Dynamics and Thermodynamics of Crystalline Polymorphs. 3. γ-Glycine, Analysis of Variable-Temperature Atomic Displacement Parameters, and Comparison of Polymorph Stabilities

Dynamics and disorder: on the stability of pyrazinamide polymorphs

The enantiotropic relationship between the four polymorphs of pyrazinamide is analyzed by means of accurate X-ray diffraction measurements, normal-mode refinement and periodic DFT calculations.

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 abinitio 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.

Crystal structures

A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X-ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry.

Low-frequency lattice vibrations from atomic displacement parameters of α-FOX-7, a high energy density material

The normal mode analysis of variable-tem­per­ature anisotropic atomic displacement parameters (ADPs) of the α-phase of 1,1-di­amino-2,2-di­nitro­ethyl­ene (DADNE or FOX-7) is reported.

Highly anharmonic thermal vibrations may serve as a source of structural instabilities resulting in phase transitions, chemical reactions and even the mechanical disintegration of a material. Ab initio calculations model thermal motion within a harmonic or sometimes quasi-harmonic approximation and must be com­plimented by experimental data on tem­per­ature-dependent vibrational frequencies. Here multi-tem­per­ature atomic displacement parameters (ADPs), derived from a single-crystal synchrotron diffraction experiment, are used to characterize low-frequency lattice vibrations in the α-FOX-7 layered structure. It is shown that despite the limited quality of the data, the extracted frequencies are reasonably close to those derived from inelastic scattering, Raman measurements and density functional theory (DFT) calculations. Vibrational anharmonicity is parameterized by the Grüneisen parameters, which are found to be very different for in-layer and out-of-layer vibrations.

Theoretically derived thermodynamic properties can be improved by the refinement of low-frequency modes against X-ray diffraction data

Herein, a framework for the estimation of the thermodynamic properties of molecular crystals via the refinement of frequencies from density functional theory calculations against X-ray diffraction data is presented. The framework provides an efficient approach to including the contribution of acoustic modes in the thermodynamic properties. The obtained heat capacities for urea, the α- and β-glycine polymorphs, benzoic acid, and 4'-hydroxyacetophenone are in good agreement with those from adiabatic calorimetry.

X-ray diffraction data as a source of the vibrational free-energy contribution in polymorphic systems

In this contribution we attempt to answer a general question: can X-ray diffraction data combined with theoretical computations be a source of information about the thermodynamic properties of a given system? Newly collected sets of high-quality multi-temperature single-crystal X-ray diffraction data and complementary periodic DFT calculations of vibrational frequencies and normal mode vectors at the Γ point on the yellow and white polymorphs of di-methyl 3,6-di-chloro-2,5-di-hydroxy-terephthalate are combined using two different approaches, aiming to obtain thermodynamic properties for the two compounds. The first approach uses low-frequency normal modes extracted from multi-temperature X-ray diffraction data (normal coordinate analysis), while the other uses DFT-calculated low-frequency normal mode in the refinement of the same data (normal mode refinement). Thermodynamic data from the literature [Yang et al. (1989), Acta Cryst. B45, 312-323] and new periodic ab initio DFT supercell calculations are used as a reference point. Both approaches tested in this work capture the most essential features of the systems: the polymorphs are enantiotropically related, with the yellow form being the thermodynamically stable system at low temperature, and the white form at higher temperatures. However, the inferred phase transition temperature varies between different approaches. Thanks to the application of unconventional methods of X-ray data refinement and analysis, it was additionally found that, in the case of the yellow polymorph, anharmonicity is an important issue. By discussing contributions from low- and high-frequency modes to the vibrational entropy and enthalpy, the importance of high-frequency modes is highlighted. The analysis shows that larger anisotropic displacement parameters are not always related to the polymorph with the higher vibrational entropy contribution.

Comments on 'Hydrogen bonds in crystalline d-alanine: diffraction and spectroscopic evidence for differences between enantiomers'

The recent paper by Belo, Pereira, Freire, Argyriou, Eckert & Bordallo [(2018 ▸), IUCrJ, 5, 6-12] reports observations that may lead one to think of very strong and visible consequences of the parity-violation energy difference between enantiomers of a molecule, namely alanine. If proved, this claim would have an enormous impact for research in structural chemistry. However, alternative, more realistic, explanations of their experiments have not been ruled out by the authors. Moreover, the theoretical calculations carried out to support the hypothesis are unable to differentiate between enantiomers (molecules or crystals). Therefore, the conclusions drawn by Belo et al. (2018 ▸) are deemed inappropriate as the data presented do not contain sufficient information to reach such a conclusion.

A crystal structure prediction enigma solved: the gallic acid monohydrate system - surprises at 10 K

The seemingly unpredictable structure of gallic acid monohydrate form IV has been investigated using accurate X-ray diffraction measurements at temperatures of 10 and 123 K. The measurements demonstrate that the structure is commensurately modulated at 10 K and disordered at higher temperatures. Aided by charge-density modeling and periodic DFT calculations we show that the disorder gives a substantial stabilization of the structure.

Does Z' equal 1 or 2? Enhanced powder NMR crystallography verification of a disordered room temperature crystal structure of a p38 inhibitor for chronic obstructive pulmonary disease

The crystal structure of the Form A polymorph of N-cyclopropyl-3-fluoro-4-methyl-5-[3-[[1-[2-[2-(methylamino)ethoxy]phenyl]cyclopropyl]amino]-2-oxo-pyrazin-1-yl]benzamide (i.e., AZD7624), determined using single-crystal X-ray diffraction (scXRD) at 100 K, contains two molecules in the asymmetric unit (Z' = 2) and has regions of local static disorder. This substance has been in phase IIa drug development trials for the treatment of chronic obstructive pulmonary disease, a disease which affects over 300 million people and contributes to nearly 3 million deaths annually. While attempting to verify the crystal structure using nuclear magnetic resonance crystallography (NMRX), we measured ¹³C solid-state NMR (SSNMR) spectra at 295 K that appeared consistent with Z' = 1 rather than Z' = 2. To understand this surprising observation, we used multinuclear SSNMR (¹H, ¹³C, ¹⁵N), gauge-including projector augmented-wave density functional theory (GIPAW DFT) calculations, crystal structure prediction (CSP), and powder XRD (pXRD) to determine the room temperature crystal structure. Due to the large size of AZD7624 (ca. 500 amu, 54 distinct ¹³C environments for Z' = 2), static disorder at 100 K, and (as we show) dynamic disorder at ambient temperatures, NMR spectral assignment was a challenge. We introduce a method to enhance confidence in NMR assignments by comparing experimental ¹³C isotropic chemical shifts against site-specific DFT-calculated shift distributions established using CSP-generated crystal structures. The assignment and room temperature NMRX structure determination process also included measurements of ¹³C shift tensors and the observation of residual dipolar coupling between ¹³C and ¹⁴N. CSP generated ca. 90 reasonable candidate structures (Z' = 1 and Z' = 2), which when coupled with GIPAW DFT results, room temperature pXRD, and the assigned SSNMR data, establish Z' = 2 at room temperature. We find that the polymorphic Form A of AZD7624 is maintained at room temperature, although dynamic disorder is present on the NMR timescale. Of the CSP-generated structures, 2 are found to be fully consistent with the SSNMR and pXRD data; within this pair, they are found to be structurally very similar (RMSD₁₆ = 0.30 Å). We establish that the CSP structure in best agreement with the NMR data possesses the highest degree of structural similarity with the scXRD-determined structure (RMSD₁₆ = 0.17 Å), and has the lowest DFT-calculated energy amongst all CSP-generated structures with Z' = 2.

Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. II. Applications to L-alanine, naphthalene and xylitol

In the first paper of this series [Hoser & Madsen (2016). Acta Cryst. A72, 206-214], a new approach was introduced which enables the refinement of frequencies of normal modes obtained from ab initio periodic computations against single-crystal diffraction data. In this contribution, the performance of this approach is tested by refinement against data in the temperature range from 23 to 205 K on the molecular crystals of L-alanine, naphthalene and xylitol. The models, which are lattice-dynamical models derived at the Γ point of the Brillouin zone, are able to describe the atomic vibrations of L-alanine and naphthalene to a level where the residual densities are similar to those obtained from the independent atom model. For the more flexible molecule xylitol, larger deviations are found. Hydrogen ADPs (anisotropic displacement parameters) derived from the models are in similar or better agreement with neutron diffraction results than ADPs obtained by other procedures. The heat capacity calculated after normal mode refinement for naphthalene is in reasonable agreement with the heat capacity obtained from calorimetric measurements (to less than 1 cal mol^-1 K^-1 below 300 K), with deviations at higher temperatures indicating anharmonicity. Standard uncertainties and correlation of the refined parameters have been derived based on a Monte Carlo procedure. The uncertainties are quite small and probably underestimated.

Dynamic quantum crystallography: lattice-dynamical models refined against diffraction data. I. Theory

This study demonstrates and tests the refinement of a lattice-dynamical model derived from periodic ab initio calculations at the Γ point against elastic diffraction data (X-ray or neutron). Refinement of only a handful of parameters is sufficient to obtain a similar agreement with the data as the conventional crystallographic model using anisotropic displacement parameters. By refinement against X-ray data, H displacement parameters are obtained which compare favourably with those from neutron diffraction experiments. The approach opens the door for evaluating thermodynamic properties, and for refinement against multi-temperature data, against inelastic diffraction data, spectroscopic information and thermal diffuse scattering data.

Sarcosine and betaine crystals upon cooling: structural motifs unstable at high pressure become stable at low temperatures

The crystal structures of N-methyl derivatives of the simplest amino acid glycine, namely sarcosine (C3H7NO2) and betaine (C5H11NO2), were studied upon cooling by single-crystal X-ray diffraction and single-crystal polarized Raman spectroscopy. The effects of decreasing temperature and increasing hydrostatic pressure on the crystal structures were compared. In particular, we have studied the behavior upon cooling of those structural motifs in the crystals, which are involved in structural rearrangement during pressure-induced phase transitions. In contrast to their high sensitivity to hydrostatic compression, the crystals of both sarcosine and betaine are stable to cooling down to 5 K. Similarly to most α-amino acids, the crystal structures of the two compounds are most rigid upon cooling in the direction of the main structural motif, namely head-to-tail chains (linked via the strongest N-H···O hydrogen bonds and dipole-dipole interactions in the case of sarcosine, or exclusively by dipole-dipole interactions in the case of betaine). The anisotropy of linear strain in betaine does not differ much upon cooling and on hydrostatic compression, whereas this is not the case for sarcosine. Although the interactions between certain structural motifs in sarcosine and betaine weaken as a result of phase transitions induced by pressure, the same interactions strengthen when volume reduction results from cooling.