Diffuse scattering and partial disorder in complex structures

A solid solution to computational challenges presented by crystal structures exhibiting disorder

Crystal structues exhibiting disorder still present a barrier for many computational methods. Dittrich et al. [(2024). IUCrJ, 11, 347-358] showcase a unified approach, tackling solid solutions, near symmetry and more.

Hydrogen atoms in supramolecular chemistry: a structural perspective. Where are they, and why does it matter?

Hydrogen bonding interactions are ubiquitous across the biochemical and chemical sciences, and are of particular interest to supramolecular chemists. They have been used to assemble hydrogen bonded polymers, cages and frameworks, and are the functional motif in many host-guest systems. Single crystal X-ray diffraction studies are often used as a key support for proposed structures, although this presents challenges as hydrogen atoms interact only weakly with X-rays. In this Tutorial Review, we discuss the information that can be gleaned about hydrogen bonding interactions through crystallographic experiments, key limitations of the data, and emerging techniques to overcome these limitations.

Ligand and solvent effects on the absorption spectra of CdS magic-sized clusters

The absorption spectra of congenetic wurtzite (WZ) and zincblende (ZB) CdS magic-sized clusters are investigated. We demonstrate that the exciton peak positions can be tuned by up to 500 meV by varying the strong coupling between X-type ligands and the semiconductor cores, while the addition of L-type ligands primarily affects cluster midgap states. When Z-type ligands are displaced by L-type ligands, red shifts in the absorption spectra are observed, despite the fact there is a small decrease in cluster size. Density functional theory calculations are used to explain these findings and they reveal the importance of Cd and S dangling bonds on the midgap states during the Z- to L-type ligand exchange process. Overall, ZB CdS clusters show higher chemical stability than WZ clusters but their optical properties exhibit greater sensitivity to the solvent. Conversely, WZ CdS clusters are not stable in a Lewis base-rich environment, resulting in various changes in their spectra. Our findings enable researchers to select capping ligands that modulate the optical properties of semiconductor clusters while maintaining precise control over their solvent interactions.

Unlocking New Topologies in Zr-Based Metal-Organic Frameworks by Combining Linker Flexibility and Building Block Disorder

The outstanding diversity of Zr-based frameworks is inherently linked to the variable coordination geometry of Zr-oxo clusters and the conformational flexibility of the linker, both of which allow for different framework topologies based on the same linker-cluster combination. In addition, intrinsic structural disorder provides a largely unexplored handle to further expand the accessibility of novel metal-organic framework (MOF) structures that can be formed. In this work, we report the concomitant synthesis of three topologically different MOFs based on the same M₆O₄(OH)₄ clusters (M = Zr or Hf) and methane-tetrakis(p-biphenyl-carboxylate) (MTBC) linkers. Two novel structural models are presented based on single-crystal diffraction analysis, namely, cubic c-(4,12)MTBC-M₆ and trigonal tr-(4,12)MTBC-M₆, which comprise 12-coordinated clusters and 4-coordinated tetrahedral linkers. Notably, the cubic phase features a new architecture based on orientational cluster disorder, which is essential for its formation and has been analyzed by a combination of average structure refinements and diffuse scattering analysis from both powder and single-crystal X-ray diffraction data. The trigonal phase also features structure disorder, although involving both linkers and secondary building units. In both phases, remarkable geometrical distortion of the MTBC linkers illustrates how linker flexibility is also essential for their formation and expands the range of achievable topologies in Zr-based MOFs and its analogues.

Efficient fitting of single-crystal diffuse scattering in interaction space: a mean-field approach

The diffraction patterns of crystalline materials with strongly correlated disorder are characterized by the presence of structured diffuse scattering. Conventional analysis approaches generally seek to interpret this scattering either atomistically or in terms of pairwise (Warren-Cowley) correlation parameters. Here it is demonstrated how a mean-field methodology allows efficient fitting of diffuse scattering directly in terms of a microscopic interaction model. In this way the approach gives as its output the underlying physics responsible for correlated disorder. Moreover, the use of a very small number of parameters during fitting renders the approach surprisingly robust to data incompleteness, a particular advantage when seeking to interpret single-crystal diffuse scattering measured in complex sample environments. As the basis of this proof-of-concept study, a toy model is used based on strongly correlated disorder in diammine mercury(II) halides.

rmc-discord: reverse Monte Carlo refinement of diffuse scattering and correlated disorder from single crystals

A user-friendly Python-based program has been developed to analyze diffuse scattering from single crystals with the reverse Monte Carlo method. The approach allows for refinement of correlated disorder from atomistic supercells with magnetic or structural (occupational and/or displacive) disorder.

A user-friendly program has been developed to analyze diffuse scattering from single crystals with the reverse Monte Carlo method. The approach allows for refinement of correlated disorder from atomistic supercells with magnetic or structural (occupational and/or displacive) disorder. The program is written in Python and optimized for performance and efficiency. Refinements of two user cases obtained with legacy neutron-scattering data demonstrate the effectiveness of the approach and the developed program. It is shown with bixbyite, a naturally occurring magnetic mineral, that the calculated three-dimensional spin-pair correlations are resolved with finer real-space resolution compared with the pair distribution function calculated directly from the reciprocal-space pattern. With the triangular lattice Ba₃Co₂O₆(CO₃)_0.7, refinements of occupational and displacive disorder are combined to extract the one-dimensional intra-chain correlations of carbonate molecules that move toward neighboring vacant sites to accommodate strain induced by electrostatic interactions. The program is packaged with a graphical user interface and extensible to serve the needs of single-crystal diffractometer instruments that collect diffuse-scattering data.

Revisiting the Structure of Calcined and Hydrated AlPO-11 with DFT-Based Molecular Dynamics Simulations*

Published crystal structures of the AEL-type aluminophosphate AlPO-11 in its calcined form (space group I m a 2 ) show some peculiar features, such as unusually short Al-O and P-O bonds and near-linear Al-O-P angles. Although experimental evidence for the presence of dynamic disorder was presented, the nature of the associated distortions remained unresolved. In this study, ab initio molecular dynamics (AIMD) calculations in the framework of density functional theory (DFT) were employed to study the dynamic behaviour of this zeotype. At 100 K, static local distortions that break the I m a 2 symmetry are present in the time-averaged structures computed from the AIMD trajectories. At 300 and 500 K, the time-averaged structures approach I m a 2 symmetry. Although shortened Al-O and P-O bonds and near-linear Al-O-P angles were found in the average structures, an analysis of radial and angular distribution functions confirmed their absence in the instantaneous structures. This deviation is due to a precession-like motion of some oxygen atoms around the Al-P connection line, which moves their time-averaged positions closer to this line. In hydrated AlPO-11, some of the water molecules are coordinated to framework Al atoms, leading to an octahedral coordination of 1/5 of the Al sites. DFT optimisations and AIMD simulations on partially hydrated models delivered evidence for a preferential adsorption at the Al1 site. No dynamic disorder was observed for the hydrated form.

Opportunities and challenges in understanding complex functional materials

Understanding complex functional materials suffers from needing to capture structural features on many length scales. By quantitatively combining complementary experimental measurements, realistic models can now be generated. Here, I discuss the strengths and limits of this approach, but also advocate focusing on the interactions that drive structural complexity instead.

Inorganic co-crystal formation and thermal disproportionation in a dicyanometallate ‘superperovskite’

The dicyanometallate superperovskite co-crystal [NBu₄]Mn[Au(CN)₂]₃·[NBu₄]ClO₄ illustrates a new type of structural and phase complexity accessible to dicyanometallate perovskites.

Stabilization of Polar Nanoregions in Pb-free Ferroelectrics

The formation of polar nanoregions through solid-solution additions is known to enhance significantly the functional properties of ferroelectric materials. Despite considerable progress in characterizing the microscopic behavior of polar nanoregions (PNR), understanding their real-space atomic structure and dynamics of their formation remains a considerable challenge. Here, using the method of dynamic pair distribution function, we provide direct insights into the role of solid-solution additions towards the stabilization of polar nanoregions in the Pb-free ferroelectric of Ba(Zr,Ti)O_{3}. It is shown that for an optimum level of substitution of Ti by larger Zr ions, the dynamics of atomic displacements for ferroelectric polarization are slowed sufficiently below THz frequencies, which leads to increased local correlation among dipoles within PNRs. The dynamic pair distribution function technique demonstrates a unique capability to obtain insights into locally correlated atomic dynamics in disordered materials, including new Pb-free ferroelectrics, which is necessary to understand and control their functional properties.

Evaluation of General and Tailor Made Force Fields via X-ray Thermal Diffuse Scattering Using Molecular Dynamics and Monte Carlo Simulations of Crystalline Aspirin

We have performed a comparison of the experimental thermal diffuse scattering (TDS) from crystalline Aspirin (form I) to that calculated from molecular dynamics (MD) simulations based on a variety of general force fields and a tailor-made force field (TMFF). A comparison is also made with Monte Carlo (MC) simulations which use a "harmonic network" approach to describe the intermolecular interactions. These comparisons were based on the hypothesis that TDS could be a useful experimental data in validation of such simulation parameter sets, especially when calculations of dynamical properties (e.g., thermodynamic free energies) from molecular crystals are concerned. Currently such a validation of force field parameters against experimental data is often limited to calculation of specific physical properties, e.g., absolute lattice energies usually at 0 K or heat capacity measurements. TDS harvested from in-house or synchrotron experiments comprises highly detailed structural information representative of the dynamical motions of the crystal lattice. Thus, TDS is a well-suited experimental data-driven means of cross validating theoretical approaches targeted at understanding dynamical properties of crystals. We found from the results of our investigation that the TMFF and COMPASS (from the commercial software "Materials Studio") parameter sets gave the best agreement with experiment. From our homologous MC simulation analysis we are able to show that force constants associated with the molecular torsion angles are likely to be a strong contributing factor for the apparent reason why these aforementioned force fields performed better.

A method to perform modulated structure studies using the programZMC

The Monte Carlo simulation toolkitZMCprovides a general method for Monte Carlo simulation of disordered molecular displacements, orientations and site occupations. It is part of a suite of programs that allows convenient calculation of three-dimensional reciprocal space diffraction intensities. Such intensities are useful for extensive structure interpretations from diffraction experiments. Some physical properties can also be calculated from the simulation. This article reports the implementation of an integratedZMCmodule that facilitates the construction of modulated molecular crystals and allows the corresponding calculation of modulation satellites. Use of the module is explained and examples illustrated. The method is ideally suited for novice treatment of modulated structure features and also as a basic platform to explore complex structure/properties relationships using atomistic simulation techniques.

Local disorder in Na0.5Bi0.5TiO3-piezoceramic determined by 3D electron diffuse scattering

Local structural distortions in Na_0.5Bi_0.5TiO₃-based solid solutions have been proved to play a crucial role in understanding and tuning their enhanced piezoelectric properties near the morphotropic phase boundary. In this work all local structural disorders in a lead-free ternary system, namely 85%Na_0.5Bi_0.5TiO₃-10%Bi_0.5K_0.5TiO₃-5%BaTiO₃, were mapped in reciprocal space by 3D electron diffraction. Furthermore, a comprehensive model of the local disorder was developed by analysing the intensity and morphology of the observed weak diffuse scattering. We found that the studied ceramics consists of plate-like in-phase oxygen octahedral nanoscale domains randomly distributed in an antiphase tilted matrix. In addition, A-site chemical short-range order of Na/Bi and polar displacements contribute to different kinds of diffuse scattering. The proposed model explains all the observed diffraction features and offers insight into the ongoing controversy over the nature of local structural distortions in Na_0.5Bi_0.5TiO₃-based solid solutions.

Temperature-induced reversible structural phase transition and X-ray diffuse scattering in 2-amino-3-nitropyridinium hydrogen sulfate

The novel polar material 2-amino-3-nitropyridinium hydrogen sulfate, C5H6N3O2(HSO4) (abbreviated as 2A3NP-HS), was obtained and structurally characterized by means of single-crystal X-ray diffraction. At room temperature, 2A3NP-HS crystallizes as a non-centrosymmetric disordered phase (I) in the orthorhombicPna21space group. On cooling below 298 K, 2A3NP-HS undergoes a reversible phase transition to phase (II) with the monoclinic non-centrosymmetricP21space group. This transition might be classified as an `order–disorder' type. The structural details in both phases are analysed. Additionally, for phase (I), in the 304–365 K temperature range, diffuse scattering was found to be present in the form of elongated streaks parallel to thea* direction. This can be unravelled when implementing a short-range order affecting anionic cationic ribbons occurring in the structure, with correlations acting both in thea-direction and in thebc-plane. The results of Monte Carlo simulations, adapting a two-dimensional Ising-type model, reveal the formation of domains, which areb-elongated and thin alonga. Locally, the stacking of the ribbons in the domains reflects the ordered arrangement observed in the low-temperature monoclinic phase (II).

A rapid two-dimensional data collection system for the study of ferroelectric materials under external applied electric fields

Synchrotron X-rays on the Swiss Norwegian Beamline and BM28 (XMaS) at the ESRF have been used to record the diffraction response of the PMN-PT relaxor piezoelectric 67% Pb(Mg_1/3Nb_2/3)O₃-33% PbTiO₃ as a function of externally applied electric field. A DC field in the range 0-18 kV cm^-1 was applied along the [001] pseudo-cubic direction using a specially designed sample cell for in situ single-crystal diffraction experiments. The cell allowed data to be collected on a Pilatus 2M area detector in a large volume of reciprocal space using transmission geometry. The data showed good agreement with a twinned single-phase monoclinic structure model. The results from the area detector were compared with previous Bragg peak mapping using variable electric fields and a single detector where the structural model was ambiguous. The coverage of a significantly larger section of reciprocal space facilitated by the area detector allowed precise phase analysis.

An insight into real and average structure from diffuse X-ray scattering - a case study

Two-dimensional diffuse X-ray scattering from an organic salt [N-(3-(2,6-dimethylanilino)-1-methylbut-2-enylidene)-2,6-dimethylanilinium chloride, C21H27N2(+)Cl(-)] was interpreted with the help of an analytical model of diffuse scattering. An analysis of the relationship between symmetry and diffuse scattering for the studied system has been undertaken. The symmetry of the system explains the extinction pattern, taking the form of curves, on the diffuse scattering planes. We have also tested the relationship between the average structure model and scattering intensities. Two models, differing in their representation of overlapping atoms, were used. In the case of diffuse scattering the difference between resulting intensities is immense, while for the Bragg intensities it is much smaller. This sensitivity of diffuse scattering could potentially be used to improve the description of the average structure.

On the use of molecular dynamics simulation to calculate X-ray thermal diffuse scattering from molecular crystals

The use of molecular dynamics simulations to calculate the thermal diffuse scattering from X-ray diffraction experiments on molecular crystals is described, using the crystal structure of aspirin form I as an example system. Parameter settings that do not affect the actual simulation are varied in order to examine the effect on the final calculated diffraction pattern, and thus roughly determine a range for general settings that might be used in further experiments targeted at tailoring parameters associated with the functional forms for dispersion interaction terms commonly used in molecular simulation force fields. The proposed method is compared with that of the more widely accepted Monte Carlo technique, and possible advantages and drawbacks for the use of either method are discussed.

Recent developments in the structural science of materials

This Editorial surveys the current status and recent developments in the structural science of materials as exemplified by the articles recently published in IUCrJ.

Revealing the Mechanisms of Protein Disorder and N-Glycosylation in CD44-Hyaluronan Binding Using Molecular Simulation

The extracellular N-terminal hyaluronan binding domain (HABD) of CD44 is a small globular domain that confers hyaluronan (HA) binding functionality to this large transmembrane glycoprotein. When recombinantly expressed by itself, HABD exists as a globular water-soluble protein that retains the capacity to bind HA. This has enabled atomic-resolution structural biology experiments that have revealed the structure of HABD and its binding mode with oligomeric HA. Such experiments have also pointed to an order-to-disorder transition in HABD that is associated with HA binding. However, it had remained unclear how this structural transition was involved in binding since it occurs in a region of HABD distant from the HA-binding site. Furthermore, HABD is known to be N-glycosylated, and such glycosylation can diminish HA binding when the associated N-glycans are capped with sialic acid residues. The intrinsic flexibility of disordered proteins and of N-glycans makes it difficult to apply experimental structural biology approaches to probe the molecular mechanisms of how the order-to-disorder transition and N-glycosylation can modulate HA binding by HABD. We review recent results from molecular dynamics simulations that provide atomic-resolution mechanistic understanding of such modulation to help bridge gaps between existing experimental binding and structural biology data. Findings from these simulations include: Tyr42 may function as a molecular switch that converts the HA-binding site from a low affinity to a high affinity state; in the partially disordered form of HABD, basic amino acids in the C-terminal region can gain sufficient mobility to form direct contacts with bound HA to further stabilize binding; and terminal sialic acids on covalently attached N-glycans can form charge-paired hydrogen bonding interactions with basic amino acids that could otherwise bind to HA, thereby blocking HA binding to glycosylated CD44 HABD.