Origin of the Thermodynamic Stability of the Polymorph IV of

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Origin of the Thermodynamic Stability of the Polymorph IV of Crystalline Barbituric Acid: Evidence from Solid-State NMR and Electron Density Analyses Zahra Badri,† Kateřina Bouzková,† Cina Foroutan-Nejad,‡ and Radek Marek*,†,‡,§ †

CEITEC - Central European Institute of Technology, ‡National Center for Biomolecular Research, and §Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5/A4, CZ-62500 Brno, Czech Republic S Supporting Information *

ABSTRACT: In this contribution, the origin of the stability of the polymorph IV (enol form) of crystalline barbituric acid relative to the polymorph II (keto form) is investigated using solid-state NMR spectroscopy and electron density analysis. Electron density analysis reveals differences in the nature of the intermolecular contacts in the different polymorphs of barbituric acid. Comparing the properties of hypothetical single molecules of barbituric acid with cluster models shows that the electronic and magnetic properties of polymorphs of barbituric acid can be employed to measure the strengths of the intermolecular interactions. Changes in the magnitudes of the NMR chemical shift tensors are also shown to be parallel to the intermolecular delocalization index of Quantum Theory of Atoms in Molecules, which measures the covalency of an intermolecular interaction.

1. INTRODUCTION Polymorphism, the ability of a chemical substance to form more than one crystalline form in the solid state, is well-known in chemistry. It has been identified among different classes of compounds and for chemical elements, where it is known as allotropy. It is also found in biologically active materials. Polymorphism plays an important role in the pharmaceutical industry because it has frequently been observed that only one of several crystalline forms of a drug is sufficiently active to be useful.1 Among pharmaceutical molecules, polymorphism usually occurs as a result of differing intermolecular interactions2,3 between individual molecules in the solid state.4,5 The characterization of crystal structure based on intermolecular interactions is therefore crucial to observing the generation of different polymorphs.6 Different crystal forms of a molecule differ in properties such as stability, solubility, and bioavailability.7 A recent study on barbituric acid8 revealed that at ambient conditions the most thermodynamically stable form is polymorph IV (formed by the enol tautomer),9 whereas polymorph II, which is the commercially available form (formed by the keto tautomer depicted in textbooks), is relatively unstable (Scheme 1). However, it has been demonstrated that the keto form is generated in other conditions.10−14 These two forms of barbituric acid are trapped in specific networks of intermolecular contacts, such as hydrogen bonding (H-bonding) or π···π stacking. Theoretical calculations indicate that the intermolecular interactions in the crystal environment © 2014 American Chemical Society

Scheme 1. Keto (K) and Enol (E) Tautomeric Forms of Barbituric Acid

should favor the enol form over the keto form by 58.5 kJ·mol−1, whereas gas-phase studies suggest that the molecule in its keto tautomer is 53.7 kJ·mol −1 lower in energy. 8 Indeed, intermolecular interactions reverse the order of thermodynamic stability of the tautomers, favoring the enol form in the solid state and the keto tautomer in the gas phase and in solution. It has been demonstrated that the crystal of polymorph II consists of two different conformers of keto tautomer:9 an envelope conformation and a planar conformation (see Figure 1). In the envelope conformer, K1, the hydrogen atoms bonded to carbon atom C5 are oriented pseudo axial and pseudo equatorial with respect to the six-membered ring. In the planar conformer, K2, both hydrogen atoms of C5 assume similar angles to the plane of the molecule resulting in an Received: December 19, 2013 Revised: May 6, 2014 Published: May 7, 2014 2763

dx.doi.org/10.1021/cg401899q | Cryst. Growth Des. 2014, 14, 2763−2772

Crystal Growth & Design

Article

cross-polarization and two-pulse phase-modulated (TPPM) decoupling during the acquisition. The NMR spectra of the individual forms were compared with those found in the literature.8 The program DMFIT was used to obtain the principal components of the 13C NMR CSTs from the MAS sideband patterns.32 Several MAS rates were used to determine the CST parameters, and the average values are reported. The principal components obtained are ordered according to the IUPAC rules:33 δ11≥ δ22 ≥ δ33. 2.2. Computational Methods. The initial geometries of polymorph II (CCDC No. 250445)9 and polymorph IV (CCDC No. 794121)8 for the theoretical study were taken from X-ray diffraction studies. In the first step, the geometries of all of the atoms heavier than hydrogen (C, N, and O) were fixed, and the coordinates of all of the H atoms in three different clusters, each containing 17 molecules (one cluster for polymorph IV and two for polymorph II) were optimized. A smaller cluster containing 13 molecules was subsequently selected from each of these bigger clusters. These smaller clusters contained all of the molecules that were considered to have bonding interactions with the central molecule in each cluster. The interactions of the central molecule with its neighbors in the clusters were analyzed, and the NMR chemical shifts for the individual atoms of the central molecule were calculated. The energy optimization was performed at the B3LYP34,35/6-31G(d) level of theory. The NMR shielding tensors were computed using the GIAO36 approach at the B3LYP/6-311++G(d,p) level of theory. The same calculations were performed on the cluster of α-glycine molecules37 that was used as a secondary standard (for XYZ coordinates; see Supporting Information). The Gaussian 09 rev C.0138 suite of programs was employed for all calculations. Subsequently, the NMR chemical shifts were calculated using the following equation:

Figure 1. Side views of the two conformers (envelope K1 and planar K2) of the keto form of barbituric acid present in polymorph II (CCDC no. 250445).9 The planar keto form K2 seems to represent a disorder average of K21 and K22.

approximately C2v molecular structure (cf. Figure 1). A combined study involving X-ray diffraction and ab initio computations has suggested that the energy of K1 is very close to the energy of the free keto tautomer of barbituric acid, and K2 is a transition state that is also very close in energy to the local minimum.9 On the basis of the calculations and the crystallographic evidence, Lewis et al. have concluded that K2 appears to be present because molecular vibrations cause C5 to oscillate between two structures (K21 and K22) that resemble envelope geometry.9 In this contribution, we employ noncovalent interaction (NCI)15−17 plots to demonstrate the bonding networks in polymorphs II and IV, using global pictorial representation. In addition, we study the nature of individual intermolecular interactions in detail in light of the quantum theory of atoms in molecules (QTAIM),18 a powerful tool for studying noncovalent interactions.19−22 Solid-state NMR spectroscopy has been used to study the influence of intermolecular interactions on the 1H NMR23 and particularly the 13C NMR24 chemical shifts in different crystalline forms. It is well-known that isotropic NMR chemical shifts and, even more, NMR chemical shift tensors (CSTs), are sensitive to crystal effects, including hydrogen bonding.25−28 It has recently been demonstrated that this sensitivity is attributable to the modulation of the magnetic shielding that occurs when the electron density in the system undergoes spatial redistribution induced by the formation of intermolecular contacts.29,30 Yates et. al have demonstrated a correlation between the strengths of hydrogen bonds and the magnitudes of the variation in the chemical shift upon formation of intermolecular interactions in a crystal.31 In this work, we investigate the modulation of the NMR CSTs in detail by means of density functional theory (DFT) computations. We also try to inspect some probable relationships between variations in the NMR chemical shift tensors and the electron density redistribution in light of QTAIM.

δi = σst − σi + δst

(1)

where σst (CO) = −0.83 ppm and δst = 176.03 ppm are the C NMR shielding constant of the carbonyl carbon in α-glycine and the experimental 13C NMR chemical shift of the carbonyl carbon in αglycine, respectively; the subscript st denotes secondary standard. Because we could not determine the experimental 13C NMR CSTs for polymorph II (the keto tautomer) precisely, we used the experimental values reported in the literature.39 The RMSDs between the theoretical and experimental values were calculated as well. Total views of the intermolecular interactions in both polymorphs were obtained by applying an NCI descriptor. In the NCI plot, the reduced density gradient (RDG) s(r) is mapped onto the ρ(r).sign(λ2), where λ2 is the second eigenvalue of the Hessian electron density matrix.16 The promolecular densities were used for NCI analysis. Finally, characteristics of the (3, −1) critical points (line critical points, LCPs) of the electron density, including the electron density (ρ(r)), the Laplacian of the electron density (∇2ρ(r)), the kinetic energy density (G(r)), the energy density (H(r)), and the delocalization index (DI), were investigated by using the AIMAll suite of programs40 in order to have a detailed description of the intermolecular contacts. Single-point calculations based on the geometries of the isolated structures K21 and K22 at the MP2/aug-cc-pVTZ and B3LYP/6-311+ +G(d,p) computational levels demonstrate that the planar K2 is very slightly more stable than the conformers K21 and K22 (see Table S1, Supporting Information). However, the planar conformer K2 in a crystal arrangement of polymorph II does not represent a real local minimum. Therefore, this conformer was fully optimized at the center of a cluster consisting of 17 molecules by fixing the coordinates of the heavier atoms (C, N, and O) in the peripheral molecules. Optimization of the geometry yielded the two conformers K21 and K22 depicted in Figure 1. Indeed, the intermolecular interactions between the surrounding molecules and K21 or K22 lower the energy of their respective clusters relative to those that contain the planar K2. The bonding interactions and NMR chemical shifts of 13-molecule clusters inside 17-molecule clusters containing K21 or K22 were also studied in detail. Similar steps were repeated for the geometries obtained by reoptimizing the 17-molecule clusters of polymorph II by using 13

2. EXPERIMENTAL AND THEORETICAL METHODS 2.1. Solid-State NMR Spectroscopy. Polymorph II of barbituric acid (the keto tautomer) was purchased from Sigma-Aldrich. Polymorph IV (the enol tautomer) was prepared by grinding polymorph II, according to the method of Schmidt et al.8 Solid-state NMR experiments were performed on a Bruker Avance-500 spectrometer operating at frequencies of 500.13 MHz (1H) and 125.77 MHz (13C). All measurements were made at room temperature using a Bruker 4 mm MAS probe. A CP contact time of 2 ms and an optimized recycle delay of 5 s were used for the 13C CP/MAS experiments. Ramped amplitude (RAMP) shape pulse was used for the 2764



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B3LYP with a D3 dispersion correction as introduced by Grimme41 [B3LYP-D3/6-31G(d)] to verify the effects of the dispersion interactions on the geometry and, subsequently, on the NMR chemical shifts. To investigate the effects of the dispersion-corrected geometry on the AIM parameters, smaller clusters of five molecules were extracted from 17-molecule clusters that had been optimized with and without the D3 dispersion correction. Our comparative studies demonstrate that the dispersion correction used to optimize the geometry had a marginal effect on the NMR and bonding properties (Tables S2−S4, Supporting Information). This is not surprising because the dispersion correction does not change the geometrical parameters of the molecule in a crystal embedding very much and has no direct effect on the wave function. Indeed, the dispersion correction is an empirical Lennard-Jones-type parameter added to the energy, and it affects the wave function only indirectly by changing the geometry (see Table S2, Supporting Information for more details). All of the aforementioned findings justify employing the K2 transition structure as representing an average of structures K21 and K22 in the following analyses and discussions.

3. RESULTS AND DISCUSSION 3.1. Analysis of Electron Density. 3.1.1. NCI Analysis. Hydrogen Bonds. Several H-bonding interactions between the central molecule in a heptameric cluster (E-7) and its neighbors in this crystal arrangement of polymorph IV can be identified (see Figure 2). Because of the crystal symmetry, only five different types of hydrogen bond (A/A′, B/B′, C/C′, D/D′, and E/E′) are expected as shown in Figure 2. The reduced density gradient (RDG) surfaces for the E-7 crystal model of polymorph IV (enol) are shown in Figure 3. As shown in the work of Johnson et al.,15 the hydrogen bonds are characterized by λ2 < 0 curvatures (blue ellipses and ellipsoids). NCI analysis demonstrates that three different types of

Figure 3. NCI plot for E-7 cluster of polymorph IV highlighting the H-bonding interactions. The cutoff for the reduced density gradient, s(r), is 0.3 au and the color scale is −0.07 < ρ < 0.07 au.

relatively strong hydrogen bonds can be identified. The regions of these three types of hydrogen bonds are marked with blue ellipses for A/A′ and blue ellipsoids for B/B′ and C/C′. The ρ(r).sign (λ2) values for the O−H···O and N−H···O(C) hydrogen bonds in the enol form are −0.078 au (A/A′), −0.049 au (B/B′), and −0.039 au (C/C′), respectively. The C−H···O hydrogen bonds (D/D′ and E/E′) appear as green ellipsoids in Figure 3 and are characterized by very small negative values of λ2 (−0.01 au), approaching zero in the plot (see Figure S1, Supporting Information). Also, we report NCI plots (Figure S2, Supporting Information) for two clusters each containing five molecules of polymorph II (K-5): one with an envelope structure in the center (K1) and the other with a planar molecular arrangement in the middle (K2). The planar structure K2 was selected instead of the two local minima discussed in section 2.2 because it represents the average bonding interactions between the planar conformer and its surroundings. Because of the crystal symmetry, four different H-bonds can be identified in each of the K-5 clusters (see Figure 4). The strengths of G/G′ and K hydrogen bonds are identical in the two clusters because these hydrogen bonds are formed between the two different conformers, K1 and K2, in the both K-5 clusters. In contrast, the strengths of the F1/F1′ and the H1/ H1′ hydrogen bonds in the K1−5 cluster versus the F2/F2′ and H2/H2′ hydrogen bonds in the K2−5 cluster differ significantly (see also section 3.1.2). These hydrogen bonds are formed between conformers of the same type in both clusters (the K1···K1 conformers in the cluster K1−5 and the K2···K2 conformers in K2−5). All N−H···O hydrogen bonds in clusters K-5 are visualized as blue ellipsoids in the RDG plots in Figure S2, Supporting Information. In the cluster K1−5, two different values of

Figure 2. H-bonding pattern in cluster E-7 of polymorph IV with molecules in the enol tautomeric form. The five different types of Hbonding interactions in polymorph IV are labeled as A/A′, B/B′, C/ C′, D/D′, and E/E′. 2765



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Figure 4. H-bonding patterns in clusters (a) K1−5 and (b) K2−5 of polymorph II, with molecules in the keto tautomeric form. The four different types of H-bonding interactions in polymorph II are labeled F1/F1′, G/G′, H1/H1′, and K in cluster K1−5 and F2/F2′, G/G′, H2/H2′, and K in K2−5.

Figure 5. Total NCI surfaces for the clusters (a) E-13, (b) K1−13, and (c) K2−13. NCI surfaces correspond to s(r) = 0.3 au and the color scale is −0.07 < ρ < 0.07 au.

ρ(r).sign(λ2) for the hydrogen bonds were identified (−0.037 au and a wider spike with a value of about −0.043 au, as shown in Figure S3, Supporting Information). The weaker hydrogen bonds (C2)O···H−C5, H1/H1′, are shown with the green ellipsoids (Figure S2) whose peaks lie at around −0.01 au in the plot. The spike of the weakest hydrogen bond, K, appears near zero in the plot (see Figure S3). All H-bonds are characterized by less negative values in the K2−5 cluster, which indicates that these are somewhat weaker than those in K1−5 (Figure S4, Supporting Information). Comparison of the H-bonding interactions in polymorphs IV and II shows exceptionally strong A/A′ hydrogen bond in the enol form (polymorph IV). A more detailed QTAIM analysis of the H-bonding interactions is described in section 3.1.2.

Stacking Interactions. In addition to the H-bonding, other types of intermolecular interactions, such as π−π stacking, are present in both polymorphs. To estimate the roles that these other interactions play in stabilizing polymorphs II and IV, three bigger clusters, E-13, K1−13, and K2−13 each composed of 13 molecules were investigated (for the geometry of these clusters, see Supporting Information). In addition to the Hbonding, weaker intermolecular interactions, including stacking and some atomic contacts, were identified and appear as green surfaces in Figure 5 (with values in the s(r) vs ρ(r).sign(λ2) plot in Figures S5−S7, Supporting Information close to zero). It is worth mentioning that the more extensive green region of the RDG surface shown in Figure 5c indicates more favorable 2766



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Table 1. Descriptors of the (3, −1) Critical Points for Hydrogen Bonds between the Central Molecule and Neighboring Molecules in the E-7 Cluster: the Electron Density, ρ(r), the Laplacian of the Electron Density, ∇2ρ(r), the Lagrangian Kinetic Energy, G(r), the Potential Energy, V(r), the Ratio of the Lagrangian Kinetic Energy to the Electron Density, G(r)/ρ(r), the Energy Density, H(r), the Delocalization Index, DI (all Parameters Are Presented in Atomic Units), and the Bond Length (in Å) bond

ρ(r)

∇2ρ(r)

G(r)

V(r)

G(r)/ρ(r)

H(r)

DI

bond length

A/A′ B/B′ C/C′ D/D′ E/E′

0.0777 0.0418 0.0331 0.0088 0.0058

0.1722 0.1390 0.1097 0.0297 0.0231

0.0658 0.0368 0.0272 0.0063 0.0047

−0.0886 −0.0389 −0.0270 −0.0052 −0.0036

0.8468 0.8804 0.8232 0.7200 0.8175

−0.0228 −0.0021 0.0002 0.0011 0.0011

0.1589 0.1109 0.0977 0.0297 0.0196

1.494 1.716 1.831 2.546 2.729

Table 2. Descriptors of the (3, −1) Critical Points for the Hydrogen Bonds between the Central Molecules (K1 and K2) and the Neighboring Molecules in K-5 Clusters: the Electron Density, ρ(r), the Laplacian of Electron Density, ∇2ρ(r), the Lagrangian Kinetic Energy, G(r), the Potential Energy, V(r), the Ratio of the Lagrangian Kinetic Energy to the Electron Density, G(r)/ρ(r), the Energy Density, H(r), the Delocalization Index, DI (All Parameters Are Presented in Atomic Units), and the Bond Length (in Å) bond

ρ(r)

∇2ρ(r)

G(r)

V(r)

G(r)/ρ(r)

H(r)

DI

bond length

F1/F1′ F2/F2′ G/G′ H1/H1′ H2/H2′ K

0.0351 0.0296 0.0293 0.0074 0.0046 0.0012

0.1231 0.1059 0.1135 0.0229 0.0165 0.0047

0.0305 0.0249 0.0262 0.0049 0.0033 0.0008

−0.0302 −0.0234 −0.0240 −0.0041 −0.0025 −0.0004

0.8688 0.8412 0.8947 0.6622 0.7174 0.6970

0.0004 0.0016 0.0023 0.0008 0.0008 0.0004

0.0994 0.0883 0.0850 0.0320 0.0150 0.0049

1.7835 1.8592 1.8393 2.5637 2.9157 3.4956

hydrogen bonds. The data summarized in Table 1 reveal an interesting relationship between the delocalization index, the electron density, and the bond length (see Figure S8a,b, Supporting Information). The average values of the topological parameters of the hydrogen bonds of K1 and K2 in the K-5 clusters are listed in Table 2 (for individual values, see Tables S6 and S7, Supporting Information). In the cluster K1−5, the average DI value for the medium-strength F1 hydrogen bond, (C4)O···H−N4, is 0.0994 au. For the H1 hydrogen bond, (C2)O···H−C5, the DI value is 0.0320 au. The analogous F2 and H2 bonds in the K2−5 cluster are characterized by significantly smaller DI values (see Table 2). The G and K hydrogen bonds present in both K-5 clusters are characterized by DI values of 0.0850 au and 0.0049 au, respectively. As mentioned earlier, the properties of the bonds of the optimized structures K21 and K22 with their surrounding molecules were also studied within the context of QTAIM. Structures optimized with and without a dispersion correction were examined. As evident from Tables S2, S8, and S9, Supporting Information, including a dispersion correction in optimizing the geometry does not affect the QTAIM descriptors. The dynamic nature of the K2 conformer makes the situation regarding the bonding a bit fuzzy, but Tables S2, S8, and S9 show that the properties of the bonds are changed only slightly. Global Indices. In a bigger cluster containing 13 molecules (E-13), QTAIM analysis identifies 20 (3, −1) critical points, representing nine hydrogen bonds, seven π−π stackings, and four p → π* (electron lone pair of an oxygen atom to a πantibonding orbital of a CO bond) interactions (Table S10, Supporting Information). In general, a bonding interaction can stabilize a supramolecular system either by favorable electrostatic attraction or by electron exchange. In QTAIM, the delocalization index provides a straightforward measure of the contribution of electron exchange to the binding. In a series of similar interactions, one may assume that the bond with the

stacking interactions in the cluster K2−13 as compared to those in K1−13 and E-13 (see Figure 5b,a). The NCI surfaces provide a global view of the intermolecular interactions in these systems. However, in order to analyze the bonded interactions quantitatively, we employ the quantum theory of atoms in molecules (QTAIM). 3.1.2. QTAIM Analysis. Hydrogen Bonding. Many authors have used the characteristics of the (3, −1) critical points to classify intermolecular interactions.19−22 Because a limited number of the enol molecules are considered in the cluster E-7 for the QTAIM analysis (Table S5, Supporting Information), slightly different values have been obtained for the individual interactions A−E of the same type shown in Figure 2. The average values of the topological parameters of the individual intermolecular interactions are summarized in Table 1. As previously demonstrated, the electron density of a (3, −1) critical point and the magnitude and sign of the energy density, H(r), provide a measure of the strength of a hydrogen bond.20 Furthermore, the delocalization index (DI) measures the degree of electron sharing, i.e., the covalency, between two atoms. The O−H···O interaction (A) has quite a large negative energy density value; the relatively high delocalization index (0.1589 au) and the large electron density value (0.0777 au) of this bond suggest that it should be classified as a strong hydrogen bond with partly covalent character. On the contrary, bonds B and C have topological parameters which are typical of the N−H···O hydrogen bonds (DI = 0.1109 au and 0.0977 au for B and C, respectively). Exhibiting small negative energy density values, these interactions can be classified as medium hydrogen bonds.21 In accordance with NCI analysis, the larger DI value suggests a somewhat stronger interaction B as compared with C. The CO···H−C (D) and C−(H)O···H− C (E) contacts are characterized by low delocalization indices, 0.0297 au for D and 0.0196 au for E, and positive energy densities, which suggest classifying these interactions as weak 2767



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Table 3. 13C NMR CSTs (in ppm) of the Enol Form (Polymorph IV) of Solid Barbituric Acid Calculated at the B3LYP/6-311+ +G(d,p) Level of Theory for the Isolated Molecule and the Same Molecule in Selected Clusters, the Root-Mean-Square Deviation (RMSD) between the Calculated and Experimental Principal Components of the CST, and the Sum of the Differences between the Principal Components of the CST Calculated for the Isolated Molecule and for Each Selected Cluster, ΣΔδa E-1

E-2

E-3

E-4

E-5

E-7

E-13

exp

143.7 235 102 92 0 153.8 251 137 74 0 73.7 125 61 35 0 165.7 271 144 82 0 8.0 19.4

146.8 221b 129b 90 43 155.8 250 140 72 6 75.2 126 64 36 5 165.3 272 141 83 5 6.4 16.0

147.3 219 134 89 51 156.0 250 144 75 9 74.1 124 69 30 14 165.2 271 142 83 3 6.4 14.3

147.5 219 132 91 47 157.9 251 148 75 12 73.3 121 70 29 19 168.9 260b 163b 84 32 5.3 8.8

146.8 223 126 91 37 160.0 250 154 75 19 72.8 123 73 23 26 169.5 250b 177b 81 55 5.0 6.8

146.9 223 126 92 36 160.9 250 157 76 23 75.9 123 82 23 35 169.2 251 176 81 53 3.9 5.3

148.1 225 132 86 46 160.1 252 156 74 20 79.5 131 87 20 47 171.5 257 181 77 56 3.1 4.6

152.4 224 141 92 164.5 256 162 75 79.2 127 86 25 171.7 254 179 82 -

RMSDtot RMSDtot

δiso δ11 δ22 δ33 ΣΔδ δiso δ11 δ22 δ33 ΣΔδ δiso δ11 δ22 δ33 ΣΔδ δiso δ11 δ22 δ33 ΣΔδ (δiso) (CST)

Δδ11 Δδ22 Δδ33 ΣΔδE

(all (all (all (all

0 0 0 0

17 36 6 59

18 49 10 77

31 69 10 110

36 86 15 137

35 97 15 147

31 112 26 169

C2

C4

C5

C6

atoms) atoms) atoms) atoms)

ΣΔδ is calculated as the sum of the differences between the principal components of the CST for an isolated molecule and those for the same molecule as part of a given cluster. bBold numbers in the table highlight the most remarkable effects of the intermolecular interactions. a

higher delocalization index is more stabilizing, i.e., stronger.42,43 Comparing the magnitudes of the delocalization indices for the hydrogen bonds with those of the π−π stacking and p−π interactions indicates that H-bonds are far more stabilizing (in the sense of having more electron exchange) than the other interactions (DIH‑bond = 0.8074 au, DIStacking = 0.1221 au, and DIp−π = 0.0785 au). Analysis of the electron density of the first conformer of the keto form, cluster K1−13, shows 22 (3, −1) critical points, corresponding to 11 hydrogen bonds, nine π−π stackings, one CH−π (C−H···N) interaction, and one (C)O···C5 contact which results from a π → σ* electron transfer between the oxygen of the carbonyl group and the sp3 carbon atom. The second conformer, cluster K2−13, shows 25 intermolecular (3, −1) critical points, corresponding to 11 hydrogen bonds, 11 π−π stackings, one CH-π (C5−H···N) interaction, one H−H contact, and one (C2)O···C5 contact, similar to the one for K1 (Tables S11 and S12, Supporting Information). Scrutinizing the global QTAIM descriptors of the intermolecular interactions for the two keto conformers, K1 and K2, suggests that they have relatively similar interactions with their surroundings. Accordingly, one can expect that the two molecules are similarly stabilized in the crystal (the sum of the delocalization indices for the intermolecular interactions that are formed with the central molecule is 0.7962 au for K1− 13 and 0.7837 au for K2−13). However, although the central

molecules K1 and K2 form the same number of H-bonds with their neighboring molecules, K1 forms somewhat stronger Hbonds. The sum of the delocalization indices for K1 indicates somewhat more electron exchange between the central molecule and its surrounding molecules (DIH‑bond = 0.5637 au for K1−13 and 0.4488 au for K2−13). In contrast, the stacking involving the K2 conformer seems to be more effective than that for K1 (DIstacking = 0.1898 au and 0.2799 au for K1− 13 and K2−13, respectively), which is in agreement with the NCI analysis (see section 3.1.1). Stacking is facilitated in the cluster K2−13 by the higher degree of planarity of the K2 conformer as compared to K1. (The RMSD of the dihedral angles for the deviations from planarity of K2 and K1 are 2.4 and 15.2 degrees, respectively.) Studying the topological descriptors of the (3, −1) critical points of the intermolecular interactions confirms the conclusion drawn from studying the delocalization indices. On the basis of the positive energy density values, one can classify the hydrogen bonds between the molecules in the keto form, polymorph II, of barbituric acid as weak to medium bonds with negligible covalent character (see Tables S11 and S12, Supporting Information). Surveying the QTAIM descriptors for the two fully optimized keto tautomers K21 and K22 in cluster K-13 shows that differences from the nonoptimized planar conformer are negligible. In the crystal lattice, optimized K21 forms two new (3, −1) critical points corresponding to very weak CH···O 2768



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Table 4. 13C NMR Chemical Shifts and Principal Components of the CST (in ppm) in Two Conformers of the Keto Form of Solid Barbituric Acid Calculated at the B3LYP/6-311++G(d,p) Level of Theory for the Isolated Molecule and for the Same Molecule in Selected Clusters, the Root-Mean-Square Deviation (RMSD) between the Calculated and Experimental Principal Components of the CST, and the Sum of the Differences between the Principal Components of the CST Calculated for Isolated Molecule and for Each Selected Cluster, ΣΔδa C2

C4

C5

C6

RMSDtot RMSDtot

δiso δ11 δ22 δ33 ΣΔδ δiso δ11 δ22 δ33 ΣΔδ δiso δ11 δ22 δ33 ΣΔδ δiso δ11 δ22 δ33 ΣΔδ (δiso) (CST)

Δδ11 (all atoms) Δδ22 (all atoms) Δδ33 (all atoms) ΣΔδK (all atoms)

K1

K1−5

K1−13

K2

K2−5

K2−13

average K-13

145.0 237 111 88 0 162.3 260 144 82 0 32.7 47 37 14 0 162.6 261 144 83 0 7.8 23.1

148.3 232 122 91 19 166.7 252 165 83 30 32.5 44 37 16 5 165.6 252 160 84 26 5.6 15.5

148.6 230 128 88 24 169.7 250 178 80 46 37.7 48 42 24 16 170.1 256 173 81 36 2.4 10.7

145.0 238 108 89 0 161.2 258 145 82 0 29.0 42 39 6 0 163.3 261 146 83 0 8.4 23.4

148.0 233 119 92 19 165.6 250 164 83 28 30 41 39 11 6 166.2 252 163 84 27 5.9 15.8

148.8 229 129 88 31 167.3 251 170 81 33 33.9 49 38 15 17 170.3 253 176 82 39 3.4 11.8

148.7 230 129 88 28 168.5 251 174 81 40 35.8 49 40 20 17 170.2 255 175 81 38

0 0 0 0

25 48 7 80

23 85 14 122

0 0 0 0

23 47 10 80

31 77 12 120

27 81 13 121

exp39 151.9 216 133 106 170.4 252 191 68 41b/39c 51b/51c 41b/41c 26b/26c 170.4 252 191 68

ΣΔδ is calculated as the sum of the differences between the principal components of the CST for the isolated molecules and those for those same molecules in the selected cluster. bExperimental NMR chemical shifts for the first conformer (K1) with the out-of-plane CH2 group. cExperimental NMR chemical shifts for the second conformer (K2) with the in-plane CH2 group. a

Polymorph IV - Enol Form. The calculated isotropic 13C NMR chemical shifts and the principal components of the 13C NMR CSTs, as well as the corresponding experimental values determined in this work, are summarized in Table 3. Cluster models ranging from E-1 to E-7 (for numbering, see Figure 2) are considered in order to systematically investigate the effects of the H-bonding interactions on the NMR chemical shifts and the 13C NMR CSTs. In addition, a bigger cluster, E-13, is used to study the total crystal environment, including stacking interactions. The total RMSDs for both the isotropic 13C NMR chemical shifts and the 13C NMR CSTs generally decrease from the monomer to the biggest cluster by increasing the number of molecules (and intermolecular interactions) in the cluster. The NMR data calculated for the largest cluster, which models the full crystal environment, clearly show reasonable agreement with the experimental values (Table 3). It is worth noting that δ11 and δ22 are in-plane components, whereas δ33 is oriented perpendicular to the plane for all atoms. The orientations of the principal components of the 13C CSTs for the isolated molecule and for clusters are summarized in Table S15 and depicted in Figure S9, Supporting Information. As evident from Table 3, the in-plane component δ22 for the isolated molecule contributes the most to deviations from the experimental 13C NMR CST values.

hydrogen bonds with adjacent molecules. On the other hand, changes in the geometry of K22 cause some (3, −1) critical points corresponding to intermolecular interactions to disappear and some new (3, −1) CPs to form because of the redistribution of the electron density around the CH2 group. However, the total number of (3, −1) critical points remains the same as for the planar average form, K2. It should be mentioned explicitly that all these variations do not affect the conclusion that conformer K1 benefits more from hydrogen bonds than K2, with H-bonding/stacking DI ratio of approximately 3:1 for K1 and 2:1 for K2 (see Tables S13 and S14, Supporting Information). Indeed, even the optimized geometries K21 and K22 are considerably more planar than the K1 molecular structure. In a nutshell, QTAIM analysis reveals that a higher degree of covalency of the intermolecular bonds of the enol form is responsible for the greater stability of this polymorph under ambient conditions. 3.2. Effects of Intermolecular Interactions on the 13C NMR Chemical Shift Tensors (CSTs). Intermolecular interactions can induce significant changes in the anisotropy of the nuclear magnetic shielding reflected in the experimentally measured NMR chemical shift tensors. This is intimately connected with the redistribution of the electron density around the molecule, as characterized in section 3.1. 2769



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(polymorph II) as described by clusters K1−13 and K2−13 is 121 ppm. The RMSDs calculated with respect to the experimental values shows that the keto form is less affected than the enol form. This may result partly from the floppy nature of the K2 conformer in the crystal lattice. The X-ray diffraction data show that the proximity of the energy levels of the different conformers of K2 permits rapid changes in conformation that are much faster than the time scale of the NMR experiment. Accordingly, no single structure can properly reproduce the NMR spectrum. Besides, comparing the RMSDs as well as the total absolute values of the changes in the CSTs for the average of the two local minima, K21 and K22, with and without the dispersion correction shows that the NMR values are only marginally affected by optimization of the geometry and the inclusion of the dispersion correction (see Tables S3 and S4, Supporting Information). 3.3. Relationship between the NMR CSTs and the Intermolecular QTAIM DI. The modulations of the 13C NMR CSTs by the intermolecular interactions in polymorph IV (the enol tautomer) and polymorph II (the keto tautomer) of barbituric acid indicate bigger values of ΣΔδ for the enol form. This larger perturbation results from the stronger intermolecular interactions present in polymorph IV (Table 5).

The H-bonding effect on the NMR CSTs can be demonstrated on the C2 atom in the enol form as an example. The addition of one molecule to the monomer considerably changes the principal components of the CST for carbon C2 (the sum of changes in all principle components amounts to 43 ppm). This change results from the formation of the CO··· H−N (B) bond which is classified as a medium-strength hydrogen bond. The values in Figure S10, Supporting Information and Table 3 show that among the principal components the in-plane component δ22, which is almost parallel to the CO bond, and δ11, which is perpendicular to the CO bond, are responsible for the modulation of the CST values for carbon C2. Component δ22 increases dramatically, whereas component δ11 decreases considerably when the isolated molecule is replaced by this dimer model. Involving the stacking interactions in the cluster E-13 shows no considerable changes in the CSTs as compared to those calculated for the cluster E-7, for which only H-bonding interactions were considered. The total effect of the crystal environment on C2 CST (ΣΔδ) calculated for E-13 amounts to 46 ppm (see Table 3 and Figure S10, Supporting Information). The H-bonding effects on the NMR CSTs of the other carbon atoms in the enol form are also presented in Table 3 and Figures S11−S13, Supporting Information. ΣΔδ, the sum of the absolute differences between the principal components of the NMR CST for a particular atom in an isolated molecule and those for the same atom in the same molecule in a particular cluster, shows the magnitude of the changes induced by intermolecular interactions. This can be related to the strengths of the individual intermolecular contacts, as discussed in section 3.1. The total change in the 13 C NMR CSTs for the enol tautomer in polymorph IV, as described by cluster E-13, is 169 ppm. Polymorph II − Keto form. In the keto form (Table 4), the orientations of the principal components of the 13C NMR CSTs in both of the conformers and all of the clusters are the same, except for C5. The δ11 and δ22 components of the CST for the C5 atom exhibit reversed orientations in the two K2 conformers as compared to the K1, because of the near-axial symmetry of the CSTs for C5. (The orientations of the principal components of the 13C CSTs for the isolated molecules are summarized in Table S16, Supporting Information and depicted in Figure S14, Supporting Information.) The δ22 principal component of C5 is not significantly modulated by forming the K1−5 and K2−13 clusters, but forming the K1−13 cluster changes this component of C5 as much as the δ11 component. This suggests that in the first conformer the δ22 of this atom is more affected by the crystal packing environment in the bigger cluster, which can be rationalized by the formation of new interactions in the cluster K1−13. In addition to the weak hydrogen bonds that were already formed by one of the H5 atoms in the cluster K1−5, two new hydrogen bonds are formed by the other H5 atom in the K1−13 cluster (see QTAIM data, Tables S6 and S11, Supporting Information). The largest difference in the principal components for individual atoms between K1 and K2 has been identified for δ33 of the C5 atom, which is also significantly modulated by the formation of the cluster K-13. To investigate the effect of the full crystal environment on the CST, we calculated the absolute values of the changes in the individual principal components of the CST and the sums of these changes. The total average change in the 13C NMR CST for the keto tautomers

Table 5. Global Delocalization Index Values (in a.u.) for the Intermolecular Interactions and the Sums of Changes in the 13 C NMR CSTs Induced by Intermolecular Interactions (in ppm Relative to the Single Molecule) for Molecules in Polymorph IV (the Enol Form − E-13) and II (the Keto Form−the Average of the Values for K1-13 and K2-13)a DIH‑Bonding DIStacking DIHB+S DITotal ΣΔδ a

polymorph IV E-13

polymorph II K-13

0.8074 0.1221 0.9295 1.008 169

0.5063 0.2349 0.7412 0.7900 121

HB represents hydrogen bonding; S represents π−π stacking.

Interestingly, the ratio of the totals of the changes in the 13C NMR CSTs in the enol and keto tautomers (ΣΔδE/ΣΔδK = 1.40) is very close to the ratio of the total intermolecular delocalization indices of the two polymorphs (DITotal(IV)/ DITotal(II) = 1.28). This suggests an interesting relationship between the magnitude of the changes in the NMR CSTs and the strengths of the intermolecular interactions characterized by the QTAIM intermolecular delocalization index. It is worth mentioning that the ratio of the total of the changes in the 13C NMR CSTs in the enol and keto tautomers does not change at all if the structures of the central molecules are optimized, and the ratio of the total intermolecular delocalization index in two polymorphs (DITotal(IV)/DITotal(II)) changes negligibly, from 1.28 to 1.27.

4. CONCLUSIONS The effects of intermolecular interactions on the 13C NMR chemical shift tensors of barbituric acid in the solid state were investigated. As a first step, the convergence of the calculated isotropic NMR chemical shifts and the NMR chemical shift tensors with increasing numbers of molecules in a cluster was demonstrated for the polymorph IV (the enol tautomer). Comparing the 13C NMR chemical shifts of a hypothetical single molecule of barbituric acid (both enol and keto forms) in 2770



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its solid-state geometry with data obtained for the same molecule in clusters showed that the NMR chemical shifts of the enol form are influenced more by the intermolecular interactions than those of the keto form. This suggests that the intermolecular interactions are stronger in the crystal arrangement of polymorph IV (the enol form) than in polymorph II (the keto form). The source of the relative stability of the enol form under ambient crystal conditions was revealed by QTAIM analysis, which demonstrated the partial covalent character of some of the hydrogen bonds in the enol form. In addition, our study suggests an interesting relationship between the magnitude of the changes in the NMR CSTs induced by intermolecular interactions and the strengths of the intermolecular interactions as characterized by the delocalization index in the context of the QTAIM.

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ASSOCIATED CONTENT

S Supporting Information *

Descriptors of the (3, −1) critical points, orientations of the principal components of the 13C NMR CSTs and 13C NMR values, RDG plots and NCI surfaces, plots of the delocalization indices versus the electron density, patterns of the changes in the 13C NMR CSTs for individual carbon atoms with changing size of the cluster, and Cartesian coordinates for the individual clusters analyzed. 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]. Fax: +420-549492556. Tel: +420-549495748. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Czech Science Foundation (Grant Number P206/11/0550) and carried out at CEITEC the Central European Institute of Technologywith research infrastructure supported by the Project CZ.1.05/1.1.00/ 02.0068 financed from the European Regional Development Fund. C.F.-N. thanks the Program “Employment of Newly Graduated Doctors of Science for Scientific Excellence” (Grant Number CZ.1.07/2.3.00/30.009) cofinanced by the European Social Fund and the state budget of the Czech Republic. Access to the computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum and provided under the program “Projects of Large Infrastructure for Research, Development, and Innovations” (Grant Number LM2010005), and the CERIT-SC computing and storage facilities provided under the program Center CERIT Scientific Cloud, a part of the Operational Program Research and Development for Innovations (Grant Number CZ.1.05/3.2.00/08.0144), is acknowledged.

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REFERENCES

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Origin of the Thermodynamic Stability of the Polymorph IV of

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