Parametric Rietveld refinement applied to dehydration of sodium naproxen

The identification of the hydration and dehydration transformations of drugs is vital to establish stable pharmaceutical components. Our aim is to monitor the kinetics of hydration and dehydration processes in pharmaceutical solids, and to relate these to the molecular-level crystal structures. One of the primary tools to achieve this is parametric Rietveld refinement. The dehydration of two dihydrate polymorphs of the non-steroidal anti-inflammatory drug (NSAID) sodium naproxen was monitored using synchrotron powder X-ray diffraction measurements at Beamline I711, MAX IV Laboratory, Lund University. Diffraction patterns were measured in the range 300-400 K at 1 K increments. Both polymorphs dehydrate to form identical monohydrate then anhydrous phases. Independent Rietveld refinements were initially performed for each unique phase in order to establish initial values for the parametric refinement. The refinements were performed using TOPAS-Academic [1]. The structures are molecular and both dihydrate polymorphs display pseudosymmetry, thereby requiring an extensive set of restraints. One of the key advantages of the parametric Rietveld refinement is the possibility to introduce algebraic equations that describe the evolution of various parameters [2]. The kinetics of the dehydration processes were monitored using a sigmoid function applied to the scale factors of the various phases (see Figure). The evolution of the unit-cell parameters and atomic displacement parameters were also treated parametrically, and the influence of using multiple coordinate sets (one model per temperature) or a single common coordinate set for each phase was examined. One dihydrate polymorph shows a smooth and continuous transition to the monohydrate, whereas the other polymorph shows an abrupt transition. These differences are linked to the existence of topotactic or non-topotactic chemical transformations between the dihydrate polymorphs and the monohydrate phase.

In situ monitoring of hydration and dehydration in pharmaceutical solids

This talk will describe a multi-technique study of hydration and dehydration in pharmaceutical solids, using sodium naproxen as a case study. The aim of the work is to establish molecular-level structural understanding of the chemical changes that take place in the solid state as a function of temperature and relative humidity. Dynamic vapour sorption (DVS) analysis on the anhydrous compound carried out as a function of temperature provides a preliminary overview of the solid-form landscape and identifies static conditions to obtain four different hydrate forms [1]. Differences in the sorption and desorption cycles indicates the existence of a polymorphic dihydrate, and the two polymorphs show significant differences in their dehydration behaviour. Crystal structures are established for all phases in the system using either single-crystal or powder X-ray diffraction data, supplemented by dispersion-corrected density functional theory (DFT-D) calculations. The hydration and dehydration processes are monitored by powder X-ray diffraction (PXRD), as a function of relative humidity and temperature, and by variable-temperature solid-state 13C and 23Na NMR. Synchrotron PXRD is applied to the two dihydrate polymorphs to monitor the dehydration processes in approximately real time. The kinetic and structural details of dehydration are established by applying parametric Rietveld refinement [2] to the synchrotron data. This approach adds a structural picture to the kinetic processes. The PXRD studies indicate an essentially continuous dehydration pathway from one of the dihydrate polymorphs to the monohydrate, but a stepped dehydration pathway for the other dihydrate polymorph. The different mechanisms are linked to different degrees of structural similarity, and in particular to the existence of topotactic or non-topotactic transformations between the dihydrate polymorphs and the unique monohydrate and anhydrate phases.

Crystal structure prediction of indomethacin

Indomethacin is a non-steroidal anti-inflammatory and antipyretic agent. Because different packing arrangements of the same drug can greatly affect drug properties such as colours, solubility, stability, melting point, dissolution rate and so forth, it is important to predict its polymorphs. The computational prediction of the stable form will reduce undesirable risks in both clinical trials and manufacturing. Reported polymorphs of indomethacin include α, β, γ, δ, ε, η and ζ [1], of which only the thermodynamically stable form γ and the metastable form α are determined. Density functional theory with dispersion-correction (DFT-D) has been used extensively to study molecular crystal structures[2]. It gives better results with a compromise between the computational cost and accuracy towards the reproduction of molecular crystal structures. In the fourth blind test of crystal structure prediction in 2007, the DFT-D method gave a very successful result that predicted all four structures correctly. Rather than using transferable force fields, a dedicated tailor-made force field (TMFF) parameterised by DFT-D calculations[3] is used for every chemical compound. The force field is used to generate a set of crystal structures and delimit a candidate window for energy ranking. The powder diffraction patterns of predicted polymorphs are calculated to compare with experimental data.

Computational Pharmaceutical Materials Science: Beyond Static Structures.

The five Crystal-Structure Prediction (CSP) Blind Tests have shown that molecular-mechanics force fields are not accurate enough for crystal structure prediction[1]. The first--and only--method to successfully predict all four target crystal structures of one of the CSP Blind Tests was dispersion-corrected Density Functional Theory (DFT-D), and this is what we use for our work. However, quantum-mechanical methods (such as DFT-D), are too slow to allow simulations that include the effects of time and temperature, certainly for the size of molecules that are common in pharmaceutical industry. Including the effects of time and temperature therefore still requires molecular dynamics (MD) with less accurate force fields. In order to combine the accuracy of the successful DFT-D method with the speed of a force field to enable molecular dynamics, our group uses Tailor-Made Force Fields (TMFFs) as described by Neumann[2]. In Neumann's TMFF approach, the force field for each chemical compound of interest is parameterised from scratch against reference data from DFT-D calculations; in other words, the TMFF is fitted to mimic the DFT-D energy potential. Parameterising a dedicated force field for each individual compound requires an investment of several weeks, but has the advantage that the resulting force field is more accurate than a transferable force field. Combining crystal-structure prediction with DFT-D followed by molecular dynamics with a tailor-made force field allows us to calculate e.g. the temperature-dependent unit-cell expansion of each predicted polymorph, as well as possible temperature-dependent disorder. This is relevant for example when comparing the calculated X-ray powder diffraction patterns of the predicted crystal structures against experimental data.

Interpreting Disordered PXRD Structures using Molecular Dynamics

A central topic in the formulation of solid medicinal products is the identification of a suitable solid form of an active compound to obtain optimal physicochemical properties. To this end, disorder may be important for relevant crystal properties like stability. For example, disorder may account for more than 10% of the crystal volume. A rational approach to solid-form selection is typically based on structural information at atomic resolution. In practice, pharmaceutical compounds are not always well-behaved and especially in the study of polymorphs or compounds with flexible groups it can be challenging to obtain crystals suitable for single-crystal X-ray diffraction. Powder X-ray diffraction (PXRD) is a popular alternative, but it generally requires supplementary information like molecular connectivity in simple cases or computational models to solve larger structures. Computational modeling has come a long way and accurate and reliable structures of pharmaceutically relevant compounds can indeed be obtained using laboratory PXRD measurements and quantum-mechanical calculations [1]. The major limitation of quantum mechanical calculations, however, is that they do not consider time nor temperature but only static structures at zero temperature. Thus, these methods cannot model phenomena related to disorder. The molecular dynamics (MD) method can add temperature as well as time and spatial resolution to a model and has in recent years developed to be a scalable, reliable and increasingly available technique. As more and more groups from academia as well as industry employ MD in their work, the development will increase to gain momentum in the coming years. We use MD in a high-performance setting to study crystal properties that are relevant for pharmaceutical research. Using a combination of models from first principles and MD we are able to study highly disordered structures and polymorphs on the basis of PXRD data.