- Email: [email protected]
A new polymorph (IV) of benzamide: Structural characterization and mechanism of the I ↔ IV phase transition
Chemical Physics Letters 514 (2011) 274–277
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
A new polymorph (IV) of benzamide: Structural characterization and mechanism of the I M IV phase transition David M. Benoit a,1, Philipp Ectors b, Patrick Duchstein b, Josef Breu c, Dirk Zahn b,⇑ a
Nachwuchsgruppe Theorie – SFB 569, Universität Ulm, 89081 Ulm, Germany Lehrstuhl für Theoretische Chemie/Computer Chemie Centrum, Friedrich-Alexander Universität Erlangen-Nürnberg, Nägelsbachstraße 25, 91052 Erlangen, Germany c Lehrstuhl für Anorganische Chemie I, Universität Bayreuth, D-95440 Bayreuth, Germany b
a r t i c l e
i n f o
Article history: Received 9 May 2011 In final form 23 August 2011 Available online 27 August 2011
a b s t r a c t We present a molecular simulation study dedicated to the manifold of benzamide crystal structures. Along this line, a new polymorph (IV) is identified and structurally characterized. The new polymorph exhibits the same hydrogen bonded network as the stable form (I), but differs in the arrangement of molecular layers. From high-pressure molecular dynamics simulations, the I–IV transformation mechanism is suggested as the anti-parallel shuffling of (0 1 0) layers along the [1 0 0] direction. This results in a more compact benzole ring stacking and an increase in density. Thus, high-pressure synthesis is suggested as a route to the yet unconfirmed polymorph IV. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Since its discovery almost 200 years ago, the polymorphism of benzamide poses an ongoing challenge to both experiment and theory. Indeed, benzamide became an increasingly prominent test case system for the exploration of molecular crystal polymorphism in general and of pharmaceuticals stability in particular [1–3]. While the metabolic activity of benzamide itself is rather weak, from a chemical point of view, this molecule exhibits key characteristics of a drug compounds in general. Namely, the molecular interactions of benzamide result from a combination of p–p stacking of the aromatic moiety and hydrogen bonding. So far, molecular modeling approaches to the polymorphism of benzamide provided insights that are promising from a qualitative point of view – crystal structure searches could identify two of the known polymorphs, i.e. I and III and provide structural details in reasonable agreement with experiment. However, the assessment of phase II and quantitative information such as reliable lattice energies remains problematic. The different polymorphs of benzamide exhibit very similar (overall degrees of) hydrogen bonding and thus mainly differ in terms of the interactions of the benzole rings. As a consequence, energetic differences are small and a proper assessment requires very accurate methods. Breu and coworkers tested a small series of general purpose force-fields and observed
⇑ Corresponding author. E-mail address: [email protected] (D. Zahn). Present address: Department of Chemistry, The University of Hull Cottingham Road, Kingston upon Hull HU6 7RX, United Kingdom. 1
0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.08.071
rather strong differences in potential energy values even if the atomic arrangements were quite comparable [2]. Here, we present a more detailed molecular model of benzamide that fully considers molecular flexibility. On this basis, molecular dynamics runs at different temperature and, more importantly, at different pressure conditions are performed to further scan the configurational manifold of benzamide molecular crystals. 2. Simulation details 2.1. DFT calculations Periodic density functional theory in the GAUSSIAN and plane waves formalism [4] were performed on the different polymorphs of crystalline benzamide. We used the Perdew–Burke–Ernzerhof exchange correlation functional [5] and norm-conserving pseudo potentials [6–8] to remove core electrons, along with a triple-zeta quality GAUSSIAN basis set with double polarization [9] optimized for molecular systems (TZV2P-MOLOPT). A cutoff energy of 400 Ry for the plane waves, Ewald summation and an analytical expression for the stress tensor was applied. In order to account for the dispersion forces within the density functional approach, the empirical correction (DFT-D2) as suggested by Grimme was considered [10]. This has been shown to provide qualitative improvements for weakly bonded systems. Starting from the experimental lattice constants and atomic positions for each phase, we performed a full optimization of the system (lattice vectors and atomic positions) until both atomic gradients are below 1 10 3 Hartree/Å and the cell pressure is lower than 100 bar.
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D.M. Benoit et al. / Chemical Physics Letters 514 (2011) 274–277
2.2. Force field We used the General Amber force field [11] for parameterization of the atoms. Partial charges were derived by doing a HF/631G⁄ calculation on the optimized structure, followed by a 2-stage RESP-fit [12]. Potentials for bonds, valence angles, dihedrals, as well as Van der Waals parameters were set according to the GAFF Parameter set. 3
2
NH 2 1
4 5
7
O
6
Atom
Charge
Type
C1 C2 C3 C4 C5 C6 C7 H2 H3 H4 H5 H6 O N HN
0.0688 0.0994 0.1591 0.1252 0.1288 0.1072 0.7151 0.1158 0.1426 0.1413 0.1360 0.1326 0.5649 0.8920 0.3810
CA CA CA CA CA CA C HA HA HA HA HA O N HN
Figure 1. Stable structure of benzamide at ambient conditions. The volume per molecule amounts to 0.156 nm3. High pressure induces the anti-parallel shuffling of (0 1 0) layers as indicated by the arrows.
allow for cell shape variations. While the simulations reported in the following were performed at room temperature, for all polymorphs thermal stability was assessed up to about 400 K. 3. Results To demonstrate the validity of the force field we prepared supercell models of the three known polymorphs (I–III) as described in the Section 2. Using separate simulation models, molecular dynamics simulations at were performed ambient conditions to confirm polymorph stability. On this basis indeed all of the experimentally identified crystal structures were found to be (meta) stable. This reflects an important prerequisite to the suitability of the simulation models to describe benzamide polymorphism and represents a significant improvement to prior modeling studies which could not assess the metastable polymorph II [2]. However, while the structures are reproduced quite reasonably, a serious shortcoming is given by the limited accuracy in assessing lattice energies (Table 1). Indeed, the ordering of lattice energy levels of the polymorphs as obtained from model calculations reads III < I < II which is in contradiction to the experiment [1]. While the phase I reflects the stable form, polymorphs II and III are known to transform to I within hours and days, respectively. From a more qualitative point of view, force-fields and low level quantum models may still provide valuable insights as long as the focus is set to structural characterization. Indeed, the usage of simple and approximate interaction models is widely spread for the
2.3. Simulation models The simulation models for phases I–III were prepared as 8 9 2, 3 3 9 and 9 8 2 supercells [1] and periodic boundary conditions. This corresponds to roughly cubic simulation boxes which dimensions range from 4.2 to 4.8 nm. The overall number of explicitly considered benzamide molecules are 576, 648 and 576 for the simulation systems mimicking phases I–III, respectively. 2.4. Molecular dynamics simulations The molecular dynamics simulations were performed for supercell models of several nm dimensions. A time-step of 1 fs was used and Ewald summation with a real space cut-off of 1.2 nm was applied. The simulations were performed in the constant-pressure, constant temperature ensemble using an anisotropic barostat to
Table 1 Cell constants and potential energy as derived from molecular dynamics simulations at 300 K and 1 atm. Experimental values according to Ref. [3] are denoted in brackets. Note that the energy differences are in contradiction to the experimentally observed polymorph stability I < III II.
a/Å b/Å c/Å a/° b/° C/° Unit cell volume/Å3 Volume per molecule/Å3 Energy in kJ/mol per molecule:
I
II
III
IV (hypothetic)
5.64345 (5.6094) 5.07049 (5.0399) 22.25124 (22.1171) 90.00 (90) 90.00 (90.641) 90.00 (90) 636.72 (625.23) 159.18 (156.3075) 138.93
17.37628 (17.4317) 14.64495 (14.1944) 5.20159 (4977) 88.03 (90) 90.56 (90) 90.48 (90) 1322.8 (1231.4) 165.35 (153.925) 138.74
5.08162 (5.0569) 5.54293 (5.5159) 22.69036 (22.5010) 90.00 (90) 90.00 (91.36) 90.00 (90) 639.12 (627.50) 159.78 (156.875) 140.97
9.56105 5.10898 30.55187 90.00 55.69 89.99 1232.72 154.09 144.01
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D.M. Benoit et al. / Chemical Physics Letters 514 (2011) 274–277
Figure 2. Pressure-induced formation of a new benzamide polymorph (IV) which is metastable at ambient conditions. The volume per molecule amounts to 0.144 nm3. While the hydrogen bonded network and p–p interactions along the c-axis remain practically unchanged, the packing of layers is improved by additional p–p interactions between (0 1 0) layers (see also Figure 1).
Figure 3. (a) Illustration of the unit cell of the benzamide polymorph IV. Hydrogen bonding only occurs within (0 0 1) layers as highlighted in green and at different orientation in Figure 3b. (b) Illustration of a single (0 1 0) layer of the benzamide polymorph IV. Hydrogen bonding only occurs within such layers and is highlighted in green (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
scanning of the configurational manifold of solids whilst energetic ranking is typically performed by more sophisticated approaches [13–19]. The advantage of this concept is given by the efficient screening of putative structures and the focus of computationally more demanding approaches to local relaxation or even single point energy calculations [19]. We thus performed more accurate DFT calculations using a variety of state-of-the-art approaches as described in the Section 2. For both, force-field and DFT calculations all polymorphs discussed in this Letter were found as metastable structures, i.e. correspond to local minima in the potential energy landscape. Strikingly, the expected I < III < II ordering of energy levels could still not be assessed. It is reasonable to expect difficulties in modeling the p–p interactions to account for this inaccuracy. On the basis of the flexible GAFF force field approach Facelli and coworkers performed a polymorph search for a series of organic crystals, including benzamide [17]. From this, the experimental structure, polymorph I, was ranked 38 whilst the top 300 struc-
tures are within less than 10 kJ/mol. The closeness of the energy levels of the different polymorphs indicates that force fields represent a reasonable basis for assessing structures, but call for better accuracy to allow proper polymorph ranking. Similarly, we can expect force fields to provide reasonable qualitative insights into the transition mechanisms of polymorphic transformations which is the aim of the present study. We performed a series of molecular dynamics simulations to further scan the configurational manifold of benzamide crystals. While heating ? cooling ? heating runs were found to either exhibit the polymorph used as starting point or melting and glass formation, low-pressure ? high-pressure ? low-pressure cycles succeeded in stimulating solid state phase transitions. Starting from supercell models of phases I–III, high-pressure was applied for 50 ps, followed by 50 ps relaxation at ambient conditions and further 50 ps for sampling the (putatively) new configuration. Applying elevated pressure of 10, 50, 100 and 250 bar most runs resulted in amorphisation rather than inducing II ? I or III ? I transformations.
D.M. Benoit et al. / Chemical Physics Letters 514 (2011) 274–277
However, the overall approach is much more promising for the search of high-pressure polymorphs which was indeed identified from a simulation run starting from the stable form I. The new polymorph, suggested as IV, is obtained by a pressureinduced a I ? IV transformation as illustrated in Figures 1 and 2. The overall mechanism is given by the sliding of (0 1 0) layers in an anti-parallel fashion along the a-axis. This layer shuffling by ±a/2 leads to a more compact stacking of the benzole rings which are now arranged as quartets of parallel pi-systems, whilst phase I may be interpreted in terms of pairs of staggered pi-systems. This increase of p–p interactions is accompanied by a considerable reduction of the distance of the benzole groups. In phase I the pairs of staggered benzole rings are separated by 3.7 Å, in phase IV the quartets of parallel rings split into two pairs separated by 3.1 and 2.7 Å, respectively. Strikingly, the hydrogen bonded network of benzamide in phase I is only marginally deformed, but not altered during the I ? IV transition (Figure 3a and b). Thus, the hydrogen bonded (0 1 0) layers are shifted as a whole and phase stability of both polymorphs is triggered by p–p-interactions, intramolecular deformation and volume work. The latter provides a guide to the synthesis of benzamide IV. While the density of phases I–III are very similar at room temperature and ambient pressure, the density of polymorph IV is larger than that of phase I. The volume difference was observed as 12% at zero Kelvin (assessed from force-field and DFT calculations) and 8% at room temperature (assessed from force-field based molecular dynamics simulations, only). Hence, we suggest highpressure experiments to confirm the predicted polymorph IV. 4. Conclusions Molecular modeling of benzamide and its variety of crystalline forms represents an ongoing challenge. Here, we presented significant progress, namely the outline of a flexible force-field that offers the study of all known polymorphic structures. While reliable lattice energies exceeded the scope even of state-of-the
277
art DFT calculations, more qualitative insights are at reach. Along this line, we used molecular dynamics simulations to predict a new polymorph (IV). This polymorph may be obtained from phase I via a pressure-induced phase transformation that leads to a more compact packing of the benzole rings. The mechanism is suggested as the anti-parallel shuffling of (0 1 0) layers by ±a/2 along the [1 0 0] direction. Acknowledgments We gratefully acknowledge financial support from the Deutsche Forschungs-gemeinschaft (DFG), and the states of Bayern and Baden-Württemberg for computation time on the RRZE and the bwGRID cluster, respectively. References [1] J. Thun, L. Seyfarth, J. Senker, R.E. Dinnebier, J. Breu, Angew. Chem. Int. Ed. 46 (2007) 6729. [2] J. Thun, M. Schoeffel, J. Breu, Mol. Simulation 34 (10) (2008) 1359. [3] J. Thun, L. Seyfarth, C. Butterhof, J. Senker, R.E. Dinnebier, J. Breu, Cryst. Growth Des. 9 (5) (2009) 2435. [4] J. VandeVondele, M. Krack, F. Mohamed, M. Parinello, T. Chassaing, J. Hutter, J. Comput. Phys. Commun. 167 (2) (2005) 103. [5] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (18) (1996) 3865. [6] S. Goedecker, M. Teter, J. Hutter, Phys. Rev. B 54 (3) (1996) 1703. [7] C. Hartwigsen, S. Goedecker, J. Hutter, Phys. Rev. B 58 (7) (1998) 3641. [8] M. Krack, Theor. Chem. Acc. 114 (1–3) (2005) 145. [9] J. VandeVondele, J. Hutter, J. Chem. Phys. 127 (11) (2007) 114105. [10] S. Grimme, J. Comput. Chem. 27 (15) (2006) 1787. [11] J. Wang, R.M. Wolf, J.W. Caldwell, P.A. Kollmann, D.A. Case, J. Comput. Chem. 25 (2004) 1157. [12] C.I. Bayly, P. Cieplak, W. Cornell, P.A. Kollmann, J. Phys. Chem. 97 (1993) 10269. [13] C. Schön, M. Jansen, Angew. Chem. Int. Ed. 35 (1996) 1286. [14] M. Jansen, Angew. Chem. Int. Ed. 41 (2002) 3746. [15] A. Gavezzotti, Cryst. Eng. Commun. 5 (2003) 429. [16] M. Jansen, J.C. Schön, Angew. Chem. Int. Ed. 45 (2006) 3406. [17] S. Kim, A.M. Orendt, M.B. Ferraro, J.C. Facelli, J. Comp. Chem. 30 (2009) 1973. [18] M. Jansen, K. Doll, J.C. Schön, Acta Cryst. A 66 (2010) 518. [19] J. Anwar, D. Zahn, Angew. Chem. Int. Ed. 50 (2011) 1996.
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
A new polymorph (IV) of benzamide: Structural characterization and mechanism of the I M IV phase transition David M. Benoit a,1, Philipp Ectors b, Patrick Duchstein b, Josef Breu c, Dirk Zahn b,⇑ a
Nachwuchsgruppe Theorie – SFB 569, Universität Ulm, 89081 Ulm, Germany Lehrstuhl für Theoretische Chemie/Computer Chemie Centrum, Friedrich-Alexander Universität Erlangen-Nürnberg, Nägelsbachstraße 25, 91052 Erlangen, Germany c Lehrstuhl für Anorganische Chemie I, Universität Bayreuth, D-95440 Bayreuth, Germany b
a r t i c l e
i n f o
Article history: Received 9 May 2011 In final form 23 August 2011 Available online 27 August 2011
a b s t r a c t We present a molecular simulation study dedicated to the manifold of benzamide crystal structures. Along this line, a new polymorph (IV) is identified and structurally characterized. The new polymorph exhibits the same hydrogen bonded network as the stable form (I), but differs in the arrangement of molecular layers. From high-pressure molecular dynamics simulations, the I–IV transformation mechanism is suggested as the anti-parallel shuffling of (0 1 0) layers along the [1 0 0] direction. This results in a more compact benzole ring stacking and an increase in density. Thus, high-pressure synthesis is suggested as a route to the yet unconfirmed polymorph IV. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Since its discovery almost 200 years ago, the polymorphism of benzamide poses an ongoing challenge to both experiment and theory. Indeed, benzamide became an increasingly prominent test case system for the exploration of molecular crystal polymorphism in general and of pharmaceuticals stability in particular [1–3]. While the metabolic activity of benzamide itself is rather weak, from a chemical point of view, this molecule exhibits key characteristics of a drug compounds in general. Namely, the molecular interactions of benzamide result from a combination of p–p stacking of the aromatic moiety and hydrogen bonding. So far, molecular modeling approaches to the polymorphism of benzamide provided insights that are promising from a qualitative point of view – crystal structure searches could identify two of the known polymorphs, i.e. I and III and provide structural details in reasonable agreement with experiment. However, the assessment of phase II and quantitative information such as reliable lattice energies remains problematic. The different polymorphs of benzamide exhibit very similar (overall degrees of) hydrogen bonding and thus mainly differ in terms of the interactions of the benzole rings. As a consequence, energetic differences are small and a proper assessment requires very accurate methods. Breu and coworkers tested a small series of general purpose force-fields and observed
⇑ Corresponding author. E-mail address: [email protected] (D. Zahn). Present address: Department of Chemistry, The University of Hull Cottingham Road, Kingston upon Hull HU6 7RX, United Kingdom. 1
0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.08.071
rather strong differences in potential energy values even if the atomic arrangements were quite comparable [2]. Here, we present a more detailed molecular model of benzamide that fully considers molecular flexibility. On this basis, molecular dynamics runs at different temperature and, more importantly, at different pressure conditions are performed to further scan the configurational manifold of benzamide molecular crystals. 2. Simulation details 2.1. DFT calculations Periodic density functional theory in the GAUSSIAN and plane waves formalism [4] were performed on the different polymorphs of crystalline benzamide. We used the Perdew–Burke–Ernzerhof exchange correlation functional [5] and norm-conserving pseudo potentials [6–8] to remove core electrons, along with a triple-zeta quality GAUSSIAN basis set with double polarization [9] optimized for molecular systems (TZV2P-MOLOPT). A cutoff energy of 400 Ry for the plane waves, Ewald summation and an analytical expression for the stress tensor was applied. In order to account for the dispersion forces within the density functional approach, the empirical correction (DFT-D2) as suggested by Grimme was considered [10]. This has been shown to provide qualitative improvements for weakly bonded systems. Starting from the experimental lattice constants and atomic positions for each phase, we performed a full optimization of the system (lattice vectors and atomic positions) until both atomic gradients are below 1 10 3 Hartree/Å and the cell pressure is lower than 100 bar.
275
D.M. Benoit et al. / Chemical Physics Letters 514 (2011) 274–277
2.2. Force field We used the General Amber force field [11] for parameterization of the atoms. Partial charges were derived by doing a HF/631G⁄ calculation on the optimized structure, followed by a 2-stage RESP-fit [12]. Potentials for bonds, valence angles, dihedrals, as well as Van der Waals parameters were set according to the GAFF Parameter set. 3
2
NH 2 1
4 5
7
O
6
Atom
Charge
Type
C1 C2 C3 C4 C5 C6 C7 H2 H3 H4 H5 H6 O N HN
0.0688 0.0994 0.1591 0.1252 0.1288 0.1072 0.7151 0.1158 0.1426 0.1413 0.1360 0.1326 0.5649 0.8920 0.3810
CA CA CA CA CA CA C HA HA HA HA HA O N HN
Figure 1. Stable structure of benzamide at ambient conditions. The volume per molecule amounts to 0.156 nm3. High pressure induces the anti-parallel shuffling of (0 1 0) layers as indicated by the arrows.
allow for cell shape variations. While the simulations reported in the following were performed at room temperature, for all polymorphs thermal stability was assessed up to about 400 K. 3. Results To demonstrate the validity of the force field we prepared supercell models of the three known polymorphs (I–III) as described in the Section 2. Using separate simulation models, molecular dynamics simulations at were performed ambient conditions to confirm polymorph stability. On this basis indeed all of the experimentally identified crystal structures were found to be (meta) stable. This reflects an important prerequisite to the suitability of the simulation models to describe benzamide polymorphism and represents a significant improvement to prior modeling studies which could not assess the metastable polymorph II [2]. However, while the structures are reproduced quite reasonably, a serious shortcoming is given by the limited accuracy in assessing lattice energies (Table 1). Indeed, the ordering of lattice energy levels of the polymorphs as obtained from model calculations reads III < I < II which is in contradiction to the experiment [1]. While the phase I reflects the stable form, polymorphs II and III are known to transform to I within hours and days, respectively. From a more qualitative point of view, force-fields and low level quantum models may still provide valuable insights as long as the focus is set to structural characterization. Indeed, the usage of simple and approximate interaction models is widely spread for the
2.3. Simulation models The simulation models for phases I–III were prepared as 8 9 2, 3 3 9 and 9 8 2 supercells [1] and periodic boundary conditions. This corresponds to roughly cubic simulation boxes which dimensions range from 4.2 to 4.8 nm. The overall number of explicitly considered benzamide molecules are 576, 648 and 576 for the simulation systems mimicking phases I–III, respectively. 2.4. Molecular dynamics simulations The molecular dynamics simulations were performed for supercell models of several nm dimensions. A time-step of 1 fs was used and Ewald summation with a real space cut-off of 1.2 nm was applied. The simulations were performed in the constant-pressure, constant temperature ensemble using an anisotropic barostat to
Table 1 Cell constants and potential energy as derived from molecular dynamics simulations at 300 K and 1 atm. Experimental values according to Ref. [3] are denoted in brackets. Note that the energy differences are in contradiction to the experimentally observed polymorph stability I < III II.
a/Å b/Å c/Å a/° b/° C/° Unit cell volume/Å3 Volume per molecule/Å3 Energy in kJ/mol per molecule:
I
II
III
IV (hypothetic)
5.64345 (5.6094) 5.07049 (5.0399) 22.25124 (22.1171) 90.00 (90) 90.00 (90.641) 90.00 (90) 636.72 (625.23) 159.18 (156.3075) 138.93
17.37628 (17.4317) 14.64495 (14.1944) 5.20159 (4977) 88.03 (90) 90.56 (90) 90.48 (90) 1322.8 (1231.4) 165.35 (153.925) 138.74
5.08162 (5.0569) 5.54293 (5.5159) 22.69036 (22.5010) 90.00 (90) 90.00 (91.36) 90.00 (90) 639.12 (627.50) 159.78 (156.875) 140.97
9.56105 5.10898 30.55187 90.00 55.69 89.99 1232.72 154.09 144.01
276
D.M. Benoit et al. / Chemical Physics Letters 514 (2011) 274–277
Figure 2. Pressure-induced formation of a new benzamide polymorph (IV) which is metastable at ambient conditions. The volume per molecule amounts to 0.144 nm3. While the hydrogen bonded network and p–p interactions along the c-axis remain practically unchanged, the packing of layers is improved by additional p–p interactions between (0 1 0) layers (see also Figure 1).
Figure 3. (a) Illustration of the unit cell of the benzamide polymorph IV. Hydrogen bonding only occurs within (0 0 1) layers as highlighted in green and at different orientation in Figure 3b. (b) Illustration of a single (0 1 0) layer of the benzamide polymorph IV. Hydrogen bonding only occurs within such layers and is highlighted in green (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).
scanning of the configurational manifold of solids whilst energetic ranking is typically performed by more sophisticated approaches [13–19]. The advantage of this concept is given by the efficient screening of putative structures and the focus of computationally more demanding approaches to local relaxation or even single point energy calculations [19]. We thus performed more accurate DFT calculations using a variety of state-of-the-art approaches as described in the Section 2. For both, force-field and DFT calculations all polymorphs discussed in this Letter were found as metastable structures, i.e. correspond to local minima in the potential energy landscape. Strikingly, the expected I < III < II ordering of energy levels could still not be assessed. It is reasonable to expect difficulties in modeling the p–p interactions to account for this inaccuracy. On the basis of the flexible GAFF force field approach Facelli and coworkers performed a polymorph search for a series of organic crystals, including benzamide [17]. From this, the experimental structure, polymorph I, was ranked 38 whilst the top 300 struc-
tures are within less than 10 kJ/mol. The closeness of the energy levels of the different polymorphs indicates that force fields represent a reasonable basis for assessing structures, but call for better accuracy to allow proper polymorph ranking. Similarly, we can expect force fields to provide reasonable qualitative insights into the transition mechanisms of polymorphic transformations which is the aim of the present study. We performed a series of molecular dynamics simulations to further scan the configurational manifold of benzamide crystals. While heating ? cooling ? heating runs were found to either exhibit the polymorph used as starting point or melting and glass formation, low-pressure ? high-pressure ? low-pressure cycles succeeded in stimulating solid state phase transitions. Starting from supercell models of phases I–III, high-pressure was applied for 50 ps, followed by 50 ps relaxation at ambient conditions and further 50 ps for sampling the (putatively) new configuration. Applying elevated pressure of 10, 50, 100 and 250 bar most runs resulted in amorphisation rather than inducing II ? I or III ? I transformations.
D.M. Benoit et al. / Chemical Physics Letters 514 (2011) 274–277
However, the overall approach is much more promising for the search of high-pressure polymorphs which was indeed identified from a simulation run starting from the stable form I. The new polymorph, suggested as IV, is obtained by a pressureinduced a I ? IV transformation as illustrated in Figures 1 and 2. The overall mechanism is given by the sliding of (0 1 0) layers in an anti-parallel fashion along the a-axis. This layer shuffling by ±a/2 leads to a more compact stacking of the benzole rings which are now arranged as quartets of parallel pi-systems, whilst phase I may be interpreted in terms of pairs of staggered pi-systems. This increase of p–p interactions is accompanied by a considerable reduction of the distance of the benzole groups. In phase I the pairs of staggered benzole rings are separated by 3.7 Å, in phase IV the quartets of parallel rings split into two pairs separated by 3.1 and 2.7 Å, respectively. Strikingly, the hydrogen bonded network of benzamide in phase I is only marginally deformed, but not altered during the I ? IV transition (Figure 3a and b). Thus, the hydrogen bonded (0 1 0) layers are shifted as a whole and phase stability of both polymorphs is triggered by p–p-interactions, intramolecular deformation and volume work. The latter provides a guide to the synthesis of benzamide IV. While the density of phases I–III are very similar at room temperature and ambient pressure, the density of polymorph IV is larger than that of phase I. The volume difference was observed as 12% at zero Kelvin (assessed from force-field and DFT calculations) and 8% at room temperature (assessed from force-field based molecular dynamics simulations, only). Hence, we suggest highpressure experiments to confirm the predicted polymorph IV. 4. Conclusions Molecular modeling of benzamide and its variety of crystalline forms represents an ongoing challenge. Here, we presented significant progress, namely the outline of a flexible force-field that offers the study of all known polymorphic structures. While reliable lattice energies exceeded the scope even of state-of-the
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art DFT calculations, more qualitative insights are at reach. Along this line, we used molecular dynamics simulations to predict a new polymorph (IV). This polymorph may be obtained from phase I via a pressure-induced phase transformation that leads to a more compact packing of the benzole rings. The mechanism is suggested as the anti-parallel shuffling of (0 1 0) layers by ±a/2 along the [1 0 0] direction. Acknowledgments We gratefully acknowledge financial support from the Deutsche Forschungs-gemeinschaft (DFG), and the states of Bayern and Baden-Württemberg for computation time on the RRZE and the bwGRID cluster, respectively. References [1] J. Thun, L. Seyfarth, J. Senker, R.E. Dinnebier, J. Breu, Angew. Chem. Int. Ed. 46 (2007) 6729. [2] J. Thun, M. Schoeffel, J. Breu, Mol. Simulation 34 (10) (2008) 1359. [3] J. Thun, L. Seyfarth, C. Butterhof, J. Senker, R.E. Dinnebier, J. Breu, Cryst. Growth Des. 9 (5) (2009) 2435. [4] J. VandeVondele, M. Krack, F. Mohamed, M. Parinello, T. Chassaing, J. Hutter, J. Comput. Phys. Commun. 167 (2) (2005) 103. [5] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (18) (1996) 3865. [6] S. Goedecker, M. Teter, J. Hutter, Phys. Rev. B 54 (3) (1996) 1703. [7] C. Hartwigsen, S. Goedecker, J. Hutter, Phys. Rev. B 58 (7) (1998) 3641. [8] M. Krack, Theor. Chem. Acc. 114 (1–3) (2005) 145. [9] J. VandeVondele, J. Hutter, J. Chem. Phys. 127 (11) (2007) 114105. [10] S. Grimme, J. Comput. Chem. 27 (15) (2006) 1787. [11] J. Wang, R.M. Wolf, J.W. Caldwell, P.A. Kollmann, D.A. Case, J. Comput. Chem. 25 (2004) 1157. [12] C.I. Bayly, P. Cieplak, W. Cornell, P.A. Kollmann, J. Phys. Chem. 97 (1993) 10269. [13] C. Schön, M. Jansen, Angew. Chem. Int. Ed. 35 (1996) 1286. [14] M. Jansen, Angew. Chem. Int. Ed. 41 (2002) 3746. [15] A. Gavezzotti, Cryst. Eng. Commun. 5 (2003) 429. [16] M. Jansen, J.C. Schön, Angew. Chem. Int. Ed. 45 (2006) 3406. [17] S. Kim, A.M. Orendt, M.B. Ferraro, J.C. Facelli, J. Comp. Chem. 30 (2009) 1973. [18] M. Jansen, K. Doll, J.C. Schön, Acta Cryst. A 66 (2010) 518. [19] J. Anwar, D. Zahn, Angew. Chem. Int. Ed. 50 (2011) 1996.