GASP: software for geometric simulations of flexibility in polyhedral and molecular framework structures

Dynamics in the ordered and disordered phases of barocaloric adamantane

High-entropy order-disorder phase transitions can be used for efficient and eco-friendly barocaloric solid-state cooling. Here the barocaloric effect is reported in an archetypal plastic crystal, adamantane. Adamantane has a colossal isothermally reversible entropy change of 106 J K^-1 kg^-1. Extremely low hysteresis means that this can be accessed at pressure differences less than 200 bar. Configurational entropy can only account for about 40% of the total entropy change; the remainder is due to vibrational effects. Using neutron spectroscopy and supercell lattice dynamics calculations, it is found that this vibrational entropy change is mainly caused by softening in the high-entropy phase of acoustic modes that correspond to molecular rotations. We attribute this difference in the dynamics to the contrast between an 'interlocked' state in the low-entropy phase and sphere-like behaviour in the high-entropy phase. Although adamantane is a simple van der Waals solid with near-spherical molecules, this approach can be leveraged for the design of more complex barocaloric molecular crystals. Moreover, this study shows that supercell lattice dynamics calculations can accurately map the effect of orientational disorder on the phonon spectrum, paving the way for studying the vibrational entropy, thermal conductivity, and other thermodynamic effects in more complex materials.

Dynamic tilting in perovskites

A new computational analysis of tilt behaviour in perovskites is presented. This includes the development of a computational program - PALAMEDES - to extract tilt angles and the tilt phase from molecular dynamics simulations. The results are used to generate simulated selected-area electron and neutron diffraction patterns which are compared with experimental patterns for CaTiO₃. The simulations not only reproduced all symmetrically allowed superlattice reflections associated with tilt but also showed local correlations that give rise to symmetrically forbidden reflections and the kinematic origin of diffuse scattering.

Cisplatin uptake and release in pH sensitive zeolitic imidazole frameworks

Cancer remains hard to treat, partially due to the non-specificity of chemotherapeutics. Metal-organic frameworks (MOFs) are promising carriers for targeted chemotherapy, yet, to date, there have been few detailed studies to systematically enhance drug loading while maintaining controlled release. In this work, we investigate which molecular simulation methods best capture the experimental uptake and release of cisplatin from UiO-66 and UiO-66(NH₂). We then screen a series of biocompatible, pH-sensitive zeolitic imidazolate frameworks (ZIFs) for their ability to retain cisplatin in healthy parts of the patient and release it in the vicinity of a tumor. Pure-component GCMC simulations show that the maximum cisplatin loading depends on the pore volume. To achieve this maximum loading in the presence of water, either the pore size needs to be large enough to occupy both cisplatin and its solvation shell or the MOF-cisplatin interaction must be more favorable than the cisplatin-shell interaction. Both solvated and non-solvated simulations show that cisplatin release rates can be controlled by either decreasing the pore limiting diameters or by manipulating framework-cisplatin interaction energies to create strong, dispersed adsorption sites. The latter method is preferable if cisplatin loading is performed from solution into a pre-synthesized framework as weak interaction energies and small pore window diameters will hinder cisplatin uptake. Here, ZIF-82 is most promising. If it is possible to load cisplatin during crystallization, ZIF-11 would outcompete the other MOFs screened as cisplatin cannot pass through its pore windows; therefore, release rates would be purely driven by the pH triggered framework degradation.

Using geometric simulation software ‘GASP’ to model conformational flexibility in a family of zinc metal–organic frameworks

Synthesis with different solvents leads the same metals and ligands to assemble into geometrically and topologically distinct frameworks, aided by intrinsic flexibility of the ligand.

Determining the structure of zeolite frameworks at high pressures

The study of porous materials under high-pressure conditions is crucial for the understanding and development of structure–property relationships.

The steric influence of extra-framework cations on framework flexibility: an LTA case study

The theoretical extent of framework flexibility of Zeolite A (LTA) in response to the steric and geometric effects of different Si/Al compositions and extra-framework cation content has been explored using GASP software. Flexibility windows and compression mechanisms for siliceous LTA and aluminosilicate Na-LTA, Ca-LTA and K-LTA have been modelled. As expected, relatively small cations in the zeolite pores have little effect on the range of flexibility observed. Aluminosilicate LTA, Na-LTA and Ca-LTA frameworks exhibit identical flexibility windows and these frameworks also follow the same compression mechanisms. The introduction of larger K+ ions, however, results in greater steric hindrance. This restricts the flexibility of the framework and alters the compression mechanism to accommodate these larger cations. It is shown that the limits of the flexibility window of Zeolite A are dependent on framework aluminium content and extra-framework cation size.

Pressure-induced symmetry changes in body-centred cubic zeolites

Previous work has shown a strong correlation between zeolite framework flexibility and the nature of structural symmetry and phase transitions. However, there is little experimental data regarding this relationship, in addition to how flexibility can be connected to the synthesis of these open-framework materials. This is of interest for the synthesis of novel zeolites, which require organic additives to permutate the resulting geometry and symmetry of the framework. Here, we have used high-pressure powder X-ray diffraction to study the three zeolites: Na-X, RHO and ZK-5, which can all be prepared using 18-crown-6 ether as an organic additive. We observe significant differences in how the occluded 18-crown-6 ether influences the framework flexibility-this being dependent on the geometry of the framework. We use these differences as an indicator to define the role of 18-crown-6 ether during zeolite crystallization. Furthermore, in conjunction with previous work, we predict that pressure-induced symmetry transitions are intrinsic to body-centred cubic zeolites. The high symmetry yields fewer degrees of freedom, meaning it is energetically favourable to lower the symmetry to facilitate further compression.

Advances in Sustainable Catalysis: A Computational Perspective

The enormous challenge of moving our societies to a more sustainable future offers several exciting opportunities for computational chemists. The first principles approach to "catalysis by design" will enable new and much greener chemical routes to produce vital fuels and fine chemicals. This prospective outlines a wide variety of case studies to underscore how the use of theoretical techniques, from QM/MM to unrestricted DFT and periodic boundary conditions, can be applied to biocatalysis and to both homogeneous and heterogenous catalysts of all sizes and morphologies to provide invaluable insights into the reaction mechanisms they catalyze.

Intrinsic Flexibility of the EMT Zeolite Framework under Pressure

The roles of organic additives in the assembly and crystallisation of zeolites are still not fully understood. This is important when attempting to prepare novel frameworks to produce new zeolites. We consider 18-crown-6 ether (18C6) as an additive, which has previously been shown to differentiate between the zeolite EMC-2 (EMT) and faujasite (FAU) frameworks. However, it is unclear whether this distinction is dictated by influences on the metastable free-energy landscape or geometric templating. Using high-pressure synchrotron X-ray diffraction, we have observed that the presence of 18C6 does not impact the EMT framework flexibility-agreeing with our previous geometric simulations and suggesting that 18C6 does not behave as a geometric template. This was further studied by computational modelling using solid-state density-functional theory and lattice dynamics calculations. It is shown that the lattice energy of FAU is lower than EMT, but is strongly impacted by the presence of solvent/guest molecules in the framework. Furthermore, the EMT topology possesses a greater vibrational entropy and is stabilised by free energy at a finite temperature. Overall, these findings demonstrate that the role of the 18C6 additive is to influence the free energy of crystallisation to assemble the EMT framework as opposed to FAU.

Adventures in boron chemistry - the prediction of novel ultra-flexible boron oxide frameworks

Recent periodic density functional calculations have predicted the existence of ultra-flexible low-energy forms of boron oxides in which rigid boron-oxygen heterocycles are linked by flexible B-O-B bridges. The minima in the energy landscapes of these frameworks are remarkably broad, with widths in excess of those of many hybrid metal-organic frameworks. Enormous changes in cell volume, which can exceed a factor of two, are accompanied by negligible changes in energy. Here we explore the underlying reasons for this behaviour using molecular electronic-structure calculations, periodic density functional theory and template-based geometric simulations. The angular flexibility of the B-O-B bridge depends only upon the geometry of the local B2O5 unit, independent of the configuration of neighbouring bridges. Unique cooperativity between the bending and twisting motions of the bridges leads to considerable anisotropy in framework flexibility. Exceptional flexibility is conferred not only by the intrinsic bending flexibility of the bridges but by topological factors, crucially the relaxation of torsional constraints when B3O3 rings are present. We test these conclusions by showing how the flexibility of the frameworks can be tuned by decoration with isoelectronic rings. The new nanoporous boron oxides presented in this work are predicted to be potential novel guest-host materials because of their flat energy landscapes. Furthermore, such structures can be generated systematically from silicates by the substitution of B2O54- for SiO44-. A borate analogue of β-cristobalite is shown to be isoenergetic with the known B2O3-I polymorph. We raise the possibility of new families of frameworks and zeolite analogues.

Coupling of emergent octahedral rotations to polarization in (K,Na)NbO3 ferroelectrics

Perovskite potassium sodium niobates, K_1−xNa_xNbO₃, are promising lead-free piezoelectrics. Their dielectric and piezoelectric characteristics peak near x = 0.5, but the reasons for such property enhancement remain unclear. We addressed this uncertainty by analyzing changes in the local and average structures across the x = 0.5 composition, which have been determined using simultaneous Reverse Monte Carlo fitting of neutron and X-ray total-scattering data, potassium EXAFS, and diffuse-scattering patterns in electron diffraction. Within the A-sites, Na cations are found to be strongly off-centered along the polar axis as a result of oversized cube-octahedral cages determined by the larger K ions. These Na displacements promote off-centering of the neighboring Nb ions, so that the Curie temperature and spontaneous polarization remain largely unchanged with increasing x, despite the shrinking octahedral volumes. The enhancement of the properties near x = 0.5 is attributed to an abrupt increase in the magnitude and probability of the short-range ordered octahedral rotations, which resembles the pre-transition behavior. These rotations reduce the bond tension around Na and effectively soften the short Na-O bond along the polar axis – an effect that is proposed to facilitate reorientation of the polarization as external electric field is applied.

Advancing reverse Monte Carlo structure refinements to the nanoscale

Over the past decade, theRMCProfilesoftware package has evolved into a powerful computational framework for atomistic structural refinements using a reverse Monte Carlo (RMC) algorithm and multiple types of experimental data. However, realizing the full potential of this method, which can provide a consistent description of atomic arrangements over several length scales, requires a computational speed much higher than that permitted by the current software. This problem has been addressedviasubstantial optimization and development ofRMCProfile, including the introduction of the new parallel-chains RMC algorithm. The computing speed of this software has been increased by nearly two orders of magnitude, as demonstrated using the refinements of a simulated structure with two distinct correlation lengths for the atomic displacements. The new developments provide a path for achieving even faster performance as more advanced computing hardware becomes available. This version ofRMCProfilepermits refinements of atomic configurations of the order of 500 000 atoms (compared to the current limit of 20 000), which sample interatomic distances up to 10 nm (versus3 nm currently). Accurate, computationally efficient corrections of the calculated X-ray and neutron total scattering data have been developed to account for the effects of instrumental resolution. These corrections are applied in both reciprocal and real spaces, thereby enabling RMC fitting of an atomic pair distribution function, which is obtained as the Fourier transform of the total-scattering intensity, over the entire nanoscale distance range accessible experimentally.

Defining the flexibility window in ordered aluminosilicate zeolites

The flexibility window in zeolites was originally identified using geometric simulation as a hypothetical property of SiO₂ systems. The existence of the flexibility window in hypothetical structures may help us to identify those we might be able to synthesize in the future. We have previously found that the flexibility window in silicates is connected to phase transitions under pressure, structure amorphization and other physical behaviours and phenomena. We here extend the concept to ordered aluminosilicate systems using softer 'bar' constraints that permit additional flexibility around aluminium centres. Our experimental investigation of pressure-induced amorphization in sodalites is consistent with the results of our modelling. The softer constraints allow us to identify a flexibility window in the anomalous case of goosecreekite.

An Exhaustive Symmetry Approach to Structure Determination: Phase Transitions in Bi2Sn2O7

The exploitable properties of many materials are intimately linked to symmetry-lowering structural phase transitions. We present an automated and exhaustive symmetry-mode method for systematically exploring and solving such structures which will be widely applicable to a range of functional materials. We exemplify the method with an investigation of the Bi2Sn2O7 pyrochlore, which has been shown to undergo transitions from a parent γ cubic phase to β and α structures on cooling. The results include the first reliable structural model for β-Bi2Sn2O7 (orthorhombic Aba2, a = 7.571833(8), b = 21.41262(2), and c = 15.132459(14) Å) and a much simpler description of α-Bi2Sn2O7 (monoclinic Cc, a = 13.15493(6), b = 7.54118(4), and c = 15.07672(7) Å, β = 125.0120(3)°) than has been presented previously. We use the symmetry-mode basis to describe the phase transition in terms of coupled rotations of the Bi2O' anti-cristobalite framework, which allow Bi atoms to adopt low-symmetry coordination environments favored by lone-pair cations.

Intrinsic flexibility of porous materials; theory, modelling and the flexibility window of the EMT zeolite framework

Framework materials have structures containing strongly bonded polyhedral groups of atoms connected through their vertices. Typically the energy cost for variations of the inter-polyhedral geometry is much less than the cost of distortions of the polyhedra themselves - as in the case of silicates, where the geometry of the SiO4 tetrahedral group is much more strongly constrained than the Si-O-Si bridging angle. As a result, framework materials frequently display intrinsic flexibility, and their dynamic and static properties are strongly influenced by low-energy collective motions of the polyhedra. Insight into these motions can be obtained in reciprocal space through the `rigid unit mode' (RUM) model, and in real-space through template-based geometric simulations. We briefly review the framework flexibility phenomena in energy-relevant materials, including ionic conductors, perovskites and zeolites. In particular we examine the `flexibility window' phenomenon in zeolites and present novel results on the flexibility window of the EMT framework, which shed light on the role of structure-directing agents. Our key finding is that the crown ether, despite its steric bulk, does not limit the geometric flexibility of the framework.