Combined Experimental and Computational Studies of Pyrazinamide

Article pubs.acs.org/crystal

Combined Experimental and Computational Studies of Pyrazinamide and Nicotinamide in the Context of Crystal Engineering and Thermodynamics Katarzyna N. Jarzembska,†,‡ Anna A. Hoser,†,⊥ Radosław Kamiński,*,†,‡ Anders Ø. Madsen,§ Krzysztof Durka,∥ and Krzysztof Woźniak†,⊥ †

Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warszawa, Poland Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260-3000, United States § Department of Chemistry, University of Copenhagen, Universitetparken 5, 2100 Copenhagen, Denmark ∥ Department of Chemistry, Warsaw University of Technology, Noakowskiego 3, 00-664, Warszawa, Poland ⊥ Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Ż wirki i Wigury 101, 02-089, Warszawa, Poland ‡

S Supporting Information *

ABSTRACT: Pyrazinamide and nicotinamide constitute small, rigid molecules, which are of importance in several areas of science, including crystal engineering, chemical synthesis, biochemistry, and pharmacy. This contribution is dedicated to the comprehensive study of experimental charge density distributions and computational analysis of the β form of pyrazinamide and α form of nicotinamide. Static electron density distribution is obtained through application of Hansen and Coppens multipolar formalism, and further analyzed via Bader’s quantum theory of atoms in molecules (QTAIM). Geometrical and electron density features of both crystals, such as atomic charges, bond critical points, electrostatic potential and experimentally derived intermolecular interactions are described and compared. The presence of the additional nitrogen atom in the aromatic ring of pyrazinamide, when compared to nicotinamide, has, as expected, a major influence on the surrounding atoms, including the amide moiety (0.2 e difference on the carbonyl group carbon atom). This, in consequence, affects the electrostatic potential in this region, and thus the favorable weak interactions of both molecules, what leads to the substantially different crystal packing motifs. These considerations were quantified in terms of computational methods (periodic DFT and PIXEL approaches), resulting in the conclusion of the α form of nicotinamide crystal being more energetically advantageous. Additionally, a proper deconvolution of thermal motion from static charge density provides precise and accurate atomic displacement parameters (ADPs). This allows for estimation of vibrational entropy contribution to the total stabilization of the studied crystal structures by means of Madsen and Larsen approach. It appeared that vibrational entropies obtained by employing ADPs after full multipolar refinement on high-resolution data are in good agreement with the corresponding values derived from ADPs after the transferred aspherical atom model (TAAM) refinement performed on the lowresolution data. This comparison, conducted here for the very first time, opens up the possibility of routine entropy evaluation for various crystal structures using multipole parameter databanks.

1. INTRODUCTION

listed by the World Health Organization on the Model List of Essential Medicines. In turn, NICO is an important watersoluble vitamin (vitamin B3), and can serve as a model compound for investigating of nicotinamide adenine dinucleotide (NAD) and its phosphate (NADP) transformations.1 PYRA, despite the rigidity of its molecule, forms at least four polymorphs according to literature reports.2 These are denoted

Small biologically active molecules are amidst the most important components of various drugs. This is due to their favorable molecular properties such as low molecular weight, simple synthetic protocols, and very often, rigidity (or semirigidity) of the structure. Among many others two organic compounds attract considerable attention, because they fulfill the above criteria rigorously. These are the pyrazinamide (hereafter PYRA) and nicotinamide (NICO) compounds (Scheme 1). PYRA is a very well-known antituberculosis drug, classified as API (active pharmaceutical ingredient) and © 2014 American Chemical Society

Received: March 17, 2014 Revised: May 12, 2014 Published: May 16, 2014 3453

dx.doi.org/10.1021/cg500376z | Cryst. Growth Des. 2014, 14, 3453−3465

Crystal Growth & Design

Article

2. MATERIALS AND METHODS

Scheme 1. Pyrazinamide (PYRA) and nicotinamide (NICO) molecules

2.1. Crystallization. The studied PYRA and NICO compounds were purchased from the Sigma-Aldrich Corporation as white powders. Charge-density-quality single crystals in both cases were grown from water/acetone (1:1) solutions by slow evaporation of solvent at room temperature. For PYRA two types of crystals, that is, α and β polymorphic forms, were simultaneously obtained. It occurred that solely the β form was suitable for high-resolution X-ray measurements (it is denoted hereafter as βPYRA). In the case of NICO, the α polymorphic form was crystallized and subjected to charge density study (hereafter αNICO). 2.2. X-ray Data Collection and Processing. High-resolution single-crystal X-ray measurements for βPYRA and αNICO were carried out at 90 K at a Bruker AXS Kappa APEX II Ultra diffractometer equipped with a TXS rotating anode (Mo−Kα radiation, λ = 0.71073 Å), 4-circle goniometer, multilayer optics, and an Oxford Cryosystems nitrogen gas-flow device (700 Series Cryostream). The determination of unit cell parameters and the integration of raw diffraction images were performed with the APEX2 program package.13 Data sets were corrected for Lorentz, polarization and oblique incidence effects. The multiscan absorption correction, frame-to-frame scaling and merging of reflections were carried out with the SORTAV program.14 Final data collection and reduction parameters for both measurements are shown in Table 1. 2.3. Structure Solution and Refinement. Both crystal structures were solved by a charge-flipping method15 with the SUPERFLIP program.16 The IAM refinements were performed with the JANA program.17

as α, β, γ and δ, and all can be found in the Cambridge Structural Database (CSD).3 The γ phase has been discovered most recently by Castro et al.2e A thorough study of stability relationships was presented by Cherukuvada et al.,2f and also lately by Tan et al.,4 who extended relevant conclusions into the high-pressure regime. Compared to the rich structural diversity of pyrazinamide structures, only two polymorphic forms are known for nicotinamide. The second reported, rare form was structurally determined only in 2011 by Li et al.5 PYRA and NICO are also frequently found as components in various cocrystals synthesized for the purpose of crystal engineering studies,6 or as compounds of potential importance in medicine and pharmacy. NICO, which is safe for human consumption and classified as GRAS (generally recognized as safe), is particularly often crystallized with different APIs to increase solubility and, in consequence, bioavaibility of a given pure API.6k Cocrystals, which contain PYRA and NICO, are based mostly on different carboxylic acids,6b−m,7 but structures containing other molecules, such as, alcohols6n or even “hostlike” macrocycles,6m have also been reported in the literature. The strong hydrogen bonding properties of PYRA, NICO, and related carboxyamides, combined with their ability to act as ligands in various complexes with transition metals, made them a powerful tool for synthesis of various discrete supramolecular complexes and highly ordered coordination polymers. Such constructs can be applied in catalysis, medicine, or as luminescent species, magnetic device components, porous zeolite-like materials, etc.8 In this contribution, we present high-quality experimental charge density studies of crystals of model molecules of pyrazinamide and nicotinamide using the multipolar approach.9 These are further supplemented by extensive theoretical computations, which provide a clear linkage between the electronic structure, intermolecular interactions, and bulk properties of solid forms.10 Additionally, calculated cohesive energies are complemented with crystal entropies. Following Madsen and Larsen approach,11 we employ the recent method of crystal entropy estimation, both to charge density structural models and to the low-resolution data refined using the transferred aspherical atom model (TAAM) approach,12 or conventional spherical atomic scattering factors (independent atom model (IAM) approach). The possibility of routine entropy evaluation, especially without the need for high resolution X-ray diffraction data, would be definitely of relevance for the crystal engineering community and, thus, shall be tested. In general, this contribution will constitute a solid base for investigations concerning cocrystal structures containing the title compounds, as well as, for further analyses of biochemical activity of PYRA, NICO, and their derivatives.

Table 1. Parameters Characterizing the X-ray Data Collection and Refinement for Data Sets of Both Compounds compound formula molecular weight, Mr (g mol−1) crystal system space group a (Å) b (Å) c (Å) β (deg) volume, V (Å3) dcalc (g cm−3) F000 absorption coefficient (μ/mm−1) crystal color and habit crystal size θ range (sin θ/λ)max (Å−1) completeness index ranges

no. of reflections collected/ unique Rint no. of reflections with I ≥ 3σ(I) no. of params/restraints R[F] (I ≥ 3σ(I))/(all data) wR[F] (I ≥ 3σ(I))/(all data) R[F2] (I ≥ 3σ(I))/(all data) S[F] (I ≥ 3σ(I))/(all data) Δϱmin/max (e Å−3) res 3454

βPYRA C5H5N3O 123.11 monoclinic P21/c 14.3396(7) 3.6211(2) 10.6131(5) 101.0440(7) 540.88(5) 1.512 256 0.112 colorless block 0.09 × 0.17 × 0.23 2.90−58.03° 1.19 98.8% −34 ≤ h ≤ 34 −5 ≤ k ≤ 8 −22 ≤ l ≤ 25 38036/7618

αNICO C6H6N2O 122.12 monoclinic P21/c 3.8563(1) 15.6302(5) 9.3702(3) 98.1880(6) 559.03(3) 1.451 256 0.103 colorless block 0.10 × 0.14 × 0.29 2.55−58.02° 1.19 97.4% −4 ≤ h ≤ 8 −37 ≤ k ≤ 37 −22 ≤ l ≤ 22 53360/7733

3.41% 6241 204/5 1.53%/2.12% 2.37%/2.47% 2.45%/2.49% 1.185/1.118 −0.14/+0.16

3.02% 6464 211/6 1.47%/2.00% 2.17%/2.28% 2.26%/2.29% 1.141/1.096 −0.12/+0.13



Article

Figure 1. Molecular graphs showing bond paths (golden solid lines) and bond critical points (small red spheres) for (a) βPYRA and (b) αNICO crystal structures. Labeling and estimation of atomic thermal motion as ADPs is included (ellipsoids are drawn at the 50% probability level).

Table 2. Selected QTAIM Parameters of Strong Intramolecular Interactions in BCPs for βPYRA and αNICOa compound

bond

d (Å)

d1 (Å)

d2 (Å)

ϱ (rBCP) (e Å−3)

∇2ϱ (rBCP) (e Å−5)

ε

βPYRA

O1−C1 N1−C1 N2−C3 N2−C4 N3−C2 N3−C5 C1−C2 C2−C3 C4−C5 N1−H1A N1−H1B C3−H3 C4−H4 C5−H5 O1−C1 N1−C1 N2−C3 N2−C4 C1−C2 C2−C3 C2−C6 C4−C5 C5−C6 C6−H6 N1−H1A N1−H1B C3−H3 C4−H4 C5−H5

1.2392(2) 1.3310(2) 1.3374(2) 1.3378(2) 1.3345(2) 1.3378(2) 1.5056(2) 1.3968(2) 1.3943(2) 1.010(1) 1.010(1) 1.083(1) 1.083(1) 1.083(1) 1.2373(2) 1.3402(2) 1.3407(2) 1.3408(2) 1.4980(2) 1.3956(2) 1.3912(2) 1.3912(2) 1.3886(2) 1.083(1) 1.010(1) 1.010(1) 1.083(1) 1.083(1) 1.083(1)

0.807 0.777 0.780 0.767 0.782 0.783 0.746 0.694 0.702 0.723 0.731 0.739 0.700 0.375 0.781 0.768 0.758 0.760 0.759 0.696 0.689 0.706 0.693 0.711 0.730 0.728 0.705 0.695 0.720

0.433 0.554 0.558 0.571 0.553 0.555 0.759 0.703 0.693 0.287 0.279 0.344 0.383 0.708 0.456 0.573 0.583 0.581 0.740 0.700 0.702 0.685 0.696 0.372 0.281 0.282 0.378 0.388 0.363

2.87 2.46 2.34 2.43 2.41 2.29 1.79 2.21 2.21 2.42 2.40 1.99 1.95 2.01 2.85 2.44 2.39 2.41 1.82 2.13 2.16 2.18 2.19 1.96 2.39 2.43 2.04 2.00 1.94

−32.1 −27.9 −21.9 −22.5 −23.4 −20.4 −14.2 −21.1 −20.6 −37.7 −40.9 −24.6 −22.6 −24.9 −32.4 −22.8 −18.7 −18.9 −12.9 −17.1 −17.5 −17.9 −17.8 −22.3 −37.8 −39.8 −25.2 −23.5 −21.7

0.10 0.26 0.12 0.14 0.12 0.12 0.23 0.24 0.27 0.04 0.04 0.07 0.08 0.07 0.09 0.21 0.09 0.12 0.17 0.22 0.20 0.25 0.20 0.03 0.05 0.02 0.06 0.07 0.04

αNICO

a d, distance between bonded atoms; d1 and d2, distances from 1st and 2nd atom to the bond critical point, respectively; ϱ, electron density; ε, bond ellipticity.

Multipole refinements of βPYRA and αNICO were carried out in the MOPRO suite18 combined with the newest version of the University at Buffalo Data Bank (UBDB),19 based on the Hansen-Coppens multipole model.9 The multipolar refinement procedure was analogous to the ones applied in our previous charge density and related studies.10b,c,20 The refinement details are available from the Supporting Information. The final charge density distribution models are characterized with very flat and almost featureless residual density distribution (Δϱres = −0.14/+0.16 e Å−3, and Δϱres = −0.12/+0.13 e Å−3 for βPYRA and αNICO, respectively; properties evaluated with the JNK2RDA program21). All final refinement statistics are summarized in Table 1. CIF files for both refinements are present in the Supporting Information, or can be retrieved from the Cambridge Structural Database3 (deposition numbers CCDC 991917 and CCDC 991918). 2.4. Properties Derived from the Experimental Charge Density. The experimental charge density distributions obtained

with the multipolar approach were analyzed by means of Bader’s quantum theory of atoms in molecules (QTAIM).22 The VMOPRO module (part of the MOPRO package) was used for Fourier syntheses and bond critical point evaluation. Visualization of bond paths and surfaces was accomplished with the MOPROVIEWER program.23 The neighboring molecules selected for the bond path search were prepared using the CLUSTERGEN program,24 locally modified for the purpose of molecular dimer analysis in the solid state. Evaluation and integration of atomic basins were performed with the WINXPRO program.25 2.6. Theoretical Calculations. The CRYSTAL package26 (version CRYSTAL09) was used for the evaluation of crystal cohesive energy values and dimer interaction energies. B3LYP/pVTZ level of theory27 was employed with both Grimme dispersion28 and BSSE corrections.29 General procedures are described elsewhere.10b,c,30 The input files were prepared using the CLUSTERGEN program.24 3455



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Additionally, the cohesive energy and dimer interaction energy values were estimated with the aid of the PIXEL approach31 at the MP2/6-31G** level of theory,32 which enabled total energy decomposition into electrostatic, polarization, dispersion and repulsion contributions. 2.7. Crystal Entropy Evaluation. Bürgi and co-workers33 have shown that analysis of multitemperature X-ray diffraction data may afford thermodynamic information, for example, specific heats, when a rigid-body or semirigid body approach is applied to ADPs. Subsequent results reported by Madsen and Larsen11,34 indicate that in the case of low-temperature structures a single-temperature high-resolution X-ray measurement may be sufficient if only good quality ADPs are provided. Having accurate estimates of ADPs, it is possible to calculate vibrational entropies (STLS) corresponding to the low-frequency lattice vibrations. To derive the vibrational entropy associated with the lowfrequency modes, one needs to conduct the translation-libration-screw (TLS) analysis35 and compute the related frequencies (and some estimated standard uncertainties, based on the standard uncertainties given for the eigenvalues of the TLS-fit matrix in the THMA program35a). On the basis of such evaluated frequencies, the vibrational entropy of crystals as a function of temperature can be calculated as a sum of the contributions from each oscillator:

3.1. Charge Density Distribution of the Studied Molecules. Molecular graphs of βPYRA and αNICO are shown in Figure 1, whereas the bond distances and topological parameters are presented in Table 2. The obtained set of interatomic bond paths (BPs) and bond critical points (BCPs) indicates consistent topology of the derived charge density distribution in both cases. All values presented in Table 2 are in typical ranges for organic molecules. Thus, here we note only some more relevant observations: (a) the distance from the bond critical point to the hydrogen atom is shortest for the amide hydrogen atoms, which is due to their increased positive charge; (b) analysis of ellipticity and electron density values does not provide a clear picture of preferred resonance forms of the 6-membered rings; (c) the highest electron density values are observed for the C1−O1 bonds, what corresponds to their short lengths (1.2392(2) and 1.2373(2) Å, respectively) and confirms the expected double bond character; these bonds are also highly polarized and exhibit large values of negative Laplacian at BCPs; (d) the highest values of negative Laplacian are observed for the N−H bonds; (e) the lowest electron density values are found for the C1−C2 bonds, indicating their single bond character; (f) all other C−N and C−C bonds exhibit intermediate nature between single and double bonds. A closer look at the atomic Bader charges (Table 3) reveals significant differences between the two molecules. Atoms C1,

⎛ ⎤−1 ⎡ ⎛ hv ⎞⎤⎞ hvi ⎡ ⎛ hvi ⎞ ⎜ ⎢ exp⎜ − 1⎥ − ln⎢1 − exp⎜ − i ⎟⎥⎟ STLS(T ) = R ∑ ⎟ ⎜k T ⎢ ⎝k T ⎠ ⎥⎦ ⎢⎣ ⎝ kBT ⎠⎥⎦⎟⎠ B i ⎝ B ⎣

where R is the gas constant, kB is the Boltzmann constant, and vi is a frequency of a given ith oscillator. Following the above procedure, vibrational entropy was estimated for βPYRA and αNICO, on the basis of the collected high-resolution X-ray diffraction data with different resolution cut-offs and approaches of obtaining ADPs. To estimate the total entropy, the frequencies related to the high-frequency vibrational modes were calculated using the CRYSTAL code. To guarantee that the geometries used for the frequency calculations reached stationary points on the potential energy surface (PES), the geometry optimizations were performed. Solely the atomic coordinates were optimized, whereas the lattice constants were kept fixed. Subsequently, the high-frequency vibrational modes were computed and used to estimate the “internal” contribution to the crystal entropy (SCRY). The geometry optimizations and frequency calculations were carried out at the B3LYP/6-31G** level of theory36 for both compounds. For more details see the Supporting Information.

Table 3. Bader Charges (QAIM) and Atomic Basin Volumes (VAIM) for βPYRA and αNICO Molecules Present in the Crystal Lattice βPYRA

3. RESULTS AND DISCUSSION Application of an aspherical electron density model to highresolution X-ray diffraction data allows for a proper deconvolution of static charge density and thermal motion features. This is especially important for obtaining accurate atomic positions, and thus molecular geometries suitable for further energetic characterisations of the studied crystals, but also for good ADP estimations, which in turn influence crystal entropy values. Therefore, good-quality charge-density-distribution models of βPYRA and αNICO crystals were crucial for our subsequent investigations and, thus, were evaluated with great care. To obtain a common ground for βPYRA and αNICO, which enables reliable comparisons, charge density measurement strategy, as well as further data treatment were performed following the same procedures described in our latest study by Kamiński et al.20a It should be noted here that, whereas the charge density data for the β form of PYRA are, to the best of our knowledge, presented here for the first time, the α form of nicotinamide has been already a subject of the experimental charge density study by Miwa et al.37 Nevertheless, in that contribution the maximum entropy method was applied for the determination of the dynamic electron density, what makes the findings difficult to be directly compared with our multipolar model9 which describes static electron density distribution.

αNICO

atom

QAIM (e)

VAIM (Å3)

QAIM (e)

VAIM (Å3)

O1 N1 N2 N3 C1 C2 C3 C4 C5 C6 H1A H1B H3 H4 H5 H6

−1.14 −1.03 −0.92 −0.92 +1.39 +0.36 +0.31 +0.32 +0.35

18.81 17.91 14.70 14.57 5.18 8.12 10.19 10.45 10.13

−1.21 −1.10 −0.91

17.87 17.85 15.53

+0.42 +0.48 +0.18 +0.06 +0.12

3.99 2.66 5.44 6.94 5.92

+1.19 +0.05 +0.37 +0.34 −0.12 −0.05 +0.46 +0.44 +0.13 +0.12 +0.15 +0.14

5.73 9.71 9.36 9.64 12.28 11.11 2.75 3.16 5.54 5.94 7.51 5.51

C2, and C5 are the most differing ones, with the emphasis on the latter, for which even the sign of the atomic charge changes between βPYRA and αNICO. Such observations become easily understood when one notices that these atoms, particularly C2 and C5, are in the closest neighborhood of either N3 (βPYRA) or C6 (αNICO) which are clearly dissimilar in nature. The N3 atom is very negative (−0.92 e) and, consequently, the C5 and C2 atoms gain the positive charge in the case of pyrazinamide molecule. For αNICO, where the aromatic ring is more uniform, both atoms, C2 and C5, are much less positive. Significant changes of the C2 atom charge propagate further onto the C1 atom, and thus also some differences are observed for the O1 atom, which is more negative in the αNICO crystal. Similar discrepancies are also visible for other atoms, such as, N1, C3, 3456



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Table 4. Selected QTAIM Parameters for Weak Intermolecular Interactions at the Positions of Respective BCPs for βPYRA and αNICO (G, Kinetic Energy Density; V, Potential Energy Density)a compound

interaction

motif

d (Å)

d1 (Å)

d2 (Å)

ϱ (rBCP) (e Å−3)

∇2ϱ (rBCP) (e Å−5)

G (rBCP) (kJ mol−1 a0−3)

V (rBCP) (kJ mol−1 a0−3)

βPYRA

H1B···O1#1 H1A···O1#2 N3···H3#2 H4···N2#3 H5···N2#4 C2···O1#5 N1···N1#5 C4···N2#5 N3···C2#5 O1···N1#6 N1···N1#6 H4···H5#7 H1A···O1#8 N2···N1#8 H3···O1#8 N2···H1B#9 H3···O1#9 N2···H4#10 H4···H4#10 N2···C2#11 C3···N1#11 C4···C6#11 O1···H5#12 H6···H6#12 O1···H5#13 C5···H6#13 C4···C4#14

D1 D2

1.896(1) 2.339(3) 2.328(3) 2.462(3) 2.310(3) 3.3085(3) 3.6211(2) 3.3736(3) 3.3582(3) 3.5013(3) 3.6049(4) 2.626(8) 1.953(1) 3.8652(3) 2.522(4) 2.077(1) 2.460(4) 2.642(2) 2.1651(2) 3.5373(3) 3.4785(2) 3.5689(3) 3.006(4) 1.971(9) 2.858(4) 2.800(4) 3.2794(3)

0.692 0.939 1.427 0.998 0.917 1.721 1.811 1.673 1.709 1.741 1.803 1.296 0.722 1.967 1.038 1.295 1.030 1.572 1.083 1.769 1.747 1.780 1.729 0.986 1.655 1.651 1.640

1.204 1.411 0.903 1.471 1.401 1.622 1.827 1.793 1.654 1.766 1.803 1.409 1.231 1.923 1.486 0.785 1.454 1.086 1.083 1.769 1.797 1.804 1.282 0.986 1.205 1.151 1.640

0.21 0.07 0.09 0.08 0.11 0.04 0.02 0.03 0.04 0.02 0.02 0.02 0.18 0.01 0.05 0.18 0.06 0.04 0.03 0.02 0.02 0.02 0.02 0.06 0.02 0.03 0.03

1.2 0.8 1.0 0.8 0.9 0.5 0.3 0.4 0.4 0.3 0.3 0.3 1.3 0.2 0.9 0.9 0.7 0.4 0.9 0.3 0.3 0.3 0.2 1.0 0.3 0.5 0.5

45.55 17.22 23.97 18.21 23.84 9.55 4.95 8.63 9.25 5.50 5.24 6.08 40.72 3.00 17.60 34.74 15.29 9.56 17.32 6.27 6.18 5.82 4.51 21.85 6.49 10.59 10.01

−58.42 −13.90 −19.94 −15.57 −23.12 −6.64 −2.98 −5.99 −6.49 −3.29 −3.13 −3.63 −46.43 −1.68 −12.04 −43.97 −11.72 −7.35 −10.20 −4.10 −3.86 −3.85 −2.70 −15.61 −4.01 −6.75 −6.29

αNICO

D3 D4 S1

H1 H2 D1′

D2′ D3′ S1′

H1′ H2′ H3′

Only symmetry-independent BPs are listed for dimers. The selected dimers are depicted in Figure 2. Symmetry transformations: (#1) −x + 1, −y + 1, −z; (#2) x, −y + 0.5, z − 0.5; (#3) −x + 2, y − 0.5, −z + 0.5; (#4) x, −y − 0.5, z − 0.5; (#5) x, y − 1, z; (#6) −x + 1, −y, −z; (#7) −x + 2, −y, −z; (#8) x, −y + 0.5, z − 0.5; (#9) x − 1, −y + 0.5, z − 0.5; (#10) −x − 1, −y, −z + 1; (#11) x − 1, y, z; (#12) −x + 1, −y, −z + 2; (#13) −x, −y, −z + 2; (#14) −x, −y, −z + 1. a

Table 5. Geometry of Selected Specific Weak Interactions Present in the βPYRA and αNICO Crystal Structuresa compound βPYRA

αNICO

interaction #1

N1−H1B···O1 N1−H1A···O1#2 C3−H3···N3#3 C4−H4···N2#4 C5−H5···N2#5 N1−H1A···O1#6 C3−H3···O1#6 N1−H1B···N2#7 C3−H3···O1#8 C4−H4···N2#9

motif

dX−H (Å)

dY···H (Å)

dX···Y (Å)

θX−H···Y (deg)

D1 D2

1.010(1) 1.010(1) 1.083(1) 1.083(1) 1.083(1) 1.010(1) 1.083(1) 1.010(1) 1.083(1) 1.083(1)

2.9047(3) 3.1876(3) 3.3301(3) 3.4510(4) 3.3214(3) 2.9601(2) 3.2210(2) 3.0750(2) 3.3006(3) 3.6664(3)

1.896(1) 2.339(3) 2.328(3) 2.462(3) 2.310(3) 1.953(1) 2.522(4) 2.077(1) 2.460(4) 2.642(2)

176.01(1) 141.00(3) 153.10(3) 151.20(3) 154.64(3) 174.49(1) 121.34(3) 169.31(1) 133.51(3) 157.50(2)

D3 D4 D1′ D2′ D3′

For topological parameters see Table 4. Symmetry transformations: (#1) −x + 1, −y + 1, −z; (#2) x, −y + 0.5, z − 0.5; (#3) x, −y + 0.5, z + 0.5; (#4) −x + 2, y − 0.5, −z + 0.5; (#5) x, −y − 0.5, z − 0.5; (#6) x, −y + 0.5, z − 0.5; (#7) x + 1, −y + 0.5, z + 0.5; (#8) x − 1, −y + 0.5, z − 0.5; (#9) −x − 1, −y, −z + 1. a

3.2. Supramolecular Structures. To show the full picture of the charge density distribution in the crystals of the studied compounds, we have also analyzed specific contacts and motifs formed by pyrazinamide and nicotinamide molecules, which are particularly interesting from the crystal engineering point of view. The topological and geometrical parameters for various weak interactions found in both crystal structures are tabulated in Tables 4 and 5. Apart from the analysis of numerical data, modern charge density methods allow for visualization of electron density

and H4, but according to our recent studies all the latter differences (i.e., for C1, N1, C3, and H4) are comparable with the method precision.20a Interestingly, the atomic charges are not correlated with the atomic volumes, which may suggest non-negligible influence of the crystal environment. Intermolecular interactions may also contribute to some of the observed differences among atomic charges, especially for the atoms involved in strong hydrogen bonds which shall be discussed further in the text. 3457



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Figure 2. Selected dimers for studied pyrazinamide (left panels a, c, e, g, i) and nicotinamide (right panels b, d, f, h, j) crystal structures (golden lines, BPs, small red spheres, BCPs). Color coding is the same as in Figure 1

solid state, and substantially contribute to the crystal stability. Selected dimers are presented in Figure 2 (their symbols are related to the third column in Tables 4 and 5). In addition to

features in crystals. Parallel with the determination of the weak interaction BCPs, full BP set was also evaluated. This resulted in the selection of characteristic dimers, which occur in the 3458



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Table 6. Interaction Energies for Dimers Observed in the Solid Statea compound

dimer

n

−1 ECRY int (kJ mol )

−1 EEL int (kJ mol )

e (%)

−1 EPIX int (kJ mol )

major interactions

βPYRA

D1 D2 D3 D4 S1 H1 H2 D1′ D2′ D3′ S1′ H1′ H2′ H3′

1 2 2 2 2 1 1 2 2 1 2 1 1 1

−62.6 −25.3 −12.5 −10.7 −12.4 −10.5 −3.3 −35.9 −36.1 −11.1 −8.0 −10.5 −18.1 −6.0

−58.4 −16.9 −7.8 −11.6 −11.1 −4.9 −3.6 −30.1 −27.9 −12.5 −5.9 −17.0 −10.8 −3.2

6.6 33.1 37.8 8.4 11.1 53.7 10.0 16.1 22.9 11.9 25.8 62.3 40.5 47.8

−57.0 −26.6 −12.5 −10.7 −9.7 −10.1 −4.3 −32.8 −35.3 −13.9 −8.0 −11.2 −18.0 −7.6

hydrogen bond hydrogen bond C−H···N interaction C−H···N interaction π-stacking O1···N1 and N1···N1 H···H contacts hydrogen bond hydrogen bond C−H···N interaction π-stacking H···H contacts C5···H6 C4···C4

αNICO

a CRY CRY EL CRY Eint is the energy computed in CRYSTAL; EEL int is the energy based on the Espinosa−Lecomte estimation; e = |Eint − Eint |/Eint ; n is the number of dimer occurrences in the cluster around the central molecule.

Table 7. Cohesive Energy Values for the βPYRA and αNICO Crystal Structuresa

the geometrical parameters for the encountered dimeric species, charge density analysis provides the estimation of energetics of intermolecular interactions. This is realized within the Espinosa−Lecomte (EL) estimation protocol,38 which works best for interactions with high electrostatic energy component, such as hydrogen bonds. Information on the intermolecular interaction energies can be also obtained from the supermolecular computations, here performed using the CRYSTAL package, and is compared with the EL method results in Table 6. The differences between the two approaches are, as expected, most significant for dispersive in nature intermolecular contacts, however, the energy values do not differ more than of about 50%, except for one dimer present in the αNICO form (namely H1 one). For the strongest interactions, and thus the ones contributing to the stability of the crystal most, differences are visibly smaller (around 20%). Even though both compounds crystallize in the P21/c space group, significant differences can be found in their molecular packing, what is reflected in the formed structural motifs. In the case of βPYRA, a major synthon (dimer D1) characterized by definitely most favorable interaction energy reaching −60 kJ mol−1 can be distinguished (all the energy computation methods provided very close energy results here). This synthon is further surrounded by weaker hydrogen-bond-type contacts, expanding the motif toward the molecular chain, and then into the 3D structure, supported by secondary dispersive interactions. In the case of αNICO, there are two distinctive hydrogen-bonded dimers, D1′ and D2′, which saturate all the hydrogen bond donor and acceptor centers. These two motifs form an effective 3D network supported by other less significant interactions given in Table 6. The important factor contributing to the differences between the crystal networks of the two studied molecules is the conformation of the amide group in respect to the aromatic ring plane. Whereas the pyrazinamide molecule is flat, in the nicotinamide crystal, the amide moiety is slightly rotated which enables effective intermolecular contacts. It would be thus interesting to investigate how these differences affect the cohesive energy and entropy of both crystals. As shown in Table 7, periodic cohesive energy calculations resulted in about 10 kJ mol−1 difference in favor of the nicotinamide α polymorph. The PIXEL method gave systematically lower amplitudes of the cohesive energy values,

compound energy (kJ mol−1)

βPYRA

αNICO

ECRY coh ECRY est EEL est EPIX coh EPIX coul EPIX disp EPIX rep EPIX pol

−105.6 −99.1 −80.8 −100.2 −89.7 −90.0 +112.3 −32.9

−115.1 −102.8 −85.5 −107.4 −91.6 −95.3 +115.9 −36.4

a

Calculated with the CRYSTAL program at the DFT(B3LYP)/pVTZ level of theory (ECRY coh ), estimated on the basis of the dimer energy values derived with CRYSTAL at the DFT(B3LYP)/pVTZ level of theory (ECRY est ), estimated on the basis of the Espinosa−Lecomte interaction energies for the same set of molecular dimers (EEL est ), and calculated with the aid of the PIXEL (MP2/6-31G**) program (EPIX coh ), together with its division into the Coulombic, dispersion, repulsion, PIX PIX PIX and polarization subcomponents (EPIX coul, Ecoul, Erepl, and Epol ).

however, the final conclusion remains the same. It should be noted here that this observation is more general, as recently shown by Maschio et al. 39 According to the energy decomposition obtained using the latter approach, αNICO outnumbers slightly the βPYRA crystal in each of the total energy components. Additionally, we attempted to estimate the cohesive energy on the basis of the dimer interaction energy results derived with the three methods, Espinosa-Lecomte approach, periodic DFT (CRYSTAL) and PIXEL method. The cohesive energy of the examined crystals was calculated taking into account a set of the closest molecules surrounding a given nicotinamide or pyrazinamide moiety in a crystal lattice, using a simple formula 1 Eest = ∑ niE int , i 2 i where n and Eint have the same meaning as in Table 6. Cohesive energies estimated that way were related to the corresponding values computed using the periodic approach. The results are summarized in Table 7. Clearly, for both compounds, the relative differences amount to about 10% and 25% in respect to 3459



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Figure 3. Electrostatic potential mapped onto the Hirshfeld surface: (a) D1 and D2 dimer interactions in βPYRA; (b) chains based on D2′ dimer interactions in αNICO.

between both compounds is observed in the vicinity of the oxygen atom. Whereas the integrated Bader charges are not that different in that region (Table 3), the electrostatic potential visibly exhibits larger negative values for αNICO. Consequently, the NH2 group seems to be less positively charged, which might be responsible for different binding preferences of both molecules in the crystal lattice (D1-type motif is absent in the αNICO crystal structure). These findings also show that the analysis of crystal molecular packing cannot be analyzed in terms of integrated or point properties (such as atomic charges), but the full description of fine details in the periphery of a molecule may play a crucial role. This also indicates the importance of crystal environment which should not be neglected in the analyses, as has been shown by our recent reports.10b,c 3.4. Entropy Evaluation. In general, it is a very demanding task to compute crystal entropies of desired accuracy by means of ab initio simulations. This is because such calculations require a lattice dynamical description, which is based on interatomic forces obtained by investigating the potential energy surface near the equilibrium. It is though difficult to describe accurately the shape of the intermolecular potential energy surface for molecular crystals dominated by weak interactions. Estimation of dispersion forces occurs to be particularly problematic, although currently some empirical corrections to the DFT methods are available. Nevertheless, it is important to calculate vibrational crystal entropy as this quantity, together with intermolecular interaction energies, dominates crystal stability. Thus, its value is crucial when comparing thermodynamic stabilities of crystal structures of related compounds, such as, βPYRA and αNICO. It should be noted here that low-frequency lattice vibrations are essential for the vibration entropy estimation, whereas the contribution from intramolecular vibrations are of minor importance. This is because the difference in frequencies of internal modes is small between the solid state and the gas phase. When examining the quoted relation of entropy in respect to the oscillator frequency, it can be also seen that the low-frequency modes give the largest contribution to the entropies. According to literature investigations,36b however, among the frequencies obtained from periodic ab initio calculations used to compute atomic Debye−Waller factors, the important low-frequency modes are most difficult to be estimated with high accuracy. Consequently, it was proposed to obtain low-frequency modes from X-ray diffraction exper-

the reference values (periodic computation results), for CRYSTAL and EL-based estimations, correspondingly. This illustrates the impact of the system periodicity on the cohesive energy values, as well as neglecting of some of the energy components. The relation between Ecoh and EEL est is particularly interesting, because it shows the reliability of the total cohesive energy estimation directly from the experimental charge density data. Although the difference amounts to about 25%, such an estimation may provide some idea about the relative stabilities of crystals, as at least in our case the trend is somewhat preserved. Such considerations are though case-dependent and may obviously bias the results when cohesive energy differences for given compared crystals are very small. Furthermore, this approach applied to crystals, where the dispersive interactions predominate the electrostatic forces, would be much less effective and sensible. As mentioned before, the cohesive energy is clearly lower for the αNICO form, regardless the computation method. This can result from the differences in the molecular packing briefly described above. In the case of βPYRA the structure is dominated by strong and directional hydrogen bonds, which have major contribution to the stability of the crystal, making it more compact (the molecule is completely flat). In the case of αNICO the crystal is less compact (unit cell is slightly larger), but the conformation of the molecule allows more intermolecular contacts to be involved in the overall stability of the crystal. 3.3. Electrostatic Potential. A property which can be readily obtained from the experimental electron density distribution is the electrostatic potential (ESP). ESP mapped onto the Hirshfeld surface40 was proved to be a useful tool in the analysis of weak interactions in molecular crystals, as shown by Spackman and co-workers.41 Therefore, we utilize here this approach to show the importance of selected molecular motifs in the case of βPYRA and αNICO forms. Figure 3 shows the chosen types of dimers for both crystal structures. In the case of the βPYRA structure, the D1 and D2 dimers clearly exhibit the complementary regions of negative and positive ESP (e.g., the negative potential near O1 atom matches the positive potential in the vicinity of H1B atom). Essentially the same ESP pattern is observed for the αNICO crystal structure, where D2′ dimeric motifs form chains in the crystal lattice, interacting mostly electrostatically. We note that for αNICO the D1′ dimers behave similarly. The presented results indicate that the complementarity of positive and negative ESP regions might be considered as a driving force in the crystal formation. A striking difference 3460



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Table 8. Vibrational Entropy Values from CRYSTAL Computations of Internal Modes (SCRY) and External from TLS Model (STLS) Evaluated for βPYRA and αNICO after Different Refinement Modelsa compound

model

RTLS (%)

βPYRA

MR-vs-HR TAAM-vs-HR TAAM-vs-LR IAM-vs-LR MR-vs-HR TAAM-vs-HR TAAM-vs-LR IAM-vs-LR

3.8 3.7 5.8 7.0 3.6 3.5 3.9 5.0

αNICO

normal mode frequencies, νi (cm−1) 40.5, 40.6, 40.1, 37.6, 36.5, 36.0, 34.7, 33.0,

44.2, 43.8, 42.0, 40.6, 40.7, 40.2, 39.1, 38.8,

46.4, 46.2, 46.0, 45.5, 46.5, 46.0, 44.3, 40.6,

71.5, 72.7, 75.3, 68.1, 68.6, 68.6, 68.5, 65.1,

79.7, 78.2, 76.3, 73.6, 72.6, 72.8, 72.4, 68.7,

−1 −1 S90K K ) TLS (J mol

−1 −1 S90K K ) CRY (J mol

−1 −1 S298K K ) TLS (J mol

−1 −1 S298K K ) CRY (J mol

54.9 54.9 55.1 56.8 57.2 57.5 58.5 60.2

5.9

112.6 112.7 112.9 114.7 115.2 115.4 116.5 118.3

53.2

90.4 91.1 93.6 95.6 91.7 92.2 90.4 93.0

4.7

52.1

a

MR-vs-HR (full multipolar model refined versus high-resolution data), TAAM-vs-HR (TAAM model versus high-resolution data), TAAM-vs-LR (TAAM model versus low-resolution data; (sin θ/λ) ≤ 0.7 Å−1), and IAM-vs-LR (IAM versus low-resolution data), and at two temperatures (90 and 298 K). Estimated standard deviation (e.s.d.) values on entropy amounts for about 1.0 J mol−1 K−1.

imental data.11 It occurred that frequencies of low-frequency modes can be calculated successfully from the TLS analysis on the basis of high quality ADPs, and subsequently applied to compute entropies and associated standard uncertainties. In the case of nicotinamide and pyrazinamide crystal structures, the Hirshfeld rigid-bond test42 is fulfilled for a series of structural models given in Table 8, what indicates sufficient quality of the obtained ADPs in all the cases. Thus, the TLS analysis was conducted for both compounds for the high-resolution charge density crystal structures and also for the data of high or low resolution refined using transferred aspherical atom and independent atom models (MR-vs-HR (full multipolar model refined vs high-resolution data), TAAMvs-HR (TAAM model vs high-resolution data), TAAM-vs-LR (TAAM model vs low-resolution data; (sin θ/λ) ≤ 0.7 Å−1), and IAM-vs-LR (IAM vs low-resolution data). The obtained residual RTLS are very low, which implies a good rigid body fit and reflects the rigidity of the analyzed molecules. Numerical values of entropies estimated for αNICO and βPYRA for various refinement schemes are listed in Table 8. The entropy values were calculated for 90 K, which corresponds to the X-ray diffraction measurement temperature, but also were extrapolated to room temperature (RT) values, what may be of relevance for future studies. It appears that the difference between TLS vibrational entropies for nicotinamide and pyrazinamide is equal to 2.3, 2.6, and 3.4 J mol−1 K−1 at 90 K for MR-vs-HR, TAAM-vs-HR, and TAAM-vs-LR refinements, respectively (similar values are obtained for the RT estimation). Such values, with their estimated standard deviations of approximately 1.0 J mol−1 K−1, indicate only a small difference between the vibrational entropies for the two compounds. Evaluation of the entropy corresponding to internal modes of vibration gives a difference of −1.2 and −1.1 J mol−1 K−1 at 90 K and RT, respectively. Therefore, differences in stability between the two crystals would primarily result from differences in their enthalpies. The TLS entropy difference of 2.3 J mol−1 K−1 at 90 K corresponds to about 0.21 ± 0.09 kJ mol−1 at this temperature (i.e., 2.3 ± 1.0 J mol−1 K−1 at 90 K). Such a small difference, with slightly higher entropy for nicotinamide, is in good agreement with a somewhat larger volume of the nicotinamide unit cell: 559 versus 541 Å3 for pyrazinamide. The larger unit cell volume allows the nicotinamide molecules to vibrate with greater amplitudes, that is, with smaller frequencies (similar correlation has been observed previously11).

As it was mentioned earlier, to estimate vibrational entropy of the low-frequency modes, good quality ADPs are required. Such ADPs can be obtained after charge density refinement of high-resolution X-ray diffraction data. However, because of the different scattering power of crystals, it is not always possible to obtain a high-resolution data set. On the other hand, it is known, that application of databanks (e.g., the used UBDB,19 or other, Invarioms43 or ELMAM44) during the refinement significantly improves ADP values.12b,45 Therefore, we decided to verify a magnitude of discrepancies between vibrational entropies calculated after TAAM refinement for high- and for low-resolution data sets (sin θ/λ) ≤ 0.7 Å−1). It appears that differences between TAAM-vs-HR and TAAM-vs-LR are in the range of error bars when compared to the charge density data estimates. In both cases (αNICO and βPYRA), slightly higher entropies were obtained for TAAM-vs-LR refinements, which is in agreement with the size of ADPs for non-hydrogen atoms. The difference resulting from using low-resolution data is more emphasized for αNICO. The entropy values obtained after the IAM refinement against low-resolution data are, as expected, noticeably larger. In addition, it should be noted that the ADP values obtained from the TAAM refinement are resolutiondependent, as shown by Dittrich et al.46 This issue somewhat limits the general application of our method to relative comparisons between crystal structures. Nevertheless, the idea of estimating vibrational entropy of low-frequency modes, not necessarily from high-resolution data set, but from lowresolution data supplemented by TAAM refinement, seems to be a promising alternative and shall be investigated more carefully in the nearest future.

4. CONCLUSIONS In this contribution, we provide a deep insight into the solidstate forms of β polymorph of pyrazinamide and α polymorph of nicotinamide, both compounds being very important in the field of crystal engineering, chemical synthesis and pharmacy. Our work covers precise experimental electron density study of the two crystal structures, analysis of weak interactions in respect to energetic features in the crystalline state, and an attempt to generalize the entropy evaluation from X-ray diffraction data. The application of multipolar formalism, coupled with the QTAIM approach, allowed us to determine bonding patterns in both crystal structures. This served as a starting point for the evaluation of energetic features, with the special emphasis on 3461



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data collection and its computational studies. A.Ø.M. gratefully acknowledges the support from the Danish Research Council. Calculations were carried out using resources provided by the Wrocław Centre for Networking and Supercomputing (Grant 285).

dimer interactions and possible retrieval of cohesive energy from high-resolution X-ray diffraction data. The presence of the additional nitrogen atom in the aromatic ring of pyrazinamide has a major influence on the surrounding atoms, what is reflected in their atomic charges. The differences in the atomic charges between the two molecules propagate to the amide moiety, and, in consequence, have a substantial impact on the electrostatic potential in this region (clearly visible when ESP is mapped on Hirshfeld surfaces). This, in turn, influences the weak interaction preferences of the studied compounds within the crystal lattice. Therefore, the observed crystal packing motifs are substantially different in the case of βPYRA and αNICO. Whereas the pyrazinamide forms the outstanding strongly bound hydrogen-bond dimeric motif (D1), the nicotinamide crystal structure exhibits a large variety of more uniform weak interactions expanded in 3 dimensions. These considerations were quantified in terms of computational methods (periodic DFT and PIXEL approaches), and indicated that the nicotinamide crystal is more energetically favorable. Interestingly, the simple estimations on the basis of dimeric interactions provided the same conclusions. Charge density data resulted additionally in the very precise APDs which were used for crystal vibrational entropy estimations. The differences in entropies evaluated for βPYRA and αNICO are very small, and show that the nicotinamide crystal is slightly more advantageous in terms of entropy. Interestingly, the entropy values obtained on the basis of lowresolution X-ray diffraction data refined using TAAM appeared to be statistically the same. This suggests that the entropy evaluation could be routinely performed using low-resolution X-ray diffraction data sets. Nevertheless, to draw binding conclusions some additional studies shall be conducted in the future, especially regarding the relative stability of polymorphic and cocrystal structures. We believe that this approach would be of importance for the crystal engineering and crystal structure prediction community.

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ASSOCIATED CONTENT

* Supporting Information S

Multipole refinement details, theoretical computations and entropy estimation details, figures showing residual and static deformation density maps and overlay of molecular geometries obtained by the experiment and after optimization, and additional references. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

K.N.J. and A.A.H. contributed equally to this work Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.A.H. and K.N.J. gratefully acknowledge the National Science Centre in Poland (Grant 2011/03/N/ST4/02943) for financial support which enabled the nicotinamide charge density quality data collection and its computational studies. R.K. would like to thank the Polish Ministry of Science and Higher Education for financial support within the Iuventus Plus grant (Grant 120000501/59 PM-121) enabling the pyrazinamide X-ray diffraction 3462



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