Interpretation of Crystal Effects on NMR Chemical Shift Tensors

Article pubs.acs.org/JPCA

Interpretation of Crystal Effects on NMR Chemical Shift Tensors: Electron and Shielding Deformation Densities Martin Babinský,†,‡ Kateřina Bouzková,† Matej Pipíška,† Lucie Novosadová,† 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, 62500 Brno, Czech Republic S Supporting Information *

ABSTRACT: The relationship between the NMR observables and the supramolecular structure of any system is not straightforward. In this work we examine the influence of the crystal packing for three purine derivatives (hypoxanthine, theobromine, and 6-(2methoxy)benzylaminopurine) on the principal components of the NMR chemical shift tensors (CSTs). We employ density functional calculations to obtain various molecular properties (the ground-state electron density, the magnitudes and orientations of the components of NMR chemical shift tensor, and the spatial distribution of the isotropic magnetic shielding) for the isolated molecules and for the molecules embedded in supramolecular clusters modeling the crystal environment and evaluate their differences. The concept has enabled us to rationalize the effect of the crystal packing on the NMR CSTs in terms of the redistribution of the ground-state electron density induced by intermolecular interactions in the solid state.

1. INTRODUCTION The crystal structure of any chemical compound can be understood in terms of the intermolecular interactions and the dynamics acting during the crystallization process. Depending on the initial conditions as solvent, temperature, or stirring, a compound may develop into various crystal forms characterized by different networks of intermolecular contacts. This phenomenon, known as polymorphism, is of great importance for the pharmaceutical, agrochemical, and food industries, because the different crystal forms may have considerably different properties such as stability, solubility, and bioavailability.1 Therefore, recognition of the individual forms based on descriptions of the most important intermolecular contacts has become important for controlling their generation.2 Solid-state NMR spectroscopy is an especially powerful tool for structural studies of crystalline compounds at molecular and supramolecular levels.3 Of the defined NMR parameters, isotropic chemical shifts are used most routinely to distinguish between different crystal forms of a given compound.4 The multinuclear capability of NMR enables probing the electronic environments of various nuclei in a molecule and providing a pattern of the intermolecular interactions present. Much more informative, but not as widely used as the isotropic NMR chemical shifts, are the NMR chemical shift tensors.5 Whereas the isotropic chemical shift (δiso) gives the average value of the three principal components (δ11, δ22, δ33) δiso = (δ11 + δ22 + δ33)/3

Figure 1. Schematic representation of the NMR chemical shift tensor (CST) and its principal components.

established or understood. Therefore, in the work discussed herein, we try to establish the relationship between the nature of the intermolecular interactions and the redistribution of the ground-state electron density. More importantly, we investigate the influence of this modulation on the NMR chemical shift tensors. A simplified approach (neglecting the contribution of the internal dynamics and the deformation of the molecular geometry caused by strong noncovalent interactions)6 to characterizing the redistribution of the ground-state electron density induced by the crystal packing is to describe these changes for rigid geometries of the interacting objects.7,8 We define the property obtained in this way as the electron deformation density (EDD). The EDD (Δρ) is calculated and visualized as the difference between the electron density of a molecule placed in its crystal environment (ρ1) and the sum of the electron densities of the isolated molecule (ρ2) and its crystal environment (ρ3):

(1)

Δρ = ρ1 − (ρ2 + ρ3 )

the chemical shift tensor (CST) describes the distribution of the magnetic shielding in the three principal directions from the nucleus (Figure 1). However, the connection between the observed chemical shift and a particular intermolecular contact is not always easily © 2012 American Chemical Society

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Received: November 6, 2012 Revised: December 17, 2012 Published: December 19, 2012 497

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several MAS rates, and the obtained principal components were averaged. The average standard deviations of the fit of the CST components are 1.4 and 7.8 ppm for 13C and 15N NMR data, respectively. 2.2. Preparation of Structural Models for Theoretical Calculations. Single-crystal X-ray structures (CCDC Codes GEBTUC13 for 1 and SEDNAQ14 for 2, and CCDC No. 249264 for 3) reported previously were used as inputs for the cluster model building. The identity of the structures with the samples used for CP/MAS experiments was confirmed with Xray powder diffraction. The cluster approach was employed to simulate the crystal environment, although the GIPAW15,16 method may be more efficient and was successfully used in a number of studies to predict the solid-state NMR parameters.17−19 However, the main advantage of the cluster model is the possibility of studying the effect of individual intermolecular interactions and their additivity on the molecular properties, simply by altering the cluster size or geometry. In this study, the size of a supramolecular cluster was chosen in a way that takes into account both the hydrogen bonding and stacking interactions between the central molecule and its crystal environment, although, for the nuclei of interest, the calculated modulations in the NMR CSTs were caused mainly by the presence of the hydrogen bonds (e.g., see Figure S5 in the Supporting Information). The final cluster size was 21 monomer units for compound 1 (1-HBS21), 13 molecules for compound 2 (2-HBS13), and 16 molecules for compound 3 (3-HBS16). Finally, the positions of the protons in these clusters were optimized at the B3LYP20/6-31G*21 level of theory using the Gaussian 09.A222 suite of programs. The resulting structures were used in subsequent calculations (see the Supporting Information for XYZ coordinates). 2.3. Software and Methods Employed for QuantumChemical Calculations. The Gaussian 09.A2 suite of programs was also employed for the calculations of the electron deformation density (EDD), the shielding deformation density (EDD), and the NMR chemical shift tensors (CSTs) using the B3LYP functional and the 6-311G**23 basis set. Because of the quite modest size of the basis set used, the counterpoise correction by Boys and Bernardi24 was used during the calculations involving only parts of molecular clusters. Single-point interaction energy calculations were performed using TURBOMOLE 6.0325 suite at the SCS-MP226 level of theory and employing Dunning’s aug-cc-pVTZ27,28 basis set. The counterpoise correction was used also in this case. Resolution of identity29 approximation was employed in order to speed up the calculations, and all orbitals with energies lower than −3.0 hartree (ca. −1883 kcal mol−1) were kept frozen. 2.4. Calculation of Chemical Shift Tensors. For each molecular cluster two sets of data were calculated. First, the nuclear shielding tensors were obtained for the central molecule embedded in the cluster. Then the crystal environment was removed and the shielding tensors were recalculated for the isolated central molecule. The values of nuclear shielding constants (σi) were then converted to the NMR chemical shifts (δi) using the equation

When visualized, the EDD reveals regions where the electron density in the ground state decreases (shown as red lobes in this work) or increases (blue lobes) due to the crystal contacts. To correlate the EDD with the experimentally obtained changes in CSTs, we further introduce the isotropic shielding deformation density (SDD). This is defined similarly to the EDD, but instead of changes in the electron density, it gives changes in the isotropic values of the magnetic shielding (Δσ) in real space:9,10 Δσ = σ1 − (σ2 + σ3)

(3)

This concept, derived from the ground-state electronic structure recoded into the magnetic shielding influenced by the excited states, represents a simple and rather intuitive bridge between the quantum chemical model of the supramolecular system and the experimental observables represented by the NMR CSTs. Visualization of the real-space changes in the electron and isotropic shielding densities represents a powerful tool for understanding the consequences of several intermolecular interactions that drive the formation of the crystal and is demonstrated here on examples of the hydrogen bonding interactions present in the crystalline samples of hypoxanthine (1), theobromine (2), and 6-(2-methoxy)benzylaminopurine (3) shown in Figure 2.

Figure 2. Structures of hypoxanthine (1), theobromine (2), and 6-(2methoxy)benzylaminopurine (BAP, 3).

2. MATERIALS AND METHODS 2.1. Solid-State NMR Spectroscopy. Hypoxanthine (1, triclinic polymorph) and theobromine (2, monoclinic polymorph) were purchased from Sigma-Aldrich and used without further purification. 6-(2-Methoxy)benzylaminopurine (3) was prepared according to a published procedure.11 Solid-state NMR experiments were performed at room temperature on a Bruker Avance 500 spectrometer operating at frequencies of 500.13 (1H), 125.77 (13C), and 50.69 MHz (15N). A Bruker 4 mm cross-polarization/magic angle spinning (CP/MAS) probe was used for all measurements. 13C and 15N CP/MAS spectra were recorded with 1.8 and 4 ms contact times, respectively, and optimized recycle delays of 30−240 s. Ramped amplitude (RAMP) shape pulse was used during the cross-polarization and two-pulse phase-modulated (TPPM) decoupling during the acquisition. The spectral assignments were carried out with the use of NQS and CPPI pulse sequences. The program DMFIT12 was used to obtain the principal components of the 13C and 15N CSTs from the MAS sideband patterns. The obtained principal components were subsequently ordered according to the IUPAC rules: δ11 ≥ δ22 ≥ δ33. To minimize the error arising from the analysis and to estimate the standard deviation, the CST parameters were determined at

δi = (σref − σi) + δref

(4)

where σref is the nuclear shielding of a reference compound calculated using the same method, and δref is the experimental value of the NMR chemical shift of the reference compound. In 498

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Figure 3. Visualization of (a) the EDD for a hydrogen-bonded cluster of hypoxanthine (1) and (b) in-plane slice of the EDD with calculated changes in the 1H NMR chemical shifts for the individual hydrogen atoms trapped in standard and weak hydrogen bonds.

this study, α-glycine cluster was used as a reference system (σC‑13 = 0.51 ppm, δC‑13 = 176.03 ppm for the CO group; σN‑15 = 203.0 ppm, δN‑15 = 34.1 ppm for the amino group). 2.5. Calculations of EDD and SDD. Figure S1 in the Supporting Information demonstrates the process of calculating the electron deformation density. First, the electronic wave function of the cluster calculated in section 2.3 was used to obtain a three-dimensional (3D) grid of points representing the spatial distribution of electron density. The geometry of the cluster was then divided into a central molecule and its surroundings, and for each of these systems the wave function and 3D grid of electron density were calculated. The sum of these partial densities (ρcent and ρenv) was then subtracted from the electron density map of the whole complex (ρclust) to yield the final electron deformation density (EDD). The shielding deformation density (SDD) was calculated in a manner similar to that for the EDD. The 3D grid representing the spatial distribution of isotropic magnetic shielding around the system was calculated by placing ghost atoms at selected points in space and evaluating the isotropic shielding at these points. 2.6. Calculation of Point Charges for Simplified Model of Theobromine Dimer. The point charge of the acceptor oxygen atom used in the simplified model of theobromine dimer was obtained using the RESP30,31 methodology. An inhouse version of RED II32 software modified to use the B3LYP functional and 6-311G** basis set for the charge derivation was employed. The molecular electrostatic potential was computed for two distinct orientations of the whole cluster to address the problem of the orientation dependence of RESP-derived point charges. The point charge of oxygen atom O76 (−0.2631 e) was then used in the simplified model. 2.7. Evaluation of Interaction Energies. In order to qualitatively estimate the strength of individual hydrogen bonds between the central molecule and its environment, the structures of clusters 1-HBS21 and 3-HBS16 were split into dimers featuring the desired interaction (see Figure S2 in the Supporting Information). These dimers were then subjected to single-point calculations of interaction energy as described previously.

structural applications accompanying the development and availability of ultrafast magic-angle-spinning techniques, and sophisticated multidimensional solid-state NMR experiments.33 Despite the difficulties in observing and analyzing 1H NMR resonances in the solid state (caused by the large magnitudes of the homonuclear direct spin−spin couplings), there are a substantial number of studies correlating 1H NMR parameters with the nature of hydrogen bonding (HB) interactions in the solid state.34−37 Because the interpretation of the EDD patterns is straightforward in this case, we first analyze and demonstrate the modulations in 1H NMR chemical shifts caused by the formation of a hydrogen bond. We have calculated the differences in the NMR chemical shifts between a single molecule and a cluster of 21 molecules of hypoxanthine (1-HBS21), as well as the electron deformation density (EDD) for this arrangement. The results shown in Figure 3 clearly demonstrate that changes in the calculated isotropic 1H NMR chemical shifts (CSs) are directly correlated with the magnitudes of the EDD. For example, the small red lobes (representing decreases in the electron density) at the positions of atoms H2 and H8 correspond to the changes in the NMR CSs of approximately 1.5−2 ppm, whereas the larger ones at the positions of H1 and H9 correspond to Δδiso values of about 4.5 ppm and about 6.5 ppm, respectively. This is evidence that not only the presence but also the strength of a hydrogen bond is straightforwardly encoded in the EDD pattern. To confirm the assumed strengths of the individual hydrogen bonds, we have calculated the interaction energies (IEs) for various pairs of molecules. For the pair including only the weak C−H···N hydrogen bond (H2),38 the calculated IE is −3.61 kcal mol−1. For the other two pairs that are also connected by standard hydrogen bond of N−H(9)···N and N−H(1)···O types, the IE values are −11.15 and −21.51 kcal mol−1, respectively. These numbers support the EDD model obtained and confirm that the changes in the calculated 1 H NMR data are due to the formation of hydrogen bonds of different strengths (based on the calculated interaction energies). This seems to be a straightforward and general behavior applicable to all hydrogen atoms in organic and pharmaceutical substances. 3.2. Modulation of 13C NMR CSTs by Intermolecular Interactions. As our next step, we investigated the 13C NMR CSTs, which are easily determined at natural abundance, and a good agreement between the experiment and theory can be achieved even for compounds with poor signal dispersion and low 13C CST anisotropy.39 The protonated aromatic carbons are especially quite sensitive to the crystal packing (e.g., HB). It has been demonstrated that the formation of a hydrogen bond

3. RESULTS AND DISCUSSION 3.1. Influence of Crystal Packing on 1H NMR Chemical Shifts. In a majority of cases the intermolecular interactions in organic and pharmaceutical crystals include hydrogen atoms (e.g., hydrogen bonding, C−H···π interactions) because they are located on the molecular surface. 1H NMR chemical shifts are assumed to be of rapidly increasing importance for the 499

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Table 1. Calculated Values (and Their Differences from the Experimental Data) of the Isotropic NMR CSs and CSTs for Selected Atomsa chemical shift (ppm) δiso

a

δ11

δ22

δ33

model system

atom

calc

exp − calc

calc

exp − calc

calc

exp − calc

calc

exp − calc

2-HBS13 3-HBS16

C8 N3 N7 N9

143.3 211.9 242.3 164.9

+0.8 +6.1 +6.2 +5.7

208.3 353.0 426.7 244.2

+0.3 −7.0 −0.30 +16.2

152.9 313.9 294.9 180.6

+4.9 +20.9 +8.9 +1.6

68.8 −13.0 5.2 69.9

−2.2 +4.00 +10.2 −0.1

See Figures S3 and S4 in the Supporting Information for a graphical comparison of the experimental and theoretical data.

the electron density in the π part of the C8 subspace is significantly reduced (Figure 4, left). Employing the natural chemical language of molecular orbitals, an increase in the electron density in the σC8−H region close to C8 and a decrease in the πC8 space (see also Figure S5 in Supporting Information) could enhance the σCH → π* orbital magnetic interactions.42,43 This would result in an increased paramagnetic deshielding contribution to the CST of the C8 atom mainly in the direction of the applied magnetic field, i.e., perpendicular to the plane of the σC8−H → π* orbitals. In other words, the magnetic shielding in the direction perpendicular to the C8−H bond and lying in the plane of the purine ring will be modulated the most (see Figure S6 in the Supporting Information). Indeed, the largest changes in the CST were observed in δ22, the principal component possessing this orientation in the space (orange color, Δδ22 = 20 ppm). In order to visualize changes in the magnetic shielding induced by crystal packing, we calculated and visualized the isotropic SDD (Figure 4, right), which unequivocally supports the model introduced above. To investigate the effect of the electrostatic interaction between the interacting objects on the EDD, iso-SDD, and CST, we analyzed the simple model, where an acceptor oxygen atom participating in hydrogen bonding with the H8 atom of the central molecule was simulated by an RESP-derived point charge. The observed behavior was very similar to that observed for the whole cluster. 3.3. Modulation of 15N NMR CSTs by Intermolecular Interactions. The C−H···X and C−H···π interactions are important since they are highly populated in supramolecular assemblies of organic compounds, pharmaceutical substances, and biomolecular systems. However, N−H···N(O) interactions are generally characterized by significantly larger interaction energies. How are these interactions encoded in the EDD,

predominantly influences only one of the three principal components of the 13C CST of these carbons.40,41 Here we have used our EDD and iso-SDD models to rationalize this observation. As a specific example representing a weakly hydrogen bonded C−H group, we analyzed the C8 atom in theobromine (2), where we had obtained excellent agreement between the experimental and the DFT calculated 13 C CSTs (see Table 1 and Figure S3 in the Supporting Information). Details of the real-space distribution of the EDD and the isotropic SDD around atom C8 in 2 are shown in Figure 4 together with a schematic representation of the

Figure 4. Visualization of the (a) EDD and (b) SDD for atom C8 in theobromine (2). The arrows schematically represent the calculated relative orientations of the in-plane principal components of the 13C CST, whereas the numbers denote the calculated changes in the magnitude of these components upon formation of the molecular cluster.

changes in the CST originating from the crystal packing. The HB interaction clearly polarizes the C8−H bond, resulting in a decrease in the electron density at H8 (red lobe) and an increase of electron density close to C8 (blue lobe). Further,

Figure 5. Visualization of the (a) EDD, (b) SDD, and principal components of the 15N CSTs in the central molecule of 6-(2methoxy)benzylaminopurine (3). The arrows represent the relative orientations of the principal components of the CSTs, whereas the numbers denote the calculated changes in the magnitudes of the individual components (in ppm) caused by the formation of the molecular cluster. 500

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Figure 6. Visualization of slices of the EDD (a) in the plane δ11|δ33 around the N9 atom and (b) in the plane δ22|δ33 around the N3 atom of 6-(2methoxy)benzylaminopurine (3) highlighting changes in σ (left) and π (right) subspace. Changes in the EDD are schematically shown in a manner to resemble the orbital rotation model. The in-plane (δ11|δ22) cut of isotropic SDD is shown in (c). The arrows represent the relative orientations of the principal components of the 15N NMR CSTs.

lone pair of electrons close to the nitrogen atom (Figure 6b, left) and the increase in the electron density in the π part of the nitrogen subspace (Figure 6b, right) should result in less efficient nLP → π* orbital magnetic interaction (see schematic representation in Figure 6b) that produces less deshielding mainly in the direction of δ11 (red color, Δδ11 = −45 ppm). The reverse EDD patterns for the N9 and N3 atoms (Figure 6a and Figure 6b) are recoded to the reverse isotropic SDD shown in Figure 5b and also as an in-plane slice in Figure 6c. As is clear from this straightforward analysis, the presence of a hydrogen bond is always predominantly manifested in the principal component of the 15N NMR CST that is oriented perpendicular to the hydrogen bond.45 Hence, in the case of the HB donor, it is the δ22 principal component (orange), and in the case of the HB acceptor, it is the δ11 principal component (red). This difference in the orientation of the principal components of the CST between the N−H and N−LP types of nitrogen atoms has been previously described by Grant et al.46 15 N NMR CSTs can also be used to estimate the strength of the intermolecular interactions, as we demonstrate for the two bare nitrogen atoms (bearing lone pairs of electrons) trapped in two different types of N···H−N hydrogen bonds, namely N3 and N7. The N3 is trapped in the dimer through two N3···H− N9 interactions. The formation of this dimer is associated with the calculated elongation of the N9−H distance by 2.1 pm and an interaction energy of −19.36 kcal mol−1. In contrast, N7 is included in the formation of another dimer via two N7···H− N10 bonds characterized by an interaction energy of −11.94 kcal mol−1 and elongation of the N10−H distance by 1.3 pm. Clearly, these two dimers differ significantly in the strength of the interaction between their individual parts, with one of these interactions being characterized by an approximately 50% increase in the corresponding descriptors. Is this difference

SDD, and CSTs? And can we obtain CST, EDD, and SDD patterns for N−H similar to those for C−H? To reveal these dependencies, we analyzed the 15N NMR CSTs for 6-(2-methoxy)benzylaminopurine (3), specifically two principally different types of atoms: N3, a bare nitrogen atom bearing a lone pair (LP) of electrons, and N9, part of an N−H group (being constitutionally similar to the abovementioned C8−H). We obtained a good correlation between the experimentally determined and calculated principal components of the 15N NMR CST (see Table 1 and Figure S4 in the Supporting Information). The EDD for the central molecule is shown in Figure 5a (see also Figure S7 in the Supporting Information). This ground-state EDD is related to the isotropic SDD shown in Figure 5b, a fact which can serve as a basis for rationalizing the changes in the principal components of the CSTs. The analogy between C8−H (see section 3.2) and N9−H is obvious from the results obtained; the CST of the nitrogen atom that represents the HB donor (N9−H) changes predominantly in its δ22 principal component (orange color, Δδ 22 = +55 ppm), which is oriented approximately perpendicularly to the N9−H bond and lies in the plane of the purine ring. Analogously to the C8−H, an increase in the electron density in the σN9−H region close to N9 (Figure 6a, left) and a decrease in the πN9 space (Figure 6a, right) could enhance the σNH → π* orbital magnetic interaction. These changes in the EDD resembling the orbital rotation model (σNH → π* interaction)44 are schematically visualized in Figure 6a (see also Figure S8 in the Supporting Information). The EDD pattern for the second type of nitrogen atom, the one bearing a lone pair of electrons (N3), is approximately the reverse relative to those of the C−H and N−H types (Figures 4 and 5). The decrease in the electron density in the region of the 501

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ABBREVIATIONS NMR, nuclear magnetic resonance; CST, chemical shift tensor; EDD, electron deformation density; SDD, shielding deformation density; LP, lone pair

reflected equally in the nuclear magnetic shielding, and can we observe it experimentally via the CSTs? The DFT calculated difference in the isotropic NMR chemical shift clearly correlates with the interaction energy as shown schematically in Figure S7 in the Supporting Information. Analyzing changes in the individual components of the CST reveals that perturbation of the principal components δ33 (perpendicular to the purine ring, +4 ppm vs +8 ppm; not shown) and δ22 (radial with the HB direction, both are −15 ppm) is almost identical for both HBs, independent of the related interaction energy. Therefore, we emphasize that the strength of the HB interaction is mostly encoded in the change of only a single principal component of the CST of the HB acceptor atom (see Figure 5b). This component, which is oriented perpendicularly to the HB direction, undergoes changes (−30 ppm vs −45 ppm) which are proportional to the differences in the descriptors mentioned above (interaction energy and N−H bond elongation).

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ASSOCIATED CONTENT

S Supporting Information *

Calculated interaction energies, additional figures, simulated CP/MAS NMR spectra, and XYZ coordinates of molecular clusters. This material is available free of charge via the Internet at http://pubs.acs.org.

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4. CONCLUSIONS All of the examples we have discussed in this article confirm that visualization of the real-space changes in electron and isotropic-shielding densities represents a powerful tool for rationalizing and understanding the relationship between the crystal structure and the experimental NMR CSTs. We have demonstrated how the presence and the strength of the hydrogen bonds are reflected in the isotropic 1H NMR chemical shifts and in the principal components of the 13C and 15 N CST. Application of this computational model to interpret effects of the stacking interactions and the interactions with ions is underway in our laboratory. Our approach can be used together with experimental chemical shifts for diverse practical applications, for example, to differentiate between various crystal forms of a compound.

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AUTHOR INFORMATION

Corresponding Author

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

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Czech Science Foundation (P206/11/0550). Access to the computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum provided under the program “Projects of Large Infrastructure for Research, Development, and Innovations” (LM2010005) is highly appreciated. 502

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dx.doi.org/10.1021/jp310967b | J. Phys. Chem. A 2013, 117, 497−503