Received 13 September 2013
A top-down approach to crystal engineering of a racemic 2-isoxazoline
The crystal structure of racemic dimethyl (4RS,5RS)-3-(4-nitrophenyl)-4,5-dihydroisoxazole-4,5-dicarboxylate, C13H12N2O7, has been determined by single-crystal X-ray diffraction. By analysing the degree of growth of the morphologically important crystal faces, a ranking of the most relevant non-covalent interactions determining the crystal structure can be inferred. The morphological information is considered with an approach opposite to the conventional one: instead of searching inside the structure for the potential key interactions and using them to calculate the crystal habit, the observed crystal morphology is used to define the preferential lines of growth of the crystal, and then this information is interpreted by means of density functional theory (DFT) calculations. Comparison with the X-ray structure confirms the validity of the strategy, thus suggesting this top-down approach to be a useful tool for crystal engineering.
The common approach to crystal engineering is based on structural analysis of crystal packing aimed at highlighting the most relevant non-covalent interactions that could make it possible to control and design the synthesis of the solid state for compounds of interest. The information gained from the solid-state arrangement of the building blocks of the crystal allows a wide range of speculations on possible chemical and physical ways to enhance or deplete some of these key interactions. In this framework, insight into packing arrangements provided by the increasingly powerful and easy-to-control X-ray diffraction instruments makes this task easier to carry out. However, it is often limited to inspection of the packing geometry to identify the shortest intermolecular contacts from which the main interactions responsible for the crystal cohesion are inferred. Moreover, these are usually ascribed a priori to well established categories such as various kinds of hydrogen bonds, - interactions, and so on. The pitfalls of this kind of approach have recently been discussed and might present the risk of subjectivity when ranking structural motifs only on the basis of geometrical evidence, without also calculating the interaction energy (Gavezzotti, 2013).
In this paper we invert this conventional approach to crystal engineering by looking at the crystal morphology, by recalling that the outer shape of a crystal must contain valuable information on the microscopic behaviour at the molecular level (Weissbuch et al., 1991, 1995, 2003). According to previous examples (Bacchi et al., 2011), we adopt a rational protocol that starts by identifying the morphologically important (MI) faces that are necessarily related to the main factors that build up the crystal, then performing a geometrical analysis to find objectively the directions of the main interactions. We then derive a quantitative ranking of the energies involved in the process of the crystal building by means of DFT calculations. We do not perform a crystal morphology prediction (Bacchi et al., 2011; Lazo Fraga et al., 2013; Li Destri et al., 2011, 2013; Punzo, 2011, 2013), but consider the real crystal morphology that is experimentally measured and indexed on the diffractometer. Possible inconsistencies between predicted and experimental crystal morphologies could be interpreted on the basis of molecular structures and bond anisotropies, as well as on the fact that computational methods do not fully take into account some relevant experimental factors such as temperature, supersaturation and growth mechanism, or the key role played by the solvent in solution crystallization.
We interpret the experimental morphology on the basis of the periodic bond chain (PBC) theory (Hartman & Bennema, 1980; Bennema et al., 2004), thus assuming that the surface area corresponding to the most prominent MI faces belongs to those showing a slower growth rate, which is in turn proportional to the attachment energy (Ea). Although the attachment energy was originally defined as `the bond energy released when a building unit is attached to the surface of the crystal face concerned' (Hartman & Perdok, 1955), accordingly to current literature (Punzo, 2011) we define it as the energy released by attaching a molecule, or a growth slice, to a growing crystal surface. More specifically, for our purposes, we consider the energy released as a consequence of the interactions normal to the surface of the formula unit within an underlying slice (Punzo, 2011). For this reason, instead of limiting the structural analysis to the crystal packing we consider the structural and energy landscape provided by each MI face as resulting from cutting a slab parallel to that face, thus corresponding to a picture of that particular crystallographic environment. By attaching successive formula units to the slab, we interpret in fine detail the overall process of crystal growth, explained on the basis of the final crystal morphology.
For this work we consider well shaped crystals of dimethyl (4RS,5RS)-3-(4-nitrophenyl)-4,5-dihydroisoxazole-4,5-dicarboxylate (1) (Quilico & Grunanger, 1955), which belongs to the 2-isoxazoline class of compounds that are reported to show antifungal activity (Konopíková et al., 1992) as well as to act as herbicides (Munro & Bit, 1986), and which have also been studied in relation to cycloaddition reactions (Chiacchio et al., 1996, 2002, 2003, 2004; Quadrelli et al., 2004).
The crystal structure of (1), synthesized as reported in the literature (Quilico & Grunanger, 1955), was determined by single-crystal X-ray diffraction on a crystal selected from a batch crystallized from benzene by slow evaporation. Data were collected with Cu K radiation ( = 1.5418 Å) at room temperature (293 K) on a Bruker APEX-II CCD diffractometer; H atoms were located from the difference Fourier map and their coordinates were refined. Crystal data and structure refinement details are reported in Table 1.
From inspection of the crystallization batch, it was evident that all crystals presented a similar growth morphology. This was quantitatively analysed for the selected crystal by measuring crystal dimensions and indexing the faces by means of the SCALE procedure embedded in the APEX2 software (Bruker, 2008). The morphology was analysed using stereographic projections created by the programs KrystalShaper (JCrystalSoft, 2013) and WinWullf (JCrystalSoft, 2009).
All calculations were performed in the gas phase using the GAUSSIAN09 package (Frisch et al., 2009) using the 6-311G(d,p) basis set with the DFT functional wB97XD, which includes empirical dispersion and long-range corrections (Chai & Head-Gordon, 2008). Single-point energy calculations were performed on monomers, dimers, trimers and tetramers, as taken from the X-ray crystal structure, in order to assess their relative stability. Moreover, in order to gain information on the interaction of a single molecule with the (001), (010) and surfaces, models were built by considering a single molecule within the crystal with the 6 (or 7) nearest molecules from the adjacent slab with the proper Miller indices. For these latter models, the calculations were performed on the 6 (or 7) slab molecules and on the nearest interacting single molecule belonging to the adjacent slab.
Prediction and study of the possible crystal morphologies were performed using a preliminary equilibration protocol, by means of the Discover module included in Materials Studio 4.4 (Accelrys, 2003), adopting the molecular mechanics approximation and the COMPASS forcefield (Sun, 1998). The established single-crystal structure was used as the input for energy minimization. A distance cutoff was selected for interactions between molecules, applied as 1.5 times the value calculated in terms of the centroid-to-centroid distance along each lattice vector. An energy cutoff of -2.49 kJ mol-1 was also applied and only interactions with a more stabilizing energy were considered. The morphology protocol itself is based on the so-called GM method, based on the PBC theory. For this purpose, the calculations were performed allowing a minimum interplanar distance (dhkl) of 1.300 Å and a maximum value of 3 for each of the three Miller indices. The overall number of growing faces was limited to 200. All of these calculations correspond to 0 K and surface relaxation was not applied. Furthermore, the surface is considered to be a perfect termination of the bulk. A detailed description of the calculation performed can be found in Punzo (2013).
Compound (1) crystallized from benzene as a racemic mixture in the space group P21/c (Table 1). As shown in Fig. 1, the molecule consists of a nearly planar core comprising the nitro group, the phenyl ring and the isoxazoline heterocycle. The latter bears two methoxyacetyl substituents that stick out almost perpendicularly in opposite directions from the planar molecular core [N2-C7-C8-C10 -101.7 (1), N2-O3-C9-C11 -98.3 (1)°]. The isoxazoline ring is slightly distorted in an envelope conformation, with the C9 atom deviating by 0.38 Å from the ring plane. The molecule bears no obvious functional groups that suggest strong intermolecular interactions. In such a case, the classical approach adopted in most papers is to analyse the shortest intermolecular contacts and to infer that interactions shorter than the sum of van der Waals radii are possibly stabilizing. This approach has been criticized, because without any energy estimation there is no reason to exclude the possibility that such short contacts might be repulsive (Gavezzotti, 2013). We report here this conventional kind of discussion based on interatomic distances, then contrast it with experimental evidence about preferred growth directions derived from the macroscopic crystal morphology.
| || Figure 1 |
Molecular structure of (1), showing displacement ellipsoids at 50% probability for non-H atoms.
Analysis of the shortest intermolecular contacts indicates a possible interaction between one O atom of the nitro group and one electron-poor carboxylic C atom [O2C11i = 3.211 (2) Å; symmetry code: (i) -x,1-y,-z]. The directionality of the contact suggests donation of electron density from the O lone pair perpendicular to the plane of the sp2 carboxylate group. The charge density map calculated by DFT methods (as specified in §2) on the isolated molecule supports the possibility of this interaction (Fig. 2a). This interaction defines a centrosymmetric supramolecular dimer (Fig. 2b). All other short interactomic contacts would usually be interpreted as weak CHO interactions.
| || Figure 2 |
(a) Molecular charge density map resulting from the DFT calculations. (b) Geometrical analysis of the crystal packing, showing the NO2COOCH3 short contact (black dashed lines), building a centrosymmetric supramolecular dimer, and showing all other short CHO contacts as blue dashed lines.
The indexing of the macroscopic crystal morphology allows verification of whether the shortest contacts correspond to stronger interactions in a top-down approach (Bacchi et al., 2011). In Fig. 3 the experimental indexing of the MI faces is shown (a), associated with the corresponding contacts between an incoming molecule and the growing crystal face (b). Relevant faces are , being the largest, followed in order of importance by (010) and , along with their equivalents according to monoclinic symmetry. The relation between outer shape and inner packing was investigated and rationalized with the help of stereographic projections (Fig. 4) according to the procedure outlined previously (Bacchi et al., 2011). The experimentally visible faces (a) are reported on the sphere (inset). The observed faces (hkl) (labelled in white) are built by pairs of non-parallel arrays [uvw] (labelled in red) of intermolecular interactions that actively contribute to the crystal packing through periodic bond chains (PBC), and whose orientations [uvw] may be identified by looking at the stereographic projection of the observed faces (Fig. 4b). Active PBCs should be represented by the [uvw] zone axes (red arcs) corresponding to the directions that intersect at the poles (hkl) of the faces observed experimentally (labelled in black). In summary: we plot on the Wullf sphere all poles representing the low-index faces (black dots in Fig. 4b); we identify the experimentally visible faces (labelled in Fig. 4a); we pick zone axes (red lines in Fig. 4b) that intersect at the poles representing visible faces; these zone axes correspond to the PBCs building up the faces.
| || Figure 3 |
Experimental indexing of the MI faces (a); corresponding contacts between an incoming molecule and the growing face (b).
| || Figure 4 |
Graphical determination of the [uvw] PBC vectors that span the observed faces. (a) Face indices are represented with white labels; inset: position of the projection of the poles corresponding to the experimental faces. (b) Stereographic projection of the low-index faces (black dots). Experimental faces are labelled in black. The [uvw] vectors are represented by the red zone arcs, labelled in red, square brackets. The same [uvw] directions are also labelled in (a), to show how the faces are built.
The resulting PBCs for (1) are PBC1 = , PBC2 = , PBC3 = , and the relation with the experimental crystal faces is indicated at the top of Fig. 5. According to the different development of the crystal along these directions, the strength of the interactions along the PBC should be ranked as PBC1 > PBC2 > PBC3, since the crystal shape is most elongated along  and least along . These directions can be interpreted by looking at the intermolecular interactions along the PBC directions in the crystal packing (Fig. 5). We immediately note that the basic structural building units are the centrosymmetric dimers shown in Fig. 2(b). These are assembled along PBC1 and PBC2 by CHO contacts involving the phenyl H atoms to give sheets that are stacked along PBC3 with CHO contacts involving methyl groups. This is in agreement with the qualitative concept that aromatic CH is a better hydrogen-bond donor than aliphatic CH.
| || Figure 5 |
Ranking of the arrays of the main interactions (periodic bond chains, PBC) in the packing as derived by the analysis of the experimental morphology: chains of supramolecular dimers along PBC1  and along PBC2  build a sheet; the sheets are stacked along PBC3 .
A parallel analysis has been carried out by computing interaction energies based on the morphological considerations. On the basis of the performed indexing, we chose the most relevant crystal growth directions, considering that generally the growth rate for the face is inversely proportional to the surface area of each face (Prywer, 1995, 2001, 2002, 2003, 2004), i.e. the slower the growth, the larger the face surface. On the other hand, the direction perpendicular to the less developed face is the fastest direction of growth and therefore the one bearing the most relevant intermolecular interactions. Once the MI faces are selected, we cut the unit cell for the crystal structure along those directions. It is useful to recall that the choice of these directions was not made on the basis of theoretical or speculative considerations, but on the experimental evidence of crystal growth.
Now that we know along which directions to concentrate our efforts, we analyse for each MI face the stability of molecular dimers, trimers and tetramers. These were chosen considering the architecture giving rise to the most stable setup of aggregates, irrespective of any geometrical consideration. Each successive monomer added to the previously determined building block - i.e. a monomer added to another monomer to generate a dimer, a monomer added to the previously generated dimer to generate a trimer, and so on - was identified by means of the symmetry operations required to generate it. After having ranked the stability of the so-built dimers, trimers and tetramers, we consider a slab of finite area, corresponding to the environment of each MI face, and simulate the attachment of a single molecule.
This approach allows us to confirm by DFT calculations whether the energy involved in the growth process can be predicted at the molecular stage (i.e. considering very simple building blocks, when the crystal is already formed), by attaching new units to the growing surface. The considered geometries are the result of the molecular configuration and relative arrangement of the crystal building blocks, as inferred from the X-ray structure. The geometries were not optimized in order to avoid any possible shift of the atomic positions. As a result, the proposed examples are selected among real experimental landscapes, and not among simulated ones. The resulting interactions are reported in Table 2.
We start by analysing two possible interactions between monomers as shown in Fig. 6, which correspond to the two most stable dimers. In the first case (dimer 1) the two monomers lie edge-on to each other, while in the second case (dimer 2) they form a face-to-face interaction. Taking the reference unit as x,y,z, the first dimer corresponds to the interaction with the molecule generated by the symmetry operator x,y-1,z, that is along the direction of PBC1 (Figs. 5 and 6, top left), while the second dimer corresponds to the interaction with the molecule generated by -x,1-y,-z (Figs. 5 and 6, top right). The second case is stabilized by -stacking interactions as reported in Table 3 and by the contact between the electron-rich O atom of the NO2 group and the electron-poor carboxylic sp2 C atom, as already suggested by the geometrical analysis of the short interactions and by the analysis of the molecular electron density. The relative energies of the two systems, calculated as explained in §2, are reported in Table 4, where the most stable system, i.e. the one with the lower energy, is considered to be zero. The significantly greater stability of dimer 2 (> 41.9 kJ mol-1), which is assembled head-to-tail, thus favouring dipole association, could suggest a possible explanation for why the crystallization yields a racemic mixture. Dimer 2 is centrosymmetric and it gives rise to a characteristic crystal packing where the basic building blocks are chains of dimers.
| || Figure 6 |
(a) The two most stable dimers as inferred by DFT calculations, corresponding to two experimental crystallographic landscapes; dimer 2 is the most stable. (b) The two most stable trimers; trimer 1 is the most stable. (c) The three most stable tetramers. The unit cell is represented to visualize the orientation of the supramolecular aggregates, with the a axis shown in red (along PBC2), b axis in green (along PBC1) and c axis in blue.
We analyse two different possible trimeric arrangements, as reported in Table 4 and Fig. 6. Trimer 1, the most stable, is the result of the attachment to dimer 1 of a molecule generated by the operator x,y+1,z, corresponding to the arrangement present in the (010) face when another molecule attaches on this surface along PBC1. This confirms the suggestion of the stereographic projection being the direction of fastest growth of the crystal perpendicular to this face. A slightly higher energy is calculated for trimer 2, generated by considering the interaction along PBC2 of a molecule generated by 1+x,y,z to dimer 2, thus showing another -stacking interaction (Table 3). This geometry resembles that present on the face, which is actually a face of intermediate surface development among the MI faces along PBC2, once again in agreement with the information in the Wulff plot.
A similar approach can be applied to tetramers (Fig. 6), and we have considered only three different tetramers representative of the MI faces (see Table 4). Tetramer 1 is the most stable and results from the attachment of a molecule generated by 1-x,2-y,-z to trimer 1, approaching it from below along PBC1. This is the growth direction of the (010) face, and the picture could be interpreted as a description of the possible crystal nucleation, where the original most stable dimer is approached by new building blocks to give rise to fast crystal growth along the PBC1 direction. Tetramer 2 is slightly less stable, in spite of the already mentioned -stacking interactions (Table 3), as in dimer 2. It results from the attachment of two molecules to dimer 2, one generated by x-1,y,z and another by 1-x,1-y,-z. This is the direction of growth of the face along PBC2 , confirming the overall face growth by means of the energy ranking. The robustness of trimer 1 as the basic building unit is shown by considering that tetramer 3, generated by the addition to trimer 2 of a monomer along PBC1 (symmetry operator x, y-1,z) is less stable by far.
After having performed the basic interaction analysis at the molecular level, we extend our study by considering different slabs of the crystal, corresponding to finite portions of the MI faces. For this purpose, we first calculate the energy for the single standalone monomer (Em), as in the previous case. Then, after considering all of its interactions with a definite slab representing the considered MI face, whose energy was already calculated (Es), we compute the overall energy of the system (Esm). We subtract Es from Esm in order to compare the energy of the standalone monomer with the interacting one. Furthermore, we compute the possible energy surplus by defining Em = Esm - Es - Em. In order to avoid any possible inequality as a result of the different number of interactions considered for a single monomer and, more critically, having dealt with slabs containing different numbers of fragments, we normalize these calculations for a single monomer (Em/Ns). The results obtained are reported in Table 5. They illustrate the landscape more completely and clearly than in the previous analysis which was confined to discrete numbers of aggregates, and they confirm the results already obtained. In summary: (010) has the greatest attachment energy Ea and this is the smallest face but the fastest direction of growth; the  direction, normal to this face, corresponds to PBC1 according to morphology considerations (see Fig. 4). The face has the second largest Ea, and the morphological analysis shown in Fig. 4 confirms that the growth direction  normal to this face corresponds to PBC2. Finally, face (001) has the smallest Ea, confirming that the direction normal to it, , is the weakest periodic bond chain, i.e. PBC3.
| || Figure 7 |
(a) (001), (b) and (c) (010) slabs corresponding to each MI face with each incoming monomer. Dashed yellow lines are the shortest contacts reported in Table 2.
The results obtained were compared with those inferred by a morphology prediction, performed as described in §2. The obtained crystal habit is provided in the supporting information,1 together with a table reporting the computed MI faces. Although the overall crystal shape is roughly confirmed as expected (Punzo, 2011), the specific list of the MI faces is only partially reproduced by the prediction. In fact, only the (001) face [reported as (002)] is present, while the other MI faces are not even reported as less important ones. These results suggest that the standard (Punzo, 2013) forcefield-based approach to morphology prediction is not completely reliable. As always, the pitfalls of the theoretical predictions are not only due to the chosen algorithms and forcefields, but more often to the role of solvent. The calculations are carried out in vacuo, but no more realistic results are achieved whether the solvent is considered explicitly or not. However, arguments about the role of the solvent can be interpreted as a potential tool for fine tuning of the crystal habit.
All experimental attempts to use other solvents gave rise to thinner crystals, such as in the case of a 1:1 mixture of n-hexane and benzene. This feature can be related to an even faster growth along the PBC1 direction perpendicular to the (010) face. As a consequence, we can assume that the presence of a fraction of a different solvent allows further stabilization in terms of Ea, thus speeding up the crystal growth along that face. This should be due to an even weaker interaction by n-hexane molecules with those cropping out from the (010) face. A possible interpretation could be the diminished possibility of -stacking interactions, which can be offered by benzene and not by n-hexane, which could influence the crystal growth relative to that in pure benzene solution, thus altering the final habit.
The experimental indexing, being directly related to the evidence observed, is in principle more reliable than a computationally inferred crystal morphology. The algorithms used for morphology prediction have a well known tendency to overestimate the amount and relative percentage of the MI faces (Punzo, 2011; Lazo Fraga et al., 2013; Punzo, 2013). This is proved by the results of our morphology prediction (in the supporting information ) which confirm, in principle, the landscape inferred by the experimental measurements, but predict the existence of some less relevant MI faces in the apical part of the crystal which were not actually present in the real sample. The demonstrated computational analysis, on the other hand, provides a complete picture of the key interactions in the crystal. It is based on, and driven by, the experimental morphological inspection, and allows more specific considerations about the cooperative role of all of the considered non-covalent interactions, compared with the traditional analysis of a crystal structure. The present study shows that, starting from the macroscopic observation of the crystal, we can considerably aid the crystal engineering approach. Instead of relying on purely speculative considerations, our analysis is guided at the molecular level on the basis of the real experimental crystal growth.
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