Structure and interactions in benzamide molecular crystals Philipp Ectors 1, Dominique Ectors 2, Dirk Zahn 1 1) Lehrstuhl für Theoretische Chemie/Computer-Chemie-Centrum Friedrich-Alexander- Universität Erlangen-Nürnberg, Nägelsbacher Str. 25, D-91052 Erlangen, Germany. 2) Lehrstuhl für Mineralogie, Friedrich-Alexander-Universität Erlangen-Nürnberg Schlossgarten 5a, 91054 Erlangen, Germany. This is the pre-peer reviewed version of the following article: Structure and interactions in benzamide molecular crystals Philipp Ectors, Dominique Ectors, Dirk Zahn; Molecular Simulation Vol. 39, Iss. 13, 2013, which has been published in final form at DOI:10.1080/08927022.2013.794274. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self- Archiving.
Structure and interactions in benzamide molecular crystals Philipp Ectors, 1 Dominique Ectors, 2 Dirk Zahn 1,* 1 Lehrstuhl für Theoretische Chemie/Computer-Chemie-Centrum Friedrich-Alexander-Universität Erlangen-Nürnberg, Nägelsbacher Str. 25, D-91052 Erlangen, Germany. 2 Lehrstuhl für Mineralogie, Friedrich-Alexander-Universität Erlangen-Nürnberg Schlossgarten 5a, 91054 Erlangen, Germany. *Corresponding author E-mail: dirk.zahn@chemie.uni-erlangen.de
ABSTRACT We resolve discrepancies concerning the experimentally determined structure of benzamide molecular crystals from dispersion-corrected density functional calculations. A clear energy ranking is obtained for the two candidates of the stable (P1) modification of benzamide. This is rationalized by subtle differences of the molecular interactions in the molecular crystal. The potential energy of the different structures is dominated by the interplay of intermolecular attraction and molecular torsion/deformation to accommodate favourable hydrogen bonded networks. Using suitable proxies arranged in pseudocrystalline setups we discriminate the contribution of electrostatics, π-π interactions and intra-molecular interactions to the lattice energies. KEYWORDS Crystal Structure Molecular simulation Molecular Interactions
Introduction The identification and understanding of the structure of molecular crystals is of considerable importance to both academia and industry, namely for controlling pharmaceutics production and metabolism. This ongoing challenge to both experiment and theory is nicely reflected by benzamide molecular crystals which, since its discovery almost 200 years ago, became an increasingly prominent test case system for the exploration of molecular crystal polymorphism in general and of pharmaceuticals stability in particular [1-3]. Despite this attention, there is a serious discrepancy concerning the experimentally refined crystal structures of the stable form (P1) of benzamide. In figure 1 the two qualitatively different structure candidates of Gao et al. (ref. [4], named P1) and Thun et al. (refs. [1,3], named P1 ) are illustrated. While the packing of benzene rings and the arrangement of the hydrogen bonded network are very similar, the main difference is given by the interaction of the polar moieties with the π-system. In principle, one of these structures could be a yet unnoticed part of the still ongoing search for polymorphs of benzamide. This however would impose that both structures are of similar formation energy. In what follows, we discriminate the two structure candidates for the benzamide crystal from state-ofthe-art quantum calculation. Moreover, by constructing artificial crystals comprising fragments of benzamide we contrast benzene and amide pseudo crystals arranged at lattice sites and orientations corresponding to the benzamide crystal structure, thus isolating different types of molecular interactions that constitute the differences of P1 and P1 type structures of benzamide crystals.
Theory Density-functional theory calculations were perfomed for benzamide, formamide and benzene molecular crystals, based on the P1 and P1 structures of benzamide [5] (see also figure 1). Both unit cells comprise 4 explicit molecules, whilst the remaining molecular interactions are mimicked by periodic boundary conditions. We use the Perdew-Burke-Ernzerhof exchange corrleation functional [6], ultrasoft pseudopotentials with a plane wave cutoff of 35 Ry and a secondary cutoff of 180 Ry along with an empirical dispersion correction as proposed by Grimme [7]. A Monkohorst k-point grid of 4x4x1 is applied throughout all crystal calculations [8]. For the investigation of isolated molecules a single molecule was placed in a pseudo-crystal of sufficiently large unit cell (corresponding to a 3 3 1 supercell) to avoid intermolecular interactions from periodic boundary conditions. Results Unit cells for the two structure candidates P1 and P1 as obtained from experiment of Gao et al. [4] and Thun et al. [1,3], respectively, were subjected to dispersion corrected density-functional theory calculations. Structure optimisation was performed from potential energy minimization at variable cell size and shape without imposing symmetry operations other than periodic boundary conditions. The fully relaxed crystal structures are shown in figure 1 and the relaxed cell parameters are denoted in table 1. Despite much similarity between the two structures, we found a significant energetic difference for the two arrangements of benzamide. Indeed, the structure P1 is disfavoured by almost 3 kj mol -1 per molecule, over the P1 structure. Moreover, the volume of the P1 unit cell (at 0 Kelvin) is 1.5 % smaller than for the P1 structure, hinting at a denser and stronger packing of the molecules.
The difference in potential energy might appear surprising, because at first sight both crystal structures exhibit strong similarities. Indeed, the packing of benzene rings is practically identical and also the hydrogen bonded network is analogous in both structures (fig. 1 and table 2). Nevertheless, the two structures differ in terms of interactions of the benzene rings with the polar amide groups which N-benzene and O-benzene contacts can be interpreted as (preferred) cation-π and (less favoured) anion-π interactions, respectively. Figure 2 highlights the exchanged roles of N and O in P1 and P1 for this interaction. To confirm this interpretation, it is educative to rationalize the different interaction types by means of artificially arranged pseudocrystals of proxy molecules that mimic selected interaction types on an exclusive basis. For example, the role of hydrogen bonding in P1 and P1 may be illustrated by investigating a formamide pseudocrystal of the same hydrogen bonded network as observed in the P1 and P1 structures of benzamide crystals. This was accomplished by freezing the atoms of the amide moiety according to the benzamide crystal whilst replacing the aromatic fragment by a hydrogen atom (and exclusively relaxing the newly formed C-H bond). Similarly, the role of the π -π interactions can be mimicked by a virtual benzene crystal using identical atomic positions as in P1/P1 but replacing the amide group by a hydrogen atom (and again relaxing the newly formed C-H bond). Apart from such discrimination of contributions to intermolecular interactions in benzamide, we also calculated the intramolecular energy resulting from deformation of the molecules in terms of torsion and N-C-O valance angle. For this, isolated benzamide molecules as cut from the P1 and P1 crystal structures (i.e. freezing the atomic positions) were compared to the freely relaxed molecular structure.
Within the obvious limitations of accepting formamide and benzene as proxies for hydrogen bonding and π-π interaction, respectively, This allows to attribute the preference of P1 over P1 to the following sum of contributions: ΔE (P1-P1 ) = - 3.9 kj mol -1 (intramolecular deformation) + - 1.6 kj mol -1 (hydrogen bonding) + + 3.7 kj mol -1 (π-π interaction) + - 9.5 kj mol -1 (amide group - π interaction) = - 11.3 kj mol -1 per molecule. Note that the cation/anion -π type interaction could not be calculated directly, but (in lack of a suitable proxy molecule) were taken as the rest in the above energy balance to reach the overall preference of 3 kj mol -1. In view of the observed misconception concerning the alignment of benzamide molecules in the P1 structure, we furthermore checked on the known polymorphs P2, P3 and a recently suggested highpressure form P4 [4,9-11]. While the crystal structures of P3 and P4 [11] were confimed, our DFT calculations including full cell optimization showed inversion of the amide group to be drastically preferred for P2 [9,10]. Indeed, the energy per molecule was found as 14.1 lower upon 180 rotation of the amide group and subsequent relaxation for P2. Moreover, improved molecular packing is concluded for this structure from a reduction of the volume demand per molecule V(P2)-V(P2 ) which amounts to 17,4 Å 3 per molecule. Conclusion
It is noteworthy that the packing of benzene moieties and the hydrogen bonded network exhibits only minor differences for both P1 type structures (table 1). Because of this structural similarity it appears rather unlikely to us that by use of specific solvent or template surface a syntheses route could be designed to discriminate between the P1 and P1 structures of benzamide. Without preference from such external parameters both structure types compete on the basis of potential energy. The latter favours P1 by about 3 kj mol -1 per molecule, mainly as a consequence of the different N-benzene and O- benzene contacts in P1 and P1, respectively. Our calculation furthermore suggest that the experimentally derived P2 should be corrected to P2.
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a b c Fig.1a Illustration of phase P1 as obtained from ab-initio relaxation of the crystal structure suggested by Gao et al. [4] from neutron diffraction. The hydrogen bonded network is indicated by dashed grey lines. Nearest intermolecular distances of O C and N C contacts are illustrated in red and blue respectively.
a b c Fig 1b Analogous to figure 1a, but shown for the phase P1 as derived from ab-initio relaxation of the structure suggested by Thun et. al [1,3] Note that the tilting of the amide group with respect to the phenyl group implies that P1 and P1 (21,54 and 24,10, respectively) cannot be matched by symmetry operations. This results in subtle but important differences of the distance distribution as shown in fig. 3 and table 1.
Potential energy per molecule / kjmol -1 P1(confirmation run) P1 P1 Volume per molecule / Å 3 Fig.2 Energy versus volume diagram of the benzamide crystal structures after relaxation from ab-initio calculations. To confirm the different structural features of P1 and P1, an additional simulation was prepared from exchanging the amino and carbonyl groups in P1. After relaxation, the corresponding structure was found as practically identical to that of P1.
P1 N C O C P1 1 Å 2 Å 3 Å 1 Å 2 Å 3 Å Fig. 3 Occurrence profile of the N C and O C contacts in structures P1 (top) and P1 (bottom). Note that the N C and O C distances are practically exchanged in both structures.
P1 P1' (P1 ) (confirmation run) alpha 89.96 (90 ) 92.50 (90 ) 90.11 beta 86.30 (89.22 ) 86.76 (90.641 ) 86.76 gamma 90.09 (90 ) 88.91 (90 ) 90.10 a / Å 5.438 (5.549) 5.420 (5.6094) 5.408 b / Å 4.973 (5.033) 5.056 (5.0399) 4.971 c / Å 20.316 (21.548) V / Å -3 per molecule E / kj mol -1 per molecule 137.069 (150.435) 20.321 (22.1171) 138.837 (156.3075) 20.399 136.891-117.6 E(P1) + 2.8 E(P1) + 0.02 Table 1: Unit cell parameters as obtained for the different crystal structure candidates of P1 after full relaxation of atomic positions and cell size and shape. The values in brackets refer to experimental data measured at ambient conditions. The confirmation run (P1 ) refers to amide rotation in P1 and subsequent relaxation. Note the closeness of resulting structure with P1.
Distance / Å P1 P1 N C 3,217 3,326 / 3,369 (two peaks) O C 3,331 3,130 (double peak) H-bond (dimers) 1,815 / 1,814 1,817 / 1,796 H-bond (layers) 1,873 / 1,874 1,902 / 1,968 Table 2 Nearest neighbor distances of intermolecular contacts in the benzamide crystal structures P1 and P1 as obtained from ab-initio relaxation of the experimentally determined structures from Gao et. al and Thun et al., respectively. Note that d(n C) < d(o C) in P1, whilst the opposite relation is observed in P1. The energetic disfavoring of P1 over P1 may also be attributed to a less ordered distribution of H- O distances in the else wise analogous network of hydrogen bonds. Therein, benzamide is organized as dimers (along the horizontal direction in fig.1) which are interconnected by further hydrogen bonds leading to (001) layers.