The low/room-temperature forms of the lithiated salt of 3,6-dihydroxy-2,5-dimethoxy-p-benzoquinone:...

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COVER ARTICLEFrayret et al. The low/room-temperature forms of the lithiated salt of 3,6-dihydroxy-2,5-dimethoxy-p-benzoquinone: a combined experimental and dispersion-corrected density functional study

CE015015_cover_PRINT.indd 1CE015015_cover_PRINT.indd 1 3/12/2013 10:42:42 AM3/12/2013 10:42:42 AM

Cite this: CrystEngComm, 2013, 15,2809

The low/room-temperature forms of the lithiated saltof 3,6-dihydroxy-2,5-dimethoxy-p-benzoquinone: acombined experimental and dispersion-correcteddensity functional study3

Received 18th September 2012,Accepted 15th November 2012

DOI: 10.1039/c2ce26523k

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Gaetan Bonnard,a Anne-Lise Barres,ab Olivier Mentre,c Damian G. Allis,d Carlo Gatti,e

Philippe Poizota and Christine Frayret*a

Following our first experimental and computational study of the room temperature (RT) form of the

tetrahydrated 3,6-dihydroxy-2,5-dimethoxy-p-benzoquinone dilithium salt (Li2DHDMQ?4H2O), we have

researched the occurrence of hydrogen ordering in a new polymorph at lower temperature. The study of

polymorphism for the Li2DHDMQ?4H2O phase employs both experimental (single crystal X-ray diffraction)

and theoretical approaches. While clues for disorder over one bridging water molecule were observed at

RT (b form), a fully ordered model within a supercell has been evidenced at 100 K (a form) and is discussed

in conjunction with the features characterizing the first polymorphic form reported previously. Density

functional theory (DFT) calculations augmented with an empirical dispersion correction (DFT-D) were

applied for the prediction of the structural and chemical bonding properties of the a and b polymorphs of

Li2DHDMQ?4H2O. The relative stability of the two polymorphic systems is evidenced. An insight into the

interplay of hydrogen bonding, electrostatic and van der Waals (vdW) interactions in affecting the

properties of the two polymorphs is gained. This study also shows how information from DFT-D

calculations can be used to augment the information from the experimental crystal diffraction data and

can so play an active role in crystal structure determination, especially by increasing the reliability and

accuracy of H-positioning. These more accurate hydrogen coordinates allowed for a quantification of

H-bonding strength through a topological analysis of the electron density (atoms-in-molecules theory).

Introduction

Large-scale installations using current lithium ion batteries(LIB) would leave large ecological footprints and face resource

restrictions, as rare metals are used as cathodes on one handand high temperature syntheses are required on the otherhand. Redox-active organic materials, which have beenenvisaged with rising interest for a decade, do not requiresuch materials. To date, various classes of redox-active organiccompounds have been investigated vs. Li+/Li0, including inparticular materials derived from electron-donating/acceptingmolecules (either in the form of polymers or low-molecular-weight crystalline compounds).1–15 In most of these experi-ments, (mono- or polycyclic-) quinone-based materials oroxocarbon salts were envisaged. Many of these compounds arelow-cost, while some might even be biomass in origin.2,3,6,7

Additionally, they are more easily recycled products. However,dissolution issues may pose critical safety and cyclabilityproblems with some of these compounds. Such features mightbe however attenuated if ionic functional groups are present inthe quinonic system.

Taking the benefits from our various observations onquinonic-type structures,2,3,6,7 we have recently designedvarious series of organic salts able to reversibly de-intercalatelithium. One of them corresponds to the lithiated salt of 3,6-

aLaboratoire de Reactivite et Chimie des Solides – UMR CNRS 7314, Institut de

Chimie de Picardie – FR 3085 CNRS, Universite de Picardie Jules Verne, 33, rue

Saint-Leu, 80039 Amiens cedex, France. E-mail: christine.frayret@u-picardie.frbLaboratoire des Glucides – FRE CNRS 3517, Institut de Chimie de Picardie – FR

3085 CNRS, Universite de Picardie Jules Verne, 33, rue Saint-Leu, 80039 Amiens

cedex, FrancecUnite de Catalyse et de Chimie du Solide, equipe de Chimie du Solide – UMR CNRS

8181, ENSC Lille-UST Lille, Cite Scientifique – Bat. C7 – BP 80108, 59655 Villeneuve

d’Ascq cedex, FrancedDepartment of Chemistry, Syracuse University, Syracuse, NY 13244, USAeCNR-ISTM, Istituto di Scienze e Tecnologie Molecolari, Via Golgi 19, 20133, Milano,

3 Electronic supplementary information (ESI) available: Details of thermalanalysis measurements (DSC curve), details of single crystal characterizations (X-ray crystallographic information) as CIF files, and predicted (DFT-D optimized)crystal structures (lattice parameters, AIM analysis and positions of all hydrogenatoms) for the two polymorphic forms. CCDC 910541 (a-phase) and 856689(b-phase). For ESI and crystallographic data in CIF or other electronic format seeDOI: 10.1039/c2ce26523k

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dihydroxy-2,5-dimethoxy-p-benzoquinone (Li2DHDMQ),16 anintermediate structure between the tetralithium salt oftetrahydroxy-p-benzoquinone (Li4THQ) and the tetramethoxy-p-benzoquinone (TMQ) molecule, which is characterized by itsredox amphoteric nature. In this work, we complete ourstructural examination of the tetrahydrated form ofLi2DHDMQ, named as Li2DHDMQ?4H2O, which proved to bean interesting cathode material for Li-ion batteries working atan average potential of 3 V vs. Li+/Li0. As described in ourprevious work,16 concerning the RT polymorph (named asb-phase), a disorder over one bridging water molecule wasevidenced. In order to check the occurrence of a form at lowtemperature, possibly characterized by higher ordering, itscrystal structure was first studied in the present work throughsingle crystal X-ray diffraction at 100 K and differentialscanning calorimetry. At 100 K, a fully ordered model within asupercell has been observed. Structural features of this newform (labeled as a-phase) are discussed in connection withthose characterizing the RT polymorphic form. The experi-mental study is complemented by theoretical approaches,which were successfully applied recently to the study of organiccrystals.16–18 The relative abilities of various exchange-correla-tion functionals: local density approximation (LDA),19 Perdew–Burke–Ernzerhof (PBE) variant of the generalized-gradient-approximation (GGA),20 PBEsol,21 and revPBE22 to account forboth intra- and inter-molecular geometries were alreadyaddressed in our initial work dealing with the RTLi2DHDMQ?4H2O phase.16 As expected, standard DFT methodsfailed in describing the long-range vdW interactions. Especially,among widely used exchange-correlation functionals, neitherLDA nor PBE balances the strong intramolecular chemicalbonding and the weak intermolecular attractions, resulting inincorrect equilibrium structural features. We thereforeextended our study to the incorporation of dispersion correc-tions in the PBE density functional. An indication of the muchbetter agreement with the experiment by including suchcorrections was found. More precisely, the concomitant rescal-ing of vdW radii of the damping function and the modulation ofthe s6 parameter in the dispersion energy term16 was proven tobe very efficient for the adequate structural description of suchcompounds. In particular, it was possible to establish that theinteraction between Li2DHDMQ?4H2O layers should be domi-nated by vdW interactions due to the large difference betweenthe inter-plane distance d calculated with a particular disper-sion corrected method and unmodified PBE. Therefore, in thiswork, we restricted our computational approach to thedispersion-corrected DFT treatment by using similar processes.However, in the work dealing with the RT phase16 only the GGA–PW method was used. In this paper, we compared critically thepotential of the two DFT approaches, hybrid B3PW9123 LCAOand GGA–PW (see the ‘Computational details’ section of theESI3), to calculate the structural and chemical properties of thetwo Li2DHDMQ?4H2O polymorphs, especially regarding hydro-gen bonding. Indeed, hybrid functionals usually obtain moreaccurate H-bonding data than non-hybrid (traditional GGA andLDA) functionals.

Additionally, we should stress that hydrogen positions incrystal structures are often very difficult to locate due to theweak ability of the hydrogen atom to scatter X-rays. It shouldbe noted that it is quite common that hydrogen positions arealso dynamically disordered at RT. Even for the RT cases, theexercise of pinpointing hydrogen positions is not futile; it mayshed light on local conformations as well as hint at the modesof stabilization in possible low-temperature forms. In thiswork, even if it is difficult to get reliable scattering data fromhydrogen atoms using X-ray diffraction, a first estimation ofthe hydrogen atom locations was provided when the structurewas solved by X-ray diffraction techniques, which werecompared to those issued from the theoretical approach.More realistic D–H bond lengths were gained from theoptimization by starting from this trial location.

We shall also outline that getting an accurate picture of thehydrogen coordinates is a prerequisite for correctly revealingthe strength of hydrogen bonds (HB) within each polymorph.Indeed, stabilization due to stacking in the Li2DHDMQ?4H2Ocompound originates from both vdW forces and H-bondinginteractions. While the vdW energy for both polymorphs can bedirectly compared, there is a need to quantify the magnitude ofH-bonding from chemical bonding analyses. To this latterrespect, it is possible to use a topological study of the electrondensity to complement the geometrical considerations.Developed by Bader and co-workers,24 the Atoms-In-Molecules(AIM) theory, which was built through the implementation ofpurely physical arguments, offers a rigorous way to partition anymolecular system into atomic fragments by considering thegradient vector field of its electron density. Such partitioning ofthe electron density allows for the evaluation of atomiccharges,25–29 which can be useful, for instance, in order toappreciate the occurrence of charge transfer. It also describes themolecular topology through the determination of Bond CriticalPoints (BCPs) between two bonded atoms. At each BCP, severalproperties may be calculated, such as the electronic density (r)and the Laplacian field +2r(r). These properties are related to thecharge distribution and to the extent of electron sharing betweenthe linked atoms and allow for a classification of the interactionas shared (covalent) or closed-shell (ionic/HB) when theelectronic density is concentrated or depleted, respectively.Here we report the topological features of charge densitiesissued from our theoretical analysis on the two crystal forms.

Methods

Crystallization conditions for Li2DHDMQ?4H2O were alreadydescribed in our previous paper.16 Differential scanningcalorimetry (DSC) measurements were carried out with aNetzsch DSC204 under argon flow using sealed aluminumcrucibles with cap layers perforated just before the analysis toallow for gas release.

Single crystal XRD measurements were accomplished atboth RT and 100 K using a Bruker X8 Apex2 CCD4K (Mo Karadiation, l = 0.71073 Å) equipped with an Oxford Cryostream

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cooling system. Absorption corrections were performed usingthe multiscan SADABS program.30 Structures were solved bydirect methods using SHELX31 and least-squares refinementwas conducted with the JANA2006 software package.32

Hydrogen positions have been located through Fourierdifference maps. Crystallographic data for both polymorphsare listed in Table 1.

The optimized structures of the two bulk crystals wereobtained from the VASP33 and the CRYSTAL0934,35 packages bytaking into account the empirical dispersion of Grimme.36

Calculations were carried out at the PBE-D and B3PW91-Dlevels of theory. Inclusion of vdW radii modification proposedby Civalleri et al.37 and additional adjustment of the s6 valuessuggested by King et al.17 to this latter method wererespectively labelled PBE-D* and corr-PBE-D*_0.52.16 Optimals6 values were identified to be 0.36 and 0.52 for the RT and100 K phases, respectively. BCPs for the two polymorphs wereanalyzed through the AIM24 theory by using the TOPOND38

program. Further details of thermal analysis, X-ray datacollections and computations are available from the ESI.3

Results and discussion

Structure descriptions

b-Li2DHDMQ?4H2O phase at RT. Li2DHDMQ?4H2O crystal-lized in the monoclinic space group P21/n with one-halfp-benzoquinone derivative molecule,16 one lithium and twowater molecules in the asymmetric unit (Table 1). Onehydrogen atom from a water molecule is disordered over twohalf-occupied positions, H2b9 and H2b99. As already describedfor anionic p-benzoquinone salts39,40 and in particular forlithium chloranilate salts,41,42 the dianionic organic moleculeconsists of two resonance sub-systems with delocalized

electrons separated by two C–C single bonds (Fig. 1). Thismesomeric effect is corroborated by the bond length analysis(Table 2). Indeed, the same distance value is measured for alldelocalized C–O bonds (average distance of 1.26 Å) and fordelocalized C–C bonds (average distance of 1.39 Å), respec-tively, named a and b in Fig. 1. The 1.53 Å length of theremaining non-delocalized C–C bond, named c, is in agree-ment with a single bond. As the negative charge is distributedon a one-half symmetric part of the molecule, oxygen atoms ofthe carbonyl groups are characterized by a similar electronicenvironment, thus explaining the comparable distance separ-ating these atoms from lithium. The first coordination shell ofthe lithium can be described as a distorted square pyramidconsisting of five independent oxygen atoms, two of thembelonging to water molecules and the three others belongingto the quinone molecule (two carbonyl and one methoxygroups (Fig. 2a)). Molecules are stacked along the crystal a axisand linked together through a lithium coordination networkin the bc plane, thus creating a layered structure. One watermolecule is located within the layers while the second onebridges two layers (Fig. 3a). Furthermore, the bulky methylterminal groups prevent a face-to-face stacking of thep-benzoquinone, inducing a slipping from one layer to theother. Contrary to the tetramethoxy-p-benzoquinone, thepacking is not stabilized by a p…p stacking interactionbetween parallel layers, as identified by the long centroid–centroid distance (5.33 Å).43 The large inter-plane distance(4.66 Å) is essentially due to the presence of the intercalatedwater molecule between the layers. In this structure, crystalpacking essentially relies on the HB network, confirmingprevious conclusions on the predominant contribution ofthese interactions on the stacking of quinoid rings.41,44 Thisstrong hydrogen network is based on the interplay of hydrogenatoms belonging to water molecules with four of the fiveindependent oxygen atoms of the structure, i.e. two from thecarbonyl groups of the organic molecule and two other onesfrom water molecules (Fig. 4a). HBs and their geometricaldescription are summarized in Table 2.

a-Li2DHDMQ?4H2O phase at low temperature. At first, DSCanalyses were carried out in order to check the existence of apotential phase transition. Upon one cooling–heating cycle(RT-92 K), no specific thermal event occurred, i.e. no phasetransition is expected (in ESI,3 Fig. S1). Considering singlecrystal X-ray diffraction data recorded at 100 K, the reciprocallattice is characterized by the presence of a supercell reflectionset, as shown in ESI,3 Fig. S2. From the latter, we compared the(h0l) precession frame calculated from both data collections.

Table 1 Crystallographic data for the two polymorphic forms of theLi2DHDMQ?4H2O compound. Data of b-phase were already published in ref. 16

Crystal data a-Phase b-Phase

Formula C8H14Li2O10 C8H14Li2O10

T/K 100 298Mr/g mol21 284.1 284.1Crystal system Monoclinic MonoclinicSpace group P21/n P21/na/Å 10.5610(8) 5.3318(5)b/Å 9.4941(7) 9.5162(9)c/Å 13.2344(8) 12.7812(13)b/u 107.394(3) 96.490(10)V/Å3 1266.30(15) 644.34(11)Z 4 2Dcalcd/Mg m23 1.4896 1.464F(000) 592 2962hmax/u 62.36 52.28Measured reflections 41 727 26 652Unique reflections (Rint) 4098(0.0415) 1284(0.0466)Number of parameters 237 120GOF (S) 1.15 1.07R1, wR2 [I . 3s(I)] 0.0327, 0.0488 0.0316, 0.0266R1, wR2 (all data) 0.0501, 0.0538 0.0422, 0.0321D(r)/e A23 0.63, 20.23 0.17, 20.14

Fig. 1 Delocalization scheme of the negative charges in the DHDMQ22 ionwithin the crystal phase indicating the bond distances (a = 1.26 Å; b = 1.39 Å; c =1.53 Å).

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The relationship between the two forms is given by aAa = 2aAb

bAa = 2bAb, cAa = 2cAb 2 aAb, where a and b refer to the low-temperature and RT form, respectively. The occurrence of thissuperlattice does not affect the symmetry of the whole crystalsince the space group (P21/n) is retained. As already men-tioned, the cell volume at 100 K (a-form) is doubled comparedto the b-form. The expansion of the cell occurs in the (ac) planewhile the b parameter remains almost unchanged. Fig. 3highlights the transformation from one phase to the other. Atfirst glance, there is no obvious difference between the twoforms since the molecules occupy nearly the same positionsand remain similarly oriented. The relationship between thetwo forms concerning the water molecule is shown in Fig. 5.The low-temperature superstructure is driven by the orderingof the two randomly disordered hydrogen atoms (H2b9 andH2b99), assorted with high thermal motion parameters. Ofcourse, this ordering along with related thermal effects isaccompanied by intermolecular rearrangements that, even ifminor at first glance, are sensitive since the set of supercell

reflections appears relatively intense. Ow1(b) is split into thetwo independent Ow1(a) and Ow3(a) atoms, which roughlypreserve their O–H orientations. The corresponding disor-dered Ow2(b) molecule is split in the two independent ones(Ow2(a) and Ow4(a)), each of them taking one specific O–Horientation from the parent multi-configuration. As a conse-quence of the hydrogen ordering, the novel extended networkis modified from one layer to the other due to the antagonistHw2b and Hw4b locations (Fig. 4). The corresponding HBsinvolve other water molecules for the first one (Hw2a), whereasthe second one (Hw4b) points towards the oxygen atom of thecarbonyl group. Similarly, in the a- and b-forms, weak HBsexist between two hydrogen atoms from methyl groups and anoxygen from water or quinone molecules but with a very lowimpact on the crystal packing compared to the strong HBnetwork induced by water molecule hydrogen atoms. HBdistances and angles relative to a-phase are given in Table 3. Adeeper inspection into the structure revealed a slight motionof the quinone molecules. The stacking of the organic

Table 2 Theoretically and experimentally determined intramolecular and intermolecular bond distances for the polymorphic b-form

EXP Theoretical calculation

RT corr-PBE-D*_0.52 corr-PBE-D*_0.36 B3PW91-D*_0.36

Intramoleculard(C–C) d(C1a–C2a) 1.390(2) 1.404 1.404 1.398

d(C2a–C3a) 1.397(2) 1.412 1.412 1.410d(C3a–C1a) 1.532(2) 1.535 1.535 1.534,d(C–C). 1.440 1.450 1.450 1.447,d(C–C) except (C3–C1). 1.394 1.408 1.408 1.404

d(C–O) d(C4a–O2a) 1.427(2) 1.447 1.447 1.430d(C1a–O1a) 1.263(2) 1.277 1.278 1.267d(C2a–O2a) 1.394(2) 1.389 1.390 1.378d(C3a–O3a) 1.259(2) 1.268 1.268 1.254,d(C–O). 1.336 1.345 1.346 1.332,d(delocalized C–O). 1.261 1.273 1.273 1.261

RMSD C–C, C–O 0.013 0.013 0.009d(C–H) d(C4a–H4a) 1.00(2) 1.095 1.095 1.089

d(C4a–H4b) 1.02(3) 1.099 1.099 1.093d(C4a–H4c) 0.94(3) 1.099 1.099 1.094,d(C–H). 0.99 1.098 1.098 1.092

d(O–H) d(OW1–HW1a) 0.90(2) 1.000 1.000 0.986d(OW1–HW1b) 0.89(2) 0.994 0.994 0.989d(OW2–HW2a) 0.78(2) 0.995 0.995 0.978d(OW2–HW2b9) 0.96(8) 0.977 0.977 0.980,d(O–H). 0.88 0.992 0.992 0.983

Intermoleculard(O…H–Cmethyl) d(O3

…H4a–C4) 2.81(2) 2.670 2.689 2.660d(O…H–O) d(O1

…H2b9–OW2) 2.27(9) 2.005 2.027 1.983d(O1

…H1b–OW1) 1.88(2) 1.745 1.752 1.787d(O3

…H1a–OW1) 1.82(3) 1.679 1.686 1.713d(OW1

…H2a–OW2) 2.07(3) 1.735 1.745 1.789d(Li…O) d(Li…O1) 2.113(3) 2.188 2.185 2.156

d(Li…O2) 2.379(3) 2.338 2.347 2.3823d(Li…O3) 2.015(3) 2.063 2.070 2.0525d(Li…OW2) 1.949(3) 1.935 1.945 1.940d(Li…OW1) 2.004(3) 2.030 2.038 2.021

RMSD Li…O 0.046 0.046 0.027,(O…H–Cmethyl) ,(O3

…H4a–C4) 114(2) 113.3 112.9 112.4,(O…H–O) ,(O1

…H2b9–OW2) 140(6) 149.9 149.6 152.1,(O1

…H1b–OW1) 168(2) 170.3 170.5 169.9,(O3

…H1a–OW1) 175(2) 175.4 175.5 177.6,(OW1

…H2a–OW2) 151(3) 157.9 158.0 155.3

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molecules is modified since they are no longer strictly parallelto each other but deviated by 7.23u with respect to the planedefined by the molecular ring from the upper layer. Thisdeviation does not strongly affect inter-planar distances, with

the average distance of 4.61 Å remaining close to the initial4.66 Å distance in the b-structure (Fig. 3). Similarly to thecrystal structure of the b-form, each negative charge isdelocalized on one-half molecule (for both A and B p-benzo-quinone molecules) as demonstrated by C–C and C–Ointeratomic distances (in ESI,3 Table S1). Concerning the twoindependent lithium coordination polyhedra, the initialgeometry is preserved. Oxygen group ligands are the sameand, as in the b structure, the shortest Li…O distances are alsoassigned to oxygen atoms from water molecules (,2 Å) (Fig. 2).Li1 and Li2 are five-fold coordinated (to two oxygen atoms fromwater molecules, to one oxygen atom from the methoxy groupof molecule A, and to the two oxygen atoms from the carbonylgroups of molecule B (Fig. 2b)). However, small differences inthe Li…O distances can be pointed out. In particular, ashrinking of the Li2–O bonds involving the oxygen from watermolecule Ow2 and the O2b from the methoxy group is observedcompared to the other ‘‘LiO5’’ polyhedron existing in thea-phase and the one from the b-form. This difference clearlyoriginates from the Ow2 and Ow4 water molecules ordering atlow temperature. Such small changes in the HB network canhowever affect the electronic environment of oxygen atomsand their interactions with lithium atoms, resulting in slightdistance modifications.

DFT calculations

Relative stability and inter-/intra-molecular structural fea-tures for the a- and b-forms of the Li2DHDMQ?4H2Ocompound. From total energy results, we observed that thea-phase is more stable than the b-phase. According to ourvarious results, we noticed that changing the methods forcalculating vdW interactions did not modify the relative energyordering, but did lead to larger or smaller relative energy

Fig. 2 (a) Lithium coordination polyhedron in the b-phase with Li…O distances:a = 1.951(3) Å, b = 2.380(3) Å, c = 2.003(3) Å, d = 2.113(3) Å, e = 2.016(3) Å; (b)the two lithium coordination polyhedra in the a-phase with Li…O distances: a =1.923(2) Å, b = 2.260(2) Å, c =2.046(2) Å, d = 2.168(2) Å, e = 2.035(2) Å, a9 =1.947(2) Å, b9 = 2.434(2) Å, c9 = 1.967(2) Å, d9 = 2.056(2) Å, e9 = 1.998(2) Å.

Fig. 3 Unit cell transformation from RT b-phase (a) to low temperature a-phase (b).

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differences between both polymorphs. In order to consider atreatment taking into account the best reproduction ofgeometrical features, we have to perform a comparisonbetween results linked to distinct s6 scaling factors. We thusadjusted the vdW energy according to the ratio between thetwo optimal s6 values identified within the corr-PBE-D*_0.xxformalism (see the ‘Computational details’ section of the ESI3):0.52 for the a-phase against 0.36 for the b-one; see below. Thisallowed us to adjust the total energy subsequently in order toget meaningful values, which now can be directly compared.The energy difference between the structure with the lowestenergy and the one with the highest energy was 14.18 kJ mol21

per formula unit (p.f.u.). On the other hand, the difference invdW energy between both phases amounted to only 1.83 kJmol21 in favor of the a-phase, showing the higher extent ofvdW interactions within the low-temperature phase. Thesevalues thus might be an indication that the H-bondingconformational energy is important to the overall energy ofthe system. Such considerations will be discussed hereafterthrough the accurate analysis of the HB’s relative strength. Onthe other hand, varied kinds of electrostatic interactions arepresent in the crystal, involving especially Li…O interactions.From both experimental and computational data, Li…Odistances appeared to be longer (by 0.01 Å on average) in the

Fig. 4 Compared hydrogen bond networks of: (a) b-phase and (b) a-phase. Hydrogen atoms from methyl groups and their weak associated hydrogen bonds areomitted for clarity.

Fig. 5 Hydrogen atoms ordering from RT b-phase to low temperature a-phase.

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b-phase, also explaining the differentiation in energy betweenboth phases (due to the lower stabilization ascribable toelectrostatic interactions in the b-form).

The optimized cell parameters for the a- and b-forms aregiven in ESI,3 Table S2. Fig. 6a–c, respectively, highlight thechanges in unit cell volume or monoclinic angle, in latticedimensions and in inter-plane distance d, with respect to theexperimental X-ray data for the full-geometry optimizations ofthe a- and b-unit cells. From the comparison with theexperimental values, it may be concluded that both corr-PBE-D*_0.52 and corr-B3PW91-D*_0.52 treatments accurately pre-dict the unit cell volume for the a-form, the discrepancy withexperiment (DV/V) being almost nonexistent for the firstmethod and lower than 1% for the second one. These resultsappear to be slightly better than the ones found for the PBE-D*calculation, which lead to a DV/V value of y1.5%. However, byexamining the changes in the lattice parameters of thea-phase, we can draw more explicit conclusions concerningthe ability of the distinct methods to account for theintermolecular interactions of the system. Indeed, the resultsof the optimization with the corr-B3PW91-D*_0.52 functionalare in much better agreement with experiment, with only avery slight underestimation of the a and b lattice parameters(lower than 1%) and a tiny overestimation of the c one. In

comparison, larger deviations with respect to experiment arefound for the corr-PBE-D*_0.52 treatment. Therefore, the lackof volume variation for the latter method was only due to acompensation of the positive and negative evolutions in latticeparameters. The extent of deviation from the experiment forthe calculated interlayer spacing, d, is only slightly enhancedfor corr-B3PW91-D*_0.52 (+0.9%) as compared to that of thecorr-PBE-D*_0.52 method (20.4%). For the intermolecularfeatures, the corr-B3PW91-D*_0.52 method thus appears onthe whole as the best suited for the a-phase. Concerning theb-phase, an improvement has been evidenced compared to ourprevious studies on this polymorphic form16 by selecting thecorr-PBE-D*_0.36 method instead of the corr-PBE-D*_0.52 one(Fig. 6a and ESI,3 Table S2). Using this improved dispersionparameter (s6 = 0.36), the unit cell volume was neitheroverestimated nor underestimated (DV/V = 0%), whereas itundergoes an underestimation of 21.1% for s6 = 0.52. Fromthe lattice parameter consideration, this can be correlated to adecrease in the discrepancy with experiment of the b unit cellparameter, while the error relative to other lattice parametersis roughly the same in the two polymorphic forms. Finally, thelowest relative error in inter-plane distance d is also found forcorr-PBE-D*_0.36 (Dd/d = 0%), whereas corr-PBE-D*_0.52 andcorr-B3PW91-D*_0.36 methods are characterized by only slight

Table 3 Theoretically and experimentally determined distances for intermolecular interactions in the polymorphic a-form

EXP Theoretical calculation

100 K PBE-D* corr-PBE-D*_0.52 corr-B3PW91-D*_0.52

d(O…H–Cmethyl) d(O1b…H2a–C4a) 2.77(1) 2.710 2.746 2.841

d(O3a…H3b–C4b) 2.70(1) 2.596 2.592 2.524

d(O3b…H1a–C4a) 2.79(1) 2.7299 2.7502 2.712

d(OW2…H2b–C4b) 2.81(1) 2.6757 2.6873 2.730

d(O…H–O) d(O1a…H4Wb–OW4) 2.01(1) 1.870 1.874 1.871

d(OW3…H4Wa–OW4) 1.91(1) 1.633 1.644 1.732

d(O1a…H3Wa–OW3) 1.93(1) 1.753 1.755 1.827

d(O3b…H3Wb–OW3) 1.86(1) 1.613 1.635 1.673

d(OW4…H2Wa–OW2) 2.10(2) 1.812 1.824 1.812

d(OW1…H2Wb–OW2) 2.05(1) 1.766 1.785 1.797

d(O1b…H1Wb–OW1) 1.88(1) 1.678 1.695 1.736

d(O3a…H1Wa–OW1) 1.88(2) 1.700 1.705 1.707

d(Li…O) d(Li1…OW1) 1.966(2) 2.008 2.011 1.986

d(Li1…OW4) 1.947(2) 1.975 1.986 2.000

d(Li1…O2a) 2.434(2) 2.298 2.327 2.438

d(Li1…O1b) 2.055(2) 2.089 2.100 2.054

d(Li1…O3b) 1.997(2) 2.070 2.070 2.020

d(Li2…OW2) 1.922(2) 1.934 1.946 1.921

d(Li2…OW3) 2.045(2) 2.097 2.105 2.087

d(Li2…O1a) 2.169(2) 2.204 2.190 2.228

d(Li2…O3a) 2.036(2) 2.095 2.087 2.067

d(Li2…O2b) 2.257(2) 2.213 2.251 2.227

RMSD Li…O 0.061 0.054 0.033,(O…H–Cmethyl) ,(O1b

…H2a–C4a) 125(1) 120.7 121.0 117.6,(O3a

…H3b–C4b) 116(1) 115.8 116.5 112.5,(O3b

…H1a–C4a) 117(1) 113.5 113.4 112.3,OW2

…H2b–C4b) 174(1) 173.4 175.1 177.9,(O…H–O) ,(O1a

…H4Wb–OW4) 158(1) 152.3 152.9 156.1,(OW3

…H4Wa–OW4) 155(1) 158.5 158.2 150.0,(O1a

…H3Wa–OW3) 167(1) 166.9 167.1 168.0,(O3b

…H3Wb–OW3) 175(1) 177.1 177.0 178.5,(OW4

…H2Wa–OW2) 171(1) 174.7 175.0 173.3,(OW1

…H2Wb–OW2) 168(2) 168.7 168.4 165.0,(O1b

…H1Wb–OW1) 170(1) 168.9 169.3 165.0,(O3a

…H1Wa–OW1) 173(1) 174.1 174.3 175.3

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underestimation (20.9%) or overestimation (+1.0%), respec-tively.

In addition to intermolecular geometry features, we shallalso consider the influence of the various selected methods onbond lengths. The overall agreement between the differentlevels of theory and experiment is characterized by the rootmean square deviations (RMSDs) with respect to the experi-mental data, which quantify the deviations from the experi-mental bond lengths. Due to the uncertainty of H positioninggained from X-ray diffraction, RMSD evaluation was restrictedto C–O and C–C bonds. The relative ability of the various

methods to reproduce bonding distances for the a-formroughly follows the same ranking already noted for the latticeparameter reproductions (in ESI,3 Table S1): the corr-B3PW91-D*_0.52 provides the most correctly described intramoleculargeometry (with RMSD = 0.007 Å). However, we should stressthat RMSD values for corr-PBE-D*_0.52 and PBE-D* (0.009 Åfor both), although more elevated, are not very far from theone characterizing the best method. With the corr-B3PW91-D*_0.52 treatment, the departure from the experimentgenerally corresponds to a slight overestimation of the C–Cbonds (except two, which are underestimated) and to a slightunderestimation of the C–O bonds (except two, which areoverestimated). By looking at averaged distances for thedelocalized C–C bonds, the departure from the experiment(1.40 Å) appears to be negligible (1.41 Å) or nonexistent (1.40 Å)for corr-PBE-D*_0.52 and corr-B3PW91-D*_0.52, respectively.The non-delocalized C1–C3 bond distance for these twomethods is only very slightly shorter (1.53 Å) than theexperiment (1.54 Å) as well. Similarly, the delocalized C–Odistance is 1.27/1.26 Å for corr-PBE-D*_0.52 and corr-B3PW91-D*_0.52, respectively, which agrees quite well with theobserved bond length (1.26 Å). As expected, due to theuncertainty on the H positions, higher discrepancies withthe experiment are observed regarding bonds involving Hatoms. For this latter ground, the D–H bond lengths of thea-phase will be discussed in the section relative to theH-positioning.

Calculated bond lengths of the b-form are presented inTable 2, along with RMSD values for the C–C and C–O bonds.For the reproduction of lengths related to these latter bonds,corr-PBE-D*_0.52 and corr-PBE-D*_0.36 exhibit nearly identi-cal results, leading to an overestimation of all interatomicdistances except one (d(C2a–O2a)), which is slightly under-estimated. Accordingly, the same RMSD value (0.013 Å) isobserved for both levels of theory. A lower extent of deviationwith respect to the experiment is found by using the corr-B3PW91-D*_0.36 treatment, with an RMSD value of 0.009 Å.The maximum discrepancy between experimental and compu-tational results concerning C–C bond distances is around0.01 Å for both the corr-PBE-D*_0.36 and corr-B3PW91-D*_0.36 methods, while a slightly higher extent (0.02 Å) isfound in the case of C–O bonds for the corr-PBE-D*_0.36treatment compared to the corr-B3PW91-D*_0.36 one (0.01 Å).

Examination of intermolecular distances, namely Li…O(ionic interaction) and O…H (HB) (in ESI,3 Tables S3a andS3b for the a- and b-phase, respectively), is restricted here tothe first kind of interaction while the HBs will be describedhereafter. For a same s6 value, we observe that the hybridfunctional always leads to a lower extent of RMSD values (forboth phases) among the various set of methods. The extent ofdiscrepancy with experiment is however higher for the Li…Ointeractions compared to the bonded interactions, even withthe corr-B3PW91-D*_0.36/0.52 methods (in the RT/100 Kphase). In the RT phase, switching from s6 = 0.52 to the 0.36value does not affect significantly the reliability of thetheoretical treatment for Li…O distances, resulting in identicalRMSD values (0.05 Å).

Topological features can be used to complement the above-mentioned theoretical results by providing some quantitative

Fig. 6 Relative errors (%) of the DFT or DFT-D calculated values to theexperimental ones: (a) for the unit-cell volume V and monoclinic angle b; (b) forthe optimized lattice parameters, a, b and c; (c) for the inter-plane distance d.

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descriptors of the chemical bonding. Such data were collectedfor the a- and b-phases. A BCP corresponding to zero gradientof electron density is found between each pair of nuclei, whichare considered to be linked by a chemical bond with twonegative curvatures (l1 and l2) and one positive curvature (l3),denoted as a (3,21) critical point. The Laplacian value is ameasure of the local curvature of r(r) and indicates whetherthe electron density is locally concentrated (+2r(r) , 0) ordepleted (+2r(r) . 0) at a given point in space. The bondellipticity, e, defined in terms of the two negative curvatures l1

and l2 as e = (l1/l2 2 1), shows the deviation of the chargedistribution of a bond path from axial (cylindrical) symmetry.The ellipticity at the BCP can thus be interpreted as a measureof the anisotropy of the curvature of the electron density in thedirections normal to the bond (a zero value indicating noanisotropy), and therefore serves as a sensitive index tomonitor the p-character of double bonds. The calculatedvalues of electron density (r), Laplacian of electron density(+2r), and bond ellipticity (e) at BCPs of C–C, C–H, O–H andC–O bonds as well as Li…O interactions at the corr-B3PW91-D*_0.52/6-31G(d,p) and corr-B3PW91-D*_0.36/6-31G(d,p) levelsof theory for the a- and b-phase are given in Table 4 and in ESI,3Table S3. All covalent bonds of Li2DHDMQ?4H2O (except thecovalent/polar C3–O3 bond in the b-phase and the covalent/polar C3a–O3a, C3b–O3b and C1b–O1b bonds in the a-form) arecharacterized by negative values of the Laplacian of r at theBCPs. In the two polymorphic forms, the C–C bonds showvalues of r and absolute values of +2r systematically decreasingwith increasing length of the bond, i.e. with an increasing singlebond character. As a demonstration of the sensitivity of e to thepresence of p-bonds, in the b-phase the ellipticity at the C1–C2

and C2–C3 BCPs is around y0.3, whereas at C3–C1 BCP it is onlyy0.1, thus clearly increasing with p character. This result thusconfirms the delocalization scheme issued from the considera-tion of experimental C–C bond lengths, which is also identicalfor the a-phase, for which same features of ellipticity areobserved. Similar evolution of r and absolute values of +2r as afunction of bond lengths are observed for C1–O1, C2–O2 and C4–O2 bonds in the b-phase, although low ellipticity values aremaintained for these three bonds due to the well-knowncovalent/polar character of C–O linkages. Among this series,the weakest bond is the C4–O2 one, because it is associated tothe methoxy group. This observation is completely transferableto the features characterizing the a-phase. All Li…O interactionsin the two forms exhibit a r value smaller than 1, a positiveLaplacian and a ratio l1/l3 , 1. They can therefore be classifiedas closed shell interactions (ionic type) as expected. A shortercalculated average distance is found for such Li…O interactionsin the case of the a-form (2.07 Å versus 2.11 Å for the b one), withassociated higher extent on average for the r(rC) and +2r(rC)values of the low-temperature form. Other electrostatic interac-tions of similar or weaker strength such as Li…C or O…O arealso noticed in both polymorphs (along with one H…Hinteraction present in the a-form exclusively).

H-positioning and H-bonding in the a- and b-forms of theLi2DHDMQ?4H2O compound

Exact knowledge of the H positions is most often crucial forunderstanding organic molecular crystal arrangement due totheir implication in the stability and global reactivity of thesystem. This is especially relevant when a HB network ispresent in the crystal for which the accuracy of non-covalent

Table 4 AIM analysis for the a and b-phases at the corr-B3PW91-D*_0.52 and the corr-B3PW91-D*_0.36 level of theory, respectively. Calculated interatomic distance,RA–B, electron density at BCP, r(rC), Laplacian of electron density at BCP, +2r(rC) and H-bond energy, HBE

RA–B (Å) r(rC) (e Å23) +2r(rC) (e Å25) HBE (kJ mol21)

a-phaseO…H–Cmethyl OW2

…H2b–C4b (HB1) 2.730 0.040 0.482 23.65O3a

…H3b–C4b (HB2) 2.524 0.061 0.843 26.78O3b

…H1a–C4a (HB3) 2.712 0.047 0.650 24.87OW4

…H2a–C4a (HB4) 2.801 0.034 0.507 23.42OW3

…H3b–C4b (HB5) 2.985 0.027 0.386 22.51OW4

…H2b–C4b (HB6) 2.978 0.027 0.361 22.40OW2

…H2a–C4a (HB7) 2.885 0.027 0.386 22.51O–H…Ccarbonyl OW3–HW3b

…C1a (HB8) 2.642 0.223 2.289 236.04OW4–HW4b

…C1a (HB9) 2.662 0.196 2.096 230.20C–H…C C4b–H1b

…C2a (HB10) 2.788 0.047 0.507 24.22C4a–H3a

…C2b (HB11) 2.838 0.047 0.507 24.22O…H–O O1a

…HW3b–OW39 (HB12) 1.827 0.223 2.289 236.04O1a

…HW4b–OW49 (HB13) 1.871 0.196 2.096 230.20O3a

…HW1a–OW1 (HB14) 1.707 0.290 3.132 253.96OW3

…HW4a–OW4 (HB15) 1.732 0.283 3.060 252.05OW1

…HW2a–OW2 (HB16) 1.797 0.236 2.532 239.69OW4

…HW2b–OW2 (HB17) 1.812 0.243 2.435 240.65O3b

…HW3a–OW2 (HB18) 1.673 0.317 3.350 261.31

b-phaseO…H–Cmethyl OW2

…H4a–C4 (HB1) 2.707 0.044 0.578 24.34OW2

…H4c–C4 (HB2) 3.219 0.015 0.228 21.32O…H–O O1

…H2b9–OW2 (HB3) 1.983 0.155 1.633 221.40O1

…H1b–OW1 (HB4) 1.787 0.237 2.548 239.96O3

…H1a–OW1 (HB5) 1.714 0.283 3.068 252.09OW1

…H2a–OW2 (HB6) 1.789 0.247 2.655 242.47

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D–H…A bond lengths is mandatory. For a long time, it wasindeed widely assumed that H-bonding interactions (related toelectrostatics and charge transfer effects) were much strongerthan stacking interactions, mainly referring to vdW and p–pinteractions. From this, it was anticipated that H-bonding wasthe key player in determining molecular structure andproperties where an HB network was present. A recent workfrom Deringer et al.45 sheds more light on the fruitful role thatcan be played by quantum chemistry in order to complementX-ray diffraction data by providing accurate relaxed Hpositions in organic crystals. They especially proved that theiroptimized C–H, N–H, O–H and B–H bond lengths coincidewell with results issued from neutron diffraction studies. Suchvalidation of the density functional computations, even withinthe PBE functional, is encouraging for further similar studies.Moreover, this work also outlined the fact that no systematicerror was found between X-ray and neutron-derived D–H bondlengths, therefore proving that no simple additive correctionwas possible in view of reproducing neutron data from X-raydiffraction results. This constitutes another striking indicationthat quantum chemical approaches might be required in somecases, especially where neutron data is not available.

Comparing experimental heavy-atom distances with thosecalculated globally (with the optimized method, namely corr-B3PW91-D*_0.52) shows minimal differences for the a

structure. Li…O distances differed by a maximum of 0.05 Å,whilst the maximum bonded distance between heavy atomsdiffered by at most 0.01 Å (Li2DHDMQ22 anion), well withincomputational boundaries. Such observations are confirmedby the overlay of the a-phase structure at 100 K and theminimized structure by using the corr-B3PW91-D*_0.52method (Fig. 7), confirming both that the calculated minimumenergy structure corresponds to the one obtained fromexperiment and that such DFT-D treatments are able tocorrectly reproduce interactions between heavy atoms withinthe crystal. Therefore, a confident appreciation from theviewpoint of H positioning should be gained through theconsideration of the corr-B3PW91-D*_0.52 calculation. TableS1 in the ESI3 gathers the experimental and computed D–Hbond lengths of the a-phase while Table S4, ESI,3 provides thecomparison between H positions obtained either from theexperiment or from the calculation. C–H and O–H distancesare roughly elongated by 0.1 Å and 0.2 Å after DFT-Doptimization, respectively. It should be noted as a firstcomment that such a feature is comparable to the overalltoo-short bond lengths observed from the X-ray diffractionstudies by Deringer et al.45 in the case of paracetamol or othermolecular crystals, which validated their computational datathrough neutron studies. Therefore, such observations tend tohighlight once more the deficiency of the X-ray data concern-ing H positioning, since d(D–H) found for the b-phase arearound 1.1 Å according to the calculation versus 1.0 Å fromX-ray data, similarly to what was observed for the paracetamolcrystal by these authors (same extent of discrepancy withexperiment). On the other hand, we shall also stress thatCmethyl–H distances significantly shorten over the temperaturerange due to thermal motion of the methyl group. Somecaution should thus be taken concerning the direct compar-ison between X-ray results obtained at ambient temperature

and those issued from the calculations, which imply inher-ently a static, classical nuclear description of the atom at atemperature of 0 K. Similarly, very satisfying positioning of theheavy atoms were found for the b-phase as can be seen fromthe overlay presented on ESI,3 Fig. S3. Maximum discrepancieswith the experiment fall exactly in the same ranges as thosealready mentioned for the a-phase for both Li…O and bonded(C–C/C–O) distances, therefore demonstrating the reliability ofthe computational approach. C–H and O–H bond lengths wereroughly elongated by 0.1 Å as a consequence of relaxationsimilarly to the a-phase for which the elongation was larger forO–H bonds (0.2 Å). Therefore, we can be confident in Hpositions provided from the calculation for this phase as well(ESI,3 Table S5).

It is well known that the geometric parameters of the HBreflect the strength of the bond. One of the most well knownfeatures of the D–H bond within D–H…A systems are theirelongation in comparison with free D–H bonds. Usually, theshorter the H…A distance, the stronger the HB. In the case ofthe O–H…O bond (which corresponds to the predominantkind of HB here), this HB is accompanied by the lengtheningof the O–H bond and shortening of H…O distance. First of all,we should remark that O–H…O bonds issued from the X-raydiffraction data and from the computational work aredifferentiated in terms of lengths. For instance, HB4 andHB6 are identical in the computed data (1.79 Å) whereas they

Fig. 7 (a) Overlay of the a-phase for the structure at 100 K (red) and theminimized structure by using the corr-B3PW91-D*_0.52 method (blue) vieweddown the a axis; (b) zoom in the overlay of the Li2DHDMQ22 anion and watermolecules.

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are farther from each other in the experiment (1.88 Å and2.07 Å, for a- and b-phases, respectively). There is thus acrucial need for quantification of the HB strength fromtopological approaches.

Different studies have pointed out that the formation of HBsleads to the appearance of a BCP between the hydrogen atomand the acceptor atom, which are linked by the concomitantbond path.46–48 For the RT Li2DHDMQ?4H2O compound, theintermolecular HBs were indeed characterized by the presenceof a BCP between the hydrogen atom and the acceptor oxygen(O) atom, except for one of the intermolecular HBs (O3

…H4a–C4). Additionally, two BCPs were also found for the O…H–Cmethyl HBs corresponding to OW2

…H4a–C4 (labeled HB1) andOW2

…H4c–C4 (labeled HB2). On the other hand, there is noexperimental electron density-based topological evidence forthe occurrence of an intramolecular HB within the compound.The bond critical points identified for O–H…O bonds havetypical properties of a closed-shell interaction: the value of theelectron density at the BCP, r(rC), is relatively low, the |l1|/l3

ratio is ,1 and the Laplacian of the electron density, +2r(rC), ispositive, indicating that the interaction is dominated by thecontraction of charge away from the interatomic surfacetoward each nuclei. More quantitatively, AIM criteria to definea HB consider that r(rC) and +2r(rC) must be within the 0.002–0.035 and 0.024–0.139 ranges, respectively (both in atomicunits),48,49 corresponding to 0.0134–0.235 e Å23 and 0.579–3.350 e Å25 ranges, respectively. Such criteria are fulfilled forHB3, HB4, HB5 and HB6 in the RT Li2DHDMQ?4H2Ocompound, with the slightly larger values for r(rC) in HB4and particularly in HB5 and HB6 denoting their greaterstrength with respect to conventional HBs. Indeed, their bondlength is intermediate between the case of the so-calledpolarized-assisted and resonance-assisted HBs.50 HB1 ispractically within this range (with +2r(rC) = 0.578 e Å25) whileHB2 exhibits a Laplacian of the electron density lower than thelowest +2r(rC) of this range. Moreover, in several works,51,52

the HB length and electron density or Laplacian of the electrondensity revealed an inverse correlation. Therefore, according toTable S3 in ESI,3 the ordering of these two properties allows forthe following classification of HB in terms of strength orderingresulting from r(rC) and +2r(rC) values: HB5 . HB6 y HB4 .

HB3 (as already mentioned through bond length analysis).Results using the AIM approaches are thus in full agreementwith geometrical parameters issued from our calculation.

Other topological parameters might also be considered inorder to characterize the HB strength. For instance, the l3

parameter shows how easily the BCP can be moved along thebond path24 and thus the larger this parameter, the stronger theHB. Therefore, the lower values of l3 also point to a weakeningof the HB. Once more, the ordering of O–H…O bonds in termsof relative strength is validated by the consideration of l3 values.As expected, the two O…H–Cmethyl HBs (HB1 and HB2) exhibittopological features, which clearly evidence the weaker char-acter of these bonds compared to the O–H…O ones, withnoticeably lower values of r(rC), +2r(rC) and l3.

Due to the perfect agreement concerning relative HBstrength between geometrical features and topological ana-lyses for the b-phase, it was possible to propose a directranking of the HBs according to their bond lengths in the

a-phase. For this polymorphic form, O–H…O distances liewithin the range: 1.67–1.87 Å, with the following ordering:HB18 . HB14 . HB15 . HB16 . HB17 . HB12 . HB13 (withone of the O–H…O interactions not identified as a bondcritical point). Similarly, the O…H–Cmethyl HB, with bondlengths lying in between 2.52 and 2.99 Å, can be classified asfollows: HB2 . HB3 . HB1 . HB4 . HB7 . HB6 . HB5. Inboth cases (O–H…O and O…H–Cmethyl bonds), the ranking isperfectly justified by the continuously decreasing values ofelectron density or Laplacian of the electron density revealedfrom the TOPOND package. The evaluation of HB energieswere also carried out by first estimating the potential energydensities, V(rC), at BCPs through the Abramov’s approach53

and by using such V(rC) values in the Espinosa equation.54 Theestimated HB energy values presented in Table 4 corroboratethe already established trends in bond lengths, r(rC) and+2r(rC) values for both phases.

On average, calculated O–H…O bond lengths are equal to 1.77and 1.82 Å for the a- and b-phases, respectively. Therefore, theHB network should be of higher strength in the a-phase forprevailing interactions. This is completely corroborated by thehigher extent of average values observed in the a-phase for bothr(rC) (0.255 e Å23 and 0.231 e Å23 for the a- and b-phases,respectively) and +2r(rC) (2.699 e Å25 and 2.476 e Å25 for the a-and b-phases, respectively). Moreover, the l3 parameter isapproximately 1.1 times larger in the a-phase compared to the b

one, which is also evidence of the higher strength of the O–H…OHB network in the low-temperature form. On the other hand, ahigher number of weak O…H–Cmethyl HBs are present in thea-form compared with the b-one, whereas some additionalinteractions (O–H…Ccarbonyl and C–H…C ones) are also presentin the a-form. In conclusion, as suggested previously, the higherstability of the a-form may also be ascribed to the higher HBconformational energy in this phase, occurring especiallythrough O–H…O bonds but thanks to much weaker HBs as well.

Conclusions

In conjunction with our first study of the Li2DHDMQ?4H2Ophase at RT, experimental evidence of a lower temperaturephase at 100 K was provided through X-ray diffraction. Astructural distinction between the two phases occurred in theform of an ordering phenomenon of H atoms within asupercell at low temperature.

An important prerequisite for the theoretical study ofpolymorphism in crystal structures is the ability of acomputational method to correctly reproduce geometryfeatures of the crystal structures. From this study, the DFT-Dcalculations were established to be sufficiently reliable to actas a validation tool for crystal structures obtained byexperiment, outlining once more the critical role of thedispersion parameter adjustment. Moreover, while DFT-D isoften considered to be relegated to a rather passive role byusing an initially refined crystal structure, this study hasclearly demonstrated that computational work can provideslightly different and likely more reasonable H positioningthan previously proposed by X-ray diffraction experiments.

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Additionally topological features of the electron densityissued from the calculation may serve as a precise tool for thecomparison of HBs within the global HB network of thestructure. Within the AIM approach performed for both a- andb-forms, an inverse correlation between the HB distance,electron density and Laplacian of electron density have beenestablished, allowing an accurate ranking of the HBs accord-ing to their relative strength within the crystals (alsocorroborated by the l3 values evolution). Such analysis alsoallowed us to extract a quantitative differentiation in terms ofrelative HB network strength between both phases.

From the decreasing values of the total energy, it was seenthat temperature diminution stabilizes the structure, with adifference between the total energy of the phases at 298 K and100 K equal to 14.18 kJ mol21 p.f.u. It was proven that such avalue was partly ascribable to the distinction in energiescharacteristic between the two forms for dispersion (vdW)interactions (1.83 kJ mol21 p.f.u.). On the other hand, weakerLi…O interactions and smaller HB network’s strength wererevealed for the b-phase in comparison with the a-one, fromthe topological analysis of the electron density.

Acknowledgements

The authors gratefully acknowledge the GCEP sponsors withinthe GCEP program (http://gcep.stanford.edu/) as well as theRegion Picardie and the FEDER program for financial supportof the project. The authors deeply thank Matthieu Courty(Laboratoire de Reactivite et Chimie des Solides, France) forDSC measurements. We thank the DSI-CCuB from theUniversity of Bourgogne, the computer center MCIA of theUniversity of Bordeaux and Pays de l’Adour and the CINESfrom Montpellier for allowing us to access their computerfacilities. We gratefully acknowledge generous allocations ofcomputing time from the CINES.

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The low/room-temperature forms of the lithiated salt of 3,6-dihydroxy-2,5-dimethoxy-p-benzoquinone:...

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