Crystal Structure Prediction for Powder XRD of Polymorph toward Intractable Metal Complexes

Abstract

Originating from the challenges of using ordinary methods for determining the structure of salen-type nickel(II) complexes and the limitations of crystallography of unknown organic powders, which has not been reported for many years, this chapter mainly reviews crystal structure prediction, polymorphism, phase transitions, and the application of computational methods. It also states that new research is incorporating computational chemistry for analyzing powder XRD. In particular, we will explore the possibility of predicting polymorphic crystal structures, which are of academic and industrial interest and applying them to metal complexes and organic-inorganic hybrid materials. There are also high hopes for the recent development of electron diffraction.

1. Introduction

Powder X-ray structural analysis is sometimes used when conventional single-crystal X-ray structural analysis is difficult. However, analysis of powder requires “favorable conditions” to be met, and it is not uncommon for the analysis to fail. Crystal polymorphism and crystal solvents are an inherent difficulty. The focus here will be on the crystal structure of compounds based on powder analysis, which can potentially take on different crystal structures depending on temperature and solvent conditions.

Several well-known examples of inorganic compounds exhibiting structural phase transitions and crystal polymorphisms are known. For example, ZnS (sphalerite and wurtzite), TiO₂ (anatase and rutile), and BaTiO₃ (rhombohedral-orthorhombic-tetragonal [dielectric]-cubic) are widely known. As we learn in basic chemistry, ionic bonding is based on low directionality, and ions that can approximate a spherical shape can differ in packing. This is due to the difference in ion arrangement.

On the other hand, many examples of organic compounds exhibiting structural phase transitions and crystal polymorphisms are also known. In general, organic compounds have more “flexibility” in their three-dimensional structures, and intermolecular interactions than inorganic compounds, so structural phase transitions and crystal polymorphisms that accompany changes and differences in molecular structure are common. In addition, although not polymorphic, the same molecule can have different crystal structures depending on the presence or absence of a crystal solvent (often water), which is an important aspect of drug development. Now, in the case of a metal complex in which a metal ion and an organic ligand are combined, it is necessary to consider both elements (although it can be treated in the same way as an organic compound in many cases).

Structural phase transitions and crystal polymorphisms of metal complexes have recently been reported by Miyamura and Honda [1, 2]. Salen-type nickel(II) complexes with long-chain alkyl groups exhibit the “cold-crystallization” phenomenon, which is often seen in conventional high-molecular compounds, even though they are low-molecular-weight compounds. Here, we do not refer to the “anomalous thermal behavior” of “cold-crystallization” related to structural phase transitions and crystal polymorphisms. In terms of structural chemistry, conformational changes in long-chain alkyl groups and accompanying crystal structural changes are important. Alkyl chains tend to assemble parallel to each other as a result of van der Waals interactions, and this interaction affects the crystal structure. Therefore, the structure of alkyl derivatives depends on the chain length. Therefore, alkylation of rigid molecules can significantly change their physical properties, such as thermal properties, crystal structure, and the structure of adsorbed monolayers. However, although there are many examples of salen-type metal complexes, the fact that this phenomenon was observed in nickel(II) complexes requires consideration of special circumstances. In fact, salen-type ligands can be distorted into the coordination structure oriented by metal ions while maintaining planarity [3, 4]. Furthermore, it is known that salen-type nickel(II) complexes tend to form a dimer structure in the crystal. The structure is built up in a centrosymmetric dimer characterized by a weak but significant Ni-Ni intermolecular interaction with a Ni-Ni distance of about 3.16–3.20 Å.

Upon successful recrystallization, microscopic observation of the crystal quality revealed two different crystal habits depending on the solvent used. Crystals grown from acetone, ethyl acetate, toluene, and N-methyl-2-pyrrolidone (“NMP”) were plate-like, while those grown from chloroform, dichloromethane (“DCM”), dimethyl-formamide (“DMF”), acetic acid, and methanol were needle-like. Crystals grown from ethanol were either plate-like or very fine needle-like. X-ray crystallography revealed that the plate-like crystals always corresponded to the solvent-free compound, and the needle-like crystals to the five solvates of Ni(salen): Ni(salen)-chloroform, Ni(salen)-DCM, Ni(salen)-DMF, Ni(salen)-AcOH, and Ni(salen)-1.5MeOH. Crystals of the ethanol solvate were not successfully isolated.

When crystals were grown by evaporation from ethanol solutions near room temperature, they were very fine and needle-like, but their quality was not sufficient for X-ray crystal structure determination. All successful recrystallizations took several hours to several days. Recrystallization from pure dimethyl sulfoxide (hereafter DMSO) or pure ethylene glycol still did not yield crystals; recrystallization from water failed because Ni(salen) is insoluble in water; recrystallization from a mixture of DMSO and water (9:1) yielded crystals of solvent-free 1. No attempt was made to recrystallize Ni(salen) from other mixed solvents.

The nature of the weak but important metal-metal interactions observed in square-plane d⁸ complexes has been explained by the concept of overlapping metal-metal orbitals, i.e., the overlap of the p_z (empty) and d_z2 (fully occupied) orbitals of one d⁸ atom with those of the neighboring d⁸ atom. The intermetallic distance is then governed by the amount of overlap between metal-metal orbitals. In the reported structures of solvent-free compounds and their solvates, neighboring Ni(salen) molecules always exhibit weak intermetallic interactions, which can be found along centrally symmetric dimers or one-dimensional chains. In this series of compounds, the metal-metal interactions found in the dimer units appear to be slightly stronger than those found in the one-dimensional chains, but the intermetallic distances in the former group differ significantly [Δ(Ni---Ni) max-min ≈ 0.26 Å]. However, there is no apparent correlation between the strength of the metal-metal interactions and the nature of the intermolecular solvent-salen interactions; further investigation of the metal-metal interactions found in 1 should be done in a separate paper. The reason for the preferential formation of either dimeric or one-dimensional chain structures in the seven structures of Ni(salen) and its solvates is still unclear. While dimeric units seem to be preferred in these structures, one solvated structure contains one-dimensional chains, which are linked by solvent molecules via the motif Ni(salen)---solvent---solvent. Such a motif may provide extra rigidity to the monomer units and favor the construction of one-dimensional chains.

There are also reports of the crystal structures of salen-type nickel(II) complexes with some simple substituents such as ethylenediamine, 1,2-diaminocyclohexane, 1,2-diphenylethylendiamine [5, 6, 7]. Therefore, not only the characteristic dimer structure but also from the powder X-ray diffraction pattern applicable to structural phase transitions and crystal polymorphisms, or in combination with other related techniques, (racemic) propylenediamine derivatives salen-type (Figure 1). An attempt was made to analyze the crystal structure of nickel(II) complexes.

Figure 1.

Chemical structure of the racemic nickel(II) complex.

The first difficulty was that single crystals of sufficient size could not be grown, although single crystals of small size could be obtained by X-ray diffraction. Therefore, the in-house apparatus could not obtain a decent diffraction peak.

The next difficulty was that the structural analysis of unknown organic crystals from synchrotron radiation powder X-ray diffraction patterns failed at the stage of lattice parameter indexing. Taking advantage of simple substituents, we were preparing for Rietveld analysis and fitting using the optimized structure by density functional theory (DFT) calculation as a model, but we did not proceed to that stage. Synchrotron radiation X-ray diffraction was able to be measured on a very small single crystal sample and a randomly oriented fine powder sample (Figure 2).

Figure 2.

Powder XRD patterns of the nickel(II) complexes as (a) powder and (b) single crystal.

A final difficulty arose when electron diffraction was attempted in order to perform diffraction data measurements and structural analysis on “single crystals” that were too small. Unexpectedly, a weak regular diffraction pattern was observed for a specific one-dimensional (probably c-axis) direction, and no diffraction pattern was observed for other directions (Figure 3). This suggests that although there is barely regular molecular alignment in one direction (stacking of planar ligands due to the formation of the dimer structure typical of nickel(II) complexes), there is order in the direction perpendicular to it. It was speculated that the crystal packing is weakly regular and unique. Under these circumstances, we have come to believe that there have been no reports of single-crystal X-ray structural analysis of nickel(II) ion-containing molecules, which are the simplest class of molecules.

Figure 3.

Electron diffraction patterns (along the c-axis) of the nickel(II) complex.

Based on these backgrounds and motives, are there any research examples or findings that can provide hints for crystal structure analysis of such difficult crystal polymorphs (structural phase transitions) by X-ray powder diffraction? Although there are many organic compounds, we decided to investigate research examples of structure analysis by powder X-ray diffraction or three-dimensional electron diffraction while predicting the crystal structure of crystal polymorphs.

2. Crystal structure prediction polymorph for powder XRD

In addition to cases where it is difficult due to the reasons mentioned above, a number of crystal structures have been reported by powder analysis of compounds that can have different crystal structures. Particularly in the case of organic compounds for applied purposes, strong motivation and great significance are the driving force. However, in general, analysis is often not easy and is done on a case-by-case basis. Here, the characteristics of compounds, analysis methods, and additional methods for analysis (other measurements and computational chemistry) will be reviewed.

Watt et al. [8] reported the crystal polymorphism of 5-aminouracil derivatives. In order to obtain polymorphic single-crystal samples, sublimation or methods using various solvents were employed, and data with different crystal shapes and XRD patterns were obtained. A comparison of the molecular structures of the polymorphs revealed different hydrogen bonding patterns and differences in the tetrahedral conformation of the proton-donor amino groups. The difference in lattice energies is mentioned. They are discussing the crystal structure based on synchrotron radiation X-ray diffraction data from single crystals. However, the powder XRD pattern does not give uniform and clean data due to the influence of “phase impurities.” Indeed, the nucleobase derivative 5-aminouracil (AUr) is intriguing for its biological activity, but the solid-state structure of this compound remains elusive because of its tendency to crystallize as an aggregate of microcrystalline particles. Both crystallization of AUr from solution and crystallization by sublimation were revisited, and large, albeit difficult, single crystals of AUr were grown. Synchrotron X-ray diffraction of the single crystal revealed the structure of this compound for the first time. The structure obtained was one of the previously calculated structures, but the corresponding calculated structure was more than 10 kJ mol⁻¹ above the minimum and was not considered experimentally feasible (early efforts to predict crystal structures had assumed that AUr was rigid in an optimized conformation of isolated molecules). Periodic electron-level modeling (PBE-TS optimization) revisited these crystal structures and yielded more realistic relative lattice energies, but it required the use of experimental cell parameters in good agreement with the experimental powder model. Powder X-ray diffraction of the precipitated material and mirror image Raman analysis of individual crystal aggregates indicated the possible presence of at least one other polymorph in small amounts, which is consistent with the thermodynamic validity of the computer-generated polymorphs. This experimental polymorph was isolated from multiple crystal growth methods and identified as one of the computationally generated crystal structures. Although only one polymorph of this compound was structurally characterized, there is evidence that additional polymorphs are likely present in the bulk growth product. This structural information provides useful insight into the effect of 5-position substitution on uracil derivatives. This study illustrates the utility of inexpensive crystal structure prediction (CSP) studies using rigid molecules and the challenges faced by current computational modeling of electronic and geometric changes associated with -NH₂ group delocalization and thermal expansion in the organic solid state. Nevertheless, the energetic competitiveness of the various crystal structures provides evidence that AUr molecules offer a variety of hydrogen bonding interactions and are important nucleobase derivatives in novel oligonucleotide assemblies.

Gushurst et al. [9] discovered a new polymorph of the organic compound ROY, for which 11 polymorphs have already been discovered. In this study, the structure was analyzed by Rietveld analysis of powder X-ray diffraction as a matching polymorph in order to match the previously reported experimental data and crystal structure prediction. A novel polymorph of ROY was discovered using a thermal method. The crystal structure was elucidated by matching experimental data with powder X-ray diffraction patterns calculated from previously published crystal structure predictions. The structure was further refined by the Rietveld method. This new polymorph was named PO13 because of its pumpkin-orange color. At room temperature, PO13 is not as stable as Form Y. After 5 years, a sample of 99% pure PO13 was converted to a mixture of 45% PO13 and 55% Form Y. A new polymorph of ROY was discovered in 2013. Recently, the structure was refined using the Rietveld method on the PXRD pattern collected in 2013, as this structure correctly matched the predicted crystal structure. The refined structure is in very good agreement with the predicted structure, demonstrating the excellent results of crystal structure prediction by Vasileiadis. This study demonstrates the value of combining computational and experimental methods, especially in screening for polymorphs PO13 melts at 100.0°C. PO13 melts at 100.0°C. Due to the amorphous content, minor form impurities in the starting material, and overlapping thermal events, the exact heat of melting could not be determined, but the total enthalpy was about 25.6 kJ mol⁻¹ and compared well with other known forms. Because of the imprecision of the heat of fusion during melting, the relative stability of PO13 relative to other forms cannot be predicted solely from the thermal data. However, samples were stored at room temperature for approximately 5 years. During this time, the relative percentage of PO13 decreased from 99% to 45% in favor of Form Y. Thus, at room temperature, Form Y is more stable than PO13.

Zhang et al. [10] discussed the metastable polymorph of the amide compound tuberculosis (pharmaceutical), of which three polymorphs are known. Single crystal results were used to identify which known polymorph it is. The polymorphs have structural differences in torsion angles and hydrogen bonds, as well as significant differences in lattice energies. Two new metastable polymorphs of the tuberculosis drug isoniazid, considered monomorphic for 60 years, were discovered using melt crystallization and nanoscale confinement. The two new forms were easily distinguished from the known forms by optical microscopy, Raman spectroscopy, and powder X-ray diffraction. For one of the new polymorphs, a single crystal structure was obtained. Melt crystallization yielded three crystalline polymorphs that were easily distinguished by polarized light microscopy. One of them was identified as Form I by Raman spectroscopy and powder X-ray diffraction. The other two were new polymorphs (forms II and III). These polymorphs were strongly temperature-dependent. The sublimation method produced needle crystals of morphology II and flake crystals of morphology I. Morphology II was identified by single-crystal X-ray diffraction; for type II, space groups were identified by single-crystal X-ray diffraction. The calculated powder X-ray diffraction patterns are consistent with the experimental geometry patterns; the hydrogen bonding modes for types I and II are different; the lattice energies for types I and II were calculated using the Vienna ab initio simulation package (VASP 5.3.5) and density functional theory (DFT). The energy cutoff for the plane wave expansion is 500 eV and was described using the Projector Augmented Wave (PAW) method. The Generalized Gradient Approximation (GGA) of the revised Perdew-Burke-Ernzerhof (rPBE) function was employed to account for electron exchange and correlation. Grimme’s D2 method was used to estimate van der Waals forces. Thus, crystal morphology, growth characteristics, PXRD, Raman spectroscopy, and single crystal X-ray diffraction clearly indicate the presence of two new polymorphs of INZ obtained by crystallization from melt. These results indicate that melt crystallization and crystallization under nanoconfinement are promising experimental methods for screening polymorphs, which is important for the development and efficacy of active pharmaceutical ingredients. This is especially important for high-Z structures that cannot be tested by computational crystal structure prediction methods. Furthermore, these results further support McCrone’s conjecture that “in general, the number of forms known for a compound is proportional to the time and money spent on the study of that compound.”

Bhardwaj et al. [11] discuss more than 10 crystal polymorphs and various crystal structures with and without “crystallization solvents.” There are differences in conformation and hydrogen bonding patterns among the polymorphs. Predictive calculations of crystal structures have been very difficult due to the effects of pressure and crystallization solvents. Rietveld analysis of powder X-ray diffraction was performed using single crystal results. Calculated results were organized by creating a (lattice) energy landscape and a search was made for energetic global minima. Polymorphs for which single crystal X-ray diffraction was not possible were submitted to powder X-ray diffraction, and similar ones were clearly distinguished by solid-state NMR. In the first CSP study, the Z′ = 2 polymorph was examined for possible crystal packing in various space groups determined by the three torsion angles, energy landscapes were generated, and plausible structures were found for several polymorphs. In the next CSP study, GRACE was used for the Z′ = 2 polymorph, sampling crystal filling in the Z′ = 1 or Z′ = 2 space group, which accounts for 99.9% of the distribution observed in the Cambridge Structural Database. Energy landscapes were calculated using Perdew-Burke-Ernzerhof (PBE) functions and empirical one-atom dispersion models (NP). Crystal structures were determined by Rietveld refinement of structural models using single crystal X-ray diffraction or powder X-ray diffraction combined with solid-state NMR. The relative positions of hydrogen bond donors and acceptors varied widely between polymorphs; DSC measurements were complemented by calculations of relative lattice energies using various periodic dispersion corrected DFT methods.

Jeziorna et al. [12] discuss the polymorphism and “co-crystallization” of meloxicam. They use energy landscapes for crystal structure prediction calculations, characterized by DFT calculations that search for conformations. Rietveld analysis of powder X-ray diffraction is based on limited single-crystal analysis and is characterized by large differences in hydrogen bonding modes between polymorphs. Thermal analysis related to phase transitions and solid-state NMR (observation of hydrogen bonding sites) experiments, described below, were also performed. All structures within the first 15 kJ/mol of the total energy of the global minimum (GM) structure in this energy landscape were further evaluated. Conformational searches for MLX neutral and two amphoteric ionic types are performed using Spartan 18’s grid search. All rotatable bonds are included. All unique stereostructures were further subjected to DFT calculations using Gaussian 16 software, evaluated at the level of theory in B3LYP-GD3BJ/6-311G (d, p), and later evaluated in the basis set using an additional diffusion function (6-311G++ (d, p)), specifically for amphoteric The ranking of the conformational energies was confirmed to be correct with respect to the ionic form. Finally, an additional relaxation scan calculation was performed in Gaussian 16 with a small step size of 8° for this torsion in order to evaluate the energetic impact of the thiazole ring orientation. CSP calculations were performed independently for each of the selected related stereostructures; the Z′ = 1 and Z′ = 2 crystal structure generation steps were performed using Global Lattice Energy Explorer. Based on quasi-random searches, between 2000 and 10,000 geometrically minimized crystal structures were generated in the 10 most common crystallographic space groups. The generated structures were geometrically minimized with respect to intermolecular interactions using FIT repulsive dispersion potentials. Atom-centered multipoles up to rank 4 (generated from Gaussian calculated electron density in GDMA 2.2.11 software) and a cutoff value of 25 Å for van der Waals interactions were used for the minimization. The force-field optimized structures were evaluated for overlap based on PXRD patterns and similarity of density and energy data, with cutoff values of 0.02 g/cm³ and 0.1 kJ/mol, respectively. The unique structures generated and optimized at this stage constitute the energy landscape of the force field. In this energy landscape, all structures within the first 15 kJ/mol total energy for global minimum (GM) structures were further evaluated. Selected MLX-predicted crystal structures were further shape-optimized with a k-point spacing of 0.07 Å⁻¹ and an energy cut of 600 eV using PBE-D2 level theory. In the first run of shape optimization, all atom positions were relaxed with fixed cell parameters, and in the second run, the cell parameters were also relaxed. This was done to speed up the convergence to the local minimum: a fully geometrically optimized structure in the PBE-D2 level constitutes an intermediate-level crystalline energy landscape called the DFT-D2 level. From this DFT-D2 landscape, the lowest energy structures found within the first 15 kJ/mol relative energy range of the DFT-D2 GM structure were further targeted for PBE-MBD geometry optimization.

To calculate the ¹³C shielding constants MLX-I, MLX-IV, and SDMSO, they used the reconstructed experimental crystal structures as a starting point and optimized the geometry with CASTEP using the same approach as the structures generated with the CSP NMR shielding constants to support ¹³C resonance assignments. For the optimized structure, the structure was calculated with the GIPAW approach; based on the analysis of the CSP energy landscape, new crystallization experiments were devised and performed to obtain polymorphic crystals; the lattice and intramolecular energies of crystals containing neutral and charged species of PRX, a molecule closely related to MLX The implications of the comparison of the lattice and intramolecular energies of crystals containing neutral and charged species of PRX, a molecule closely related to MLX, are also briefly discussed. Usually, when considering crystallization from a solvent, evaluating the energies of chemical species present in solution can provide some clues as to possible conformations in the crystal. In fact, zwitterionic species tend to have higher gas-phase energies than neutral species, justifying the omission of such studies. As a result, the crystal lattice energy of the charged species is 17% higher than that of the neutral species, and the crystal structure of the zwitterionic species has an intramolecular energy of more than 40 kJ/mol higher than that of the neutral molecules. This is important not only for solution crystallization studies but also for CSP calculations, which must take into account that the intramolecular energy of the zwitterionic species is higher than that of the neutral case.

Some examples of studies feature methods to obtain polymorphic crystals: Askin et al. [13] obtained a new polymorph of olanzapine, a pharmaceutical compound with more than 60 reported crystal structures including polymorphs and crystal water, by crystallizing it in a polymeric PVP solution. The dimer structure in the crystal is characteristic. Melting and crystallization were directly observed by simultaneous thermal analysis and powder XRD measurements. The results of lattice energy calculations are discussed as landscape. A new polymorph of olanzapine, type IV, was identified and isolated; CSP accurately predicted the presence of type IV, which had not been obtained experimentally prior to this study because solution-based crystallization methods form olanzapine dimers and further polymorphs based on the SC 0 motif. Crystallization from the amorphous phase of solids allows crystallization of different structures, which is thought to be due to the prevention of dimer formation. DSC-PXRD has been important in confirming the presence of new morphologies. On the other hand, Braun et al. [14] reported surface-induced polymorphism of the antiepileptic drug phenytoin. In surface adsorption, it is hypothesized that polymorphism can occur due to a decrease in local entropy at the surface due to the interaction between the adsorbed molecule and the substrate. The polymorphs were screened from the landscape of lattice energy calculations (information that polymorphs could be obtained). Two crystalline polymorphs were obtained when crystallized on the surface of silicon wafers. These were confirmed by grazing incidence X-ray diffraction (scattering vector values) corresponding to the surface, rather than by the usual powder XRD measurements of bulk samples. Detailed features and differences in molecular conformation and crystal packing (hydrogen bonding mode differences) are discussed. The structure of phenytoin in thin films is difficult to assess for many reasons; a combination of CSP calculations, GIXD experiments, and Raman spectroscopy allowed us to elucidate the structure of the thin film form (Form II) of phenytoin. The results suggest that differences in the steric H-bonding network are likely the reason for the faster dissolution of the thin film form (Form II) induced at the surface, as opposed to the bulk form, Form I. In general, CSP-based structural solution methods can provide information on the packing arrangement of organic molecules with limited experimental data. This can be applied to low-quality data such as GIXD data for thin films, X-ray diffraction for single crystals, neutron diffraction, electron diffraction, etc., minimizing the requisite for high-quality crystal growth. Regarding entropy in normal crystal polymorphs, there is also a study of benzamide by Fellah et al. [15]. A new highly metastable benzamide Form IV polymorph was found by melt crystallization in parallel with growth under nanoconfinement in very small pores. Under nanoscale configurations, the melting behavior of the more stable benzamide Form III crystallized in larger pores was strongly affected by pore size. The interfacial energies calculated by the Gibbs-Thomson equation were consistent with those obtained by the semiempirical model. A number of candidate structures for benzamide IV were obtained by a combination of powder X-ray diffraction analysis and computational methods. Several possible disorder models were narrowed down based on a two-dimensional parquet-like tiled tape consisting of four benzamide molecules. The disorder can be explained by various stacking defect configurations corresponding to random displacement and orientation of the tape. Taken together, these observations reveal that although the crystallographic complexity of such a simple molecule is impressive, new methods for determining solid-state structure are within reach. Moreover, this analysis suggests that many structures that might have been abandoned due to overarching defects such as low crystallinity, twinning, and disorder can be resolved. Yao et al. [16] discovered two new polymorphs of piroxicam (forms VI and VII) by melt crystallization and crystal structure prediction (CSP). They grew high-quality single crystals from molten microdroplets and analyzed their structures by X-ray diffraction. Melt crystallization is an important complement to solution analysis in polymorph discovery because it is thermodynamically less stable than the known polymorphs, which are mainly obtained by solution analysis. One thing has been confirmed. Piroxicam was reported to be thermally unstable and unsuitable for melt crystallization, but this problem was circumvented by exposing the molten droplets to high temperature for a short time.

If there are differences in hydrogen bonding modes between crystal polymorphs, a method that can combine spectroscopic experiments with XRD would be promising to detect them. Vibrational spectroscopy is available for hydrogen bonding, but solid-state NMR is more useful when compared to computational chemistry, and Mathew et al. [17] used a combined experimental and computational approach to distinguish between different polymorphs of the drug aspirin. In this method, DFT calculations of NMR parameters and solid-state NMR experiments using isotopes of natural abundance are combined with a DFT-based crystal structure prediction method, the ab initio random structure search method (AIRSS method), to predict polymorphic structures. Prediction with high accuracy AIRSS was used to predict the crystal structures of two polymorphs of aspirin, and information from powder XRD was also used. The root-mean-square deviation of the experimental and calculated proton chemical shifts was used to identify the polymorphs present in the experimental samples. This was successful despite the very similar molecular environments in the crystals of the two polymorphs; Smalley et al. [18] investigated the crystal structure of a new polymorph (β-polymorph) of the typical amino acid L-tyrosine by a combined analysis of three-dimensional electron diffraction data and powder X-ray diffraction. Three-dimensional electron diffraction data have been shown to be a useful structure determination method for reliable unit cell determination and space group assignment. The use of solid-state NMR and AIRSS resulted in an approach that greatly outperformed attempts at powder XRD analysis, which could not even be indexed (due to weaker XRD peak intensities) due to randomly oriented samples. A new polymorph of L-tyrosine (β polymorph) was prepared by crystallization from the gas phase, and the crystal structure was determined by combined analysis of 3D-ED and PXRD data and cyclic DFT-D calculations. The final structure of the β polymorph obtained from Rietveld purification was confirmed by (i) cyclic DFT-D geometry optimization, which confirmed that the crystal structure was very close to the minimum on the energy landscape; (ii) isotropic ¹³C NMR for the crystal structure calculated using DFT-D methods chemical shifts and excellent agreement with values observed in experimental high-resolution solid-state ¹³C NMR spectra. Furthermore, DFT-D calculations at the PBE0-MBD level suggest that the crystal structure of the β polymorph determined here is metastable compared to the previously reported crystal structure of the α polymorph. Structure prediction calculations using the AIRSS method generated five promising polymorphic crystal structures for L-tyrosine. The lowest energy structure was the alpha polymorph, the beta polymorph was at about 4 kJ mol⁻¹ higher energy, and the other three predicted structures were at more than 11 kJ mol⁻¹ higher energy than the alpha polymorph. In determining the crystal structure of materials that are difficult to characterize structurally by single-crystal XRD, the important advantages of using a combination of these methods within a robust protocol that incorporates consideration of periodic DFT-D calculations and solid-state NMR data, in addition to the combination of 3D-ED and PXRD data are highlighted. This has expanded our understanding of the structural properties of L-tyrosine in its crystalline state.

There is also a paper by Pawlak et al. [19] on combining solid-state NMR with experiments and crystal structure prediction calculations for single crystals, which is more reliable than powder XRD. The complementary application of CSP and solid-state NMR has significant advantages. Furthermore, while CSP describes well the range of thermodynamically preferred crystal structures, even the most robust algorithms do not take into account the static/dynamic molecular disorder that is often observed in experimental techniques. Solid-state NMR can be easily applied to systems that exhibit conformational flexibility and different molecular interactions. Thus, they demonstrate the synergistic effects of experimental solid-state NMR and single-crystal X-ray diffraction, as well as thermal analysis and crystal structure prediction techniques based on DFT calculations, in the analysis of systems that form polymorphs, undergo phase transitions, and local dynamic processes. One of the simplest and most common applications of solid-state NMR is the use of one-dimensional ¹³C CP/MAS experiments to determine the number of non-equivalent molecules, or crystallographic Z′ values. This is the first step in a strategy called NMR crystallography, the core of which is the GIPAW method. The GIPAW method is a breakthrough development in the theoretical prediction of NMR parameters for solid materials, and this approach can be readily applied to provide experimental validation of CSP solutions. Specifically, we show whether the possible solutions identified by the CSP strategy are consistent with the experimental form. In this study, we present for the first time the X-ray diffraction structure and MAS NMR characterization of a new room temperature polymorph of TFM (labeled TFM RT) recently reported by Gunnam et al. and a low-temperature TFM polymorph (TFM LT) at −40°C that undergoes thermal transition to the TFM RT polymorph. The phase transition is clearly visible in the DSC plots and is reversible. Crystals mounted on a goniometer head can be cooled and heated without cracking, producing diffraction patterns characteristic of TFM LT and TFM RT lattices, respectively. This reversible process occurs by varying the Z′ value while maintaining the crystal system, and the two forms have different lattice parameters and exhibit different reflection patterns. Reflections per second corresponding to TFM LT lattice direction a, both structures vanishing in TFM RT diffraction images, for the same type of crystal Reflections per second corresponding to TFM LT lattice direction a, both structures vanishing in TFM RT diffraction images, were determined based on diffraction experiments performed on the same type of crystal, highlighting that The differences between TFM LT and TFM RT will be discussed, focusing on the change in aromatic ring orientation related to the C4-NH-C5-C6 torsion angle. In the room temperature bimolecular structure, up to 50% disorder is modeled between torsion angles of −7.8° and 28.6°. These observations are consistent with the broad energy minima observed in the DFT calculations when the C4-NH-C5-C6 torsion angle is varied; PISEMA solid-state NMR experiments show that the static limits of the aromatic CH portion are 75% and 51% at 20 and 40°C, respectively, while the C-H The difference in crystal lattice energies between TFM LT and TFM RT is up to 2.4 kJ/mol, as calculated using DFT-D. This small difference supports the reversible conversion between both forms observed experimentally. The TFM RT polymorph also exhibits molecular disorder of the CF 3 group, and thus, the disorder of the two parts of the molecule may be correlated. The conversion from TFM LT and TFM RT appears to be driven by the same entropy preference as previous studies. The transformations from TFM LT and TFM RT appear to be driven by the same entropy preference as in previous studies. It is interesting to compare the TFM cases here: impairment in TFM RT is associated with a change in Z′ value from 2 to 1 compared to TFM LT in the case of Szell et al. However, there were clear differences in the calculated PXRD patterns that could not be explained by thermal expansion alone, and the ¹³C chemical shifts observed by solid-state NMR were different at all sites, not just those showing disorder. Furthermore, the crystal structure prediction procedure, which does not account for disorder in the output format, explained both the experimental TFM polymorphism in the global minimum region of energy. In conclusion, this study demonstrates that DFT calculations and CSP, in combination with experiments such as DSC, X-ray diffraction, and MAS NMR, can be used to investigate and understand the role of solid-state states, especially dynamics, in pharmaceutical molecules.

3. Three-dimensional electron diffraction for crystal structure analysis

Methods for powder structure analysis of organic compounds were reviewed, including additional techniques (other measurements and computational chemistry) and prediction of (polymorphic) crystal structures. However, the biggest experimental difficulty is that the (single) crystal is small, and there are great expectations that advances in equipment such as electron diffraction will be able to overcome this issue. Recent advances in instrumentation and technology [20, 21] have made it possible to use electron diffraction for crystallography (3-D structural analysis) rather than traditional electron microscopy (which has been used for morphological observation of metal compound nanocrystals.). In 1994, Vincent and Midgley developed a new data acquisition tool, precession electron diffraction (PED), which alleviates some of these problems. In 2007, Kolb et al. used a TEM goniometer to tilt a substrate in a series of discrete angular steps (ADT) and proposed to collect a series of tomographic diffraction patterns. ADT is intentionally designed so that most diffraction patterns are collected in the off zone, providing ideal conditions for observing quasi-kinematic scattering; ADT was rapidly combined with beam precession by Mugnaioli et al. Although PEDT required special external hardware to achieve beam precession, structural PEDT was the first electron diffraction technique to gain some traction as a general method for structure elucidation. Hovmöller, Zou, et al. also devised a method to slice the reciprocal lattice space into finer slices by supplementing the coarse mechanical tilting with electron beam tilting. This method, called Rotational Electron Diffraction (RED), utilizes custom software to collect data at very fine angular steps (Δη < 0.1°), surpassing the accuracy of TEM goniometers. These developments paved the way for continuous rotation, arguably the most impactful methodological advance in 3D electron crystallography. Continuous rotation was formulated almost in parallel by Nederlof et al. in 2013 and Nannenga et al. in 2014, respectively; unlike PEDT and RED, no auxiliary hardware or software is strictly necessary to perform continuous rotation ED, and most commercially available TEMs can collect continuous rotation data with little or no reconstruction. In this technique, the irradiated crystal is periodically sampled in reciprocal space at periodic intervals while being rotated in one direction around the axis of the TEM goniometer.

A review paper by Simoncic et al. [22] was written for crystallographers unfamiliar with 3D electron diffraction (i.e., XRD users). There are also solutions to some of the problems and challenges in the analysis of crystal structures from salen-type nickel(II) complexes and powder XRD data. Neutrons are scattered by their interaction with nuclei, whereas electron beams, like X-rays, are scattered by their interaction with the electron clouds of atoms and nuclei (electrons are electronegative, so they interact electrostatically with the positive site). However, electron diffraction, which can measure single crystals of even smaller size (thinner than 1 μm thick) than X-ray diffraction, is useful when single crystal growth is difficult. Since electron beams have a different wavelength range and diffraction angle than X-rays, the problem of overlapping diffraction peaks in samples with long lattice constants (which hinders indexing and analysis) can be avoided. Electron diffraction requires only a small amount of sample and is not easily affected by small amounts of impurities (multiple crystalline phases mixed together).

From the work of Zhou et al. [23], we illustrate the advantages of electron diffraction, keeping in mind other problems of single crystal size in salen-type nickel(II) complexes (low crystallinity and presumably also anisotropic molecular orientation ordering). Some organic compounds, such as covalent organic frameworks (COFs), have low crystallinity and pores in the crystal. Of course, the resolution of diffraction is low. Such macromolecular crystalline compounds are affected by a mixture of kinetically and thermodynamically favorable products, the difficulty of obtaining large single crystals, and the influence of structural disorder on the Bragg reflection. Crystal structure analysis is difficult because of the susceptibility to radiation damage. This is a successful example of structural analysis by 3D electron diffraction, combining high-quality single-crystal data obtained separately with refinement calculations using simulated annealing (rather than conventional methods). The use of SA (simulated annealing) enables us to obtain a structural model that is comparable to the reference model, even though it contains skeletal distortions. This indicates the possibility of solving low crystallinity COF structures with SA. On the other hand, structural analysis using low-resolution data is difficult with the dual-space method, the charge inversion method, and the classical direct method. In addition, we performed simulations with different resolution data and investigated how they affect the structural elucidation by SA. The results show that a resolution of 1.5 Å or higher produces a good structural model. However, when the resolution is reduced below 2.0 Å, distortion increases significantly and prevents meaningful interpretation of the framework structure. Since crystallization is not a problem limited to COFs, it is hoped that the use of SA for low-resolution 3DED data will allow the determination of the structures of other framework materials, such as metal-organic frameworks (MOFs), hydrogen bond frameworks (HOFs), and zeolites.

4. Conclusions

In a metal complex containing a specific nickel(II) metal ion, the single crystal becomes brittle when it exhibits a structural phase transition. However, structural analysis from powder XRD data often does not go smoothly. Even with single-crystal size and crystallinity issues, the potential for beams to reach real-space goals as well as reciprocal space data (diffraction patterns) would improve things. It is also expected that the real crystal structure of the nickel(II) complex mentioned above will eventually be solved. If it is allowed to “fit” the prediction results to the XRD pattern, the current style of “solving” the crystal structure (overcoming the so-called phase problem and obtaining the atomic arrangement in the real space from the measured information in the reciprocal space) may be in danger.

Acknowledgments

The authors thank Dr. Dohyun Moon (Pohang Light Source II, Korea) for the measurement of XRD and Dr. Akane Samizo (Rigaku Cooperation, Japan) for electron diffraction. We apologize for not being able to analyze the crystal structures.

Conflict of interest

The authors declare no conflict of interest.