Predicting the Position of the Hydrogen Atom in the ... - ACS Publications

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Predicting the Position of the Hydrogen Atom in the Short Intramolecular Hydrogen Bond of the Hydrogen Maleate Anion from Geometric Correlations Lorraine A. Malaspina,† Alison J. Edwards,‡ Magdalena Woińska,§ Dylan Jayatilaka,∥ Michael J. Turner,∥ Jason R. Price,⊥ Regine Herbst-Irmer,# Kunihisa Sugimoto,¶ Eiji Nishibori,△ and Simon Grabowsky*,† †

Institute of Inorganic Chemistry and Crystallography, University of Bremen, Leobener Str. NW2, 28359 Bremen, Germany Australian Nuclear Science and Technology Organisation, New Illawarra Road, Lucas Heights, NSW 2234, Australia § Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Zwirki i Wigury 101, 02-089 Warsaw, Poland ∥ School of Molecular Sciences, Chemistry M313, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia ⊥ Australian Synchrotron, 800 Blackburn Road, Clayton, VIC 3168, Australia # Institute of Inorganic Chemistry, University of Göttingen, Tammannstr. 4, 37077 Göttingen, Germany ¶ Japan Synchrotron Radiation Research Institute (JASRI) 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan △ Division of Physics, Faculty of Pure and Applied Sciences, TIMS and CiRfSE, University of Tsukuba, Tsukuba, Japan ‡

S Supporting Information *

ABSTRACT: The position of the hydrogen atom inside the strong and short intramolecular hydrogen bond of the hydrogen maleate anion strongly varies depending on the crystalline environment. Therefore, it has not been possible in the past to accurately determine it using X-ray diffraction data although there are 292 hydrogen maleate crystal structures with different cations in the literature. In this study, a geometric correlation for the accurate prediction of the hydrogen position in the short intramolecular hydrogen bond is presented. The results used to derive the correlation are obtained from low-temperature neutron-diffraction studies on nine different hydrogen maleate salts that span the whole range from perfectly symmetric to highly asymmetric intramolecular hydrogen bonds. Since the only variable in the correlation as derived from the neutron data is the O···O distance, the hydrogen atom position in question can subsequently be predicted using information that is accurately available from routine X-ray data. The procedure is tested using high-resolution low-temperature synchrotron X-ray diffraction structures of the same compounds, before it is applied to X-ray data sets found in the literature in which the hydrogen atom position was not determined accurately or not determined at all, e.g., using a riding model.

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INTRODUCTION

There is a large number of crystal structures of hydrogen maleate salts in the Cambridge Structural Database (CSD)7−9 which show that the O···O distance varies from 2.36110 to 2.540 Å11 with a large variety of intermediate distances. Neutron diffraction studies establish that the O−H distances vary from 1.07912 up to 1.215 Å.13,14 Dayananda et al.,15 Vanhouteghem et al.,16 and Olovsson et al.12 report that a symmetric hydrogen bond is often related to crystallographic mirror symmetry, but not necessarily. It can also be observed in compounds without any symmetry constraints. However, Catti and Ferraris17 suggest that the symmetric position of the H

The hydrogen maleate (HM) anion has been investigated extensively in the past due to its very short intramolecular hydrogen bond. This hydrogen bond closes the HM anion to a seven-membered ring configuration in a resonance-assisted hydrogen bond (RAHB) fashion (see Figure 1).1 Strong hydrogen bonds such as RAHBs are often also called lowbarrier hydrogen bonds, and small molecules that comprise them are used as model systems for different states of enzymatic reactions.2−4 Specifically, hydrogen maleate compounds have been investigated spectroscopically and theoretically with this respect.5,6 It has been stated that one of the important features of the strong hydrogen bond is that it makes the molecule very rigid in contrast to the trans-isomer hydrogen fumarate.6 © XXXX American Chemical Society

Received: March 19, 2017 Revised: May 2, 2017

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DOI: 10.1021/acs.cgd.7b00390 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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from a normal O−H bond is of interest. In the riding model, an O−H distance of 0.82 Å is normally adopted. •Constraint to neutron data. The hydrogen atom position can be constrained in the refinement to a value obtained from neutron-diffraction experiments on the same compound. This strategy is, of course, not generally applicable unlike the two previous strategies. For example, the neutron structure of deuterated methylammonium hydrogen maleate was used to ensure a suitable starting model for an experimental electrondensity investigation of methylammonium hydrogen maleate using multipoles.22 •Normalization. It is a common practice in experimental electron-density modeling to elongate the covalent X−H bonds to averaged values obtained from neutron-diffraction studies as listed by Allen and Bruno28 and fix them in further refinement steps.29 For X−H bonds involved in intermolecular interactions, this might still not be sufficiently accurate. Therefore, different normalization formulas based on geometric correlations have been introduced by Lusi and Barbour.30 Alternatively, normalization terms that do not involve neutron data, but a direct application of the quantum theory of atoms in molecules, can be used.31 •Constraint to values f rom theoretical calculations. It has been shown recently that hydrogen atom positions obtained purely theoretically are in good agreement with those obtained from neutron diffraction when environmental effects are taken into account.32,33 This strategy could be used to constrain the hydrogen atom position. •Hirshfeld atom ref inement (HAR). The hydrogen atom can be treated freely with an improved method of X-ray structure refinement that employs aspherical atomic scattering factors in contrast to the commonly used IAM. HAR34,35 has shown to be capable of reproducibly generating hydrogen atom positions that are as accurate and precise as those obtained from neutrondiffraction experiments.36 HAR has already been used for Lphenylalaninium hydrogen maleate where the symmetric hydrogen atom position is not related to crystallographic symmetry. The hydrogen position could be reproduced with HAR but not with alternative models using multipoles.37 There are alternative methods that use transferable and fixed multipole parameters, such as the invariom formalism, that can reproduce hydrogen atom positions with a similar accuracy as HAR.33 HAR will be exploited in a forthcoming study for further hydrogen maleate X-ray data sets, so it is not applied in this investigation. It is obvious that it is necessary to derive simple methods that are applicable to routine X-ray data sets to accurately determine the hydrogen atom position in the important compound class of hydrogen maleates. Those strategies might be transferable to other compound classes. Our aim is to predict the hydrogen atom position in the intramolecular hydrogen bond based only on information about the non-hydrogen atoms and the intermolecular interaction network. All evidence suggests that changes in O···O distances might play a very important role in the location of the hydrogen atom in the intramolecular hydrogen bond between the oxygen atoms.38,39 Additionally, Olovsson et al.12 derived a correlation between the O−H and O··· H distances when using data sets of only three neutronderived geometries of hydrogen maleate and one hydrogen chloromaleate structure. We extend the idea proposed by Olovsson et al.12 in several aspects:

Figure 1. Hydrogen maleate structure and labeling scheme.

atom is only allowed by a perfect bilateral symmetry, such as required by crystallographic symmetry elements, or in the case of disorder, when in fact, neutron-diffraction experiments have shown that the hydrogen atom in this hydrogen bond is hardly ever disordered over two positions, but its position is highly dependent on the countercation and hence on the intermolecular interaction pattern.12,16,18−21 In some cases, neutron-diffraction experiments and the derived reliable hydrogen atom positions are crucial to solve ambiguities during space group determination.22,23 The hydrogen bond varies from perfectly symmetric to highly asymmetric, which has been established by a total of 17 single-crystal neutron-diffraction studies involving the hydrogen maleate anion with different cations: 9 structures presented in this work, and 8 structures based on a CSD search (REFCODE, reference: CAHMAL11 and IMZMAL11,18 CIRVAA01,16 IMZMAL13,24 MALOQZ03,19 NAHMAL01,12 POVHEN02,22 MALAQZ0125). There is a significantly larger number of published hydrogen maleate structures determined using single-crystal X-ray diffraction, namely, a total of 292 studies.8 In all of these studies, the treatment of the hydrogen atom in the intramolecular hydrogen bond is critical, and its position is questionable and mostly inaccurate. This is not due to carelessness of the authors but due to a lack of available simple methods to accurately determine the position from Xray data only. Hydrogen atom positions from those eight neutron-diffraction studies in the literature cannot be universally used for all of the 292 X-ray structures because the hydrogen atom position depends on the crystalline environment. In general, there are six different ways of dealing with the hydrogen atom position within X-ray-determined molecular structures: •Free ref inement. The hydrogen atom coordinates can be refined freely without constraints and restraints within an independent atom model (IAM). This will always lead to X−H bond distances that are too short because the hydrogen atom does not possess a core electron density. With X-ray diffraction data of exceptionally high quality an accurate distribution of the valence electron density can be determined, but the hydrogen atom will still be displaced toward the bonding partner because the valence electron density of the X−H bond does not coincide with the position of the hydrogen atom nucleus. •Geometric placement and riding model. The hydrogen atom can be placed according to previously established geometric criteria. Then a refinement strategy needs to be adopted that retains a sensible geometry such as the “riding model”26 in SHELX.27 It is obvious that this strategy cannot lead to the correct position of the hydrogen atom in question, particularly in the case of hydrogen maleate anions where the displacement B



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Table 1. Neutron Diffraction Measurement and Refinement Details for the Nine Hydrogen Maleate Compounds Used in This Studya compound crystal system space group formula formula Z a (Å) b (Å) c (Å) α (°) β (°) γ (°) volume (Å3) crystal dimensions (mm) reflections measured refl. at least 2x redundant unique refl. (2x red.) observed refl. (I > 3σ(I)) no. of refined parameters (restraints) resolution (Å) completeness wavelength range (Å) Rint for all 2x red. (obs.) extinction correction number of parameters on Chebyshev weighting final R (I > 3σ(I)) final wR (I > 3σ(I)) GooF deposition number compound crystal system space group formula formula Z a (Å) b (Å) c (Å) α (°) β (°) γ (°) volume (Å3) crystal dimensions (mm) reflections measured refl. at least 2x redundant unique refl. (2x red.) observed refl. (I > 3σ(I)) no. of refined parameters (restraints) resolution (Å) completeness wavelength range (Å) Rint for all 2x red. (obs.) extinction correction number of parameters on Chebyshev weighting final R (I > 3σ(I)) final wR (I > 3σ(I)) GooF deposition number

K HM orthorhombic Pbcm C4H3KO4 4 4.5071 (9) 7.7017 (15) 15.921(3)

PhAla HM37

Ba HM

Mg HM

4AP HM

monoclinic P21 C13H15N1O6 2 10.905(2) 5.2338(10) 11.439(2)

monoclinic P21 C16H28Ba2O24 2 6.4162(13) 19.016(4) 11.412(2)

monoclinic P21/c C8H18MgO14 2 10.192(2) 11.756(2) 6.6189(13)

monoclinic P21 C9H10N2O4 2 7.8515(16) 5.5447(11) 10.921(2)

101.36(3)

92.90(3)

103.66(3)

96.39(3)

552.66(19) 1.6 × 1.5 × 0.4 20678 16079 946 695 57(0) 0.65 0.884 0.850 to 1.700 6.5 (4.8)% not refined 4

640.1(2) 1.8 × 1.6 × 0.7 40536 31922 2487 2231 317(1) 0.60 0.804 0.850 to 1.700 6.4 (4.1) % 5.6(10) 4

1390.6(3) 0.4 × 0.2 × 0.2 28141 17394 1702 1575 631(80) 0.90 0.851 0.850 to 1.700 10.9 (7.7)% not refined 3

770.63(15) 1.5 × 1.5 × 0.9 38875 30530 3046 2295 188(0) 0.60 0.818 0.850 to 1.700 6.4 (4.4)% 7.4(9) 4

472.46(17) 1.6 × 1.2 × 0.9 34502 26407 1601 1496 227(1) 0.65 0.877 0.850 to 1.700 6.5(3.1)% 2.0(4) 3

0.0237 0.0230 1.0000 CCDC-1538844 Ca HM

0.0291 0.0250 0.9998 CCDC-977783

0.0253 0.0197 0.9986 CCDC-1538842

0.0332 0.0301 0.9964 CCDC-1538846 Na HM

0.0256 0.0209 0.9991 CCDC-1538840 8HQ HM

Li HM

orthorhombic Pnma C8H16CaO13 4 11.724(2) 19.637(4) 6.3269(13)

monoclinic P21/n C4H7LiO6 4 5.8334(12) 5.9257(12) 18.803(4)

1456.6(5) 1.8 × 0.7 × 0.7 53225 40818 2444 1636 185(0) 0.65 0.889 0.850 to 1.700 13.6 (8.9)% 22(6) 4

649.80(13) 1.8 × 0.3 × 0.2 24002 18499 2139 1158 164(0) 0.65 0.860 0.850 to 1.700 11.1 (7.6)% 1.4(14) 4

triclinic P1̅ C4H9NaO7 2 5.9390(12) 6.2687(13) 11.247(2) 103.95(3) 91.49(3) 99.82(3) 399.43(15) 1.2 × 0.9 × 0.8 33469 26890 3713 2981 191(0) 0.55 0.743 0.850 to 1.700 4.9 (3.1)% 19.9(7) 3

0.0551 0.0495 0.9987 CCDC-1538843

0.0498 0.0453 0.9968 CCDC-1538845

0.0309 0.0287 0.9998 CCDC-1538847

91.30(3)

C

orthorhombic P212121 C13H11NO5 4 5.3526(11) 10.014(2) 22.411(4)

1201.3(4) 2.0 × 0.9 × 0.6 37566 27634 2031 1937 271(0) 0.65 0.889 0.850 to 1.700 5.9 (3.4)% not refined 4 0.0380 0.0294 0.9997 CCDC-1538841



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Table 1. continued a

Cell parameters and space group obtained from synchrotron X-ray diffraction experiments at 25 K. In order to use the optimum Chebyshev weighting, the refinements were carried out against structure factor magnitudes F. Alternative models using refinement against F2 are deposited in the CIF format as Supporting Information.

Wilson et al.14 showed that the position of the hydrogen atom in the short intramolecular hydrogen bond is unaltered by variation of temperature or pressure. Increasing temperature only contributes to larger unit cell dimensions and atomic displacement parameters but does not introduce a qualitative difference in the potential energy curve for the hydrogen position. Therefore, the eight neutron structures reported in the literature with temperatures ranging from 120 K to room temperature (REFCODE, reference: CAHMAL11 and IMZMAL11,18 CIRVAA01,16 IMZMAL13,24 MALOQZ03,19 NAHMAL01,12 POVHEN02,22 and MALAQZ0125) were included in a final comparison in order to validate our correlation (found using the new low-temperature (12 K) neutron data sets) and assess the statement by Wilson et al.14

(i) we measured nine hydrogen maleate salts with different counterions at 12 K using Laue-type neutron diffraction at the Bragg Institute of the Australian Nuclear Science and Technology Organisation which provided 12 independent experimental hydrogen maleate geometries for the new modified correlation; (ii) we investigate the intermolecular interaction network in detail to find rules that define how the environment determines to which oxygen atom the hydrogen atom will be closely bonded (always labeled O1, for the labeling see Figure 1) without knowledge of the hydrogen atom position; (iii) we propose a modified correlation, outlined in this paper (compared to that presented by Olovsson et al.12), that will allow us to introduce a practical application of this equation in the case when neither O−H nor O···H distances are known. This means that we derive a formula to predict the hydrogen bond lengths from only the knowledge of the O1···O2 distances that are accurately available from routine X-ray diffraction data; (iv) we apply the correlation to X-ray data sets found in the CSD in which the riding model was used in order to determine the hydrogen atom position in these compounds. The compounds measured at the Bragg Institute are (in the order from symmetric to asymmetric, together with the abbreviation used throughout the manuscript, the chemical formula, the reference to the figures where the neutron-derived structures are depicted, and the references to previous X-ray and neutron structure determinations): • potassium hydrogen maleate (K, K[C4H3O4], Figure 3a13,14,23,40−42); • L -phenylalaninium hydrogen maleate (PhAla, [C9H12NO2][C4H3O4], Figure 3b37,43); • barium bis(hydrogen maleate) tetrahydrate (Ba, Ba[C4H3O4]2·4H2O), four independent hydrogen maleate anions in the asymmetric unit labeled 1Ba to 4Ba with different degrees of symmetry/asymmetry, Figure 3c44); • magnesium bis(hydrogen maleate) hexahydrate (Mg, Mg[C4H3O4]2·6H2O, Figure 3d16,45); • 4-aminopyridinium hydrogen maleate (4AP, [C5H7N2][C4H3O4], Figure 3e46); • calcium bis(hydrogen maleate) pentahydrate (Ca, Ca[C4H3O4]2·5H2O, Figure 3f18,47); • lithium hydrogen maleate dihydrate (Li, Li[C4H3O4]· 2H2O, Figure 3g20,48); • sodium hydrogen maleate trihydrate (Na, Na[C4H3O4]· 3H2O, Figure 3h12,49−52); • 8-hydroxyquinolinium hydrogen maleate (8HQ, [C9H8NO][C4H3O4], Figure 3i53). These hydrogen maleate salts span the whole range from perfectly symmetric (K) to highly asymmetric intramolecular O1−H1···O2 hydrogen bonds. The asymmetry in the 8HQ structure is the highest ever reported (Δ = 0.306 Å; Δ = d(O2···H1)−d(O1−H1)).

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EXPERIMENTAL DETAILS

Crystallization. All compounds were crystallized using the slowevaporation method in covered embryo dishes. Solvents, reagents, size, and color of the crystals for each compound are listed in Table 1 and in Table S1 in the Supporting Information. Obtaining crystals with size and quality suitable for neutrondiffraction experiments is still challenging nowadays. The average volume of the crystals used in our experiments was only 1.257 mm3, excluding Ba and Li which were even smaller. Measurements were nevertheless feasible because of the high primary intensity of the white neutron beam at the instrument KOALA (see next section). The Li HM compound presented a needle crystal habit with dimensions of 1.8 × 0.3 × 0.2 (mm), which corresponds to a volume of about 0.108 mm3. The larger specimen of the Ba HM crystals were never single crystals, and therefore the crystal used measured only 0.4 × 0.2 × 0.2 (mm) (volume ≈ 0.016 mm3), which led to a very weak diffraction pattern despite the high exposure time (5 h and 10 min per frame). All crystals were mounted on an aluminum hook using a drop of perfluorinated oil. Data Collection and Refinement. The Laue-technique neutrondiffraction experiment was carried out at the Bragg Institute of the Australian Nuclear Science and Technology Organisation (ANSTO) using the instrument KOALA54 on a thermal guide at the OPAL research reactor with polychromatic wavelength (range from 0.70 to 1.70 Å). The lower wavelength cutoff may vary for the different compounds (see Table 1). Laue patterns were recorded from the stationary crystal with a large cylindrical imaging plate camera at a temperature of 12 K using a helium cryostat. For triclinic and monoclinic space groups two different crystal orientations that differ with respect to each other by about 90° were measured to obtain a sufficiently high completeness. For orthorhombic space groups one crystal orientation was sufficient. For each orientation total exposure times between 24 and 36 h were chosen, except for Ba, for which the complete measurement took more than 4 days. Indexing, integration, normalization, and reduction of data were performed via the program LaueG,55,56 with the integration being based on the Argonne boxes procedure.57 Pertinent details about measurement and data reduction are given in Table 1. With the Laue method, indexing the diffraction pattern of an unknown compound and derivation of lattice constants is neither simple nor routine. This is due to the fact that a Laue diffraction pattern contains a continuous spectrum of wavelengths and hence involves multiple lattice planes in different orientations, making Bragg’s law difficult to solve as both d and λ are unknown parameters. Since X-ray structures below 120 K for the nine investigated compounds were unknown, we had to determine them ourselves. D



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Figure 2. Distribution of the studied structures according to the position of atom H1 in the intramolecular hydrogen bond (asymmetry Δ in Å) including the standard deviation. Therefore, low-temperature X-ray structures of all compounds were obtained using synchrotron radiation (wavelength 0.353(1) Å, resolution range 0.35−0.43 Å (0.55 Å for Ba), redundancy around 10, completeness 100%) at the beamline BL02B1 of SPring-8, Japan, at a temperature of 25 K, which is the lowest possible reasonably achievable stable temperature at the given setup using a helium gasflow low-temperature device.58 The cell parameters obtained from these experiments were used as input for LaueG. As the temperatures between the X-ray and neutron experiments are slightly different, this procedure should lead to slightly higher standard uncertainties for all neutron-derived geometric parameters. For comparison with the normalization procedures introduced in this paper, we report the freely refined hydrogen atom positions with their standard uncertainties based on an IAM of the X-ray data. R-values range from 2.4 to 4.6%. Apart from that, the high-resolution X-ray structures obtained at SPring-8 will be used in a forthcoming electron-density and Hirshfeldatom-refinement study. Therefore, no further details of the X-ray measurements are given here, except for the crystallographic details in Table 1. The CRYSTALS software59 was used to perform structure refinement of the neutron data starting with the non-hydrogen atom positions of the final IAM model from the X-ray diffraction experiments (SPring-8). It commenced from scale-factor refinement, with subsequent refinement of the positional and anisotropic displacement parameters (ADPs). Hydrogen atoms were located from the negative difference Fourier map. In those maps, no signs of hydrogen disorder were found. Final cycles of refinement used ADPs and free position refinement for all atoms, including hydrogens, except for the Ba structure where restraints had to be used on some nonhydrogen ADPs (see Supporting Information). Some of the structures also include an extinction60 parameter refinement that led to a convergent geometry of high precision and quality. For details about the refinements see Table 1, and the CIFs (CCDC-977783 and 1538840−1538847) deposited with the Cambridge Structural Database. They can be downloaded free of charge from https://www.ccdc. cam.ac.uk/structures/.

In contrast to a previous determination of the Ba HM structure at room temperature,44 we observe a noncentrosymmetric crystal packing with four crystallographically independent HM ions. Home X-ray measurements indicate signs of inversion twinning at temperatures lower than room temperature. The weak neutron-diffraction pattern of the barium salt caused by the small crystal size (see Experimental Details) led to a poor ratio of reflections over parameters (2.40) plus 80 restraints; however, this data set was sufficient to determine the hydrogen atom positions in all four HM ions freely with a precision from 0.008 to 0.010 Å, which is high enough to assign the four HM units to the groups defined above: three HM units are in the intermediate group, and one unit is symmetric (Figure 3c). Nevertheless, alternative models of the Ba HM structure (e.g., isotropic refinements) are deposited in the CIF format as Supporting Information. K HM is the only case where the H1 atom is located on a special position, here a mirror plane perpendicular to the c axis (Figure 3a). In the Ca HM structure, two of the water molecules are disordered across a mirror plane (Figure 3f). In the synchrotron X-ray diffraction experiments a weak superlattice pattern was found that could not be resolved since it vanished already during the first run; i.e., the structure could not be refined successfully in a bigger unit cell. However, it is likely that the superlattice reflections are related to the discussed disorder across the mirror plane. In the Li HM structure, pseudotranslation symmetry occurs. Here, the solution in a bigger unit cell is preferable over refinement in a smaller unit cell (space group P21/m) because weak superlattice reflections can be incorporated, and the solution is free of disorder (Figure 3g) in the bigger cell. All the other compounds (PhAla, Mg, 4AP, Na, 8HQ) do not show special features and are determined precisely. Their structures are also shown in Figure 3. Corresponding distances for all bonds of the HM moiety are summarized in Figure 4. It becomes clear that the resonance system that is connected via the RAHB mainly involves the carboxyl and the carboxylate groups but not the CC double bond which remains constant around 1.345 Å within all three groups. For the symmetric group (Figure 4a) a high extent of resonance in the carboxyl/carboxylate groups is visible through the fact that the C−O distances on both sides of the RAHB are similar, whereas in the asymmetric group (Figure 4c) carboxylate and carboxyl groups can be discerned from each other in terms of the C−O distances, showing that the resonance does not extend through the hydrogen bond as much when it is not placed symmetrically. In summary, the asymmetry of the hydrogen atom position is reflected in the extent of the resonance, or vice versa, mirrored in terms of C− O bond length variations. However, there is no statistically significant correlation between the O−H and C−O distances that could be used for generalizations. It will be discussed in the

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RESULTS Intramolecular Geometry. Regarding the position of atom H1, all structures can be sorted into three groups (Figure 2): • a (nearly) symmetric hydrogen bond with (nearly) equal distances for O1−H1 and O2−H1 bonds (Δ = 0− 0.038(6) Å and d(O···O) = 2.4035(10)−2.427(2) Å); • a group with intermediate asymmetry of the hydrogen bond (Δ = 0.185(6)−0.210(6) Å and d(O···O) = 2.4263(18)−2.443(5) Å); • an asymmetric hydrogen bond with asymmetry Δ = 0.287(2)−0.306(8) Å and d(O···O) = 2.4483(8)− 2.450(2) Å. These three groups do not overlap since the differences of the asymmetries are bigger than the standard deviations associated with them. This feature is supported by the high precision of the determination of the proton position in all structures. E



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Figure 3. Neutron-derived geometries for hydrogen maleate (HM) salts. Ellipsoids shown with 50% probability. Symmetry-generated network shown in blue. Distances of most important intra- and intermolecular O−H contacts in Å.

next chapter how the intermolecular interaction pattern induces the asymmetry into the HM moiety.

The averaged angle involving the atoms in the intramolecular hydrogen bond for all structures is 175.9 ± 0.8°, pushing the F



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Figure 4. Bond lengths (in Å) for the HM anion: (a) in the symmetric group (from top line down K, PhAla, 2Ba, Mg, and 4AP HM); (b) in the intermediate group (from top line down Ca, 1Ba, 3Ba, 4Ba, and Li HM); and (c) in the asymmetric group (from top line down Na and 8HQ HM).

in Figure 3 and listed in Table S3. A complete list of hydrogen bonds and close contacts for all structures can also be found in the Supporting Information in Tables S8−S26. It is common to all structures that hydrogen bonds are mainly responsible for the packing directed along the HM molecular plane. The HM ions in PhAla, 4AP, K, Ba, and 8HQ salts are packed in a herringbone pattern perpendicular to (110), and in Mg, Ca, Li, and Na they are packed in layers along the HM L.S. plane (perpendicular to b for Li and Na salts and perpendicular to c for Ca and Mg salts). The PhAla, 4AP, K, and 8HQ salts do not contain any cocrystallized solvent; the remaining salts contain at least two molecules of water in the asymmetric unit which intermediates these bonding patterns. For all compounds the cation contains at least one HM ion in its coordination sphere. The Mg salt is the only exception, where the Mg atom is coordinated exclusively by water molecules, and therefore the HM geometry is the closest to an isolated anion. The Ca HM crystal structure contains three crystallographically independent water molecules that coordinate the calcium atom. Two of these water molecules are stabilized by two intermolecular hydrogen bonds directed toward the carboxyl group in the HM ions. The third water molecule presents only one intermolecular interaction directed toward one of the previously mentioned water molecules and does not coordinate any HM ion, only contributing to the coordination

hydrogen atom outward from the ring. This value agrees with all the reported structures from neutron-diffraction and theoretical calculations for HM anions.6 There is no obvious relation of this angle with the symmetry or asymmetry of the hydrogen bond. Thus, the averaged value will be used for all structures in our calculations to derive our correlation. For all structures the least-squares (L.S.) plane calculation through atoms C1 to C4 shows that the HM anion possesses an essentially planar rigid geometry as expected.6 The planarity is broken, however, if the O1−H1···O2 atoms are included in the least-squares plane. The hydrogen atom H1 can move out of this plane either in a conrotatory or disrotatory fashion. In all cases, the O2 atom shows the largest deviation from the plane, being pulled toward an intermolecular hydrogen bond. The maximum deviation was found for the 4AP salt, with O2 being 0.0961(13) Å away from the L.S. plane and the minimum deviation for the Na salt with O2 being 0.0163(6) Å away. A second L.S. plane was calculated encompassing C1, O1, H1, O2, and C4 atoms for dihedral angle calculations between the first and the second L.S. planes. These values can be seen in Table S2. Atoms O3 and O4 are rotated out of either definition of the L.S. planes in a disrotatory fashion. Crystal Packing and Intermolecular Hydrogen-Bond Analysis. The final neutron-derived geometries showing the hydrogen bonding network for all compounds and the most important intra- and intermolecular O···H distances are shown G



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Figure 5. (a) Hirshfeld surfaces and (b) fingerprint plots of: Mg HM (I), Li HM (II), and 8HQ HM (III). All Hirshfeld surfaces were generated using the same color range from −0.598 (de + di smaller than the sum of the vdW radii - red) to 0.821 (de + di bigger than the sum of the vdW radii blue). The Hirshfeld surfaces and fingerprint plots are labeled using different colors according to the contact types (see legend).

or metal−oxygen contacts with O3 and O4 are present. For a full list of contacts, see Tables S11−S26. These contacts polarize the two oxygen atoms O1 and O2 to different extents. The bigger the difference in the polarization of the two oxygen atoms, the higher the asymmetry in the hydrogen atom position of the intramolecular RAHB. Consequently, hydrogen atom H1 is located more closely to the oxygen atom that is less polarized by the environment. Hirshfeld Surface Analysis. Hirshfeld surfaces were introduced by Spackman62 using the stockholder partitioning idea originally described by Hirshfeld.63,64 A weight function ω is constructed as the ratio of the procrystal electron density of the molecule of interest, relative to the total procrystal electron density. The surface is then delineated by ω = 0.5, which means that the contribution of the molecule of interest to the total electron density is 50% on the Hirshfeld surface. Hence, Hirshfeld surfaces are highly sensitive to the immediate environment as they can be regarded as the molecules’ vander-Waals envelopes.65 They are especially useful to compare different crystal structures incorporating the same molecule66,67 and will be used in this study to depict and analyze the differences in the environment of the HM anion that are decisive for the position of hydrogen atom H1 (Figure 5). The Hirshfeld surfaces were generated using the CrystalExplorer software68 and color coded using the normalized contact distance (dnorm) property. dnorm is defined in terms of the distances from a point of the surface to the nearest nucleus outside (de) and inside (di) the surface. The color code ranges from red (negative), for distances shorter than the sum of vander-Waals radii, through white to blue (positive) for distances longer then the sum of van-der-Waals radii.69 The information on dnorm on the Hirshfeld surfaces can be broken down into 2-dimensional fingerprint representations consisting of di and de pairs.70 They visually summarize the types of intermolecular contacts experienced by molecules in their environments. The map is color coded from blue (fewer points) through green to red (many points). The Hirshfeld surfaces and the respective fingerprint plots for all HM anions in this study are given in Figures S1−S4.

sphere of the calcium atom. Its oxygen atom is disordered across a crystallographic mirror perpendicular to the b axis, and therefore one of the hydrogen atoms is disordered with 50% occupancy (one on each side of the mirror plane). The lack of intermolecular interaction contributes to the high atomic displacements of this water molecule. Averaged over all independent and nondisordered water molecules in all determined structures except Ba (for that the precision is lower and restraints had to be used), the O−H distance in crystal water is 0.971 Å with a relatively narrow spread (sample standard deviation) of 0.006 Å. This value agrees with the equilibrium O−H distance in the isolated state, whereas the average H−O−H angle of 106.0° with a relatively wide spread of 2.1° is significantly larger than the equilibrium angle of 104.5°.61 Another configuration common to all compounds is the existence of a classic intermolecular hydrogen bond toward the neighboring cation or water molecules involving only one of the oxygen atoms in the intramolecular RAHB but not the other oxygen atom (Figure 3). Hydrogen atom H1 in the RAHB is always closer to the oxygen that is not involved in an intermolecular hydrogen bond. This relationship holds without exception for all 11 HM anions in this study and all reported ones for which neutron-diffraction data exist (except for K HM that is perfectly symmetric). The labeling scheme shown in Figure 1 is chosen so that the oxygen atom for which H1 is closer is referred to as O1, whereas the one with the additional intermolecular interaction is O2. It is important to note that for any predictions of the hydrogen atom position in cases where it is previously unknown (see below) the first step is the identification of the oxygen atom that is involved in the classic intermolecular hydrogen bond. In other words, the labels O1 and O2 must be assigned before a prediction about the hydrogen atom H1 can be made. The asymmetry of the RAHB is therefore in direct relationship with the asymmetry of the intermolecular interaction pattern. In addition to the mentioned classic hydrogen bond with O2, more distant contacts such as C− H···O hydrogen bonds involving O1 as well as hydrogen bonds H



Article

The Hirshfeld surfaces for all the compounds show close intermolecular contacts to the carbonyl oxygen atoms of the hydrogen maleate molecule (O3 and O4) (Figures S1−S4). Another common feature already mentioned in this work is the presence of one hydrogen bond involving atom O2 as well as the lack of classic hydrogen bonds to O1. These features can qualitatively be shown in Figure 5 where the Hirshfeld surfaces and fingerprint plots of Mg HM (symmetric group), Li HM (intermediate group), and 8HQ HM (asymmetric group) are depicted. The close contacts (red areas in Figure 5a plotted onto these surfaces are associated with O−H···O, C−H···O, H···H, and C···C contacts, which are highligted by ellipses colored in black, green, orange, and red for each one of these contact types, respectively. On all Hirshfeld surfaces the O− H···O contact involving O2 is largely pronounced, while weak contacts involving O1 vanish progressively with increasing asymmetric positioning of the H1 atom. The fingerprint plots (Figure 5b reveal a H···H contact involving atom H1 in the asymmetric position (8HQ HM). The fine spikes associated with O−H···O contacts do not involve O1 and are located below the diagonal de = di, which indicates hydrogen bonds with the donor atoms inside the surface. C···C contacts (interpreted as π···π interactions) are mostly pronounced for structures with H1 in the symmetric position. These structures are more densely packed than in the other cases. The packing density can be identified by the area extent of the fingerprint plot (smaller area indicating better packing); fuzzy areas with de and di around 2.2 Å associated with voids are detected for fingerprint plots of HM structures involving H1 in nonsymmetric positions (Figure 5(b), III). The fingerprint plots for all hydrogen maleate molecules presented in this study are significantly different from each other, exemplifying the flexibility of this compound regarding intermolecular interactions in crystalline environments. This also holds for the four independent HM anions of the Ba HM structure whose Hirshfeld surfaces and fingerprint plots (Figures S1 and S3a to S3d) are sufficiently different from each other which confirms that they experience a different crystalline environment. On the other hand, two pairs are similar to each other which confirms the existence of a pseudoinversion center that is the reason for the inversion twinning and phase transition between room temperature and low temperature. Correlations and Predictions. While trying to find a correlation for the hydrogen position, the final geometries obtained by neutron diffraction were used. The idea is to establish this correlation so that it can subsequently be used to determine the correct location of the H1 atom while having information only about the non-hydrogen atoms that are accurately available from an X-ray diffraction experiment. As mentioned previously in this paper, the averaged angle involving the atoms in the intramolecular hydrogen bond is 175.9 ± 0.8°. This value is obtained by averaging the angle of O1−H1···O2 for all the 12 independent HM ion units (Table S3). Since this angle is never 180°, the projections of the O1− H1 (y′) and O2···H1 (x′) bond lengths onto the line connecting the atoms O1 and O2 atoms were calculated using the averaged angle (Figure 6). Hence, the sum of the projections, x′ and y′, equals the O1−O2 distance (d). d = y′ + x′ ⇒ y′ = d − x′

Figure 6. Relationship between bond lengths and projections x′ and y′.

the O−H bond distances. The 11 (values for K HM were not included in the linear fit since the result may be affected by the imposed crystallographic symmetry) new points provided us the new correlation that is shown in Figure 7. The standard

Figure 7. Linear correlation between the projected distances x′ and y′ (see Figure 6), including the standard deviations in the linear regression.

uncertainties of the bond distances as well as the population standard deviation obtained through averaging the O1−H1··· O2 angle are accounted for in the linear fit. The parameters of the fit, their uncertainties, and the R2 value are also shown in Figure 7. The dependency of x′ with y′ is explicitly determined by the linear fit (eq 2). y′ = (2.1424 ± 0.0019) Å − (0.7783 ± 0.0015)x′

(2)

We can now combine eqs 1 and 2 leading to eq 3 x′ =

d − (2.1424 ± 0.0019) Å (0.2217 ± 0.0015)

(3)

Equation 3 describes the dependency of the O2···H1 projected distance (and consequently also the O1−H1 projected distance) on the O1···O2 distance only. By reversing the projection using the same averaged angle, the final O1−H1 and O2···H1 bond lengths can be predicted within the propagated uncertainties. In summary, the position of hydrogen atom H1 in the RAHB is only depending on the O1···O2 distance and can hence be estimated from X-ray diffraction experiments. Figure 8 shows the predicted O1−H1 distances for the 12 HM anions of this study using the O1···O2 distances derived from an IAM refinement against the synchrotron X-ray diffraction data. The results with their corresponding uncertainties are compared against the O1−H1 distances determined using neutron diffraction, determined in a free

(1)

The linear correlation between O1−H and O2···H previously reported12 can be improved when using the projections and not I



Article

estimates the symmetric behavior, but it is still a better approximation than the current ways of dealing with the hydrogen atom position within the X-ray-determined molecular structures (see Introduction). The negative slope of the linear correlation found shows that the O1−H1 distance increases with decreasing O···O distance. This characteristic was previously reported by Novak,71 where the author suggests that this feature might be a consequence of different types of potential energies (asymmetric double-well minimum, symmetric double minimum, and symmetric single minimum). In our study, the neutron-diffraction results unambiguously confirm that only a single-minimum scenario is present, and only a single hydrogen atom position is occupied. Eight neutron-diffraction-derived structures of HM salts have been reported before using temperatures ranging from 120 K to room temperature (CSD REFCODE, reference: CAHMAL11 and IMZMAL11, 18 CIRVAA01, 16 IMZMAL13, 24 MALOQZ03, 19 NAHMAL01, 12 POVHEN02, 22 and MALAQZ0125). This provides us with independent H1 atom positions at varying temperatures. The O1−H1···O2 angle agrees with our average which allows us to calculate the projections using the same values. The data points representing the projected distances involving the H1 atom in the intramolecular hydrogen bond are plotted in Figure 9. The

Figure 8. Comparison of O1−H1 bond lengths for the HM anions derived from neutron diffraction, IAM treatment of the X-ray data and calculated using the correlation from this study, and the correlation reported by Lusi and Barbour.30 In 3Ba, the H atom could not be freely refined in the IAM.

refinement against the synchrotron X-ray data in the IAM, and determined using a different correlation reported by Lusi and Barbour.30 In most cases (8 out of 12), our correlation leads to a prediction of the O1−H1 bond lengths that is within a single standard uncertainty relative to the neutron results, which means the correlation is accurate. The IAM results are surprisingly accurate and dramatically different from a ridingmodel value of 0.82 Å; however, they are still less accurate than the correlation, and they never match with the neutron results within a single standard uncertainty (except for the unreasonably large uncertainty of 4Ba, and in the case of K HM where the position is imposed crystallographically). The standard uncertainties for the prediction are considerably smaller than those of the free IAM refinement, which means the prediction is more precise, but the precision of the neutrondiffraction experiment is still highest (error bars smallest). It is also obvious from Figure 8 that the predicted results using our correlation are much more accurate than the results calculated according to Lusi and Barbour,30 who unfortunately do not report standard uncertainties for their correlations. Their correlation overestimates the O1−H1 bond lengths in most cases (7 out of 12) relative to the neutron-derived results. However, the correlations by Lusi and Barbour30 are more general, whereas our correlation is only valid for the compound class of hydrogen maleates, which explains why it is more accurate. In summary, the correlation reported in this study is the simplest and most accurate way to determine the hydrogen atom position in the RAHB of hydrogen maleates if neutrondiffraction results are out of reach. (All numerical results are summarized in Table S6.) From Figure 8 and Table S6 it can be seen that the correlation yields the best results for the asymmetric or intermediate H1 position. For the symmetric group the correlation leads to slightly less accurate predictions, and for K HM, the most symmetric one, the correlation breaks down. A correlation for O1···O2 against O1−H1 has been reported by Ichikawa38 using different classes of compounds (no HM anions). In this work the authors show that there is a split in the correlation curve separating the asymmetric cases from the symmetric ones. If this fact holds for the HM class of compounds, then it would mean that our approach under-

Figure 9. Linear correlation between the projected distances x′ and y′ (see Figure 6) with standard uncertainties, including previously reported neutron data sets at temperatures from 120 K to room temperature.

temperatures and also the intermolecular interaction network of the eight structures used from the CSD are listed in Table S5. In summary, the correlation established in this chapter holds across the temperature range from 12 K to room temperature (see Figure 9). As an independent check of this statement, the position of the hydrogen atom H1 for the reported eight neutron-diffraction-derived structures was calculated using our correlation (eq 3, only based on 12 K data), and the values are still in agreement with the refined positions (Table S7). This confirms the results by Wilson et al.,14 who state that the temperature has no effect on the H1 position. Figure 9 shows that the linear fit including all data is slightly less precise so that we will use the original one determined in Figure 7 for further application. J



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Table 2. Recalculated O-H Distances for Intramolecular Hydrogen Bonds of Previously Reported X-Ray Derived Geometries in Which the Riding Model Was Used (O−H = 0.82 Å)a D···A

calcd O−H

CSD refcode

temp.

donor

H

acceptor

(Å)

(Å)

calcd O··H (Å)

AFIREO DIPJER10 FALPEP TIMOLM01 ISICAP ISICIX NUSVUT OMIGEW OMIGEW OMIGEW QAYPUC QUWXEM RENBAN VAWPUG VAZJUD YAYYUT

173 K RT RT RT RT RT RT RT RT RT RT RT RT RT RT RT

O1S O31 O6 O6B O3 O2 O3 O1SB O4A′ O4A″ O2 O3 O3 O3A O3 O2

H1S H31 H6 H6B H3 H2 H3A H1SB H4A′ H4A″ H1O2 H3 H3 O31A H3D H1O2

O4S O25 O7 O7B O1 O3 O4 O4SB O1ABA O1A″ O3 O2 O5 O2A O2 O3

2.451(2) 2.446(4) 2.412(3) 2.437(4) 2.437(3) 2.429(3) 2.410(4) 2.445(6) 2.416(6) 2.436(6) 2.415(3) 2.4375(15) 2.4465(19) 2.414(3) 2.412(4) 2.429(3)

1.070(9) 1.077(12) 1.197(11) 1.109(12) 1.109(11) 1.137(11) 1.204(12) 1.081(14) 1.183(15) 1.112(15) 1.186(11) 1.107(9) 1.075(9) 1.190(11) 1.197(12) 1.137(11)

1.383(10) 1.370(13) 1.217(11) 1.330(13) 1.330(11) 1.294(11) 1.208(12) 1.366(15) 1.235(15) 1.325(15) 1.230(11) 1.332(10) 1.373(10) 1.226(11) 1.217(12) 1.294(11)

a

Atom labels reported as in the original structures; therefore, donor and acceptor correspond to O1 and O2 (in our labeling scheme), respectively. Calculated O−H (O1−H1) and O···H (O2···H1) distances stem from our correlation and differ substantially from the previously fixed values.

Obtaining an accurate prediction of the H1 position by starting only from the O1···O2 distance has shown to be possible in most cases using the derived correlation. Therefore, in a final step, we apply it to a selection of HM anions found in the CSD. From 292 HM X-ray derived structures in the CSD database, 61 of them present O−H bond distances ranging from 0.71 to 0.88 Å, and at least 24 of them are using the riding model (O−H = 0.82 Å). If we disregard those structures with obvious problems (disorder, twinning, low completeness of the data set, O···O distances greater than 2.50 Å), 16 independent HM anions remain (REFCODE, reference: AFIREO, 72 DIPJER10,73 FALPEP and TIMOLM01,74 ISICAP and ISICIX,75 NUSVUT,76 OMIGEW - 3 independent HM units,77 QAYPUC,78 QUWXEM,79 RENBAN,80 VAWPUG,81 VAZJUD,82 and YAYYUT83). As discussed in the Introduction, the riding model is not useful for compounds with low-barrier hydrogen bonds such as the RAHBs in the HM compound class. Therefore, in the 16 cases listed the hydrogen atom position in the RAHB can be regarded as being unknown. As a first step in the prediction the oxygen atom which is closer to H1 (label O1) has to be identified. This can be easily determined by looking at the environment. As mentioned in the previous section, one classic intermolecular hydrogen bond can always be found for one of the two oxygen atoms but not for the other. This is a surprisingly strict rule and holds for all 16 investigated cases. O1 has no close contacts and is thus bonding more closely to H1, whereas O2 accepts the intermolecular hydrogen bond. Subsequently, the O−H distances for the listed 16 cases were corrected using our correlation, and the obtained values are shown in Table 2. The results with the obtained standard uncertainties have additionally been added to the already existing data points of Figure 9, resulting in Figure 10. Instead of a fixed and physically meaningless bond length of O1−H1 = 0.82 Å, the range of O1−H1 bond distances obtained spans from 1.070(9) to 1.239(11) Å. Moreover, Figure 10 shows that the three groups (symmetric, intermediate, and asymmetric) still prevail with significantly more entries than before. This means that the linear correlation between O1−H1 and O2···H1

Figure 10. Linear correlation between the projected distances x′ and y′ (see Figure 6) with standard uncertainties, including neutron data sets of this study, previously reported neutron data sets, and corrected H1 atom positions by application of our correlation to previously reported X-ray data sets that used the riding model.

is not gradual but discrete. What this implies and what the reason for this phenomenon might be will be investigated in a forthcoming experimental electron-density study on the synchrotron X-ray data sets of the nine investigated compounds of this study.

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CONCLUSIONS The accurate treatment of hydrogen atoms in X-ray crystallography is difficult, especially if they are located inside a low-barrier hydrogen bond. In such a case, the hydrogen atom is significantly displaced from the donor atom. The more general question about correct placement of H atoms along a line connecting a donor and an acceptor is important for medicinal chemistry, where a correct assignment may be decisive for classifying a compound as a salt or a cocrystal. K



Article

In this study, we have investigated hydrogen maleate salts, a class of compounds with a prototype intramolecular low-barrier hydrogen bond. From accurate and precise ultralow temperature (12 K) neutron-diffraction data sets of 9 different hydrogen maleate salts encompassing 12 independent hydrogen maleate anions, we derive an averaged O−H···O angle and projections of the O−H and H···O distances onto the O···O internuclear vector. A linear correlation between these projections with an R2 regression factor of 98% leads to an equation in which the position of the hydrogen atom only depends on the O···O distance. Since the latter is accurately obtainable from X-ray diffraction data, we establish a procedure to easily and accurately estimate the H position in hydrogen maleate salts from routine X-ray diffraction data. We validate the estimation procedure against data sets across the full temperature range from 12 K to room temperature for which both neutron and X-ray diffraction data are available, and we subsequently apply it to 14 X-ray diffraction structures of hydrogen maleates (16 independent units of HM anions) in which the hydrogen atom position was not determined previously but placed and fixed geometrically. It becomes clear that the hydrogen atom position does not depend on temperature, and it is usually not disordered. The H atom position is in direct relationship with the crystalline environment, and especially the degree of asymmetry of hydrogen bonding interactions with the donor and acceptor atoms is decisive. In every case investigated in this study, there is a classic intermolecular hydrogen bond involving the acceptor atom of the intramolecular hydrogen bond (O2), whereas there are only weak interactions (e.g., C−H···O) involving the donor atom (O1). Hence, the asymmetry in polarization of the oxygen atoms determines the hydrogen position and is directly reflected in the O···O distance. Another curious fact is that the correlation between O1−H and H···O2 projected distances is not gradual but involves three groups of data points: a symmetric one with deviations from perfect symmetry up to ca. 0.06 Å, an intermediate one with deviations from perfect symmetry of between about 0.16 and 0.22 Å, and an asymmetric one with deviations from about 0.29 to 0.31 Å. The corresponding distribution of the potential energy and the electric field exerted by the environment onto the hydrogen atom in question will be investigated in a forthcoming study to elucidate these groupings.

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HM are included that use different sets of constraints and restraints. (ZIP) Accession Codes

CCDC 977783 and 1538840−1538847 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/ cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49(0) 421-218-63152. ORCID

Simon Grabowsky: 0000-0002-3377-9474 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the German Research Foundation (DFG) for funding within the Emmy Noether scheme (project GR4451/1-1). We further thank George Koutsantonis and Scott G. Stewart for providing laboratory infrastructure for this project. The neutron-diffraction experiments were performed on the KOALA beamline of the OPAL reactor under the Bragg Institute proposal nos. 2160, 2437, and 2707. The synchrotron radiation experiments were performed at SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (Proposal Nos.: 2013B1056 and 2014A1078).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b00390. Details of experimental procedures, geometrical parameters, Hirshfeld-surface analyses, intermolecular interactions (PDF) In order to use the optimum Chebyshev weighting, all refinements were carried out against structure factor magnitudes F. CIFs for these refinements are deposited with the Cambridge Structural Database and are accessible from https://summary.ccdc.com.ac.uk/ structure-summary-form. Alternative CIFs for all compounds that are based on refinements against structure factor magnitudes F2 are deposited as Supporting Information, including lists of the structure factors used in FCF format. In addition, five alternative models for Ba L



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