Surface Induced Phenytoin Polymorph. 1. Full Structure Solution by Combining Grazing Incidence X-ray Diffraction and Crystal Structure Prediction

Understanding the behavior and properties of molecules assembled in thin layers requires knowledge of their crystalline packing. The drug phenytoin (5,5-diphenylhydantoin) is one of the compounds that can be grown as a surface induced polymorph. By using grazing incidence X-ray diffraction, the monoclinic unit cell of the new form II can be determined, but, due to crystal size and the low amount of data, a full solution using conventional structure solving strategies fails. In this work, the full solution has been obtained by combining computational structure generation and experimental results. The comparison between the bulk and the new surface induced phase reveals significant packing differences of the hydrogen-bonding network, which might be the reason for the faster dissolution of form II with respect to form I. The results are very satisfactory, and the method might be adapted for other systems, where, due to the limited amount of experimental data, one must rely on additional approaches to gain access to more detailed information to understand the solid-state behavior.

A. COMPUTATIONAL

Electronic structure calculations
CASTEP (version 6.1) calculations: Brillouin zone integrations were performed on a symmetrised Monkhorst-Pack k-point grid with the number of k-points chosen to provide a maximum spacing of 0.07 Å −1 and a basis set cut-off of 780 eV.
The self-consistent field convergence on total energy was set to 1x10 −5 eV. Energy minimizations were performed using the Broyden-Fletcher-Goldfarb-Shanno optimization scheme within the space group constraints. The optimizations were considered complete when energies were converged to better than 2x10 −5 eV per atom, atomic displacements to 1x10 −3 Å, maximum forces to 5x10 −2 eV Å −1 , and maximum stresses to 1x10 −1 GPa. Energy minimizations with variable unit cells were restarted after the first minimization to reduce the effects of changes in unit cell on the basis set.
Phonon calculations performed with CASTEP v.6.1 do not account for dispersion. Therefore, additional calculations were undertaken using VASP (for details see next section).
VASP (version 5.4.4) calculations: All the calculations were performed using Perdew-Burke-Ernzerhof (PBE) exchange correlation functional in combination with the projector-augmented wave (PAW) pseudopotentials. The effects of the van der Waals (vdW) interactions were included with the pair-wise method D3-BJ by Grimme et al. Energy convergence could be achieved for the two polymorphs by using a plane wave energy cutoff of 800 eV, which proved to be adequate. Monkhorst-Pack k-point samplings of 2x1x1 and 1x1x2 for forms I and II were used, respectively. The k-point grid is selected in such a way to obtain the same density of sampling points in each direction and is thus dependent on the lattice parameters. Raising the cutoff energy from 800 to 1200 eV caused energy changes below 1 meV per atom, while the differences in energies between the adopted k-point grid and denser ones were below 1 meV per atom. Atomic coordinates were fully relaxed, halting when residual forces fell below 1 meV/Å, using the GADGET package. Vibrational modes, restricted to the Г point, were computed at the experimentally determined unit cell volumes through the force constants obtained with the Phonopy package in combination with VASP.

Potential Energy Scans
The deformation energy for phenytoin was computed on one 13x13 grid, equivalent to a 30° grid spacing for each dihedral angle in the range 0° to 360° for 1 and 2 ( Figure S1). At each grid point the deformation energy was calculated with the flexible torsions fixed and the rest of the molecule optimized at the B3LYP/6-31G(d,p) level of theory. Figure S1. Molecular diagram of phenytoin. The intramolecular degrees of freedom (dihedral angles) that were optimized within the crystal energy minimizations are indicated with arrows.
The potential energy surface scan grid (360 rotation of phenyl rings) results in eight energy minima (non-coplanar phenyl rings), which correspond to two equienergetic minima. In a Z'=1 CSP search only one minimum has to be considered due to the planarity of the phenytoin ring. Figure S2. Potential energy surface scan for phenytoin with respect to 1 and 2. Color coding in kJ mol 1 . Deformation energy calculated at B3LYP/6-31G(d,p) level of theory with the flexible torsions fixed and the rest of the molecule optimized. Conformational energy minima are indicated with diamonds and circles.

Representation of the Experimental Structure
The computational models were successful in reproducing the structurally characterized anhydrate (form I) of phenytoin (Table S3). The structures were compared using the Solid Form module of Mercury to determine the root mean square deviation of the non-hydrogen atoms in a cluster of 15 molecules (rmsd15). 18  Figure S3. Overlay of the 15 molecule cluster of PHYDAN01 (colored by element) and calculated PBE-TS structure, rmsd15=0.112 Å.

Scattering geometries
The deposition of crystalline material onto a substrate surface results in the reciprocal space information being located in the upper hemisphere above the surface (see Figure S4). To reach the different information, various X-ray scan can be used. The specular X-ray scan investigates the packing parallel to the surface by varying the incidence and exiting angle equally. Using a grazing incidence angle, diffracted intensities of the X-rays are collected at various exiting angles which typically has an angle in the co-planar direction and one perpendicular. A 2d -detector can collect this data very fast. Figure S4. Scheme on the sample alignment with respect to the X-ray beams and the scans in reciprocal space.

Maximizing form II within a spin coating experiment
To study the effect of concentration and temperature on the formation of the surface induced phenytoin phase, specular X-ray diffraction on various samples were performed. Using a constant spin speed of 17 rps and 60 sec, the variation of concentration allows to gain adjust the amount of the form I and form II as shown in Figure S5. At a concentration of 10 mg/ml of phenytoin in tetrahydrofuran, the spin coating result in the appearance of peaks solely from the form I ( Figure S5a). Having even the 002bulk and the 020bulk this suggests that this sample has some random powder like character. Halving the amount, this result in the peaks becoming smaller, but with an additional peak at around 9 nm -1 developing. This peaks is the 200 peak of the surface induced phase or short SIP. As the concentration further reduces, the amount of the form II is the greatest. At even lower concentration, the situation become again slightly more favourable for form I. Figure S5. Specular X-ray diffraction scans of phenytoin thin films prepared on silicon oxide surfaces. The sample vary by: variation of the concentration at constant 295 K (a), variation of temperature at 10mg/ml (b) and highly optimized sample prepared at 304 K with a solution of 1.2mg/ml (c).
Preparation of samples from a 10mg/ml but with changing temperature shows, that the amount of the form I with respect of form II can be varied (see Figure S5 b). For this high concentration a maximum of form II could be obtained at 308 K.
Using a further optimization steps, we could identify that at a concentration of 1.25mg/ml and a temperature of 304 K we were able to obtain a sample which only shows peaks of form II. Please note that the corresponding scan in Figure S5c shows a much larger scan range, to demonstrate also the presence of the higher order peaks.

Grazing incidence X-ray diffraction
Using a grazing angle, the measurement using a 2d -detector allow to detect many netplanes which are inclined to the substrate surface (see Figure S6). Using various concentration for the sample preparation but keeping the spin speed (17 rps), spin time (60 sec) and the temperature (304K) constant, shows again some more optimization steps. At a concentration of the 5 mg/ml, peaks to the form II are present, but in addition some ring like information appears. This rings results from the form I having a powder like character or results from various crystals of high mosaicity. On reducing the concentration to 1.25mg/ml, the rings of form I are vanished, and form II dominates the patter. The sharp peaks mean that the crystals are rather large and the mosaicity is very low. This can be expected for a polymorph growing at the surface. At a concentration of 0.63 mg/ml, form II peaks become broader, which typically is due to the crystal size being smaller. Figure S6. Grazing incidence X-ray diffraction of samples prepared at 304K from various concentrations.
Form the GIXD pattern of the 1.25mg/ml sample we extracted two line scans along the qz but distinct qxy of 10 nm -1 and 12 nm -1 , respectively. The data a summarized in Figure S7 showing the variation in peak intensities (full lines). To indicate the goodness of our structure solution, we plotted also the theoretical peak intensities form the Pc solution of the main manuscript for these peaks (green line) showing that the overall agreement is good. The deviation existing likely due to small statistical deviation on account of large crystals as we see by changing the samples, incorrect data corrections (e.g. flat field correction of the detector), defects, disorder, amongst others. A re-optimization using approaches often done in single crystal diffraction, Rietveld refinement or similar methods, might allow to clarify this in more detail, but was of no interest for this particular study. The reader should be aware, that this data is only a comparison with the calculation without taking into account one of the various effects shown above. Figure S7. Extracted qz scans at two in-plane vectors (qxy) from sample prepared from a 1.25mg/ml THF solution and 304K. The corresponding GIXD pattern is depicted in Fig. S6b.