Diindolylmethane - ACS Publications - American Chemical Society

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Polymorphism and Thermal Stability of Natural Active Ingredients. 3,3′-Diindolylmethane (Chemopreventive and Chemotherapeutic) Studied by a Combined X‑ray, 1H−14N NMR-NQR, Differential Scanning Calorimetry, and Solid-State DFT/3D HS/QTAIM/RDS Computational Approach Jolanta Natalia Latosińska,*,† Magdalena Latosińska,† Marek Szafrański,† Janez Seliger,‡ and Veselko Ž agar§ Crystal Growth & Design 2016.16:4336-4348. Downloaded from pubs.acs.org by MIDWESTERN UNIV on 01/21/19. For personal use only.

†

Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia § “Jozef Stefan” Institute, Jamova 39, 1000 Ljubljana, Slovenia ‡

S Supporting Information *

ABSTRACT: The compound 3,3′-diindolylmethane (DIM) is a major in vivo product of digestion of indole-3-carbinol (I3C) (phytochemical from Brassicaceae family plants) and a main mediator of its chemopreventive and chemotherapeutic effects. In our previous paper (Eur. J. Pharm. Sci. 2015, 77, 141−153), we have reported the impact of structural differences between DIM and I3C on their biological activity. In this paper, the coinfluence of two factors: polymorphism and temperature, on the topology, nature (Coulombic/polarization/dispersion/repulsion), and strength of interaction pattern in DIM are in our area of interest. Upon polymorph screening it has been found that DIM crystallizes in two polymorphic forms, form I (already known) and form II (newly obtained). differential scanning calorimetry indicated a slightly lower melting point for form I than for form II (436 versus 440 K) and the lack of phase transitions in both polymorphs. The crystal and molecular structures of both polymorphs have been determined as a function of temperature by single-crystal X-ray diffraction. The structure of polymorph I is monoclinic, space group C2/c, while polymorph II is orthorhombic, space group P212121. The DIM molecule adopts a twisted (both 1H-indole rings are aligned along the same direction, but they are twisted by about 61.5°) and a half-chair (the molecule is bent, and both 1H-indole rings make an angle of 68.9°) conformation, respectively, in forms I and II, which remain almost unaffected by temperature changes. Despite different relative orientations of both 1H-indole moieties in forms I and II, the differences in the interaction patterns revealed by quantum theory of atoms in molecules (QTAIM), reduced density gradient (RDS), Hirshfeld surfaces (3D HS), and two-dimensional molecular fingerprints (2D MF) are relatively small. The distribution of intermolecular interactions in the crystal of form II is by 5% less balanced than in that of form I. The Manhattan and Euclidean distances between the interactions do not exceed 3.76% and 2.21%, respectively, while the Bhattacharaya coefficient does not exceed 0.35. Solid state PDB/DPN calculations have revealed that in solid the twisted conformation of the molecule is less stable by 118.7 kJ/mol than that of the half-hair one, but despite this, polymorph I is more stable due to a greater number of weak intermolecular interactions stabilizing the crystalline packing. (In the gas phase the half-hair conformation of the molecule is less stable by 0.788 kJ/mol than the twisted one, which may be attributed to the existence of many weak interactions and crystal continued...

Received: March 22, 2016 Revised: June 8, 2016 Published: June 15, 2016 © 2016 American Chemical Society

4336

DOI: 10.1021/acs.cgd.6b00456 Cryst. Growth Des. 2016, 16, 4336−4348

Crystal Growth & Design

Article

packing effects in the solid state, which are absent in the gas phase.) The key interaction stabilizing the twisted versus chair conformation and determining crystalline packing in both polymorphs of DIM is the NH···π one. The factor responsible for the locked conformation of DIM in both forms is the electrostatic potential complementarity of the regions of N−H···π, linking neighboring molecules, which permits easy overcoming of any repulsive interactions that may force rotation of the molecule. The commercial sample of DIM was found to contain approximately 50% of form I and 50% of form II.

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INTRODUCTION As much as 50% of new active pharmaceutical ingredients (API) and natural active ingredients (NAI)1 show very low aqueous solubility, which constrains the dissolution rate and thereby limits in vivo bioavailability. One of the important procedures proposed to overcome this limitation2 and ensure the reproducible and stable bioavailability of drugs or dietary supplements1 is the screening of polymorphs (crystalline forms of the same compound).3 The change in conditions during the crystallization process (e.g., solvents, impurities, level of supersaturation, temperature, or stirring) allows the formation of different forms, which reveal differences in many physicochemical properties (such as solubility, dissolution rate, permeability, melting point, vapor pressure, crystal shape, compressibility, density, hardness, resistance to degradation, optical and electrical properties)3 but also chemical reactivity.4 Selection of the lowest energy polymorph, stable and easily controllable, is advisible according to the Q6A Guide of the International Council on Harmonization (ICH),5 as the polymorphism or phase transitions during the manufacture and storage may affect the bioavailability, the efficacy and safety, especially when dissolution is the absorptionlimiting factor (Biopharmaceutics Classification System, classes II and IV).6 Dietary agents contributing to health protection by offering a feasible and efficient mechanism to ward off the potentially destructive effects of ubiquitous but malicious factors such as mutagens or carcinogens belong to the substances whose polymorphism matters significantly. Many nutrients, elements normally available in a well-balanced vegetable plant-based diet, are produced by nutraceutical and pharmaceutical industries in the form of solid dietary supplements, whose solubility and bioavailability are highly important. The beneficial activity of 3,3′-diindolylmethane (DIM, C17H14N2), Figure 1, a major

(anti-angogenesis), NF-κB (anti-inflammation), Erβ (NR3A2; hormone control), AR (anti-androgen), P38,p21 (cytostasis), PI3/Akt (apoptosis), and IFNγ (IFNGR; antiviral, antibacterial, anticancer). Thus, DIM suppresses the proliferation of estrogendependent reproductive cancers of breast,12 cervical,13−15 ovarian,16 endometrial, and prostate17−23 but also thyroid,24 head and neck,25 colon,26 melanoma,27 or blood cells (leukemia).28 Its effectiveness in the inhibition of systemic lupus erythematosus (SLE or lupus), an autoimmune disease associated with estrogen, has been proven.29 (However, its contribution to the growth of breast cancer cells (in vitro) in the absence of estrogen30 has also been noted.) This unique ability of DIM to repair DNA potentiates antitumor activity of some drugs (e.g., Erlotnib).31 DIM is a potent radioprotector against ionizing and UV radiation acting by a unique mechanismrapid activation of a nuclear kinase that regulates responses to DNA damage, repair, or apoptosis and oxidative stress.32 Although DIM has been known for 40 years and is manufactured on quite a large scale by the chemical industry, only scarce physicochemical data on this compound are available. In pure crystalline form, DIM is insoluble in water and thus poorly absorbed by the human organism. This factor significantly limits it bioavailability. But DIM provides a predictable, safer response than I3C,17 whose toxicity is associated with unfavorable enzyme induction attributed to non-DIM reaction products. DIM used as a supplementary diet product remains stable and is not further metabolized; therefore, many researchers have now focused on DIM instead of I3C.33 In our previous paper we have reported the impact of structural differences in DIM and I3C on their biological activity.34 Polymorphism and thermal stability issues of DIM have been up to now outside the area of our interest. The crystal structure of only one known form of DIM has been resolved by X-ray diffraction with a final R-factor of 3.96% at 150 K.35 According to this study, DIM crystallizes in the monoclinic system with a space group C2/c, Z = 4, a = 27.142(4), b = 5.720(1), and c = 8.302(1) Å; β = 106.50°. The aim of our current study was screening of DIM polymorphic forms, their structural elucidation, and characterization of their thermal profile (stability, phase transitions). These data are expected to help elucidate the observed differences between the effectiveness of DIM preparations of the same composition but made by different producers. Thus, we decided to check whether any transformation or thermal decomposition disturbs the DIM structure and in a consequence modify its activity. We have already applied combinations of different experimental techniques (X-ray, differential scanning calorimetry (DSC), and 1H−14N NMR-NQR double resonance techniques) and solid state computational approaches (the Bader’s quantum theory of atoms in molecules (QTAIM)36; Johnson’s reduced density gradient (RDS),37 and Spackman’s Hirshfeld surface-based38,39) for investigation of the crystalline structure and topology of intermolecular interactions pattern of many purine or benzimidazole containing compounds.40−43 In our opinion, results of combined 1H−14N NMR-NQR, X-ray, DSC, and solid DFT studies provide valuable clues which

Figure 1. Structural formula of 3,3′-diindolylmethane (DIM).

in vivo product of digestion of indole-3-carbinol (phytochemical naturally found in Brassicaceae family plants) has been discovered by Wattenberg78 and Dashwood et al.,9 but is still a subject of extensive studies. The basic moiety of DIM, 1H-indole heterocycle, is a privileged substructure which, due to its isosterism with purine, may easily interact with different proteins and enzymes. It is known that DIM is capable of inducing apoptosis in human cancer cells10 and is an effective in vitro inhibitor of cytochromes P450 (CYP).11 Therefore, the National Cancer Institute screened DIM mainly as a therapeutic for numerous forms of cancer. Many target proteins have been discovered for DIM, e.g., HIF-1α 4337



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The crystal data together with experimental and refinement details are collected in Table 1. Crystallographic information files (CIF) with the DIM structures of polymorphs I and II were deposited in the Cambridge Crystallographic Database Centre as supplementary publications CCDC 1457911−1457915. 1 H−14N Double Resonance. Nuclear quadrupole resonance (NQR), a radiofrequency spectroscopic technique similar to nuclear magnetic resonance (NMR), is based on the interaction of the electric quadrupole moment of an atomic nucleus with the inhomogeneous electric field produced by surrounding electric charges. It is thus a sensitive technique for the study of electron charge distribution within the molecule. The atomic nuclei with nonzero electric quadrupole moment are those with the spin I ≥ 1. In zero external magnetic field the nuclear ground state splits into 2I + 1 nondegenerate (integer I) or I + 1/2 doubly degenerate (half-integer I) nuclear quadrupole energy levels. The transition frequencies between the nuclear quadrupole energy levels, called the NQR frequencies, depend on two parameters: the nuclear quadrupole coupling constant and the asymmetry parameter η of the electric-fieldgradient tensor.47 Nuclei of atoms lying at nonequivalent crystallographic positions have in general different NQR frequencies, so NQR can be used to determine the number of nonequivalent positions of a given atom within the crystal unit cell. In various crystal polymorphs of a given substance the intermolecular interactions generally differ. It results in a different electron charge distribution within the molecule and consequently in different NQR frequencies of a given atomic nucleus. Nitrogen atomic nucleus 14N has a spin I = 1 and consequently three nondegenerate nuclear quadrupole energy levels. The three 14N NQR frequencies ν+, ν−, and ν0 are expressed as47

considerably expand the knowledge and facilitate understanding the nature of the polymorphism of DIM. The propensity to form specific bonds or contacts provides substantial information on the stability or solubility.42 DIM is used as a dietary supplement and a drug, and thus reliable characterization of possible paths of its transformations is important from the point of view of development of techniques improving its solubility, like microencapsulation technology.44 Our study should be useful in the pharmaceutical industry fields (studies on stability, search for alternative forms of dietary supplements) and drug design (docking experiments; pharmacophore modeling; planning the synthesis of new compounds of this class).

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EXPERIMENTAL SECTION

Crystal Growth. DIM (purity ≥ 98%) was purchased from SigmaAldrich and used for crystallization without further purification. The single crystals were grown by slow evaporation of the solvent at room temperature or at 275 K. The crystallization from methanol or ethanol solutions always yielded monoclinic form I of DIM, regardless of temperature. The application of acetonitrile as a solvent resulted in the crystallization of a new orthorhombic form II. The orthorhombic crystals usually were grown at room temperature, whereas at 275 K a mixture of both forms or only form I were formed. On the basis of distinct habits (Figure S1, Supporting Information) these two types of crystals could be easily separated. Single Crystal X-ray Diffraction. The temperature-dependent single-crystal X-ray diffraction measurements were carried out with the graphite-monochromated MoKα radiation on a Gemini A Ultra diffractometer. The crystal temperature was stabilized within 0.1 K with a Cryostream Plus (Oxford Cryosystems) attachment. The data were collected and processed using the CrysAlisPro software.45 The crystal structures were solved by direct method with SHELXS97 and refined by full-matrix least-squares method on all intensity (F2’s) data using SHELXL97.46 All the heavy atoms were refined with anisotropic temperature factors. The H atoms were located from difference-Fourier maps and refined with isotropic temperature parameters. The structures were resolved at temperatures 120 and 296 K (form I) and 120, 293, and 370 K (form II).

ν± =

e 2qQ e2qQ η (3 ± η) ν0 = ν+ − ν− = 4h 2h

(1)

Here e2qQ/h is the quadrupole coupling constant and η is the asymmetry parameter of the electric-field-gradient tensor. The nuclear quadrupole double resonance technique with multiple frequency sweeps and two-frequency irradiation48,49 was used to measure the 14N NQR frequencies in DIM. The details of the double resonance spectrometer and of the measuring procedure are published in paper.50 The temperature of NQR experiments was 295 K, and the difference in the resonance

Table 1. Crystal Data and Structure Refinement Parameters for DIM Polymorph I at 120, 150, and 296 K, and for Polymorph II at 120, 293, and 370 K Form I temperature (K) empirical formula formula weight crystal system space group unit cell: a (Å) b(Å) c(Å) β (deg) V (Å3) Z, ρ(g/cm3) μ (mm−1) F(000) theta range (deg) reflections collected independent reflections/Rint data/restraints/parameters goodness-of-fit on F2 R1/wR2 (I > 2σI) R1/wR2 (all data) largest diff. peak and hole (e/Å3)

120.0(2)

35

150

Form II 120.0(2)

293(2)

370.0(1)

C17H14N2 246.30 monoclinic C2/c



296(2)

C17H14N2 246.30 orthorhombic P212121



27.103(3) 5.6993(6) 8.2865(9) 106.511(17) 1227.2(2) 4, 1.333 0.079 520 3.14−30.01 13492 1737/0.0232 1737/0/115 1.049 0.0393/0.1083 0.0419/0.1109 0.409/−0.161

27.142(4) 5.720(1) 8.302(1) 106.50(1) 1235.8(3) 4, 1.323

27.174(3) 5.7452(6) 8.4021(9) 106.451(17) 1258.0(2) 4, 1.300 0.077 520 3.13−30.16 4295 1703/0.0210 1703/0/115 1.033 0.0419/0.1048 0.0520/0.1143 0.180/−0.159

6.03711(10) 7.73585(14) 26.1863(5) 90.0 1222.96(4) 4, 1.338 0.080 520 2.75−30.26 31972 3531/0.0256 3531/0/228 1.037 0.0302/0.0790 0.0315/0.0799 0.293/−0.213

6.12885(8) 7.80868(10) 26.2298(3) 90.0 1255.31 4, 1.303 0.078 520 2.72−30.25 32729 3601/0.0250 3601/0/228 1.047 0.0351/0.0874 0.0395/0.0898 0.162/−0.179

6.1773(4) 7.8528(6) 26.257(3) 90.0 1273.7(2) 4, 1.284 0.076 520 2.71−30.19 5474 3400/0.0205 3400/0/229 1.012 0.0425/0.0784 0.0641/0.0898 0.119/−0.109

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from 3D HS will be published elsewhere.66 A further global quantitative characterization of the noncovalent interactions using the electrostatic potential mapped onto the 3D HS was delivered. The results were interpreted on the basis of the electrostatic complementarity67 within the so-called Politzer,68 approach. Comparison of the Interaction Patterns. A comparison of the differences/similarity between the intermolecular interaction patterns in both polymorphs was performed using a few metrics defined below: Manhattan metric

frequencies for temperatures differing by 2−3 K in the 1H NMR-14N NQR experiment was negligibly small. DFT Spectra Simulation. Periodic quantum chemistry calculations were carried out within the DMOL351,52 code run on the supercomputer at the Wrocław Supercomputing and Networking Center (WCSS). The DFT approach rooted in Thomas−Fermi53 model and Kohn−Sham54 theorem, later generalized by Levy,55 was applied. The generalized gradient approximations (GGA) Perdew, Burke, Ernzerhof (PBE)56 functional, which depends on both ρ and dρ/dr was used. The numerical radial functions basis DNP (double-ζ with polarization) was chosen. The Tkatchenko-Scheffler57 correction on dispersionthe so-called DFT-D correctionwas applied. Within this approach the principal components of electric field gradient (EFG) tensor, qii (i = x, y, and z), were obtained after the diagonalization of the traceless tensor. The details of the procedure are published in the previous paper.58 QTAIM/RDG. Quantum chemical calculations required for QTAIM analysis were carried out within the GAUSSIAN0959 code run at WCSS. Theoretical analysis of intermolecular interactions pattern was performed within the Bader’s quantum theory of atoms in molecules (QTAIM)25,34 supplemented with the reduced density gradient (RDG)37 technique with long-range corrected version of B3LYP using the Coulomb-attenuating method CAM-B3LYP/ 6-311**G++.60−62 The details of the combined approach are described in ref 58. Three different approaches to the evaluation of intermolecular potentials were applied. According to Espinosa−Molins−Lecomte,63 the energy of hydrogen bonds was estimated in a simplified manner from the local potential energy density as EH = 1/2V(rBCP). Lattice energy calculations and the separation of Coulombic/polarization/dispersion/ repulsion terms were performed using the CLP64 and Pixel65 techniques. 3D Hirshfeld Surfaces. Exploration of intermolecular interaction pattern and packing capacities in solid was performed within the 3D Hirshfeld Surfaces approach.38,39 The descriptors like dnorm, shape-index, and curvedness of the surface mapped over 3D HS were evaluated.38 The decomposition of the 3D Hirshfeld surfaces into a 2D “molecular fingerprint” map (plot of di versus de) which summarizes the distribution of interactions of the molecule with its environment39 was made. The details of the procedure that allows comparison of intermolecular interaction pattern via 2D molecular fingerprints derived

n

dML(p , q) =

∑ |pi − qi| i=1

(2)

Euclidean metric n

dE(p , q) =

∑ (pi − qi)2 i=1

(3)

Bhattacharaya coefficient n

dBC(p , q) =

∑ pq i i i=1

(4)

where pi, qj interactions in each polymorph and sum runs over all interactions. The details of this approach will be published elswhere.66

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RESULTS AND DISCUSSION The X-ray data for both forms I and II of DIM, collected at a few different temperatures, are listed in Table 1. Form I is monoclinic with a space group C2/c, Z = 4, a = 27.174(3), b = 5.7452(6), and c = 8.4021(9) Å; β = 106.451(17)° at 296 K, while form II crystallizes in orthorhombic P212121 space group (typical of proteins69) with a = 6.1773(4), b = 7.8528(6), and c = 26.257(3) Å at 293 K. The molecular conformation and crystal packing for both polymorphs are shown in Figure 2a−c. The space groups remain unchanged over a wide range of temperatures, irrespective of form I or II, but the unit cell parameters differ, Table 1.

Figure 2. Twisting and half-chair conformations of the molecule 3,3′-diindolylmethane (DIM), respectively in polymorph I and II (a), and the packing of the crystal structures in polymorphs I (b) and II (c). 4339



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indicate a significant thermal hysteresis, defined here as the difference between the melting and freezing points. The main endometric peaks indicating melting of form I and form II are located at 436 and 440 K, respectively. DSC indicates the lack of phase transitions in both polymorphs. A considerably large but smooth decrease in TGA mass of the commercial sample starting at 425 K results in 50% mass loss at 575 K (Figure S5, Supporting Information), which suggests melting with decomposition. DSC study, repeated many times with different speeds, suggests that there is no transition between polymorph I and polymorph II or vice versa. Both polymorphs are stable in the entire temperature range studied, which suggests a monotropic relation. The lack of a solid-state transition prior to melting indicates a high energy barrier between the forms. Any transition would require a concerted thermally activated conformational change which seems unlikely. The 14N NQR spectra of the two polymorphs of DIM and of the commercial sample were measured by the multiple frequency sweeps48,49 and two-frequency irradiation48 techniques. (In our earlier paper we described the results only for a commercial sample of DIM, and we missed two high frequency lines.) The line at ν0 is not resolved within the experimental resolution, and we expected to observe only one set of 14N NQR frequencies. By scanning frequency sweep limits we located the upper NQR frequencies for one nitrogen position and then stopped the scan. The 1H−14N double resonance spectra of the three samples are presented in Figure 4.

The root-mean-square (RMS) factor between the structures of form I and form II calculated for the cluster consisting of 15 molecules at RT reaches 1.479 Å. The RMS for form I at 120 and 296 K is as small as 0.086 Å and at 150 and 296 K is as small as 0.073 Å; for form II at 120 and 296 it does not exceed 0.092 Å, and at 120 and 370 K it slightly increases to 0.142 Å. Thus, the effect of polymorphism is much better pronounced than the influence of temperature. This conclusion is also well supported by the differences in the shape and slope of the temperature dependence of unit cell volume, Vunit cell(T), for both forms, I and II, Figure 3. Vunit cell(T) is nonlinear in both forms,

Figure 3. Volume (V) and surface (S) expansion of 3D Hirshfeld surfaces and unit cell volume (V unit cell) in both 3,3′-diindolylmethane (DIM) polymorphs upon temperature change. (■ - V, □ - S, and ● - V unit cell; polymorph I in red, polymorph II in blue).

but in form II the slope of volume (T) is a bit greater and the degree to which the crystal lattice expands is larger. Examination of the deviations from the least-squares planes through the atoms of particular 1H-indole rings indicates that the skeletons of each ring are nearly planar; thus a degree of conjugation over the entire indole units is reasonable. The key factor responsible for different crystalline packing is conformation of the 3,3′-diindolylmethane moleculetwisted (both 1H-indole rings are aligned along the same direction, the nitrogen atoms are at approximately the same side of the molecule and both 1H-indole rings are twisted by about 61.5°) versus half-chair (the molecule is bent, the nitrogen atoms are at opposite sides of the molecule and both 1H-indole rings form an angle of 68.9°) in forms I and II, respectively, Figure 2a. In both polymorphs, common structural motifs are molecules linked by NH···π interactions with the locking ability of the rings conformation,70 but, in form I two neighboring molecules are mutually linked and form hydrogen-bonded dimeric synthons, while in form II chains of molecules are formed, Figure S2 (Supporting Information). These packing motifs are kept unchanged upon cooling/heating in each form. The twisting/bending angles between the planes containing two 1H-indole moieties of DIM (form I: 61.44° at 120 K, 60.75° at 150 K; 61.61° at 293 K; form II: 68.70° at 120 K, 68.90° at 293 K, and 68.78° at 370 K) suggest that the conformation of DIM molecule in both forms I and II is fixed/locked within experimental error in the whole range of temperatures. Additionally, the −CH2 group is arranged symmetrically relative to the indole rings (0.002 Å), and thus it is not prone to reorientation. DSC measurements (Figures S3 and S4, Supporting Information)

Figure 4. 1H−14N NMR/NQR double resonance spectra of the two pure polymorphs and commercial sample of 3,3′-diindolylmethane (DIM).

In the investigation of polymorph I, we first used the technique based on multiple frequency sweeps. The proton spin system was polarized in a high magnetic field (0.75 T) for 1 min. Then the sample was pneumatically transferred to a low magnetic field B, in which the proton NMR frequency νH was equal to νH = γHB/2π. The sample was left in the low magnetic field for 0.5 s, so for the so-called relaxation period. During the relaxation period we applied multiple frequency sweeps of an rf magnetic field with the amplitude approximately equal to 2 mT. The duration of a frequency sweep was set to 10 ms, and the sweep frequency limits were set to 1.5 and 3 MHz. The νH-scan was performed in steps of 10 kHz in the range between 0 kHz and 1 MHz. As shown in Figure 4 we clearly observe in this frequency range in two dips: a broader dip at 290 kHz and a narrower dip at 145 kHz. The dip observed at 290 kHz is a single-quantum dip occurring at the proton NMR frequency νH equal to the lowest 14 N NQR frequency ν0, whereas the dip observed at 145 kHz is a two-quantum dip, which occurs at νH = ν0/2. The higher 14 N NQR frequencies ν+ and ν− were first located by varying 4340



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Table 2. 14N NQR Frequencies, Quadrupole Coupling Constant e2qQ/h and the Asymmetry Parameter η at the Nitrogen Nucleus in Solid State Polymorphs I and II 1

H−14N NMR-NQR (at 295 K)

PBE/DNP (form I at 296 K and form II at 293 K)

polymorph

T1 [s] at 32 MHz

ν+ [MHz]

ν− [MHz]

ν0 [MHz]

|e2Qqh−1| [MHz]

η [−]

I

110

2.295

2.005

0.290

2.867

0.202

II

90

2.405

2.145

0.260

3.033

0.171

motif

ν+ [MHz]

ν− [MHz]

ν0 [MHz]

|e2Qqh−1| [MHz]

η [−]

2.737 2.899 2.761 2.857 2.941 3.003

2.555 2.845 2.562 2.675 2.727 2.787

0.182 0.054 0.198 0.182 0.214 0.216

3.528 3.829 3.549 3.688 3.779 3.860

0.103 0.028 0.112 0.099 0.113 0.112

solida monomera solida monomera

a

Solid - crystalline structure; monomer - cut out of the crystalline structure.

Table 3. Contributions to the Total Energy for Solid State Polymorphs I and II Calculated at the PBE/DNP Level polymorph

phase

Etotal [H]

Ekinetic [H]

Ee [H]

EDFT‑D [H]

EEC [H]

Ebinding [H]

Ia

solid monomer monomer opt. solid monomer monomer opt.

−3060.09 −764.88 −765.0513 −3059.91 −764.92 −765.0510

−48.36 −7.12 −7.049 −48.55 −7.26 −6.793

4.59 −3.75 −3.763 4.92 −3.65 −4.018

−0.340 −0.020 −0.0198 −0.350 −0.018 −0.0209

10.62 2.67 2.431 10.67 2.65 2.431

−26.12 6.38 −6.5586 −25.94 −6.43 −6.5584

IIa

μmolecule [D] 3.06 3.03 0.76 0.88

a

Solid - crystalline structure; monomer - cut out of the crystalline structure; form I at 296 K and form II at 293 K; monomer opt. - optimized single molecule at PBE/DNP level.

the sweep frequency limits and then more precisely determined by the two-frequency irradiation technique as equal to 2295 kHz and 2005 kHz. In the same way we determined the 14N NQR frequencies in polymorph II as equal to 2405 kHz, 2145 kHz, and 260 kHz. In the commercial sample we observed broad, but unresolved, low-frequency dips. The application of the two-frequency irradiation technique shows in the high frequency range the presence of the same 14N NQR frequencies as previously observed for polymorphs I and II. So the commercial sample is a mixture of the two polymorphs. Also the intensities of the dips corresponding to polymorph I are nearly the same as those of the dips corresponding to polymorph II. So the fraction of each of the two polymorphs in the commercial sample is close to 50%. The relaxation time T1 slightly shorter for polymorph I (90s) than polymorph II (100 s) suggests smaller rigidity of protons in the former. The yet unpublished 1H NMR results also suggest that both systems are rigid and do not show conformational transitions. Indeed, the volume of the crystal voids in the unit cell in polymorph I is 7% larger (111.41 versus 104.57 Å3 for form I and form II, respectively). Nearly the same values of the NQR parameters, Table 2, for so distinct conformations like those in polymorph I and II, Figure 2a, suggest similarity in the distribution of electron density in the neighborhood of the nitrogen atom. A slightly smaller quadrupole constant and larger asymmetry parameter at the nitrogen site for polymorph II than I suggest that the differences are a combined effect of the change in conformation and hydrogen bond strength.71 According to the asymmetry parameter the NH···π should be weaker in polymorph I than in polymorph II, which is suggested also by its length (3.199 Å at 296 K versus 3.184 Å at 293 K). The asymmetry parameter describes a deviation of EFG tensor from the spherical symmetry, e.g., a weaker NH···π bond implies a lower EFG tensor symmetry, which is manifested as a higher asymmetry parameter.72,71,73

The calculations at the PBE/DNP level, augmented with TK dispersion, performed for the crystallographic structures of both polymorphs determined at room temperatures, satisfactorily reproduced 14N NQR parameters, confirming high symmetry of molecular structure (equivalence of both indole rings in each molecule, which gives the same NQR parameters for both 14 N sites in the molecule) of polymorph I, but indicated slight inequivalence of indole rings in polymorph II (small differences in the NQR parameters for both nitrogen atoms in the molecule). This effect was not determined in experiments; thus the asymmetry of the indole rings in form II is probably canceled out by thermal averaging. The results were calculated assuming the presence of monomers isolated from the polymorphs crystals differs significantly from those obtained in the experiment, but the results obtained for solids are reliable, which follows from the high sensitivity of NQR parameters to the far-range intermolecular interactions7443 and molecular dynamics.75,76 (Temperature is an averaging factor and can have impact on NQR parameters, which are overestimated due to neglect of this effect.76) The PDB/DNP calculations reveal that the half-chair conformer taken directly from solid is by 118.7 kJ/mol more stable than the twisted one, Table 3. (The two conformers were cut out of the crystalline structure; form I at 296 K and form II at 293 K.) The difference between both conformers (monomers) optimized in the gas phase is much smaller and equals to only 0.788 kJ/mol. Moreover, the optimized twisted conformer (form I) is more stable than the half-chair one (form II), which may be attributed to the existence of many weak interactions and crystal packing effects (including deformation of structures caused by interactions in crystal lattice) in the solid state. The crystal environment stabilizes molecular conformation that is relatively energetically unfavorable. The lattice energy, which in form I is much lower than in form II, Table 3, strongly stabilizes the former molecular conformation in the solid by as much as 369.45 kJ/mol. Because of a higher symmetry of the form II molecule and consequently a smaller dipole moment, Table 3, binding forces in form II are expected to be much weaker 4341



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Table 4. Contributions to the Total Energy for Solid State Polymorphs I and II Obtained within CLP and Pixel Approaches polymorph

method

T [K]

ECoulombic [kJ/mol]

Epolarization [kJ/mol]

Edispersion [kJ/mol]

Erepulsion [kJ/mol]

Etotal lattice [kJ/mol]

I

CLP Pixel CLP Pixel CLP Pixel CLP Pixel CLP Pixel CLP Pixel

120

−17.2 −60.2 −16.8 −57.8 −16.3 −52.4 −15.4 −55.1 −14.5 −48.2 −14.5 −44.6

−19.3 −32.2 −19.0 −30.5 −18.3 −26.6 −19.3 −29.5 −18.3 −24.8 −18.3 −24.0

−163.5 −182.9 −160.1 −179.2 −151.1 −167.9 −160.1 −180.0 −147.6 −164.5 −147.6 −155.8

54.8 100.8 52.0 100.0 45.0 80.1 51.8 95.5 42.1 75.7 42.1 67.0

−145.2 −174.5 −143.9 −167.5 −140.7 −166.8 −143.0 −169.1 −138.3 −161.8 −138.3 −157.3

II

150 296 120 293 370

but in a greater number than in form I. Analysis of the shape of the potential energy surface (PES) reveals that the path which would be required for the transition from form I to form II is very complex. The two conformational motions, jump by the torsional angle C−C−CH2−C Θ1 = 67° and rotation about −CH2−C by Θ2 = 60°, characterized by large energy barriers, are required. It justifies the lack of phase transitions and a significant thermal hysteresis observed in DSC. Lattice energy calculations, with the use of the CLP64 method, for both polymorphs indicate that the dispersion term brings a major contribution of about 90%, i.e., almost twice as large than in typical organic crystals, while the electrostatic terms i.e., Coulombic and polarization are small (bring a contribution of 10 and 11%, respectively) and close in absolute value to repulsion (32%). Detailed analysis of the contributions to the total lattice energy, Table 4, suggests that the discrepancy between the results for forms I and II stems mainly from the differences in dispersion and repulsion, while the changes in Coulombic and polarization terms are small. Lattice energy calculations, using the Pixel65 (more reliable method), for both polymorphs indicate a major contribution of the dispersion, but also significant Coulombic (about 34)% and repulsion (about 58%) terms. This suggests the dominating role of dispersion and repulsion in the crystal packing in both clearly different packings. Better stability of form I over form II results mainly from Coulombic and repulsion terms, Table 4. Irrespective of the form, I or II, and method, all terms contributing to the total lattice energy decrease upon heating. 3D Hirshfeld Surfaces Analysis. In order to gain more insight into the nature of NH···π interaction the Hirshfeld surfaces (3D HS) and its 2D fingerprint (2D FP) decomposition were analyzed, Figures 5 and 6. The shape of 3D HS indicates a small difference between single promolecules in form I and form II, despite different orientations of 1H-indole rings. A smaller size of the 3D HS surface in form I should result in improved solubility, but we did not observe drastic differences between form I and form II. The volume/surface ratio can be treated as an estimator of nucleation speed. (The free energy change can be described as a function of the radius of the nuclei from the volume and surface terms. Thus, volume/surface factor is related to the nucleation speed; when it is small, surface dominates, when it is large, volume dominates.77) A slightly higher value for polymorph II than I (1.055 at 296 K versus 1.065 at 293 K) suggests the crystallization of polymorph II is less preferred. Irrespective of the form, the volume and area of 3D HS expand slightly and nearly linearly with increasing temperature, which is

Figure 5. Crystal structures of (a) polymorph I, (b) polymorph II of DIM with dnorm mapped over the 3D Hirshfeld surface. 4342



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Figure 6. 2D molecular fingerprints of the interactions pattern in polymorph I (upper) and polymorph II (bottom) of DIM at different temperatures. Close contacts are divided into a few regions (C···H, H···C, H···H).

Figure 7. Close contacts of DIM molecules broken down into a few different basic interaction types. The notation A···B refers to interaction between X atoms inside the Hirshfeld surface and Y atoms outside (e.g., hydrogen bonds NH···C (depicted in light/dark green) and H···H (depicted in red)). Similarity in all areas not disturbed by temperature is evident. (Notation see Table 5)

confirmed by unit cell volume expansion observed experimentally. The effect of the increase in 3D HS area (S) upon heating is better pronounced than the 3D HS volume (V) change, Figure 3. Irrespective of the form, the volume and area of the 3D HS expand

slightly and nearly linearly with increasing temperature, which is confirmed by unit cell volume expansion observed experimentally. The effect of the increase in 3D HS area (S) upon heating is better pronounced than the 3D HS volume (V) change, Figure 3. 4343



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Table 5. Comparison of % of the Hirshfeld Surface, Total Hirshfeld Volume and Surface Characterizing Both Polymorphs of 3,3′-Diindolylmethane (DIM) form notation in Figure 7 I

II

1 2 3 4 5 6

T [K]

C···H [%]

H···C [%]

N···H [%]

H···N [%]

H···H [%]

N···C [%]

C···N [%]

C···C [%]

volume [Å3]

surface [Å2]

120 150 296 120 293 370

23.5 23.4 22.9 24.3 23.6 23.4

18.6 18.5 18.3 19.0 18.6 18.5

2.8 2.8 2.7 2.8 2.8 2.9

2.2 2.2 2.2 2.3 2.2 2.3

52.1 52.3 53.1 50.8 51.9 52.3

0.3 0.3 0.3 0.3 0.3 0.2

0.4 0.4 0.4 0.4 0.4 0.2

0.0 0.0 0.0 0.1 0.1 0.1

300.46 302.61 308.49 299.55 307.63 312.22

288.83 289.80 292.28 286.00 288.84 291.25

Figure 8. 3D-deformation density (DD) maps: charge depletion (CD) region at the hydrogen linked to nitrogen atom which is directed toward the charge concentration (CC) region spreading over the indole ring (polymorph I (left) and II (right)).

the H···π/ π···H contacts are represented by relatively wide symmetric spikes, at de + di ≈ 2.4 Å. The characteristic “‘wings’” at the top left, di < de, can be assigned to the surface around the donor (N−H), whereas those at the bottom right, de > di, correspond to the surface around the acceptor (π), Figure 6. These N−H···π interactions cover the area of 42.3% and 41.2% of the total 3D HS for form II and I, respectively. N−H···π belongs to attractive molecular forces in which stronger proton donating ability of the NH group results in the larger stabilizing effect. Indeed, 3D-deformation density (DD) maps, Figure 8, reveal a charge depletion (CD) region at the hydrogen linked to nitrogen atom which is directed toward the charge concentration (CC) region spreading over the indole ring. This facilitates formation of the NH···π bonds in the crystal. The electrostatic potential (ESP) mapped over the Hirshfeld surface, Figure 9, sheds some light on the nature of this interaction in both forms. The numerical characteristics of ESP: the average negative VS− and positive VS+ potentials and the most negative, VSmin and the most positive, VSmax potentials, their variances σ+2 and σ−2, the balance parameter (ηS) and the average deviation from the mean surface potential (π) for form I and form II significantly differ, Table 6. The variation of the positive and negative values of the potential in both forms is reflected by the highest absolute values of VSmin and VSmax potentials for form II than form I, Table 6. The difference in balance for form I and II is evident; ηS is much closer to the maximum of 0.25 for form II than form I. But a decrease in ηS with increasing temperature for both form I and II is a subtle effect. The product ηSσT2 takes high values, which indicates electrostatic interactive tendencies in the crystal. Its higher value for form II than form I means that both the positive and the negative potentials on the molecular surface of form II are stronger. It also indicates weaker NH···π bonds in form I, but stronger in form II and only a small decrease in strength with increasing temperature. The magnitude

The 2D FP derived from 3DS indicate that the difference between the distribution of interactions in forms I and II is negligible, Figures 6 and 7. The Euclidean distance of these two distributions does not exceed 2.16% at 120 K and 2.21% at 293 K, the Manhattan distance does not exceed 3.64% at 120 K and 3.76% at 293 K, while the Manhattan coefficient does not exceed 0.35 at 120 K and 0.36 at 293 K. The interactions distribution in form II is by 5% less balanced than in form I. Upon heating the whole 2D FP is similarly shifted due to volume expansion, Figure 6. Moreover, the Euclidian distance of the distribution of interactions in form I at 120 and 296 K does not exceed 1.96%, while in form II 2.06% at 120 and 370 and 1.99 K% at 120 and 293 K. The Bhattacharaya coefficient does not exceed 0.339 at 120 and 296 K (form I) and 0.358 at 120 and 293 K (form II). Thus, the effect of polymorphism on interactions pattern is stronger than that of thermal expansion. Detailed analysis of 3D HS with the normalized contact distance dnorm and shape-index, mapped over this surface, Figure 5, and decomposed 2D FP plots derived from 3D HS, Figures 6 and 7, confirm that the dispersion term, i.e., van der Waals forces (H···H interactions) and contacts (N···H/H···N, C···H/H···C) contribute mostly to the packing of species in the crystalline state. The quantitative results of analysis are collected in Table 5. Intense red areas in the 3D HS near N−H and over the benzene ring, representing the lowest value of dnorm (−0.261 for form II and −0.213 au for form I) and the flattened regions of the 3D HS with curvedness and shape-index mapped over this surface (contact patches), Figure S6 (Supporting Information), confirm the participation of nitrogen atoms in two N−H···π aromatic hydrogen bond interactions. The directions of these interactions are well characterized by the intersections of the axes of these interactions with the centers of red areas in 3D HS surface, Figure 5. In the 2D molecular fingerprint, 4344



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Figure 9. Electrostatic complementarity upon crystal packing in polymorphs I (left) and II (right) of DIM: electrostatic potential mapped onto the Hirshfeld surfaces of symmetry-related neighboring molecules, two different orientations shown. Color scale is −0.01 (red) to 0 (white) to 0.01 au (blue).

Table 6. Politzer-Type Statistical Analysis of the ESP on the HSs for 3,3′-diindolylmethane (DIM)a form I

II

T [K]

VSmax [kJ/mol]

VS+ [kJ/mol]

σ+2 [kJ/mol]

VSmin [kJ/mol]

VS− [kJ/mol]

σ−2 [kJ/mol]

π [kJ/mol]

ηS [−]

σT2 [kJ/mol]

ηSσT2 [kJ/mol]

120 150 296 120 293 370

98.200 97.925 98.202 96.119 96.258 94.591

24.030 24.030 24.030 24.585 24.446 24.585

0.420 4.181 4.278 0.374 0.374 0.369

−47.640 −46.532 −47.087 −54.449 −54.449 −53.060

−22.50 −22.363 −22.085 −25.697 −25.558 −25.002

0.128 0.124 0.125 0.172 0.171 0.160

23.200 23.057 22.919 25.141 25.002 24.724

0.180 0.174 0.174 0.216 0.215 0.211

0.550 1.026 1.021 1.032 1.029 1.000

0.098 0.179 0.178 0.223 0.221 0.211

a

The extremal values in the minimum and maximum surface potentials (VSmin and VSmax); average positive and negative surface potentials (VS+ and VS−); their variances (σ+2 and σ−2); the total variance (σT2); the average deviation from the mean surface potential (π). Balance (ηS) and indicator of electrostatic interactive tendencies ηSσT2.

of π suggests that local polarity of the molecule is higher in form II than form I, but in both forms it slightly decreases with increasing temperature. The match of positive and negative regions of the molecular surfaces, corresponding to electrostatic interactions, is well pronounced in ESP shown in Figure 9. The positive (blue) regions clearly separated from negative (red) flat smooth regions by white zero-potential lines are similar in shape for form II and I (in form I this region is twisted, which results from the opposite orientation of indole rings). The positive ESP on both sides of the molecule occupies a long belt-like region, Figure 9, which is formed mainly by H···H interactions, covering a comparable area of 51.9% and 53.1% for form II and I, respectively, Figure 5. In the 2D fingerprint plot, they are reflected by the cloud of scattered points and one common much broadened spike along the di = de line, Figure 6. (N···H/H···N interactions represented by wider, difficult to resolve spikes at de + di ≈ 2.8 Å covering only 4.9 and 5% of the total 3D HS for form II and I, respectively, can be neglected.) The negative potential comes from π electrons distributed symmetrically over the top and bottom sides of the molecule. Irrespective of the form, I or II, it makes a similar pattern indicating that the positive regions near N−H match the negative ones over the π ring, which forces crystalline packing via NH···π interactions. Thus, the NH···π bond is also partially electrostatic. QTAIM/RDS. To detect weak interactions in the crystalline structure, including atomic contacts, which are often omitted in standard X-ray data analysis, a combined QTAIM and RDS approach was applied. The temperature-induced changes in the interactions are very small, so the time-consuming BCP analysis was performed for the polymorph structures only at the two temperatures at which the NQR measurements were made.

The 3D RDS isosurfaces for DIM polymorphs cut at 0.07 au with the sign(λ2)ρBCP mapped over this surface, Figure 10, reveal weak interactions in real space, i.e., not only NH···π but also numerous additional interactions like C−H···C contacts. The topological descriptors of electron density (ρ(r), Δρ(r), ε, the HBCP, and its components GBCP and VBCP) and the strength of the intermolecular bonds estimated using the Espinosa−Molins− Lecomte formula are collected in Table 7. The N−H···π bonds of −6.79 kJ/mol in form I and of −7.68 kJ/mol in form II are the strongest interactions in DIM crystals. The sign(λ2)ρBCP of these interaction is equal to −0.0144 for form I and −0.0123 for form II, and thus it is quite a strong interaction, stronger than the other van der Waals ones. The value of electron densities at BCP, ρBCP, of 0.0113 and 0.0123 au for form I and form II, respectively, falls within a certain range of values typically between 0.001 and 0.035 au (markedly lower than for the covalent bonds). The corresponding Laplacian values ΔρBCP are positive and amount to 0.034 and 0.038 au for form I and form II, and do not exceed typical values between 0.006 and 0.130 au. The total energy density HBCP values are small but positive, which is indicative of the closed-shell interaction. N−H···π bond is stronger in form II than form I. According to the QTAIM and RDS NH···π is weaker in polymorph I than in polymorph II, which supports our earlier findings. The remaining intermolecular contacts are 2-fold weaker, Table 7. The electron densities at BCPs, ρBCP, which varies from 0.0019 to 0.0053 au for form I and from 0.0016 to 0.0070 au for form II are significantly lower than for the covalent bonds. The corresponding Laplacian values ΔρBCP are very small and positive and cover the range 0.0057−0.0166 and 0.0057−0.020 au for form I and form II, respectively. The sign(λ2)ρBCP of these interactions varies from −0.0020 to −0.0053 au for form I and 4345



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Figure 10. Molecular graph of two symmetry-related neighboring molecules of DIM in polymorphs I (left) and II (right) (BCP - green points, RCP - red points); RDG mapped onto the molecular graph (color scale: yellow - weak, red - strong).

Table 7. Topological Parameters of ρ(r) for Intermolecular Contacts in 3,3′-Diindolylmethane, DIM (Electron Density at Bond Critical Point BCP (ρBCP(r)), Its Laplacian ΔρBCP(r), Ellipticity (ε), Second Component of Hessian (λ2) the Potential Electron Energy Density (VBCP), the Kinetic Electron Energy Density (GBCP), the Total Electron Energy Density (HBCP) and Estimated Hydrogen Bonding Energy According to Espinosa EE Calculated at the CAM-B3LYP/6-311++G(d,p) Level of Theory critical R (X···Y) polymorph point type description of X···Y [Å] Ia

IIa

a

BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP BCP

C ··· HC C ··· HC C ··· HC C ··· HC CH ··· HC C ··· HN C ··· HN CH ··· HC C ··· HC C ··· HC C ··· HC C ··· HC C ··· HC C ··· HC C ··· HN

3.483 3.483 3.118 3.118 2.345 2.495 2.495 2.974 3.468 3.285 3.097 2.997 2.750 2.749 2.422

ρBCP(r) [au]

ΔρBCP(r) [au]

ε [−]

λ2 [au]

δ(rBCP) [au]

VBCP [au]

GBCP [au]

HBCP [au]

EE [kJ/mol]

0.0020 0.0020 0.0041 0.0041 0.0053 0.0114 0.0114 0.0016 0.0019 0.0032 0.0040 0.0039 0.0070 0.0070 0.0123

0.0057 0.0057 0.0123 0.0123 0.0166 0.0345 0.0345 0.0057 0.0058 0.0095 0.0118 0.0136 0.0203 0.0204 0.0383

0.293 0.293 2.884 2.884 0.146 1.572 1.572 0.709 1.413 0.368 1.238 1.818 0.926 0.921 1.984

−0.00065 −0.00065 −0.00062 −0.00062 −0.00383 −0.00401 −0.00401 −0.00063 −0.00045 −0.00089 −0.00106 −0.00073 −0.00283 −0.00284 −0.00389

0.026 0.026 0.012 0.010 0.010 0.007 0.007 0.006 0.005 0.010 0.009 0.010 0.022 0.023 0.031

−0.00079 −0.00079 −0.00192 −0.00192 −0.00266 −0.00517 −0.00517 −0.00071 −0.00080 −0.00141 −0.00191 −0.00206 −0.00331 −0.00332 −0.00584

0.00111 0.00111 0.00250 0.00250 0.00340 0.00690 0.00690 0.00107 0.00112 0.00190 0.00243 0.00273 0.00419 0.00421 0.00771

−0.00032 −0.00032 −0.00057 −0.00057 −0.00075 −0.00173 −0.00173 −0.00036 −0.00032 −0.00049 −0.00051 −0.00067 −0.00088 −0.00089 −0.00187

−1.04 −1.04 −2.53 −2.53 −3.49 −6.79 −6.79 −0.93 −1.05 −1.85 −2.52 −2.71 −4.36 −4.37 −7.68

Crystalline structure; form I at 296 K and form II at 293 K.

−0.0016 to −0.0040 au for form II, and thus they are very weak. Temperature changes (heating or cooling) only slightly disturb the strength of these interactions, which supports our earlier conclusion concerning conformational stability of both polymorphs.

in both forms I and II. According to DSC measurements both DIM polymorphs are stable with no trace of solid−solid phase transitions between 95 K and the melting points, which indicates monotropic relation. The 1H−14N NMR-NQR spectra of both forms and the commercial sample of DIM revealed approximately 50% of form I and 50% of form II in the commercial sample. The relaxation time T1 is shorter for polymorph I (90s) than for polymorph II (100 s), which is consistent with the larger volume of crystal voids in the unit cell of form I than form II, and which suggests smaller rigidity of protons in polymorph I. (This effect is under 1 H NMR study.)

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CONCLUSIONS DIM crystallizes in two polymorphic forms, form I reported earlier,35 and form II described in this study (newly obtained). The structure of polymorph I is monoclinic, space group C2/c, while polymorph II is orthorhombic, space group P212121. The unit cell volume expands nonlinearly with increasing temperature 4346



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DIM molecule adopts different conformations in each polymorph: twisted in form I and half-chair in form II. Solid state PDB/DPN calculations revealed that the twisted conformation of the molecule is less stable by 118.7 kJ/mol than that of the half-hair one, but despite this polymorph I is more stable due to different intermolecular interactions stabilizing the crystalline pattern. In the gas phase the half-hair conformation is less stable than the twisted one, by 0.788 kJ/mol. This discrepancy is attributed to the existence of many weak interactions and crystal packing effects in the solid state, which are otherwise absent in the gas phase. The distribution of intermolecular interactions in form II is by 5% less balanced than in form I, but the Manhattan and Euclidean distances do not exceed 2.21% and 3.76%, respectively, while the Bhattacharaya coefficient does not exceed 0.36. The key interaction stabilizing the twisted versus chair conformation and determining crystalline packing in both polymorphs of DIM is the NH···π one. The remaining contacts (e.g., CH···C, NH···C) are at least twice as weak. Lattice energy calculations, using CLP and Pixel techniques for both polymorphs, indicate a major contribution of the dispersion, but also significant Coulombic and repulsion terms. Although NH···π has mainly a dispersive nature, the charge depletion at the hydrogen linked to nitrogen atom directed toward the charge concentration spread over indole ring, is an important factor facilitating the formation of this bond. Therefore, electrostatic potential complementarity of the regions of N−H···π, linking neighboring molecules, is the factor responsible for locked conformation of DIM in both polymorphs, which is kept in a wide temperature range. NH···π is weaker in polymorph I than in polymorph II, which is supported by the 14N NMR-NQR asymmetry parameter of the EFG tensor (0.202 vs 0.171), bond length (3.199 Å at 296 K versus 3.184 Å at 293 K), melting points (436 versus 440 K), lattice energy (lower by 369.45 kJ/mol for form I), ηSσT2 values (0.179 versus 0.221 at RT), electron density (0.0113 versus 0.0123 au), and Laplacian values (0.034 and 0.038 au) at BCP, sign(λ2)ρBCP (−0.0114 versus −0.0123 au), ellipticity at BCP (1.572 versus 1.589), and estimated interaction energy (−6.79 versus −7.68 kJ/mol) at RT. This effect is not disturbed by temperature. The occurrence of two stable polymorphs at room temperature can explain considerable differences in the effectiveness of DIM preparations of the same composition but made by different producers. The observation that despite different conformations both DIM polymorphs can coexist and both are stable is important in the search for alternative, better soluble, forms of dietary supplements as well as drug design studies (in silico, molecular docking, pharmacophore modeling, synthesis of new compounds of this class).

DIM crystals of polymorphs I and II. The hydrogenbonded dimeric synthons in form I and chains of molecules in form II. DSC heating/cooling runs measured for both polymorphs, TGA curve measured for commercial DIM sample, 3D Hirshfeld surfaces for both polymorphs (PDF) Accession Codes

CCDC 1457911−1457915 contains 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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*Tel.: +48-61-8295277. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The study was supported by the Foundation for Development Diagnostics and Therapy, Warsaw, Poland (JNL and ML). Generous allotment of computer time from the Wrocław Supercomputing and Networking Center (WCSS) is gratefully acknowledged (JNL and ML).

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