On the puzzling case of sodium saccharinate 1.875-hydrate : structure description in (3+1)-dimensional superspace

The structure of sodium saccharinate 1.875-hydrate is presented in three- and (3+1)-dimensional space. The present model is more accurate than previously published superstructures, due to an excellent data set collected up to a high resolution of 0.89 Å(−1). The present study confirms the unusual complexity of the structure comprising a very large primitive unit cell with Z′ = 16. A much smaller degree of correlated disorder of parts of the unit cell is found than is present in the previously published models. As a result of pseudo-symmetry, the structure can be described in a higher-dimensional space. The X-ray diffraction data clearly indicate a (3+1)-dimensional periodic structure with stronger main reflections and weaker superstructure reflections. Furthermore, the structure is established as being commensurate. The structure description in superspace results in a four times smaller unit cell with an additional base centring of the lattice, resulting in an eightfold substructure (Z′ = 2) of the 3D superstructure. Therefore, such a superspace approach is desirable to work out this high-Z′ structure. The displacement and occupational modulation of the saccharinate anions have been studied, as well as their conformational variation along the fourth dimension

Solid Solution Formation in Xanthone–Thioxanthone Binary System: Experimental Investigation

Solid solutions are crystalline phases consisting of at least two components in a freely variable composition within certain limits [...

Dynamics and disorder:on the stability of pyrazinamide polymorphs

This article focuses on the structure and relative stability of four pyrazinamide polymorphs. New single crystal X-ray diffraction data collected for all forms at 10 K and 122 K are presented. By combining periodic ab initio DFT calculations with normal-mode refinement against X-ray diffraction data, both enthalpic and entropic contributions to the free energy of all polymorphs are calculated. On the basis of the estimated free energies, the stability order of the polymorphs as a function of temperature and the corresponding solid state phase transition temperatures are anticipated. It can be concluded that the α and γ forms have higher vibrational entropy than that of the β and δ forms and therefore they are significantly more stabilized at higher temperatures. Due to the entropy which arises from the disorder in γ form, it overcomes form α and is the most stable form at temperatures above ∼500 K. Our findings are in qualitative agreement with the experimental calorimetry results

Experimental and Computational Study of Solid Solutions Formed between Substituted Nitrobenzoic Acids

We present an experimental and computational study of solid solution formation in binary systems of substituted nitrobenzoic acids. Different isomers with methyl group, hydroxyl group, and chlorine substituents are studied. We show that the solid solution formation likelihood evaluated based on the observed solubility limit is notably affected by both - the exchanged functional groups and the location of the substituents in the molecular structure. This demonstrates that the component solubility limit strongly depends on the intermolecular interactions present in the crystal structure and altered by the molecule replacement. Solid solutions form in all of the studied crystalline phases. Component solubility limits from around 5% up to 50% were observed. The obtained results indicated that the calculated intermolecular interaction energy change by the functional group replacement does not allow to rationalize the experimentally observed solubilities neither considering the molecules adjacent to the replace group nor all the molecules within a 15 Å radius. The relative energy of the experimental structures and isostructural phases obtained from the computationally generated structure landscapes calculated at the level providing accurate energy ranking was found to be mostly consistent with the experimentally observed component solubilities

PhAI: A deep learning approach to solve the crystallographic phase problem

For more than 100 years, X-ray crystallography has provided a unique view on the three-dimensional structure of atoms and molecules in crystals. However, to determine even the simplest structures now and a hundred years ago, one needs to overcome a mathematical hurdle for which the solution is not known even to this day. To reconstruct the 3-dimensional electron density map, from which the structure can be inferred, the complex structure factors F = |F| exp(iφ) of a sufficiently large number of diffracted reflections must be known. In a conventional diffraction experiment, only the amplitudes |F| are obtained, while the phases φ are lost. This is the crystallographic phase problem. Seventy years of research has established successful ab initio phasing methods such as direct methods and charge flipping. However, these methods are limited to atomic- resolution data, complicating structure determination from weakly-scattering crystals. Here, we show that a neural network can solve the crystallographic phase problem at a resolution of only 2 Å. We have developed an approach to generate millions of artificial structures and respective diffraction data for training of a neural network. We demonstrate that ab initio phasing based on this neural network is possible using 10 % to 20 % of the data needed for present-day methods, breaking the paradigm that atomic resolution is necessary for ab initio structure solution. The current neural network works in common centrosymmetric space groups and for modest unit cell dimensions, and suggests that neural networks can be used to solve the phase problem in the general case. This approach will enable structure solution for weakly-scattering crystals such as metal-organic frameworks or nanometer-sized crystals investigated using electron diffraction

Comparison and Rationalization of Droperidol Isostructural Solvate Stability: An Experimental and Computational Study

In order to find a tool for comparison of solvate stability and to rationalize their relative stability, droperidol nonstoichiometric isostructural solvates were characterized experimentally and computationally. For the experimental evaluation of stability, three comparison tools were considered: thermal stability characterized by the desolvation rate, desolvation activation energy, and solvent sorption–desorption isotherms. It was found that the desolvation process was limited by diffusion, and the same activation energy values were obtained for all of the characterized solvates, while the solvent content in the sorption isotherm was determined by the steric factors. Therefore, the only criterion characterizing the solvate stability in this particular system was the thermal stability. It was found that computationally obtained solvent–droperidol and solvent–solvent interaction energies could be used for the rationalization of the isostructural solvate stability in this system and that the solvent–solvent interaction energy has a crucial role in determining the stability of solvates

Experimental and Computational Study of Solid Solutions Formed between Substituted Nitrobenzoic Acids

We present an experimental and computational study of the formation of solid solutions in binary systems of substituted nitrobenzoic acids. Different isomers with a methyl group, hydroxyl group, and chlorine substituents are studied. We show that the solid solution formation likelihood evaluated based on the observed solubility limit is notably affected by both the exchanged functional groups and the location of the substituents in the molecular structure. This demonstrates that the component solubility limit strongly depends on the intermolecular interactions present in the crystal structure and is altered by the molecule replacement. Solid solutions form in all of the studied crystalline phases. Component solubility limits from ∼5% up to 50% were observed. The obtained results indicated that the calculated intermolecular interaction energy change by the functional group replacement does not allow rationalization of the experimentally observed solubilities, considering neither the molecules adjacent to the replace group nor all the molecules within a 15 Å radius. The relative energy of the experimental structures and isostructural phases obtained from the computationally generated structure landscapes calculated at the level providing accurate energy ranking was found to be mostly consistent with the experimentally observed component solubilities

Toward Understanding High-Z′ Organic Molecular Crystals through the Superspace Method: The Example of Glycyl-L-valine

The high-Z′ (Z′ = 7) structure of glycyl-l-valine has been redetermined at 298 K, using synchrotron radiation and exploiting the superspace approach. The analysis of the diffraction data reveals that the structure can be described as a commensurately modulated crystal structure with superspace group P2$_1$2$_1$2$_1$(0σ$_2$0)000 and modulation wave vector q = (0, 2/7, 0). A new Z′ = 1 phase has been discovered for this compound at 323 K that is related to the known Z′ = 7 phase. The origin of the modulated phase has been explored by analyzing intermolecular interactions and molecular conformations in terms of t-plots and through a comparison to (1) the newly discovered high-temperature phase, (2) a hypothetical Z′ = 1 structure at 298 K, and (3) a similar Z′ = 1 structure of the related compound glycyl-l-leucine. The results show that the conformational flexibility of the glycyl-l-valine molecule ensures optimization of the hydrogen-bond network which causes the modulation and thus a high Z′ value of the supercell. This study highlights the elegance and convenience of the superspace approach to explain the occurrence of at least part of the rarely occurring high-Z′ structures of molecular compounds

On the Formation of Droperidol Solvates: Characterization of Structure and Properties

A solvate screening and characterization of the obtained solvates was performed to rationalize and understand the solvate formation of active pharamaceutical ingredient droperidol. The solvate screening revealed that droperidol can form 11 different solvates. The analysis of the crystal structures and molecular properties revealed that droperidol solvate formation is mainly driven by the inability of droperidol molecules to pack efficiently. The obtained droperidol solvates were characterized by X-ray diffraction and thermal analysis. It was found that droperidol forms seven nonstoichiometric isostructural solvates, and the crystal structures were determined for five of these solvates. To better understand the structure of these five solvates, their solvent sorption–desorption isotherms were recorded, and lattice parameter dependence on the solvent content was determined. This revealed a different behavior of the nonstoichiometic hydrate, which was explained by the simultaneous insertion of two hydrogen-bonded water molecules. Isostructural solvates were formed with sufficiently small solvent molecules providing effective intermolecular interactions, and solvate formation was rationalized based on already presented solvent classification. The lack of solvent specificity in isostructural solvates was explained by the very effective interactions between droperidol molecules. Desolvation of stoichiometric droperidol solvates produced one of the four droperidol polymorphs, whereas that of nonstoichiometic solvates produced an isostructural desolvate

Designing Solid Solutions of Enantiomers: Lack of Enantioselectivity of Chiral Naphthalimide Derivatives in the Solid State

The enantiomers of a previously reported naphthalimide derivative are shown in this study to form a solid solution; furthermore, on the basis of the knowledge of solid solution structural aspects other naphthalimide derivatives have been synthesized and shown to lack the enantioselectivity in the solid state. The structural origin of solid solution formation is the same as observed in most of the cases in the literature<i>quasi</i>-centrosymmetric structures form at nonracemic compositions where the most abundant enantiomer adjusts its conformation to mimic the absent one. Such solid solutions belong to the type showing some enantioselectivity. An extended single crystal X-ray diffraction study of the crystals of different enantiomeric compositions reveals the nature of the disorder in studied solid solutions. Intermolecular interactions are analyzed in terms of Hirshfeld surfaces and by means of density functional theory calculations to explore the differences of isostructural <i>quasi</i>-centrosymmetric (enantiopure) and genuine centrosymmetric (racemic) packings to shed light on the energetic aspects of solid solution formation as well as to explain the origin of partial enantioselectivity. Furthermore, lattice energy calculations explain why two structurally distinct solid solutions (around the racemic and near the pure enantiomer regions) form as found for one of the studied compounds