One Hydrogen BondâTwo Ways To Build a Structure. The Role of N

Article pubs.acs.org/crystal

One Hydrogen BondTwo Ways To Build a Structure. The Role of N−H···O Hydrogen Bonds in Crystal Structures of N,N‑Dimethylglycine Published as part of the Crystal Growth & Design virtual special issue Mikhail Antipin Memorial Issue. Eugene A. Kapustin,*,† Vasily S. Minkov,*,†,‡ Jernej Stare,§ and Elena V. Boldyreva*,†,‡ †

REC-008 Novosibirsk State University, Novosibirsk, Russia Institute of Solid State Chemistry and Mechanochemistry, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia § National Institute of Chemistry, Ljubljana, Slovenia ‡

S Supporting Information *

ABSTRACT: Crystal structures of amino acids are considered to mimic important interactions in peptides; therefore the studies of the structure-forming factors in these systems attract much attention. N,N-Dimethylglycine is an interesting model compound that was used to test the role of the N−H···O hydrogen bonds in forming the head-to-tail chains, the main structural unit in the crystals of amino acids. It was hypothesized previously [Kolesov, B. A.; Boldyreva, E. V. J. Raman Spectrosc. 2010, 41, 670−677] that additional side N− H···O hydrogen bonds play an important role in forming the head-to-tail chains of amino acid zwitterions linked via N−H··· O hydrogen bonds between the charged −NH3+ and −COO− terminal groups. The twice methylated amino group of N,N-dimethylglycine is able to form only one N−H···O hydrogen bond in the crystal structure, so this hypothesis could be tested. In the present article, we describe the crystal structures of two polymorphs of N,N-dimethylglycine, in which the zwitterions are packed in two different ways. In one polymorph (orthorhombic, Pbca), they form finite four-membered ring motifs not linked to each other via any hydrogen bonds but only by weak van der Waals interactions. However, in the second polymorph (monoclinic, P21/n, which was never described before), the zwitterions do form infinite head-to-tail chains though the N−H···O bond is the only interaction and is not assisted via any additional hydrogen bonds. The effect of cooling on the two crystal structures was followed by single-crystal X-ray diffraction combined with polarized Raman spectroscopy of oriented single crystals, in order to compare the response of the N−H···O bonds to temperature variations. The crystal structure of the monoclinic polymorph with infinite chain motifs compresses anisotropically on cooling, whereas that of the orthorhombic polymorph with finite ring motifs undergoes a reversible singlecrystal to single-crystal phase transition at ∼200 K accompanied by nonmerohedral twinning, reducing the space symmetry to monoclinic (P21/b) and doubling the asymmetric unit from two to four molecules. This phase transition could not be detected by Raman spectroscopy and DSC. The temperature dependent structure and relative stability of both polymorphs were studied by periodic DFT calculations. The monoclinic polymorph appears to be more stable (by 0.8−1.2 kcal/mol, depending on the density), but with the increasing density and decreasing temperature, the difference decreases. The phase transition of the orthorhombic polymorph has no detectable impact on its relative stability. solution or in the air.8 The properties of the N−H···O hydrogen bonds linking the zwitterions in a chain were discussed many times with respect to their role in the formation of “self-trapped states”, strain, and energy transfer along the chains of amino acids in a crystal and a peptide chain in a protein.9 It was hypothesized that additional N−H···O hydrogen bonds that can be formed by the same amino

1. INTRODUCTION Crystal structures of amino acids and small peptides are considered to mimic important interactions in large macromolecules of proteins and peptides.1−4 The most characteristic structural feature of these crystals is that they all have head-totail chains linked via the N−H···O hydrogen bonds between the charged −NH3+ and −COO− terminal groups. These chains resemble the peptide chains, though no covalent N−C bonds are formed. The chains are very robust and are preserved even through solid-state phase transitions at high pressures,5−7 unless a recrystallization takes place in the presence of water in © 2014 American Chemical Society

Received: January 5, 2014 Revised: February 18, 2014 Published: February 24, 2014 1851

dx.doi.org/10.1021/cg5000183 | Cryst. Growth Des. 2014, 14, 1851−1864

Crystal Growth & Design

Article

Table 1. Crystal Data, Data Collection, and Structure Refinement Parameters for Crystal Structures of DMG-Ia T, K a, Å b, Å c, Å α, deg V, Å3 Dcalc, g cm−3 μ, mm−1 no. of meas., indep. and obsd [I > 2σ(I)] reflns θmin, deg θmax, deg range of h k l Rint R[F2 > 2σ(F2)] wR(F2) S no. of params Δρmax, e Å−3 Δρmin, e Å−3 orthorhombic

295 11.2209(4) 10.0203(4) 18.7351(8) 90 2106.51(15) 1.301

275 11.2187(2) 10.0056(2) 18.7300(4) 90 2102.44(7) 1.303

250 11.20949(18) 9.98321(18) 18.7137(3) 90 2094.19(6) 1.308

225 11.20324(19) 9.96483(18) 18.7053(4) 90 2088.23(7) 1.312

200 11.1927(3) 9.9481(3) 18.6989(7) 90.406(3) 2082.00(11) 1.316

175 11.1828(4) 9.9261(5) 18.6889(10) 90.679(5) 2074.35(17) 1.321

150 11.1763(4) 9.9150(6) 18.6822(11) 90.912(6) 2069.97(19) 1.324

125 11.1668(4) 9.8988(5) 18.6714(10) 91.313(5) 2063.36(17) 1.328

100 11.1619(4) 9.8870(4) 18.6616(10) 91.493(4) 2058.75(16) 1.331

0.103 31 716

0.104 31 567

0.104 31 490

0.104 34 598

0.105 32 260

0.105 31 987

0.105 31 690

0.106 32 027

0.106 31 505

2150 1706

2144 1921

2139 2012

2486 2288

4258 3672

4246 3740

4237 3759

4233 3776

4222 3856

2.17 26.37

2.17 26.37

2.18 26.37

2.18 27.87

2.12 26.37

2.12 26.37

2.12 26.37

2.13 26.37

2.13 26.37

−14 → 14 −12 → 12 −23 → 23 0.0591 0.0455

−14 → 14 −12 → 12 −23 → 23 0.0357 0.0407

−14 → 14 −12 → 12 −23 → 23 0.0334 0.0394

−14 → 14 −13 → 13 −24 → 24 0.0321 0.0419

−13 → 13 −12 → 12 −23 → 23 0.0462 0.0566

−13 → 13 −12 → 12 −23 → 23 0.0511 0.0717

−13 → 13 −12 → 12 −23 → 23 0.0562 0.0862

−13 → 13 −12 → 12 −23 → 23 0.0666 0.1053

−13 → 13 −12 → 12 −23 → 23 0.0681 0.1156

0.1099 1.048 181

0.1003 1.079 181

0.0993 1.095 181

0.1049 1.125 181

0.1313 1.036 261

0.1719 1.036 261

0.2072 1.037 261

0.2652 1.022 261

0.2918 1.030 261

0.181

0.216

0.225

0.313

0.327

0.492

0.650

0.949

1.026

−0.152

−0.143

−0.145

−0.176

−0.212

−0.280

−0.293

−0.351

−0.351

Pbca, Z = 16, Z′ = 2

monoclinic, P21/b, Z = 16, Z′ = 4

For all structures: chemical formula, C4H9NO2, Mr = 103.12, crystal size 0.32 × 0.25 × 0.18 mm3. Experiments were carried out with Mo Kα radiation using an Oxford Diffraction Gemini Ultra R diffractometer. H atoms treated by a mixture of independent and constrained refinement. a

group with the neighboring molecules can stabilize the “main” hydrogen bond and the head-to-tail chains themselves.9,10 The twice methylated amino group of N,N-dimethylglycine is able to form only one N−H···O hydrogen bond in the crystal structure, so the hypothesis could be tested using this compound. A recent study11 has in fact shown that in the anhydrous N,N-dimethylglycine no head-to-tail chains are present, whereas in the crystal of its hydrate, when water molecules are added and form extra hydrogen bonds with the methylated amino acid, the head-to-tail chains can be formed. This seemed to support the hypothesis suggested in ref 10. However, in our further study, we have crystallized another polymorph of N,N-dimethylglycine (the structure of which is first reported in this paper), which made us reconsider this view. Although the N−H···O bond between the amino and carboxyl terminal groups remains the only type of hydrogen bond present in the crystal structure, head-to-tail chains of amino acid zwitterions are formed. The aim of the present study was to compare the crystal structures of the two polymorphs under ambient conditions and to follow their response to temperature variations (in particular, the response of the unique N−H···O hydrogen bond in finite cycles and in the infinite head-to-tail chains). A combination of single-crystal X-ray diffraction with polarized Raman spectroscopy of oriented single crystals was shown to be the strategy of choice for such studies12 and was used also in this work. In addition, the experimental crystal structure investigation was supported

by periodic quantum calculations, as tends to be the case in a number of studies and also part of the research experience of some of the authors.13−16

2. EXPERIMENTAL SECTION 2.1. Materials. Prismatic colorless single crystals of the orthorhombic polymorph of N,N-dimethylglycine (DMG-I) were obtained by sublimation as described previously.11 A purchased sample of N,N-dimethylglycine (Aldrich, CAS No. 1118-68-9) found to be a hydrate was initially ground and then placed into a vacuum chamber for drying. The desiccation conditions were set as 358 K, 15 mbar (1 bar = 105 Pa) and process time of 20 h, which is slightly milder than the conditions of the sublimation process. Prismatic colorless well-shaped single crystals of the monoclinic polymorph of N,N-dimethylglycine (DMG-II) were grown from a methanol solution of a desiccated sample by slow evaporation under ambient conditions. Solvent was purified from water impurities by distillation with magnesium just before the experiment and then kept tightly sealed with zeolites. Since N,N-dimethylglycine is very hygroscopic, all mounted crystals for single-crystal X-ray diffraction were covered with a thin layer of the low-viscosity CryoOil to protect them from contact with atmospheric humidity. In case of Raman experiments, crystals were quickly removed from the mother liquor, loaded into the cryostat, and vacuumized. Using any protectors for crystals was not appropriate because a thin film of any protective agent on a sample’s surface provokes strong fluorescence. 2.2. X-ray Diffraction. The structural changes in the crystals of two polymorphs of N,N-dimethylglycine on variation of temperature were followed using a Stoe IPDS-II and an Oxford Diffraction Gemini 1852



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Table 2. Crystal Data, Data Collection, and Structure Refinement Parameters for Crystal Structures of DMG-IIa T, K a, Å b, Å c, Å β, deg V, Å3 Dcalc, g cm−3 μ, mm−1 no. of meas., indep., and obsd [I > 2σ(I)] reflns θmin, deg θmax, deg range of h k l Rint R[F2 > 2σ(F2)] wR(F2) S no. of params Δρmax, e Å−3 Δρmin, e Å−3

295 5.4525(5) 19.9258(12) 9.8027(9) 91.760(7) 1064.52(15) 1.287 0.102 7891 2173 1625

275 5.4340(5) 19.9056(12) 9.7935(9) 91.884(7) 1058.76(15) 1.294 0.103 7855 2163 1583

250 5.4179(4) 19.8855(12) 9.7869(8) 91.958(7) 1053.80(13) 1.300 0.103 9447 2617 1828

225 5.4030(4) 19.8661(11) 9.7808(8) 92.048(6) 1049.17(13) 1.306 0.104 10 141 2827 1978

200 5.3874(4) 19.8354(11) 9.7721(7) 92.100(6) 1043.56(12) 1.313 0.104 10 080 2809 2003

175 5.3738(4) 19.8094(10) 9.7661(7) 92.152(6) 1038.89(12) 1.319 0.105 10 051 2798 2042

150 5.3615(4) 19.7898(10) 9.7622(7) 92.201(6) 1035.03(12) 1.324 0.105 10 009 2793 2084

125 5.3512(4) 19.7699(9) 9.7591(6) 92.228(5) 1031.66(11) 1.328 0.106 9964 2780 2171

100 5.3412(3) 19.7534(9) 9.7538(6) 92.255(5) 1028.30(10) 1.332 0.106 9932 2770 2213

2.04 26.37

2.05 26.37

2.05 28.27

2.05 29.12

2.05 29.13

2.06 29.13

2.06 29.12

2.06 29.13

2.06 29.13

−6 → 6 −23 → 24 −12 → 12 0.0250 0.0382

−6 → 6 −22 → 24 −12 → 12 0.0315 0.0377

−6 → 7 −23 → 26 −13 → 13 0.0328 0.0388

−6 → 7 −24 → 27 −13 → 13 0.0328 0.0399

−6 → 7 −24 → 27 −13 → 13 0.0328 0.0373

−6 → 7 −24 → 27 −13 → 13 0.0338 0.0372

−6 → 7 −24 → 27 −13 → 13 0.0354 0.0358

−6 → 7 −24 → 27 −13 → 13 0.0315 0.0347

−6 → 7 −24 → 27 −13 → 13 0.0332 0.0351

0.0973 1.005 149

0.0895 0.946 149

0.0897 0.969 149

0.0913 0.961 149

0.0864 0.997 149

0.0860 1.003 149

0.0808 1.013 149

0.0801 1.034 149

0.0813 1.039 149

0.140 −0.184

0.140 −0.183

0.158 −0.202

0.170 −0.209

0.171 −0.211

0.173 −0.236

0.215 −0.217

0.226 −0.209

0.255 −0.222

For all structures: chemical formula, C4H9NO2, Mr = 103.12, monoclinic, P21/n, Z = 8, Z′ = 2, crystal size 0.50 × 0.40 × 0.30 mm3. Experiments were carried out with Mo Kα radiation using an IPDS-II STOE diffractometer. H atoms treated by a mixture of independent and constrained refinement. a

Ultra R diffractometer (both with Mo Kα, λ = 0.71069 Å) equipped with cooling devices of 700-series Oxford Cryostreams and Oxford Cryosystems, respectively (the temperature was maintained at a precision of ±0.1 K). In the case of the crystal of DMG-I, the singlecrystal data were collected first on cooling from 250 to 100 K with a temperature step of 25 K and then on reverse heating at 225, 250, 275, and 295 K. Single-crystal X-ray diffraction data for the crystal of DMGII were collected on cooling from 295 to 100 K with a temperature step of 25 K. During cooling, DMG-I underwent a phase transition DMG-I (Pbca) → DMG-I′ (P21/b) at ∼200 K. A crystal structure of DMG-I′ was refined in a nonstandard space group with α as the monoclinic angle, in order to facilitate a comparison of DMG-I with the low-temperature phase. The transition was reversible and accompanied by nonmerohedral twinning. On further cooling, after the phase transition, the number of reflections related to the largest domain decreased, because the monoclinic angle increased. At the same time, twinning did not cause any crystal fragmentation. On heating up a reverse phase transition occurred also at ∼200 K and twinning disappeared; the unit cell parameters were almost equal to those of the structures obtained on cooling at 225 and 250 (the deviations did not exceed the esd’s). Since several domains were found and it was not straightforward to correct the intensities of the overlapping reflections, the twin law was not applied for structure refinement; the solution and refinement were carried out using the set of reflections from the largest domain. To orient the crystals for Raman spectroscopy experiments, the crystal faces of the two polymorphs were indexed using X-SHAPE software.17 Crystal structures of DMG-I and DMG-II at all temperatures were solved by direct methods using SHELXS18,19 and refined using SHELXL.20−22 All H atoms in crystal structures of the two polymorphs DMG-I and DMG-II were found in a difference Fourier map, and their thermal displacement parameters were fixed as Uiso(H) = 1.5Ueq (corresponding parent atom) for terminal methyl groups and Uiso(H) = 1.2Ueq for all the others. The exceptions were the terminal

methyl groups in DMG-II where H atoms were refined using the riding model with default distances of C−H = 0.98 Å, and all H atoms in the crystal structure of DMG-I′, where they were refined using the riding model with default distances of methyl C−H = 0.98 Å, secondary C−H = 0.97 Å, and ammonium N−H = 0.89 Å because of deterioration of data quality after twinning. Parameters characterizing data collection and refinement, as well as crystal data, are summarized in Tables 1 and 2. Strain ellipsoid for monoclinic crystal structures was calculated using the PASCal.23 Mercury24 and Platon25 were used for the visualization, analysis, and inspection of the crystal structures. Void diagrams were created in Mercury and are shown with a probe radius of 0.6 Å and a grid spacing of 0.1 Å. The structural data for two polymorphs of N,N-dimethylglycine were deposited as CIFs at the Cambridge Crystallographic Database (CCDC Nos. 978985−978993 for DMG-I and 978975−978983 for DMG-II) and can be downloaded freely from http://www.ccdc.cam.ac.uk; these structures are also submitted as Supporting Information to the article. 2.3. Raman Spectroscopy. Single-crystal Raman spectra were collected using a triple-grating Horiba Jobin Yvon Lab-Ram HP spectrometer equipped with an N2-cooled detector coupled to an Olympus BX41 microscope. Excitation was supplied by an Ar+ laser (λ = 488 nm) with a 2 cm−1 spectral resolution. The low-temperature Raman spectra were recorded using a helium cryostat JANIS ST500HT; oriented single crystal samples of N,N-dimethylglycine were wrapped in a thin indium foil to provide a better thermal contact, so that only the upper face was accessible for a laser beam. Raman spectra were measured in the temperature range of 4−295 K with a step of 20 K. The directions of the polarization vectors of the incident and scattered light coincided with each other and the crystallographic axes and were designated as aa, bb, and cc in the case of coincidence with the axes a, b, and c, respectively. 2.4. Periodic DFT Calculations. We used the established density functional theory formalism in conjunction with periodic boundary conditions, as implemented in the program package VASP 5.2.26−29 1853



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The density functional of Perdew, Burke, and Ernzerhof (PBE)30 was used together with a plane-wave basis set with a cutoff of 400 eV and atomic pseudopotentials according to the projector augmented wave (PAW) methodology.31,32 The dispersion interactions insufficiently assessed by the original functional were treated by the DFT-D2 correction method of Grimme.33 A Monkhorst−Pack mesh34 of 2 × 2 × 1 and 4 × 1 × 2 size was used in the calculation of integrals for the orthorhombic and monoclinic polymorph, respectively. The models were built on the basis of X-ray crystal structure data collected at different temperatures. For each model, we optimized the position of hydrogen atoms, keeping the unit cell parameters and the positions of C, N, and O atoms fixed to the experimental values and following all the space group symmetry constraints. The data on the crystal structures of the two polymorphs with coordinates of all non-H atoms refined based on X-ray single-crystal diffraction experiments and coordinates of H atoms optimized using DFT calculations are deposited as Supporting Information.

groups is almost the same for both A and B zwitterions in DMG-I, for N,N-dimethylglycine hemihydrate, and for the A zwitterion in DMG-II (the values of C4−N1−C2−C1 torsion angle are ca. 69°), while the methyl groups for the B zwitterion in DMG-II are considerably turned over the C2−N1 bond, so that the value of C4b−N1b−C2b−C1b angle reaches 78.47(16)°. Several overlaid conformations of N,N-dimethylglycine zwitterions are shown in Figure 1. It is clearly seen that

3. RESULTS AND DISCUSSION Different crystallization techniques of N,N-dimethylglycine, from gas phase and solution (see Experimental Section), lead to the formation of two different polymorphs, namely, DMG-I and DMG-II. The crystal structure of DMG-I has been reported in detail earlier.11 Both polymorphs crystallize in centrosymmetric space groups, orthorhombic Pbca for DMG-I and monoclinic P21/n for DMG-II; both have two molecules in the asymmetric unit. The cell volume of DMG-I is about 2 times larger than that of DMG-II, as is the number of molecules in the unit cell. Thus, at ambient temperature, the densities of the two forms do not differ much: 1.301 and 1.287 g cm−3 for DMG-I and DMGII, respectively. In contrast to the density, the crystal packing in these two forms differs greatly. In both polymorphs, N,N-dimethylglycine is present as a zwitterion with an ionized tertiary amino group and a carboxylate group. The difference between molecular conformations in the two polymorphs of N,N-dimethylglycine is related to the orientation of the carboxylate group and methyl groups. Selected torsion angles characterizing conformations of zwitterions in DMG-I and DMG-II are summarized in Table 3.

Figure 1. Overlaid conformations of N,N-dimethylglycine zwitterions in DMG-I (colored blue for A and sky blue for B zwitterion), DMG-II (colored red for A and orange for B), N,N-dimethylglycine hemihydrate (colored green for A and light green for B). Heavy atoms are labeled for clarity.

the carboxylate group is more twisted for both zwitterions in DMG-I, and the orientation of the methyl groups for the B zwitterion in DMG-II differs from that in all other molecules. Summing up, the differences in conformations of DMG zwitterions are comparable with those between three polymorphs of glycine with the values of N−C−C−O torsion angle equal to 19.0(1)°, 25.03(12)°, and 15.4(4)° for α-, β-, and γ-forms, respectively.37 Having only one hydrogen atom in the tertiary amino group, each zwitterion of N,N-dimethylglycine can be involved in the formation of only one intermolecular N−H···O hydrogen bond in a crystal structure. This holds for both polymorphs. The data on the geometry of hydrogen bonds at 295 K are summarized in Table 4. Substitution of hydrogen atoms of the amino group for −CH3 increases the acidity in the series of primary, secondary, and tertiary amines, so the N···O distance of the longest hydrogen bond in N,N-dimethylglycine (2.7541(16) Å) is still shorter than the shortest ones in N-methylglycine (2.7599(17) Å)38 and in α-, β-, and γ-glycine (2.7703(8), 2.7626(11), and 2.804(3) Å, respectively).37 The most amazing feature in the structures of the two polymorphs of N,Ndimethylglycine is that the molecular packing is so radically different for the zwitterions that are rather rigid and do not differ much in conformation (Figure 2). In the structure of DMG-II, A and B zwitterions are linked to each other to form infinite C22(10) chains of the head-to-tail type, which are typical for α-amino acids, as well as for their salts and hydrates or solvates,39−41 whereas DMG-I has four-membered hydrogen bonded R44(20) ring motifs (for more details about graph set notation see ref 42). The structural data suggests that N−H···O hydrogen bonds are only slightly stronger in the DMG-I polymorph, if they are not almost equal at all: the N···O distances in the ring motif are slightly shorter than those in DMG-II, although the N−H···O angles are somewhat smaller in DMG-I. Acceptors for hydrogen bonding in the N−H···O hydrogen bonds are not the same in two polymorphs: in DMG-

Table 3. Selected Torsion Angles Characterizing Conformations of N,N-Dimethylglycine Zwitterions in Two Polymorphs at 295 K torsion angle

DMG-I, deg

DMG-II, deg

N1a−C2a−C1a−O1a N1b−C2b−C1b−O1b C3a−N1a−C2a−C1a C3b−N1b−C2b−C1b C4a−N1a−C2a−C1a C4b−N1b−C2b−C1b

15.5(2) 22.9(2) 68.74(19) 68.36(19) −167.96(15) −167.97(15)

9.9(2) 5.8(2) 69.59(15) 78.47(16) −167.79(12) −157.09(15)

The values of N−C−C−O torsion angles show that the main backbone of the two molecules in DMG-II with infinite chains is more planar (9.9(2)° and 5.8(2)° for A and B zwitterions, respectively) than in DMG-I with finite cycles (15.5(2)° and 22.9(2)° for A and B zwitterions, respectively). The conformation of the N,N-dimethylglycine’s main backbone in DMG-II is quite close to that in N,N-dimethylglycine hemihydrate (8.71(18)° and 5.21(17)° for A and B zwitterions, respectively).11 The values of these torsion angles are still larger than those in N,N-dimethylglycine hydrochloride (2.2(2)°35) and N,N-dimethylglycine trifluoroacetate (3.2(3)°36), though in both salts N,N-dimethylglycine is in the cationic form with a protonated carboxyl group. Orientation of the two methyl 1854



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Table 4. Hydrogen-Bond Geometry (Experimental and DFT-Optimized) for Two Polymorphs of N,N-Dimethylglycine at 295 K form

D−H···Aa

DMG-I

N1a−H1a···O1b N1b−H1b···O2ai

DMG-II

N1a−H1a···O2b N1b−H1b···O2aii

a

expt DFT expt DFT expt DFT expt DFT

D−H, Å

H···A, Å

D···A, Å

D−H···A, deg

0.898(18) 1.061(1) 0.899(19) 1.085(1) 0.914(16) 1.090(1) 0.870(18) 1.074(1)

1.913(18) 1.751(1) 1.816(19) 1.626(1) 1.789(16) 1.619(1) 1.915(18) 1.727(1)

2.7363(19)

151.5(16) 152.49(9) 156.7(16) 158.72(9) 163.9(14) 162.84(6) 161.5(16) 158.52(7)

2.6655(18) 2.6799(15) 2.7541(16)

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

Per se, the possibility of formation of structural motifs such as isolated head-to-tail chains contradicts the earlier assumption that formation of these chains is strongly related to the ability of terminal amino groups to form additional hydrogen bonds to surrounding molecules outside the chains.10 In other words, DMG-II provides an example when hydrogen bonds between the terminal amino and carboxylate groups are preserved, and the proton of the amino group of one molecule is not transferred to the carboxylate group of another molecule in the same chain and also when all additional hydrogen bonds from surrounding molecules disappear. At the same time, the N−H··· O bonds in the chain motifs in DMG-II seem to be weaker than those in the ring motifs in DMG-I. It is also interesting that sublimation, when no other molecules are present in the system, gives the polymorph with ring motifs, whereas DMG-II with head-to-tail chains crystallizes from methanol solution. One can suppose that the solvent molecules can act as a template in the formation of these chains, and this hypothesis seems to be supported by the structural similarity of DMG-II and N,N-dimethylglycine hemihydrate. Besides, for zwitterions of amino acids, relatively small molecules in which the opposite ends are charged differently, the head-to-tail alignment can result from large dipole−dipole interactions between the molecules. It is also worth noting that under ambient conditions the head-to-tail packing in DMG-II is slightly less dense than the packing of finite rings in DMG-I (Figure 4). Keeping the crystals of both DMG-I and DMG-II polymorphs in an air atmosphere leads to the formation of N,Ndimethylglycine hemihydrate. Analysis of the effect of cooling on a crystal structure is known to be a useful tool to understand intermolecular interactions (ref 3 and references therein). The response of the two crystal structures of the DMG polymorphs to cooling is different: a reversible single-crystal to single-crystal phase transition is observed in the crystals of DMG-I at ∼200 K, while the structure of DMG-II is preserved at least down to 100 K. The phase transition DMG-I (Pbca) ↔ DMG-I′ (P21/b) is accompanied by nonmerohedral twinning on cooling, which entirely disappears on reverse heating. The number of molecules in the asymmetric unit doubles from 2 to 4 as a result of the transition from the orthorhombic to the monoclinic phase. Analysis of the reflections in the plane of the (0kl) reciprocal layer shows their splitting on cooling. It could be seen better in the high 2θ range (Figure 5). Twinning is caused by the rotation of several (at least 4) twin components with respect to each other around b* axis. A similar phase transition accompanied by nonmerohedral twinning without cracking of the crystal was observed for the β-polymorph of chlorpropamide at ∼257 K43 and for barbituric acid dihydrate at ∼217 K.44 The transition itself is due to the

Figure 2. Structural hydrogen bonded motifs in crystals of DMG-I (a) and DMG-II (b). Hydrogen bonds are highlighted as blue dashed lines. The oxygen and nitrogen atoms participating in hydrogen bonds are marked as balls. Symmetry codes: (i) 1 − x, 1 − y, 1 − z for panel a; (i) x, y, 1 + z and (ii) x, y, −1 + z for panel b.

II, the amino group is linked to the oxygen atom in trans position relative to N−H (here and below, the oxygen atom in cis position is labeled as O1 and that in trans position is labeled as O2), whereas in DMG-I, the amino group of the A zwitterion is connected with O1b and the amino group of the B zwitterion is connected to O2a. Interestingly, the infinite headto-tail chains in the crystal structure of N,N-dimethylglycine hemihydrate are formed by oxygen atoms in cis position, and the N···O distances in N−H···O hydrogen bonds are longer than those in DMG-II. The fragments of crystal structures of two N,N-dimethylglycine polymorphs are shown in Figure 3. In DMG-II, infinite zigzag C22(10) head-to-tail chains are directed along the crystallographic axis c. Such chains are very similar to those in N,N-dimethylglycine hemihydrate. The packing of these chains also resembles that in the crystal structure of N,Ndimethylglycine hemihydrate: in the latter, zigzag head-to-tail chains are linked to each other by hydrogen bonds via water molecules forming a layer; in DMG-II, these chains are isolated, but one still may find “pseudolayers” parallel to the (010) crystallographic plane. Since ring motifs in DMG-I are not linked to each other via hydrogen bonds, the crystal structure cannot be described in terms of layers and ribbons: one can find different planes containing ring motifs, so the packing of these motifs reminds one of the packing of balls but with some steric restrictions. 1855



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Figure 3. Fragments of the crystal packing in DMG-I (a−c) and in DMG-II (d−f). Dashed blue lines represent hydrogen bonds. A finite fourmember ring motif in DMG-I is highlighted by green color; an infinite chain in DMG-II is colored magenta.

disorientation of loosely connected four-membered ring motifs with respect to each other. Several domains were found while processing diffraction data, suggesting that twinning occurred in different parts of a crystal. Unfortunately, we could not define a twin law, but Figure 6 suggests one possible way of twinning in the crystal structure. Despite the phase transition in DMG-I with a sudden change in space symmetry, the changes in its cell volume and parameters on cooling were continuous (Figure 7); the continuous energy profile obtained by DFT calculations is in agreement with this (see below). Also the hysteresis on reverse heating was quite negligible: on reverse heating, the structure at 225 K corresponded to that obtained on initial cooling (at least the deviations did not exceed the esd’s). The bulk compression

of the crystal structure of DMG-I on cooling from ambient temperature down to 100 K was smaller than that of the DMGII: 2.27(1)% and 3.40(2)%, respectively. The value of the monoclinic angle α increased linearly on cooling after the phase transition up to 91.493(4)° at 100 K. In general, the values of linear strain on cooling were less for DMG-I than for DMG-II. The analysis of the distribution and sizes of interstitial voids within a structure can be useful when analyzing lattice strain. This method was applied in several publications to analyze structural strain in the crystals of selected amino acids with increasing pressure.45,46 For example, for the crystal structure of betaine monohydrate ((CH3)3N+−CH2−COO−·H2O) the direction of the major compression with increasing pressure could be correlated with the positions of the largest voids 1856



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Figure 6. Scheme of twinning of DMG-I during phase transition at 200 K: (a) before phase transition; (b) after phase transition. The twin interface is marked gray. Figure 4. Changes in density calculated from diffraction data of DMGI (brown) and DMG-II (orange) with variations in temperature. Curves are guides to the second-order polynomial fitting. Dashed line shows the phase-transition region. Intersection point is highlighted black. The direction of the “temperature axis” corresponds to the sequence in which the measurements were done (temperature decreasing).

acids, in general, are most rigid in the direction of these headto-tail chains on cooling, as was shown for many systems, such as three polymorphs of glycine,37 L- and DL-alanine,47 Lcysteine,48 and L-serine,49 and also on increasing hydrostatic pressure for α- and γ-glycine,50 L-alanine,51,52 DL-alanine,46 and 49 L-serine. The direction of the largest compression in DMG-II (2.04(1)%) corresponded to the crystallographic axis a characterizing a decrease in the distance between infinite chains within the “pseudolayer” in (010) crystallographic plane (Figure 3). The N−H···O hydrogen bonds of different types are known to play the main role in determining the anisotropy of structural strain on cooling for the polymorphs of glycine.37 In the double-methylated DMG polymorphs, the terminal amino groups can form only one N−H···O hydrogen bond; however, since there are two crystallographically nonequivalent molecules in the asymmetric unit, there are two different N−H···O hydrogen bonds, which behave differently on cooling. While the N1a−H1a···O2b hydrogen bond becomes shorter as the temperature decreases, the weaker N1a−H1b···O2a hydrogen bond becomes even longer (Figure 9). Such an unequal response agrees with the difference in molecular conformation of zwitterions. A comparison of the values of the N−C−C−O torsion angles at 295 K and at 100 K shows that one of the two zwitterions becomes more planar on cooling (N1b−C2b− C1b−O1b is 5.8(2)° and 4.75(13)° at 295 and 100 K, respectively), while the torsion angle of the main backbone of another zwitterion increases (N1a−C2a−C1a−O1a is 9.9(2)°

present in the structure.45 We have applied the same approach to analyze lattice strain in DMG on cooling, though the effects observed on cooling are of course significantly smaller than those with increasing pressure. Figure 8 shows the distribution of interstitial voids in DMG-I at 295 and 225 K. The size and positions of the largest voids along crystallographic axes a and c did not change significantly on cooling to 100 K. At the same time, small voids along crystal axis b collapsed, and this correlates with the largest compression in this direction. Voids volumes with probe radius of 0.6 Å were estimated as 5.4%, 4.4%, and 3.9% of the cell volume at 295, 225, and 100 K, respectively. In the monoclinic polymorph DMG-II, showing no phase transitions on cooling, the directions of the principal axes of strain ellipsoid were practically identical to the directions of crystallographic axes due to the small value of the deviation of the monoclinic angle β from 90°. The direction of the smallest compression coincided with the crystallographic axis c (0.50(2)% on cooling down to 100 K, Figure 7), which corresponds to the compression of the hydrogen bonded infinite head-to-tail chains. The crystal structures of α-amino

Figure 5. Reciprocal layer 0kl of the crystal of DMG-I at 250 K and DMG-I′ at 100 K. 1857



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Figure 8. Voids diagrams of the crystal structure of DMG-I at different temperatures: (a, c) 295 K; (b, d) 225 K.

hydrogen bonds “originating from” the longer N1a−H1a···O1b behaved after phase transition in different ways: one shortened in the trend of “original” hydrogen bond on further cooling down to 100 K (0.2(3)%); the other one rapidly became longer by 0.04(2) Å after the transition and then continuously extended on cooling (0.2(3)%). As in the case of DMG-II, in DMG-I before phase transition, the torsion angles of the main backbone of zwitterions changed oppositely to each other: in zwitterion B it became more planar by 0.4(4)°, and in zwitterion A it became more acute by 0.5(4)°. After the phase transition, the conformation of zwitterions changed differently, but in general, the deformation of the ring motif as a whole was not significant. Our primary aim was to study the behavior of the “main” hydrogen bonds in a head-to-tail chain in case of the absence of additional neighboring hydrogen bonds. In this respect, it should be noted that the decrease of temperature had a more pronounced effect on this hydrogen bond in DMG compared with the same type of hydrogen bond in glycine and L-alanine. In the three forms of glycine, the shortening of the strongest hydrogen bond in head-to-tail chains (the “main” hydrogen bond) on cooling to 150 K was less than that of the other hydrogen bonds (for instance, in α-glycine ΔdN···O is 0.002(7) Å for the shortest and 0.046(8) Å for the longest one37). Similarly to glycine, the shortest hydrogen bond in head-to-tail chains in crystalline L-alanine was less compressible than additional hydrogen bonds between layers (ΔdN···O is 0.009(4) Å and 0.023(5) Å, respectively53). During cooling of either glycine polymorphs or L-alanine, the changes of the torsion angle of the main backbone of the zwitterion do not exceed 1°, which is comparable to cooling of N,N-dimethylglycine polymorphs. The changes in density of both polymorphs on cooling are compared in Figure 4. While under ambient conditions the density calculated from diffraction data of DMG-II is less than that of DMG-I, their densities become equal at ∼138 K. Denser

Figure 7. Relative changes in cell parameters of DMG-I (a) and DMGII (b) with variations in temperature: black−crystallographic axis a; red−axis b; blue−axis c. Relative changes in cell volume of DMG-I (brown) and DMG-II (orange) with variations in temperature (c). Changes of monoclinic angle of DMG-I (brown) and DMG-II (orange) with variations in temperature (d). Dashed line shows the phase-transition region. All curves are guides to the eye.

at 295 K and 10.73(13)° at 100 K). It is worth noting that in the case of cooling of the three polymorphs of glycine down to 150 K all hydrogen bonds shorten.37 In DMG-I, the behavior of the N−H···O hydrogen bonds differs from that in DMG-II. This polymorph also has two nonequivalent molecules in the asymmetric unit under ambient conditions. Before the phase transition both nonequivalent N− H···O hydrogen bonds shortened on cooling to 225 K (0.2(1)%) (Figure 9). Since the number of molecules doubled during the phase transition, the two types of hydrogen bonds (N1b−H1b···O2a and N1a−H1a···O1b) gave rise to the four types of slightly different hydrogen bonds. While the two shorter hydrogen bonds related to the original N1b−H1b···O2a hydrogen bond (before the phase transition) shortened continuously and practically linear on further cooling (0.5(3)%), the donor−acceptor distances of the two other 1858



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Figure 9. Donor−acceptor distance of N−H···O hydrogen bonds in polymorphs with variations in temperature. Changes in the donor−acceptor distance of N1a−H1a···O1b hydrogen bond (a) and N1b−H1b···O2a (b) in DMG-I. Changes in the donor−acceptor distance of N1a−H1a···O2b (c) and N1b−H1b···O2a (d) in DMG-II. Dashed lines show the phase-transition region. All curves are guides to the eye.

crystal structures tend to have lower crystal packing energy, unless some directional interactions, like hydrogen bonds come into play.54,55 Taking into account that the conformations of zwitterions and the parameters of hydrogen bonds in both polymorphs are comparable, one can suppose that DMG-I should have a lower crystal packing energy under ambient conditions and therefore is more thermodynamically stable than DMG-II. Since no direct transitions can be observed between the two polymorphs on cooling at least down to 100 K (the lowest point at which single-crystal X-ray diffraction data are available) and on heating to the temperature of their sublimation/decomposition (additionally studied by DSC and X-ray powder diffraction), model calculations seem to be the only way to test this hypothesis. The densities of the polymorphs become practically equal at the lowest temperatures of this study and can be expected to invert their relative values on further cooling below 100 K. Therefore, the model calculations should take also the temperature into account and not be limited by a “zero K approximation”. Since the assessment of temperature effects and thermodynamic stabilities on a free energy scale is quite challenging and computationally demanding (at least with quantum methods), we used an approximate but simple and cost-effective treatment, as demonstrated below. Our periodic DFT calculations confirmed that in both polymorphs the DMG molecules preferably exist as zwitterions; there was no evidence of proton migration within the N−H···O hydrogen bonds resulting in the formation of neutral DMG molecules. During optimization, we deliberately fixed both the unit cell parameters and the position of heavy atoms, ensuring that the calculations followed the experimental findings to the

largest possible extent. However, we optimized the position of all hydrogen atoms, since they could not be refined at full accuracy from crystallographic techniques based on X-ray measurements, resulting in the fact that the C−H and N−H bond lengths are evidently underestimated. Indeed, the C−H and N−H distances elongated typically by about 0.1−0.2 Å during optimization, reaching reasonable values of about 1.08− 1.09 Å, respectively (See Table 4 for comparison between experimental and optimized hydrogen bond geometry). The valence and torsional angles involving hydrogen atoms were practically unchanged; hence no substantial displacements other than bond elongation occurred. We believe DFT optimization improves the position of hydrogen atoms, hence the optimized hydrogen coordinates are given in the deposited structures. In this way, we removed the strain originating from the “compressed” C−H and N−H bonds, facilitating concise energy comparison between the structures. Energies of the optimized structures allow for an estimation of thermodynamic stability of the polymorphs. Since experimental crystal structure data is available over a wide temperature range, we attempted to assess the impact of temperature on thermodynamic stability. It should be noted that the DFT calculations used in this study do not include temperature as a parameter (they are nominally done at zero K); hence the computed thermodynamic quantity is enthalpy rather than free energy. The temperature is included indirectly through the fact that the cell parameters (density) and heavy atom positions vary with temperature. In order to assess thermodynamic stability at the free energy level, inclusion of thermal fluctuations is required (i.e., molecular dynamics simulation), but due to high computational costs, this is 1859



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beyond the scope of the present study. “Temperature”/density dependent relative energies of both polymorphs are presented in Figure 10. There is a uniform trend of energy lowering with

Figure 11. Raman spectra of both DMG-I and DMG-II at three different polarizations at 295 K. The definitions aa, bb, cc imply the directions of polarization vectors of the incident (first symbol) and the scattered (last symbol) light with respect to the crystal axes.

Figure 10. Energy of DFT-optimized structures of DMG-I (brown) and DMG-II (orange) at different unit cell size (density) corresponding to the varying temperature. Dashed line shows the phase-transition region.

ν(COO−) in the longer N1a−H1a···O1b hydrogen bond and its weak shoulder at 1617 cm−1 to δ(N−H), which is a more intensive band at 1617 cm−1 in bb-polarization (Figure 11). The band at 1625 cm−1 in cc-polarization is assigned to asymmetric ν(COO−) vibrations in the shorter N1b−H1b··· O2a hydrogen bond. The differences between the polarized spectra of DMG-II in this spectral region are less pronounced because different N−H···O hydrogen bonds expand along the head-to-tail chains in the same crystallographic direction. Moreover, in all three different polarizations, the composite band at ∼1624 cm−1 includes not only the ν(COO−) vibrations of carboxylate groups involved in the two hydrogen bonds, but also the δ(N−H) vibrations. Judging from a small difference in the frequencies of such vibrations, hydrogen bonds do not differ significantly in the two polymorphs. The frequencies of stretching asymmetric COO− vibrations of both DMG polymorphs at ambient conditions are somewhat larger than those of L- and DL-alanine, L- and DL-cysteine, and the three polymorphs of glycine in agreement with the donor−acceptor distances of hydrogen bonds in these structures (Table 5). The blue shift of about 40 cm−1 is due to the difference in the coordination of a carboxylate group with respect to the N−H donor (monodentate in case of N,N-dimethylglycine and bidentate in case of other amino acids). Another interesting feature of Raman spectra of N,Ndimethylglycine polymorphs is the presence of two lowestwavenumber modes at 38 and 53 cm−1 in DMG-I and only one at 53 cm−1 in DMG-II (Figure 12). The pair of the lowestwavenumber bands (40 and 52 cm−1) was previously observed in the polarized spectra of L-alanine and assigned to “bending motion”.58 Recently,59 it was reconsidered that this pair of modes could be assigned to bending vibrations of “molecular cycles in the crystal”, that is, six-member molecular cycles in the crystals of L-alanine.53 Likewise, the pair of modes at 38 and 53 cm−1 is related to such vibrations of the four-membered ring motifs. In contrast, in DMG-II there are no such cycles, and this phenomenon was not observed. The changes in the polarized Raman spectra of the two polymorphs were followed on cooling to 4 K (Figure 13). In DMG-I, the red shift of ν(COO−) of about 4 and 2.5 cm−1 in aa- and cc-polarizations demonstrates that both longer and

increasing density (decreasing temperature) with both DMG-I and DMG-II; both profiles are smooth. Interestingly, the phase transition in DMG-I at ∼200 K is not reflected in the profile despite the change in space group symmetry, confirming rather subtle structural changes during transition. The DMG-II polymorph is consistently lower in energy, suggesting that the chained hydrogen bond structure of DMG-II is preferred over the circular hydrogen bonded clusters of DMG-I. However, with decreasing temperature, the energy difference tends to be smaller (from 1.2 kcal/mol at 295 K to 0.8 kcal/mol at 100 K). A full crystal structure optimization of both isomers, including unit cell parameters and all atomic positions, yields the energy difference of 0.5 kcal/mol, again in favor of DMG-II. Although the calculations give evidence for the higher stability of DMGII, the reverse situation cannot be excluded (particularly at lower temperatures) considering the “temperature”/density profile (Figure 10) and the limited precision of the applied methodology. Among the factors contributing to the stability of polymorphs, the cooperative effect enhancing the hydrogen bonds in rings (DMG-I) or infinite chains (DMG-II) is worth considering, but due to the complexity of interactions, this remains the challenge for our future work. Complementary information on the intermolecular interactions in the structure can be obtained from polarized Raman spectra (Figure 11). Interestingly, despite a completely different molecular packing, the polarized spectra of the two polymorphs do not differ dramatically. Considering that the conformations of zwitterions do not differ significantly, the largest difference in the Raman spectra could be expected for the bands of those functional groups that form the hydrogen bonds, namely, for N−H and COO− groups. Unfortunately, the N−H stretching vibrations were not observed in the Raman spectra because of their low intensity and a large band broadening resulting from the formation of a hydrogen bond. Information about the hydrogen bonds can be derived from the analysis of stretching vibrations of COO− group and bending vibrations of N−H. For instance, in the spectrum of DMG-I at 298 K, the band at 1631 cm−1 in aa-polarization could be assigned to the asymmetric 1860



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assume that a small shift of the bands at ∼1624 cm−1 on cooling in two other polarizations is related to the slight changes in δ(N−H) vibrations. The curves approximating the shifts of the asymmetric stretching vibrations of the COO− and of the δ(N−H) bands versus temperature did not give any indication of the phase transition on cooling in DMG-I. This is not surprising, however, since the subtle rotations of the fourmembered rings with respect to each other can hardly have a pronounced effect on the intermolecular hydrogen bonds. The changes of stretching C−H bands related to the vibrations of methyl groups also did not reveal any phase transition (Figure 14), which correlates with smooth and very small changes in the values of the C4−N1−C2−C1 angle of both zwitterions. In both polymorphs, a continuous shift of C−H stretching vibrations in the blue region corresponds to the shortening of C−H distances due to the compression of the crystal structure and the reduction of the volume of the interstitial voids (the largest change of ∼10 cm−1 was observed for the band at 3055 cm−1). It is interesting that the phase transition failed to manifest itself not only in Raman spectra but also in the DSC measurements. The DSC curves on cooling as well as on reverse heating were smooth and monotonic without any hint of a phase transition. Thus, one can assume that the related energy change was quite small. Similarly, the phase transition in β-chlorpropamide on cooling was also difficult to detect by DSC: a DSC curve averaged over four runs revealed a very small anomaly (ca. 2−3%) in the temperature interval from 257.5 to 259.5 K, which corresponded to the phase transition.43 Neither could this phase transition, clearly seen by single-crystal X-ray diffraction,43 be detected by Raman spectroscopy.60 It is noteworthy that the structural distortion in the course of the phase transition in DMG-I is even less than that observed on the low-temperature phase transition in β-chlorpropamide. For example, the β-angle in chlorpropamide structure became equal to 90.69(2)°, and this deviation from 90° is still larger than that observed in the case of DMG-I′ (90.406(3)° compared with the original 90°). Analysis of the Raman spectra of both N,N-dimethylglycine polymorphs reveals no N−H self-trapping states on cooling the two crystal structures. Based on the polarized Raman spectra of oriented crystals of three polymorphs of glycine and L- and DLalanine on cooling, Kolesov9 proposed that such coupled exciton−phonon(s) states cannot be formed in the head-to-tail chains, if all hydrogen bonds from surrounding molecules disappear. The present work does not contradict this hypothesis, though it cannot also prove it completely. The absence of self-trapped state in infinite head-to-tail chains in DMG-II can be due not only to the absence of the additional hydrogen bonds but also to the presence of crystallographically nonequivalent zwitterions in these chains and therefore to the presence of nonequivalent hydrogen bonds in the head-to-tail chains themselves. The absence of the self-trapped states in case of DMG-I can be explained by the finiteness of ring motifs. The response of the “main” hydrogen bonds in N,N-dimethylglycine polymorphs to cooling differ significantly from that in L- and DL-alanine and the polymorphs of glycine. This may support the assumption that the “main” hydrogen bond strongly depends to a large extent on the state of the additional hydrogen bonds with the neighboring molecules in the structure,10 though does not prove this hypothesis unambiguously.

Table 5. The Donor−Acceptor Distances of Selected N−H··· O Hydrogen Bonds and Frequencies of Asymmetric COO− Vibrations of Various Amino Acids under Ambient Conditions amino acid DMG-I DMG-II α-glycine56

β-glycine56

γ-glycine56

L-alanine

47

DL-alanine

L-cysteine

47

57

DL-cysteine

57

D···A distance of N−H···O hydrogen bond, Å

νas(COO−), cm−1

2.6655(18) 2.7363(19) 2.7541(16) 2.6799(15) 2.7703(8) 2.8505(10) 2.9516(9) 3.0749(10) 2.7626(11) 2.8509(13) 2.9795(15) 2.9785(13) 2.804(3) 2.811(4) 2.976(3) 2.858 2.833 2.809 2.863 2.821 2.811 2.792 3.017 2.762 2.781 2.829 2.809

1625 1624 1584

1606

1580

1585

1583

1579

1574

Figure 12. Polarized Raman spectra of both DMG-I and DMG-II single crystals at 5 K in the low-wavenumber range. The definitions aa, bb, and cc imply the directions of polarization vectors of the incident (first symbol) and the scattered (last symbol) light with respect to the crystal axes.

shorter hydrogen bonds become stronger on cooling. The wavenumber of bending vibrations of the amino group decreased gradually at ∼5 cm−1 per 290 K. In DMG-II in aapolarization, the red shift of about 11 cm−1 correlates with the strengthening of the N1a−H1a···O2b hydrogen bond. One can 1861



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Figure 13. Temperature dependence of COO− stretching asymmetrical vibrations and NH bending vibrations in both polymorphs DMG-I and DMG-II at three different polarizations: (a) aa polarization of DMG-I; (b) bb of DMG-I; (c) cc of DMG-I; (d) aa polarization of DMG-II; (e) bb of DMG-II; (f) cc of DMG-II. The definitions aa, bb, and cc imply the directions of polarization vector of the incident (first symbol) and the scattered (last symbol) light with respect to the crystal axes. Dashed lines show the phase-transition region. All curves are guides to the eye.

expect that the two polymorphs can have close values of crystal energy. This is also supported by DFT calculations suggesting slight thermodynamic preference of DMG-II, but the difference diminishes with decreasing temperature. The polymorphism in the system of DMG is also a unique example of completely different arrangements of molecules in a zwitterionic crystal having large dipole moments, corresponding to parallel and antipolar orientation of dipoles. Previously, these two extreme types of dipole−dipole arrangements were studied mainly using small molecular clusters in the gas phase.61 Further research using model calculations is needed to study the relative contributions of (i) Coulomb interactions between the dipoles, (ii) hydrogen bonds between the zwitterions in the cycles and in the chains, including their cooperative effect, and (iii) van der Waals interactions to the total packing energies of the two polymorphs. The two polymorphs can be expected to differ significantly in their properties: packing of polar head-to-tail chains and of the four-membered neutral ring motifs with no residual dipole moments produces structures differing much in the range to which Coulomb interactions extend. Even such a relatively subtle action as cooling reveals this difference in the properties. An unusual crystal structure of DMG-I undergoes a reversible phase transition at ∼200 K accompanied by a nonmerohedral twinning and the disordering of domains with finite ring motifs of zwitterions. A crystal structure of DMG-II, which is more common for amino acids, does not undergo phase transitions on cooling to 100 K, but compresses anisotropically; similar to the case of other crystalline amino acids, for example, three glycine polymorphs, L- or DL-alanine, L-serine, and L- or DLcysteine, the direction of minor compression coincides with the direction of head-to-tail chains.

Figure 14. Region of stretching C−H vibrations of methyl groups in Raman spectra of DMG-I in bb-polarizations at selected temperatures.

4. CONCLUSIONS N,N-Dimethylglycine is a striking example when having only one H atom in the tertiary amino group the zwitterion of DMG can form only one hydrogen bond, and still, by this only hydrogen bond, two structural motifs can be organized. One motif (infinite head-to-tail chains) is common for most αamino acids. Another motif (finite four-member cycles) is very unusual. The conformation of the DMG zwitterion is quite rigid and does not differ much, thus the polymorphism is related to molecular packing. Though the crystal packing is absolutely different in the two polymorphs, their densities differ surprisingly little, namely, 1.301 and 1.287 g cm−3. The vibrational frequencies and the N−O distances characterizing the N−H···O hydrogen bonds are also comparable. One can 1862



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ASSOCIATED CONTENT

S Supporting Information *

The structural data for two polymorphs of N,N-dimethylglycine with coordinates of all non-H atoms refined based on X-ray single-crystal diffraction experiments and with coordinates of H atoms optimized using DFT calculations. This material is available free of charge via the Internet at http://pubs.acs.org. The structural data for two polymorphs of N,N-dimethylglycine were deposited as CIFs at the Cambridge Crystallographic Database (CCDC Nos. 978985−978993 for DMG-I and 978975−978983 for DMG-II) and can be downloaded freely from the following site: http://www.ccdc.cam.ac.uk.

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AUTHOR INFORMATION

Corresponding Authors

*Elena V. Boldyreva E-mail: [email protected]. *Eugene A. Kapustin E-mail: [email protected]. *Vasily S. Minkov E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge financial support from RFBR Grant No. 12-03-31145, Integration Projects No. 108 of the SB RAS, the Ministry of Education and Science of the Russian Federation (Agreement No. 14.B37.21.1093), the Programmes of the Praesidium of the RAS (Project No. 24.38), the Department of Chemistry and Materials Sciences of the RAS (Project No. 5.6.4), and the Slovenian Research Agency (Program P1-0012).

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