential as new hydrogen storage materials due to the ability to systematically change pore size and framework chemistry, which gives rise to improved gas sorption characteristics.1a,b Gas uptake has been shown to be further enhanced by insertion of lithium into the pores,3 and so it seems logical that the incorporation of lithium as a structural element within the framework itself may lead to better sorption properties, and also because lithium is the lightest metal, to frameworks with enhanced gravimetric capacity. Second, rechargeable battery research has focused largely on lithium-containing materials because lithium has the largest standard electrode potential of all metals and is the lightest metal; it therefore has potential to offer unmatched energy density.4 Inspired by the recent discovery of high ionic conductivity in crystalline polymer electrolytes such as poly(ethylene oxide)6/LiXF6 (X=P, As, Sb),5 we are interested in the potential of unsolvated inorganic-organic frameworks

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

a C is shown as grey spheres, H as white and O as red. The sizes of the atoms are scaled to the corresponding van der Waals radii.

difficult. Harvey et al. studied the relative stabilities of the aluminum alkylenediphosphonate series, namely, aluminum ethylenediphosphonate, aluminum propylenediphosphonate, and aluminum butylenediphosphonate.11a Hypothetical computational models were generated for each compound, in which the inorganic layer was manually designed to adopt either an aligned or unaligned structure.12 The organic ligand in each computational model was forced to adopt a particular conformation, and as a result the organic C-C and C-P bonds are rather strained, as was noticed by the authors. Therefore, it is not clear if the relative stabilities of the analyzed structures can indeed be attributed to organic ligand conformation or to the bond strains, induced by the manual placement of the inorganic building blocks. Very recently, Bernini et al. have addressed the energetic contribution of the conformational states of the dimethylsuccinate ligand to the overall stability of two Er(III) based frameworks.11e Using fixed values for the dihedral angles adopted by the ligand in each compound, the authors calculated a total energy difference of 93 kJ mol-1. Although such analysis could shed light on the energetic contribution of the ligand conformation, an important aspect of electrostatic repulsion of the charged carboxylate groups in the isolated model was neglected. In addition, the functional and basis set used might be inadequate for the description of such delocalized groups as well as the use of different functionals for isolated and extended systems.13 Therefore, it seems clear that the energetic contribution of ligand conformation to the framework stability is still not understood. In the current study of lithium-containing inorganic-organic frameworks, we have synthesized solvothermally five anhydrous forms of lithium tartrate and solved their structures using single crystal X-ray diffraction methods. We have investigated both their relative stabilities using total energies calculations and the possible contributions of the vibrational modes to total energies. All the frameworks presented exhibit nonporous 3-D structures, in both chiral and achiral forms. A variety of ligand conformations and metal binding modes are observed, which exemplify the diversity of inorganic-organic frameworks obtainable from the use of isomeric ligands. Experimental Methods Synthesis. All reagents, lithium acetate dihydrate [Li(CH3COO) 3 2H2O] (98%, Fisher Scientific UK), D,L-tartaric acid (99.5%, Fisher Scientific UK), L-tartaric acid (>99%, Fisher Scientific UK) and meso-tartaric acid monohydrate (g97%, Sigma-Aldrich), and solvents, ethanol and tetrahydrofuran (THF) (both reagent grade, Fisher Scientific UK) and N,N-dimethylformamide (DMF, reagent

Yeung et al. grade, Acros Organics), were used as received under aerobic conditions. Reactions were carried out in 23 mL PTFE-lined stainless steel autoclaves obtained from Parr Instrument Company.14 [LiH(L-C4H4O6)], 1. A mixture of Li(CH3COO) 3 2H2O (2.0 mmol), L-tartaric acid (1.0 mmol), THF (7.5 mL), and ethanol (7.5 mL) was placed inside a 23 mL PTFE-lined stainless steel autoclave and stirred for 10 min. The autoclave was then sealed and heated at 100 °C for two days then cooled over 2 h to room temperature. The resulting solid, consisting of colorless plates and white powder, was washed with ethanol and dried in air at 60 °C for one day. The plates were used for structure determination by single crystal X-ray diffraction. However, the powder X-ray diffraction pattern of the product did not match the simulated pattern for 1; rather it appeared to contain multiple unknown phases. Thermogravimetric analysis indicates the presence of a solvated impurity and an unknown anhydrous phase, although it is unclear whether they are lithium hydrogen tartrates, dilithium tartrates, or other compositions (see Supporting Information). [Li2(L-C4H4O6)], 2. A mixture of Li(CH3COO) 3 2H2O (2.0 mmol), L-tartaric acid (1.0 mmol), and ethanol (9.25 mL) was placed inside a 23 mL PTFE-lined stainless steel autoclave and stirred for 10 min. The autoclave was sealed and heated at 150 °C for three days, then cooled over 2 h to room temperature. The final product, consisting of colorless flat rods (123 mg, 79%), was washed with ethanol and dried in air at 60 °C for one day. A suitable rod was selected for structure determination by single crystal X-ray diffraction, but the product contained approximately 14% 3. A phase-pure sample was prepared in the following way: A solution of L-tartaric acid (1.0 mmol) in ethanol (5 mL) was added dropwise to a solution of Li(CH3COO) 3 2H2O (2.0 mmol) in ethanol (5 mL) inside a 23 mL PTFE-lined stainless steel autoclave and the resulting mixture was stirred for 10 min. The autoclave was sealed and heated at 150 °C for six days, then cooled over 2 h to room temperature. The final product, consisting of white powder and colorless flat rods (156 mg, 96%), was washed with ethanol and dried in air at 60 °C for one day. Elemental analysis: C 29.63%, H 2.45% (calculated for C4H4Li2O6: C 29.67%, H 2.49%). [Li2(L-C4H4O6)], 3. A mixture of Li(CH3COO) 3 2H2O (2.0 mmol) in ethanol (5 mL) and L-tartaric acid (1.0 mmol) in ethanol (5 mL) was placed inside a 23 mL PTFE-lined stainless steel autoclave and stirred for 10 min. The autoclave was sealed and heated at 150 °C for 3 days and then cooled over three days to room temperature. The final product, consisting of colorless flat rods and hexagonal platelets (148 mg, 91%), was washed with ethanol and dried in air at 60 °C for one day. The platelets were used for structure determination by single crystal X-ray diffraction, but the product contained approximately 23% 2. A phase-pure sample was prepared in the following way: A solution of L-tartaric acid (1.0 mmol) in ethanol (5 mL) was combined with a solution of Li(CH3COO) 3 2H2O (2.0 mmol) in ethanol (5 mL) inside a 23 mL PTFE-lined stainless steel autoclave and the resulting mixture was stirred for 10 min. The autoclave was sealed and heated at 150 °C for one day, followed by 125 °C for three days, then cooled naturally to room temperature. The final product, consisting of colorless microcrystalline powder (66 mg, 41%), was washed with ethanol and dried in air at 60 °C for one day. Elemental analysis: C 29.60%, H 2.42% (calculated for C4H4Li2O6: C 29.67%, H 2.49%). [Li2(meso-C4H4O6)], 4. A mixture of Li(CH3 COO) 3 2H2 O (2.0 mmol), meso-tartaric acid (1.0 mmol), and DMF (5 mL) was placed inside a 23 mL PTFE lined stainless steel autoclave and stirred for 10 min. The autoclave was then sealed and heated at 180 °C for three days, then cooled over 2 h to room temperature. The resulting solid, consisting of colorless flat rods and white powder, was washed with isopropanol and dried in air at 60 °C for one day. The rods were used for structure determination by single crystal X-ray diffraction. However, the powder X-ray diffraction pattern of the product did not match the simulated pattern for 4; rather it appeared to contain two or more phases. Thermogravimetric analysis indicates the presence of two anhydrous impurities and subsequent to the review process we have determined by single crystal X-ray diffraction the structure of one of these (Li2(meso-C4H4O6), monoclinic P21/c, cell parameters a = 6.471(2) A˚, b = 5.014(2) A˚, c = 9.028(4) A˚, β = 95.83(3)°), which is present in the product’s powder X-ray diffraction

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Scheme 2. Chemical Equations Used to Calculate the Formation Energies of Lithium Hydrogen L-Tartrate 1 (1) and Dilithium Tartrates 2-5 (2)

pattern (see Supporting Information). The other phase is as-yet unknown. [Li2(D,L-C4H4O6)], 5. A mixture of LiNO3 (2.0 mmol), D,L-tartaric acid (1.0 mmol), and isopropanol (10 mL) was placed inside a 23 mL PTFE-lined stainless steel autoclave and stirred for 10 min. The autoclave was sealed and heated at 180 °C for five days then cooled over 2 h to room temperature. The final product, consisting of colorless needles (105 mg, 68%), was washed with ethanol and dried in air at 60 °C for one day. A suitable needle was selected for structure determination by single crystal X-ray diffraction, but the product contained approximately 30% 2. A phase-pure sample was prepared in the following way: A solution of D,L-tartaric acid (1.0 mmol) in ethanol (5 mL) was added dropwise to a solution of Li(CH3COO) 3 2H2O (2.0 mmol) in ethanol (5 mL) inside a 23 mL PTFE-lined stainless steel autoclave and the resulting mixture was stirred for 10 min. The autoclave was sealed and heated at 150 °C for three days, then cooled naturally to room temperature. The final product, consisting of white powder (134 mg, 83%), was washed with ethanol and dried in air at 60 °C for one day. Elemental analysis: C 29.93%, H 2.58% (calculated for C4H4Li2O6: C 29.67%, H 2.49%). Crystal Structure Determinations. The relevant details of structure determinations are presented in the Supporting Information. Crystal structure determinations by X-ray diffraction of 1, 3, and 4 were performed on a Bruker-Nonius APEX II CCD camera on κ-goniostat diffractometer equipped with 10 cm confocal mirrors, Bruker-Nonius FR591 rotating anode radiation source (Mo KR radiation, λ=0.71073 A˚) operating at 50 kV and 85 mA. Data were collected at 120(2) K using j and ω scans. The mean detector area resolution was 4096  4096 pixels/62  62 mm. Data collection, cell determination and refinement, and data reduction were performed using the COLLECT,15 DirAx,16 DENZO,17 and Scalepack17 programs. An empirical correction based on symmetry equivalent reflections was applied using the SADABS 2007/2 program.18 Crystal structure determination by X-ray diffraction of 2 was performed on a Oxford Diffraction Gemini A Ultra diffractometer equipped with confocal mirrors and Cu radiation source (λ = 1.54184 A˚) operating at 50 kV and 40 mA. Data were collected at 120 K using ω scans. The mean detector area resolution was 10.4 pixels mm-1. Data collection, cell determination and refinement, and cell reduction were performed using CrysAlisPro software.19 Structures of 1-4 were solved by charge flipping methods using the Superflip program.20 Full matrix least-squares refinements against 2 |F | were carried out using the SHELXTL-PLUS package of programs21 within the WinGX interface.22 All non-hydrogen atoms were refined anisotropically; hydrogen atoms were then found by inspection of the Fourier difference map and refined with isotropic displacement parameters constrained to 1.2 and 1.5 times those of their adjacent carbon and oxygen atoms, respectively. In the case of 5, microcrystal diffraction was carried out at the Advanced Light Source on the 11.3.1 beamline using 0.7790 A˚ radiation. Data were collected at 100 K using the APEXII software package.23 The structure was solved with direct methods and refined using the SHELXTL software suite.21 Toward the end of the refinement, Fourier peaks were observed corresponding to a second orientation of the tartrate ligand and refined using a partial occupancy model. Hydrogen atoms were added geometrically and refined using the riding model. Visualization of structures was carried out using Diamond24 and Mercury25 programs. Powder X-ray Diffraction. Data were collected on a Bruker D8 theta/theta (fixed sample) diffractometer with LynxEye position

sensitive detector, in Bragg-Brentano parafocusing geometry, reflection mode using Cu KR radiation (λ = 1.5418 A˚). Scans were taken over an angular range of 5°-60° (2θ) with step size 0.01°. Analysis of the data was carried out using the X’Pert HighScore Plus program.26 Thermal Behavior. Simultaneous differential scanning calorimetry and thermogravimetric analysis were performed using a TA Instruments Q600 SDT instrument with a nitrogen gas flow of 100 mL min-1 at a heating rate of 20 °C min-1, from room temperature to 700 °C using 2-5 mg samples. Infrared Spectroscopy. Fourier-transform infrared spectroscopy (FTIR) was carried out using a Bruker Tensor 27 Infrared spectrometer with a diamond attenuated total reflectance (ATR) attachment. Multiple spectra were recorded in the range 4000-500 cm-1 and subsequently averaged.

Theoretical Calculations The initial xyz coordinates of the five phases, 1-5, were obtained from the experimental X-ray data. Structures involving atomic disorder were simplified by removing the disordered atoms with lower site occupancy and assigning full occupancy to the remaining atoms. Multiple unit cells were used for each structure, such that the total number of formula units in each simulation cell was 24. For geometry and cell optimizations, all structures were calculated using the PBE functional,27 GTH pseudopotential28 with the DZVP Gaussian basis set,29 and 600 Ry plane wave density cutoff and 40 Ry relative cutoff as implemented in the QS module of the CP2K package.30 The convergence of the total energy with respect to the plane wave basis set was checked in the range of 200-1000 Ry, with intervals of 100 Ry (See Supporting Information). The relatively high and safe value of 600 Ry was chosen in order to avoid inconsistencies due to different cell sizes with respect to the plane wave basis set. The formation energies, ΔEelec, of 1-5 were calculated according to the equations shown in Scheme 2 and afterward normalized per formula unit of (di)lithium tartrate. The electronic energies at 0 K of the isolated molecules of lithium acetate, tartaric acid, and acetic acid were calculated with the same Gaussian basis set and plane wave density cutoff as the extended phases 1-5. The zero point vibrational energies (ZPVE) were evaluated (at the Γ-point only) within the harmonic approximation as a sum of contributions from all vibrational modes of the system. The thermal populations, Evib (298.15 K), were evaluated according to the classical approximation. Results and Discussion Single crystals of five lithium tartrate phases, 1-5, were obtained by solvothermal synthesis and their crystal structures were determined by single-crystal X-ray diffraction. A summary of the crystal data can be found in Table 1. Structure of LiH(L-C4H4O6) in P21, 1. The asymmetric unit of 1 consists of one crystallographically independent

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Table 1. Summary of Crystal Data for Lithium Tartrates 1-5 crystal size (mm3) crystal system space group T (K) a (A˚) b (A˚) c (A˚) R (°) β (°) γ (°) V (A˚3) asym. unit Z dcalc (g cm-3) μ (mm-1) refln collected unique refln observed data (I > 2σ(I)) parameters Rint R1 wR2 (I > 2σ(I)) R (all data) GOF

LiH(L-tart) 1

Li2(L-tart) 2

Li2(L-tart) 3

Li2(meso-tart) 4

Li2(D,L-tart) 5

0.10  0.07  0.02 monoclinic P21 120 5.0643(2) 8.3299(3) 7.4469(3) 90 107.585(2) 90 299.47(2) C4H5Li1O6 2 1.73 0.165 4170 1332 1267 117 0.0355 0.0326 0.0683 0.0356 1.109

0.5  0.4  0.3 orthorhombic P212121 120 5.0455(3) 14.9300(12) 16.1053(12) 90 90 90 1213.0(2) C8H8Li4O12 8 1.774 0.164 2396 2104 1694 241 0.039 0.0402 0.1006 0.0518 0.946

0.06  0.06  0.01 orthorhombic C2221 120 5.5800(6) 9.1055(6) 12.0180(11) 90 90 90 610.62(10) C2H2Li1O3 4 1.762 0.162 3280 696 578 61 0.0750 0.0462 0.1193 0.0644 0.916

0.22  0.05  0.03 monoclinic P21/c 120 6.0522(9) 5.3351(8) 9.8636(14) 90 100.474(9) 90 313.18(8) C2H2Li1O3 2 1.717 0.158 3246 713 543 62 0.0554 0.0810 0.1736 0.1059 1.014

0.08  0.05  0.015 monoclinic C2/c 120 15.988(10) 5.0193(14) 15.020(8) 90 101.50(5) 90 1181.1(10) C4H4Li2O6 8 1.821 0.168 4525 1212 854 131 0.0411 0.0673 0.1886 0.093 1.062

Figure 1. Ortep extended asymmetric unit of LiH(L-C4H4O6), 1. The long Li-OH distance is shown as a dashed line. C shown as gray, H white, Li green, O red. Thermal ellipsoids are given at 50% probability (20% probability for hydrogen).

lithium atom and one crystallographically independent tartrate ligand, which remains protonated on one carboxylate oxygen atom (Figure 1). The tartaric acid ligand coordinates to four lithium atoms via the deprotonated carboxylate oxygen group and a hydroxyl oxygen atom, with Li-O distances of 1.935-2.029 A˚. It may be classed as μ4, κ4, as it binds to four different lithium atoms through one hydroxyl oxygen and three unprotonated carboxylic oxygens. The lithium coordination environment is a distorted tetrahedron (O-Li-O angles 97.19-119.08°). The remaining ligand hydroxyl oxygen, O3, lies close to the face of the LiO4 tetrahedron nearest to which the Li atom sits (Li-O distance 2.470 A˚). The directionality of its thermal ellipsoid indicates some interaction with the lithium may occur. However, bond valence calculations31 estimate that this oxygen contributes to less than 7% of the total bonding to the lithium. The tartaric acid carbon skeleton is nearplanar with a torsion angle of 178.70°. The resulting structure is an array of isolated LiO4 nodes linked in three dimensions by tartaric acid ligands making an I0O3 network, according to the nomenclature of Cheetham et al.1d (Figure 2). Four hydrogen bonds per formula unit may contribute to the overall stability of the system. The use of a single enantiomer of tartaric acid imparts chirality to the structure.

Structure of Li2(L-C4H4O6) in P212121, 2. The asymmetric unit of 2 consists of two crystallographically independent tartaric acid ligands and four lithium atoms (Figure 3). Each lithium atom is coordinated by four oxygen atoms in a distorted tetrahedral manner. The tartrate carboxylate groups each bond to three lithium atoms, and the tartrate hydroxyl oxygen atoms bond to one lithium atom each. Li-O bond distances are in the range 1.883-2.004 A˚. Even in a dense system of such complexity, this wide range is rather surprising. However, as might be expected from electrostatic arguments, the lowest and highest values are for carboxylate and hydroxyl oxygen atoms, respectively. Bond angles within the tetrahedra also vary considerably, from 94.0° to 120.2°. The carbon skeletons of the tartaric acid moieties are almost planar; torsion angles are 178.1° and 174.8°. Both tartaric acid ligands, although crystallographically independent, may be classed as μ8, κ6; that is, they bind 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 two-dimensional (2-D) sheet (Figure 4a). The apical positions on the tetrahedra are occupied by hydroxyl oxygen atoms of the ligands in sheets above and below, which link the sheets to form a three-dimensional (3-D), I1O2 framework (Figure 4b). The structure is chiral due to the use of a single chiral enantiomer of tartaric acid, which did not racemize under the reaction conditions. Structure of Li2(L-C4H4O6) in C2221, 3. The asymmetric unit of 3 consists of half of one tartaric acid ligand and one lithium atom (Figure 5). The lithium atom is coordinated by four oxygen atoms in a severely distorted tetrahedron, with bond distances 1.918-1.956 A˚ and bond angles 84.6-121.7°. The smallest angle is between the chelating oxygen atoms, which also have the two longest Li-O bond distances. This is not uncommon for oxygen atoms which chelate lithium. Each tartaric acid ligand coordinates to six lithium atoms in a μ6, κ6 fashion with two lithium atoms chelated between the hydroxyl oxygen and one carboxylate oxygen. The resulting structure is an I1O2, 3-D framework comprised of chains of corner-sharing LiO4 tetrahedra connected

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

Figure 2. Structure of LiH(L-C4H4O6), 1: (a) viewed down the a-axis, and (b) viewed down [1 1 0]. C shown as gray, H white, O red, and LiO4 tetrahedra green.

Figure 3. Ortep extended asymmetric unit of Li2(L-C4H4O6), 2. C shown as gray, H white, Li green, O red. Thermal ellipsoids are given at 50% probability (20% probability for hydrogen).

by tartaric acid ligands (Figure 6). There is no obvious 2-D substructure of the type seen in 2. However, due to the use of a single enantiomer of tartaric acid, the compound is chiral, like 2.

Figure 5. Ortep extended asymmetric unit of Li2(L-C4H4O6), 3. Unlabeled atoms correspond to those necessary to complete one tartaric acid ligand. C shown as gray, H white, Li green, O red. Thermal ellipsoids are given at 50% probability (20% probability for hydrogen).

Structure of Li2(meso-C4H4O6) in P21/c, 4. The asymmetric unit of 4 consists of half of one tartaric acid ligand and one crystallographically independent lithium atom (Figure 7). The central tartaric acid carbon atoms and their associated hydrogen atoms exhibit disorder between two positions (C2, H2 and C20, H20), with a site occupancy ratio of 78.5:21.5. The two

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Figure 7. Ortep extended asymmetric unit of Li2(meso-C4H4O6), 4. Unlabeled atoms correspond to atoms related by inversion symmetry necessary to complete one tartaric acid ligand. Dashed gray bonds correspond to those of the disordered tartaric acid ligand with lower site occupancy (C20, H20). C shown as gray, H white, Li green, O red. Thermal ellipsoids are given at 50% probability (20% probability for hydrogen).

Figure 6. Structure of Li2(L-C4H4O6), 3: (a) viewed down [1 0 1], showing chains of corner-sharing tetrahedra, and (b) viewed down the chains of corner-sharing LiO4 tetrahedra. C shown as gray, H white, O red, and LiO4 tetrahedra green.

halves of the tartaric acid moiety are related by inversion symmetry. In a manner similar to 3, 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. It should be noted that the thermal displacement parameters for the hydroxyl oxygen O2 are unusually large in the direction perpendicular to the ring of chelation to lithium. Modeling the hydroxyl group as two distinct sites, corresponding to the disordered carbon atoms C2 and C20, resulted in an unstable refinement. However, it may not be unreasonable to suggest that this oxygen has substantial freedom to vibrate, or that the two sites are so close to each other as to be indistinguishable. Each lithium atom is coordinated by four oxygen atoms from three different tartaric acid ligands, with Li-O bond distances of 1.882-1.966 A˚. It is noted that the minimum and maximum Li-O bond distances are to the singly coordinating carboxylate oxygen and the hydroxyl oxygen, respectively. Bond angles within the distorted LiO4 tetrahedron range from 81.7° to 121.9°. In a similar manner to 3, the smallest angle is between the chelating oxygen atoms, which also have the two longest Li-O bond distances. The resulting structure is an array of parallel chains of cornersharing LiO4 tetrahedra, connected by tartaric acid ligands to form a 3-D, I1O2 framework (Figure 8). Like 3, there is no obvious 2-D substructure. However, the compound is achiral, which is enabled by the use of the meso-tartaric acid ligand.

Structure of Li2(D,L-C4H4O6) in C2/c, 5. The asymmetric unit of 5 consists of one tartaric acid ligand and two crystallographically independent lithium atoms (Figure 9). The carbon chain and one carboxylate oxygen atom exhibit disorder between two positions with a site occupancy ratio of 88:12. In a manner similar to 2, the tartaric acid 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 independent lithium atoms. Li-O bond distances are 1.90-1.959 A˚. The lowest of these values is for the disordered oxygen atom position of lower site occupancy. Each lithium atom is coordinated by four oxygen atoms in a distorted tetrahedron (bond angles 87.7-124.1°). The overall structure of 5 is very similar to that of 2, in which corner-sharing LiO4 tetrahedra form 1D chains bridged by tartaric acid moieties in a 2-D herringbone array (Figure 10a). The hydroxyl oxygen atoms link the sheets by filling the apical positions on the LiO4 tetrahedra, giving rise to a 3-D I1O2 framework (Figure 10a). In contrast to the structure of 2, there is only one crystallographically independent sheet, which, due to the presence of glide plane symmetry in space group C2/c, contains both L- and D-tartaric acid isomers in a 1:1 ratio. This results in a structure that, while being made up of individually chiral building blocks, is itself achiral. Thermal Behavior. Simultaneous differential scanning calorimetry and thermogravimetric analysis (SDT) on the pure compounds 2, 3, and 5 reveals similar behavior for each sample. Endothermic framework decomposition begins in one step around 270-315 °C, consistent with the absence of water or other solvent molecules (see Supporting Information for detailed plots). Computational Analysis. The formation energies calculated including electronic energy contributions only, ΔEelec, show that 2-5 are within a range of 4.53 kJ mol-1, which is of the same order of magnitude as the thermal energy at room temperature (Table 2). The monolithiated compound, 1, has a substantially less negative formation energy than the other phases. This may be explained in part by the electrostatic interactions in 1 being weaker (the ligand has only one

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Figure 9. Ortep extended asymmetric unit of Li2(D,L-C4H4O6), 5. Dashed gray bonds correspond to those of the disordered tartaric acid ligand with lower site occupancy (C1B - C4B, O1B). C shown as gray, H white, Li green, O red. Hydrogen atoms not labeled for clarity. Thermal ellipsoids are given at 50% probability (20% probability for hydrogen).

Figure 8. Structure of Li2(meso-C4H4O6), 4: (a) viewed down the a-axis, showing chains of LiO4 tetrahedra bridged by tartaric acid ligands, and (b) viewed down the chains of corner-sharing LiO4 tetrahedra. C shown as gray, H white, O red, and LiO4 tetrahedra green. Note that all disordered atoms, including those with lower site occupancies, are shown.

negative charge) and half as numerous as for 2-5. Other factors, such as sterics, may also be important. The inclusion of ZPVE and thermal vibrational energy, Evib, at room temperature results in 3-5 remaining within a similar range (6.56 kJ mol-1). However, the energy difference between 2 and 3 is increased from 3.85 to 14.37 kJ mol-1. The difference in the ZPVE between polymorphs 2 and 3 is 15.37 kJ mol-1 (see Supporting Information for absolute values). This suggests, in agreement with X-ray diffraction data, that although they have the same composition, they should have different topologies. To gain further insight into structural differences between 2 and 3, a normal-mode analysis was performed and compared with experimental FTIR spectra (Figure 11; a more detailed plot of the calculated normal-mode frequencies can be found in the Supporting Information). Both data sets indicate that 2 and 3 differ both in the region below 720 cm-1, which corresponds to heavy atom motion, and above 3000 cm-1, which corresponds to hydrogen atom motion. In the high frequency region of 2, calculations show two clear bands corresponding to O-H stretches at 3295.06 and 3455.07 cm-1 (corresponding to 3275 and 3406 cm-1 in

Figure 10. Structure of Li2(D,L-C4H4O6), 5: (a) viewed down the a-axis, showing chains of LiO4 tetrahedra bridged by a 2-D herringbone array of tartaric acid ligands, and (b) viewed down the chains of corner-sharing LiO4 tetrahedra with sheets horizontal. C shown as gray, H white, O red, and LiO4 tetrahedra green. The disordered atoms with lower occupancy are not shown for clarity.

the experimental spectrum). The O-H stretches associated with 3 are lower in frequency (3114.72 and 3149.78 cm-1) and differ by only 35.06 cm-1 and so appear as one broad

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Table 2. Comparison of Structures and Formation Energies of 1-5,a with and without Zero Point Vibrational Energy, ZPVE, and Thermal Vibrational Energy, Evib (Evaluated at T = 295.15 K) 1

2

3

4

5

empirical formula space group number of lithium - oxygen contacts tartaric acid carbon skeleton dihedral angleb

LiH(L-tart) P21 4 175.8°

Li2(L-tart) C2221 8 151.5°

Li2(meso-tart) P21/c 8 180.0°

formation energy ΔEelec (kJ mol-1) formation energy ΔEelec relative to 3 (kJ mol-1) formation energy including thermal vibrational contributions Δ(Eelec þ ZPVE þ Evib), relative to 3 (kJ mol-1)

-295.95

Li2(L-tart) P212121 8 176.0° 178.5° -435.60 3.85 14.37

-439.46 0.00 0.00

-437.62 1.84 2.04

Li2(D,L-tart) C2/c 8 175.3° 178.3° -434.92 4.53 6.56

a

All values are normalized to one mole of formula unit. b Calculated values.

Scheme 3. ChemDraw Representation of Tartaric Acid Ligand Binding Modes of Dilithium Tartrates 2-5

Figure 11. Experimental FTIR spectra of Li2(L-C4H4O6), 2, (dotted blue line) and Li2(L-C4H4O6), 3, (solid red line), together with calculated normal-mode frequencies for 2 (blue crosses above) and 3 (red crosses below). Starred peak at 2350 cm-1 is due to atmospheric CO2.

peak (3155 cm-1) in the experimental FTIR spectrum. In contrast to both 2 and 3, the calculated O-H stretches of the isolated L-tartaric acid molecule occur at higher frequencies (3536.46 and 3587.68 cm-1). This implies that the hydrogen atoms of the hydroxyl groups in 2 and 3 are constrained by the framework and might be involved in hydrogen bonding. Inspection of both calculated and experimentally determined structures of 2 reveals that the four crystallographically independent hydroxyl groups participate in at least four hydrogen bonds of varying distances and angles, accounting for the range of O-H stretches observed. In 3, both hydroxyl groups participate in one hydrogen bond each. The donoracceptor distances and angles of the hydrogen bonds are very similar, resulting in the O-H stretches being very close in energy. The hydrogen-acceptor distances in 2 are on average longer than those of 3; therefore, the hydroxyl bonds in 2 are perturbed to a lesser extent due to hydrogen bonding. This explains why the O-H stretches in 2 occur at a higher frequency than those in 3, and why those of the isolated tartaric acid molecule occur at higher frequencies still. The difference between the ZPVE contributions of the O-H modes in 2 and 3 is 2.90 kJ mol-1, whereas the difference of the total ZPVEs is 15.37 kJ mol-1. This implies that the major part of the destabilization of 2 relative to 3 at 0 K lies in the ZPVE arising from degrees of freedom which

involve the framework backbone heavy atoms. Fine structural features such as conformation of the ligand (the carbon skeletons are almost linear in all structures except 3, which has a C-C-C-C torsion angle of 151.5°), binding modes to lithium, and the extended metal-ligand-metal topology are possibly responsible for this. It is observed that the two most stable compounds, 3 and 4, exhibit bidentate binding of lithium between adjacent hydroxyl and carboxylate oxygen atoms forming a five-membered ring, whereas 2 and 5 do not (Scheme 3). It must be noted here that the current computational scheme (PBE functional) underestimates the long-range dispersion forces, which have a non-negligible contribution to hydrogen bonding (for example, see ref 32). The underestimation of dispersion forces enhances the calculated vibrational frequencies of the O-H stretching modes, thus artificially raising their ZPVE contribution (the population at room temperature is negligible). It is interesting to observe that although difference in formation energy including vibrational contributions between 2 and 3 is substantial, when thermal contributions to vibrational energy are ignored (i.e., including ZPVE and not Evib) this difference is even greater (19.22 kJ mol-1 rather than 14.37 kJ mol-1). It is also interesting to note that, similar to the Ba analogues,6g the calculated relative energies imply that the racemic phase Li2(D,L-C4H4O6), 5, is less stable than Li2(L-C4H4O6), 3, (although Ba(D,L-C4H4O6) was the major phase at high temperatures). In the preceding manuscript6g (and based on previous computational studies33), we assumed that relative stabilities of the alkali earth tartrates are not expected to change when vibrational contributions are added. This assumption has been confirmed by calculating the corresponding energies’ contributions (see Supporting Information).

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Conclusions The family of five new compounds presented is the first reported series of air-stable, anhydrous lithium-based inorganicorganic frameworks, which demonstrates the potential for manipulation of such structures by simple variations in ligand isomerism. Note that subsequent to the initial submission of this paper, we have discovered one more dilithium meso-tartrate polymorph and, from analysis of impure products, we predict the existence of at least three other phases: one solvate, one anhydrous L-tartrate compound, and one anhydrous meso-tartrate compound. This further emphasizes the richness of lithium tartrate phase-space. Numerous examples exist of compounds with more than one crystalline phase and many have been studied in detail both experimentally and computationally. In the field of inorganic-organic frameworks, however, exploration of multiphase behavior in general and polymorphism in particular is still in its infancy and this field remains almost unexplored. In the few preceding studies of hybrid framework energetics,6g,11 the contributions from the ZPVE and the Evib were not considered.34 We stress here that ZPVE and Evib (298.15 K) can have a notable effect on the relative enthalpies of inorganic-organic framework polymorphs, and thus their contribution should be evaluated when computational data on relative stabilities is analyzed. In this study, consideration of only electronic energies would lead to the conclusion that 2 should be within the same (qualitative) relative energy range as 3-5. However, inclusion of vibrational contributions35 to relative energies makes phase 2 significantly less stable than 3-5. The analysis of vibrational modes in turn points toward the topological details that are responsible for the energy difference between polymorphs 2 and 3. We are currently investigating the phase behavior of the compounds, which is complex due to the low energy differences between them, and we are characterizing both experimentally and computationally their lithium mobility and suitability for use as solid electrolytes in rechargeable batteries. Acknowledgment. We thank the EPSRC for funding (H.H.-M.Y.) and the European Research Council for Advanced Investigator Awards (A.K.C. and M.P.). We thank the EPSRC UK National Crystallographic Service for data collection for structures 1, 3, and 4, Oliver Presly for assistance with data collection for structure 2 at Oxford Diffraction Ltd., and Simon J. Teat for assistance with data collection for structure 5 on the 11.3.1 beamline at the Advanced Light Source. The Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DEAC02-05CH11231, support the Advanced Light Source. H.H.-M.Y. thanks A. Thirumurugan and C. Merrill for helpful discussions. Supporting Information Available: SDT of 2, 3, 5 and the impure source reactions of 1 and 4, powder X-ray diffraction patterns for 2, 3, 5 and the impure source reaction of 4, plot of total energy as a function of plane wave cutoff, plot of calculated normal-mode frequencies of 2 and 3 and table of absolute and relative calculated values of E, ZPVE and Evib, table from Appelhans et al.,6g updated to include Δ(Eelec þ ZPVE) and Δ(Eelec þ ZPVE þ Evib). X-ray crystallographic information files (CIF) are available for structures 1-5. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) (a) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keeffe, M.; Yaghi, O. M. Science 2002, 295 (5554), 469–472. (b) Kitagawa, S.; Kitaura, R.; Noro, S. Angew. Chem., Int. Ed. 2004, 43 (18),

(2)

(3)

(4) (5)

(6)

(7)

(8) (9)

(10) (11)

(12) (13)

(14) (15)

229

2334–2375. (c) Fletcher, A. J.; Thomas, K. M.; Rosseinsky, M. J. J. Solid State Chem. 2005, 178 (8), 2491–2510. (d) Cheetham, A. K.; Rao, C. N. R.; Feller, R. K. Chem. Commun. 2006, 46, 4780–4795. (e) Rao, C. N. R.; Cheetham, A. K.; Thirumurugan, A. J. Phys.: Condens. Matter 2008, 20 (8), 083202. (a) Liu, Y. Y.; Zhang, H.; Sun, L. X.; Xu, F.; You, W. S.; Zhao, Y. Inorg. Chem. Commun. 2008, 11 (4), 396–399. (b) Liu, Y. Y.; Zhang, J.; Xu, F.; Sun, L. X.; Zhang, T.; You, W. S.; Zhao, Y.; Zeng, J. L.; Cao, Z.; Yang, D. W. Cryst. Growth Des. 2008, 8 (9), 3127–3129. (c) Banerjee, D.; Kim, S. J.; Parise, J. B. Cryst. Growth Des. 2009, 9 (5), 2500–2503. (d) Banerjee, D.; Kim, S. J.; Borkowski, L. A.; Xu, W.; Parise, J. B. Cryst. Growth Des. 2009, 9 (5), 2500-2503. (e) Abrahams, B. F.; Grannas, M. J.; Hudson, T. A.; Robson, R. Angew. Chem., Int. Ed. 2010, 49 (6), 1087–1089. (a) Han, S. S.; Goddard, W. A. J. Am. Chem. Soc. 2007, 129 (27), 8422. (b) Mulfort, K. L.; Hupp, J. T. J. Am. Chem. Soc. 2007, 129 (31), 9604. (c) Mulfort, K. L.; Farha, O. K.; Stern, C. L.; Sarjeant, A. A.; Hupp, J. T. J. Am. Chem. Soc. 2009, 131 (11), 3866. (d) Yang, S. H.; Lin, X.; Blake, A. J.; Walker, G. S.; Hubberstey, P.; Champness, N. R.; Schroder, M. Nat. Chem. 2009, 1 (6), 487–493. (a) Tarascon, J. M.; Armand, M. Nature 2001, 414 (6861), 359–367. (b) Armand, M.; Tarascon, J. M. Nature 2008, 451 (7179), 652–657. (a) Gadjourova, Z.; Andreev, Y. G.; Tunstall, D. P.; Bruce, P. G. Nature 2001, 412 (6846), 520–523. (b) Stoeva, Z.; Martin-Litas, I.; Staunton, E.; Andreev, Y. G.; Bruce, P. G. J. Am. Chem. Soc. 2003, 125 (15), 4619–4626. (c) Zhang, C. H.; Gamble, S.; Ainsworth, D.; Slawin, A. M. Z.; Andreev, Y. G.; Bruce, P. G. Nat. Mater. 2009, 8 (7), 580– 584. (a) Thushari, S.; Cha, J. A. K.; Sung, H. H. Y.; Chui, S. S. Y.; Leung, A. L. F.; Yen, Y. F.; Williams, I. D. Chem. Commun. 2005, 44, 5515–5517. (b) Gelbrich, T.; Threlfall, T. L.; Huth, S.; Seeger, E. Polyhedron 2006, 25 (4), 937–944. (c) Coronado, E.; Galan-Mascaros, J. R.; Gomez-Garcia, C. J.; Murcia-Martinez, A. Chem.-Eur. J. 2006, 12 (13), 3484–3492. (d) Au-Yeung, A. S. F.; Sung, H. H. Y.; Cha, J. A. K.; Siu, A. W. H.; Chui, S. S. Y.; Williams, I. D. Inorg. Chem. Commun. 2006, 9 (5), 507–511. (e) Kam, K. C.; Young, K. L. M.; Cheetham, A. K. Cryst. Growth Des. 2007, 7 (8), 1522–1532. (f) Manna, S. C.; Zangrando, E.; Ribas, J.; Chaudhuri, N. R. Eur. J. Inorg. Chem. 2007, 29, 4592–4595. (g) Appelhans, L. N.; Kosa, M.; Radha, A. V.; Simoncic, P.; Navrotsky, A.; Parrinello, M.; Cheetham, A. K. J. Am. Chem. Soc. 2009, 131 (42), 15375–15386. (a) Seo, J. S.; Whang, D.; Lee, H.; Jun, S. I.; Oh, J.; Jeon, Y. J.; Kim, K. Nature 2000, 404 (6781), 982–986. (b) Nomiya, K.; Takahashi, S.; Noguchi, R.; Nemoto, S.; Takayama, T.; Oda, M. Inorg. Chem. 2000, 39 (15), 3301–3311. (c) Wu, C. D.; Hu, A.; Zhang, L.; Lin, W. B. J. Am. Chem. Soc. 2005, 127 (25), 8940–8941. Allen, F. Acta Crystallogr., Sect. B: Struct. Sci 2002, 58, 380–388. (a) Stouten, P. F. W.; Verwer, P.; Vaneijck, B. P.; Kroon, J. Acta Crystallogr., Sect. C: Cryst. Struct. Commun 1988, 44, 1961–1963. (b) Bott, R. C.; Sagatys, D. S.; Smith, G.; Byriel, K. A.; Kennard, C. H. L. Polyhedron 1994, 13 (22), 3135–3141. (c) Gelbrich, T.; Threlfall, T. L.; Huth, S.; Seeger, E.; Hursthouse, M. B. Z. Anorg. Allg. Chem. 2004, 630 (10), 1451–1458. See, for example, Figures 28-30 within ref 6e. (a) Harvey, H. G.; Slater, B.; Attfield, M. P. Chem.--Eur. J. 2004, 10 (13), 3270–3278. (b) Lee, C.; Mellot-Draznieks, C.; Slater, B.; Wu, G.; Harrison, W. T. A.; Rao, C. N. R.; Cheetham, A. K. Chem. Commun. 2006, 25, 2687–2689. (c) Bailey, A. J.; Lee, C.; Feller, R. K.; Orton, J. B.; Mellot-Draznieks, C.; Slater, B.; Harrison, W. T. A.; Simoncic, P.; Navrotsky, A.; Grossel, M. C.; Cheetham, A. K. Angew. Chem., Int. Ed. 2008, 47 (45), 8634–8637. (d) Gandara, F.; de la Pena-O'Shea, V. A.; Illas, F.; Snejko, N.; Praserpio, D. M.; Gutierrez-Puebla, E.; Monge, M. A. Inorg. Chem. 2009, 48 (11), 4707–4713. (e) Bernini, M. C.; de la Pena-O'Shea, V. A.; Iglesias, M.; Snejko, N.; GutierrezPuebla, E.; Brusau, E. V.; Narda, G. E.; Illas, F.; Monge, M. A. Inorg. Chem. 2010, 49 (11), 5063–5071. See Figure 1 in reference 11a. The relative stabilities of the charged anionic ligands were computed using the hybrid B3LYP functional with the 6-311G* localized basis. Such a basis set, which does not include diffuse functions, might be insufficient for the description of the delocalized anionic states of the carboxylate groups of dimethylsuccinate. The relative framework stability was computed using the PBE functional with plane-wave basis set. Parr Instrument Company, 211 53rd St., Moline, Illinois 61265 USA. Hooft, R. W. W. COLLECT Data Collection Software; Nonius B. V.: Rotterdam, The Netherlands, 1998.

230

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(16) Duisenberg, A. J. M. J. Appl. Crystallogr. 1992, 25, 92–96. (17) Otwinowski, Z.; Minor, W. In Methods in Enzymology; Carter, Jr., C. W., Sweet, R. M., Eds.; Academic Press: New York, 1997; Vol. 276: Macromolecular Crystallography, Pt A, pp 307-326. (18) Sheldrick, G. M. SADABS. Version 2007/2; Bruker AXS Inc.: Madison, Wisconsin, USA, 2007. (19) CrysAlis CCD, CrysAlis RED and Associated Programs; Oxford Diffraction Ltd.: Abingdon, U.K., 2006. (20) Palatinus, L.; Chapuis, G. J. Appl. Crystallogr. 2007, 40, 786–790. (21) Sheldrick, G. M. Acta Crystallogr., Sect. A: Found. Crystallogr. 2008, 64, 112–122. (22) Farrugia, L. J. J. Appl. Crystallogr. 1999, 32, 837–838. (23) APEX2, 2009.9; Bruker AXS Inc.: Madison, Wisconsin, U.S.A., 2009. (24) Brandenburg, K.; Putz, H. Diamond, 3.2; CRYSTAL IMPACT GbR: Bonn, Germany, 2009. (25) Macrae, C. F.; Edgington, P. R.; McCabe, P.; Pidcock, E.; Shields, G. P.; Taylor, R.; Towler, M.; van de Streek, J. J. Appl. Crystallogr. 2006, 39, 453–457. (26) X’Pert HighScore Plus, 2.0; PANalytical B.V.: Almelo, The Netherlands, 2004.

Yeung et al. (27) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77 (18), 3865–3868. (28) (a) Goedecker, S.; Teter, M.; Hutter, J. Phys. Rev. B: Condens. Matter. Mater. Phys. 1996, 54 (3), 1703–1710. (b) Krack, M. Theor. Chem. Acc. 2005, 114 (1-3), 145–152. (29) VandeVondele, J.; Hutter, J. J. Chem. Phys. 2007, 127, (11). (30) (a) Krack, M.; Parrinello, M. Forschungszentrum Julich, NIC Ser. 2004, 25, 29. (b) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Comput. Phys. Commun. 2005, 167 (2), 103–128. (c) http://cp2k.berlios.de. (31) Brese, N. E.; O’Keeffe, M. Acta Crystallogr., Sect. B: Struct. Sci 1991, 47, 192–197. (32) Karamertzanis, P. G.; Day, G. M.; Welch, G. W. A.; Kendrick, J.; Leusen, F. J. J.; Neumann, M. A.; Price, S. L. J. Chem. Phys. 2008, 128 (24), 17. (33) Rivera, S. A.; Allis, D. G.; Hudson, B. S. Cryst. Growth Des. 2008, 8 (11), 3905–3907. (34) The calculation of the ZPVE approximation (i.e., d2E/dX2) might remain challenging today with respect to the computational cost. (35) Within the harmonic approximation.