OGRe: Optimal Grid Refinement Protocol for Accurate Free Energy Surfaces and Its Application in Proton Hopping in Zeolites and 2D COF Stacking.

While free energy surfaces are the crux of our understanding of many chemical and biological processes, their accuracy is generally unknown. Moreover, many developments to improve their accuracy are often complicated, limiting their general use. Luckily, several tools and guidelines are already in place to identify these shortcomings, but they are typically lacking in flexibility or fail to systematically determine how to improve the accuracy of the free energy calculation. To overcome these limitations, this work introduces OGRe, a Python package for optimal grid refinement in an arbitrary number of dimensions. OGRe is based on three metrics that gauge the confinement, consistency, and overlap of each simulation in a series of umbrella sampling (US) simulations, an enhanced sampling technique ubiquitously adopted to construct free energy surfaces for hindered processes. As these three metrics are fundamentally linked to the accuracy of the weighted histogram analysis method adopted to generate free energy surfaces from US simulations, they facilitate the systematic construction of accurate free energy profiles, where each metric is driven by a specific umbrella parameter. This allows for the derivation of a consistent and optimal collection of umbrellas for each simulation, largely independent of the initial values, thereby dramatically increasing the ease-of-use toward accurate free energy surfaces. As such, OGRe is particularly suited to determine complex free energy surfaces with large activation barriers and shallow minima, which underpin many physical and chemical transformations and hence to further our fundamental understanding of these processes.

Exploring the phase stability in interpenetrated diamondoid covalent organic frameworks.

Soft porous crystals, which are responsive to external stimuli such as temperature, pressure, or gas adsorption, are being extensively investigated for various technological applications. However, while substantial research has been devoted to stimuli-responsive metal-organic frameworks, structural flexibility in 3D covalent organic frameworks (COFs) remains ill-understood, and is almost exclusively found in COFs exhibiting the diamondoid (dia) topology. Herein, we systemically investigate how the structural decoration of these 3D dia COFs-their specific building blocks and degree of interpenetration-as well as external triggers such as temperature and guest adsorption may promote or suppress their phase transformations, as captured by a collection of 2D free energy landscapes. Together, these provide a comprehensive understanding of the necessary conditions to design flexible diamondoid COFs. This study reveals how their flexibility originates from the balance between steric hindrance and dispersive interactions of the structural decoration, thereby providing insight into how new flexible 3D COFs can be designed.

An embedded interfacial network stabilizes inorganic CsPbI3 perovskite thin films.

The black perovskite phase of CsPbI3 is promising for optoelectronic applications; however, it is unstable under ambient conditions, transforming within minutes into an optically inactive yellow phase, a fact that has so far prevented its widespread adoption. Here we use coarse photolithography to embed a PbI2-based interfacial microstructure into otherwise-unstable CsPbI3 perovskite thin films and devices. Films fitted with a tessellating microgrid are rendered resistant to moisture-triggered decay and exhibit enhanced long-term stability of the black phase (beyond 2.5 years in a dry environment), due to increasing the phase transition energy barrier and limiting the spread of potential yellow phase formation to structurally isolated domains of the grid. This stabilizing effect is readily achieved at the device level, where unencapsulated CsPbI3 perovskite photodetectors display ambient-stable operation. These findings provide insights into the nature of phase destabilization in emerging CsPbI3 perovskite devices and demonstrate an effective stabilization procedure which is entirely orthogonal to existing approaches.

Perspectives on the Influence of Crystal Size and Morphology on the Properties of Porous Framework Materials.

Miniaturization is a key aspect of materials science. Owing to the increase in quality experimental and computational tools available to researchers, it has become clear that the crystal size and morphology of porous framework materials, including metal-organic frameworks and covalent organic frameworks, play a vital role in defining the physicochemical behaviour of these materials. However, given the multiscale and multidisciplinary challenges associated with establishing how crystal size and morphology affect the structure and behaviour of a material-from local to global structural modifications and from static to dynamic effects-a comprehensive mechanistic understanding of size and morphology effects is missing. Herein, we provide our perspective on the current state-of-the-art of this topic, drawn from various complementary disciplines. From a fundamental point of view, we discuss how controlling the crystal size and morphology can alter the mechanical and adsorption properties of porous framework materials and how this can impact phase stability. Special attention is also given to the quest to develop new computational tools capable of modelling these multiscale effects. From a more applied point of view, given the recent progress in this research field, we highlight the importance of crystal size and morphology control in drug delivery. Moreover, we provide an outlook on how to advance each discussed field by size and morphology control, which would open new design opportunities for functional porous framework materials.

Interfacial study of clathrates confined in reversed silica pores.

Storing methane in clathrates is one of the most promising alternatives for transporting natural gas (NG) as it offers similar gas densities to liquefied and compressed NG while offering lower safety risks. However, the practical use of clathrates is limited given the extremely low temperatures and high pressures necessary to form these structures. Therefore, it has been suggested to confine clathrates in nanoporous materials, as this can facilitate clathrate's formation conditions while preserving its CH4 volumetric storage. Yet, the choice of nanoporous materials to be employed as the clathrate growing platform is still rather arbitrary. Herein, we tackle this challenge in a systematic way by computationally exploring the stability of clathrates confined in alkyl-grafted silica materials with different pore sizes, ligand densities and ligand types. Based on our findings, we are able to propose key design criteria for nanoporous materials favoring the stability of a neighbouring clathrate phase, namely large pore sizes, high ligand densities, and smooth pore walls. We hope that the atomistic insight provided in this work will guide and facilitate the development of new nanomaterials designed to promote the formation of clathrates.

Large-Scale Molecular Dynamics Simulations Reveal New Insights Into the Phase Transition Mechanisms in MIL-53(Al).

Soft porous crystals have the ability to undergo large structural transformations upon exposure to external stimuli while maintaining their long-range structural order, and the size of the crystal plays an important role in this flexible behavior. Computational modeling has the potential to unravel mechanistic details of these phase transitions, provided that the models are representative for experimental crystal sizes and allow for spatially disordered phenomena to occur. Here, we take a major step forward and enable simulations of metal-organic frameworks containing more than a million atoms. This is achieved by exploiting the massive parallelism of state-of-the-art GPUs using the OpenMM software package, for which we developed a new pressure control algorithm that allows for fully anisotropic unit cell fluctuations. As a proof of concept, we study the transition mechanism in MIL-53(Al) under various external pressures. In the lower pressure regime, a layer-by-layer mechanism is observed, while at higher pressures, the transition is initiated at discrete nucleation points and temporarily induces various domains in both the open and closed pore phases. The presented workflow opens the possibility to deduce transition mechanism diagrams for soft porous crystals in terms of the crystal size and the strength of the external stimulus.

High-rate nanofluidic energy absorption in porous zeolitic frameworks.

Optimal mechanical impact absorbers are reusable and exhibit high specific energy absorption. The forced intrusion of liquid water in hydrophobic nanoporous materials, such as zeolitic imidazolate frameworks (ZIFs), presents an attractive pathway to engineer such systems. However, to harness their full potential, it is crucial to understand the underlying water intrusion and extrusion mechanisms under realistic, high-rate deformation conditions. Here, we report a critical increase of the energy absorption capacity of confined water-ZIF systems at elevated strain rates. Starting from ZIF-8 as proof-of-concept, we demonstrate that this attractive rate dependence is generally applicable to cage-type ZIFs but disappears for channel-containing zeolites. Molecular simulations reveal that this phenomenon originates from the intrinsic nanosecond timescale needed for critical-sized water clusters to nucleate inside the nanocages, expediting water transport through the framework. Harnessing this fundamental understanding, design rules are formulated to construct effective, tailorable and reusable impact energy absorbers for challenging new applications.

Chlorination of a Zeolitic-Imidazolate Framework Tunes Packing and van der Waals Interaction of Carbon Dioxide for Optimized Adsorptive Separation.

Molecular separation of carbon dioxide (CO2) and methane (CH4) is of growing interest for biogas upgrading, carbon capture and utilization, methane synthesis and for purification of natural gas. Here, we report a new zeolitic-imidazolate framework (ZIF), coined COK-17, with exceptionally high affinity for the adsorption of CO2 by London dispersion forces, mediated by chlorine substituents of the imidazolate linkers. COK-17 is a new type of flexible zeolitic-imidazolate framework Zn(4,5-dichloroimidazolate)2 with the SOD framework topology. Below 200 K it displays a metastable closed-pore phase next to its stable open-pore phase. At temperatures above 200 K, COK-17 always adopts its open-pore structure, providing unique adsorption sites for selective CO2 adsorption and packing through van der Waals interactions with the chlorine groups, lining the walls of the micropores. Localization of the adsorbed CO2 molecules by Rietveld refinement of X-ray diffraction data and periodic density functional theory calculations revealed the presence and nature of different adsorption sites. In agreement with experimental data, grand canonical Monte Carlo simulations of adsorption isotherms of CO2 and CH4 in COK-17 confirmed the role of the chlorine functions of the linkers and demonstrated the superiority of COK-17 compared to other adsorbents such as ZIF-8 and ZIF-71.

Texture Formation in Polycrystalline Thin Films of All-Inorganic Lead Halide Perovskite.

Controlling grain orientations within polycrystalline all-inorganic halide perovskite solar cells can help increase conversion efficiencies toward their thermodynamic limits; however, the forces governing texture formation are ambiguous. Using synchrotron X-ray diffraction, mesostructure formation within polycrystalline CsPbI2.85 Br0.15 powders as they cool from a high-temperature cubic perovskite (α-phase) is reported. Tetragonal distortions (ß-phase) trigger preferential crystallographic alignment within polycrystalline ensembles, a feature that is suggested here to be coordinated across multiple neighboring grains via interfacial forces that select for certain lattice distortions over others. External anisotropy is then imposed on polycrystalline thin films of orthorhombic (γ-phase) CsPbI3- x Brx perovskite via substrate clamping, revealing two fundamental uniaxial texture formations; i) I-rich films possess orthorhombic-like texture (<100> out-of-plane; <010> and <001> in-plane), while ii) Br-rich films form tetragonal-like texture (<110> out-of-plane; <110> and <001> in-plane). In contrast to relatively uninfluential factors like the choice of substrate, film thickness, and annealing temperature, Br incorporation modifies the γ-CsPbI3- x Brx crystal structure by reducing the orthorhombic lattice distortion (making it more tetragonal-like) and governs the formation of the different, energetically favored textures within polycrystalline thin films.

Quantifying the Likelihood of Structural Models through a Dynamically Enhanced Powder X-Ray Diffraction Protocol.

Structurally characterizing new materials is tremendously challenging, especially when single crystal structures are hardly available which is often the case for covalent organic frameworks. Yet, knowledge of the atomic structure is key to establish structure-function relations and enable functional material design. Herein, a new protocol is proposed to unambiguously predict the structure of poorly crystalline materials through a likelihood ordering based on the X-ray diffraction (XRD) pattern. Key of the procedure is the broad set of structures generated from a limited number of building blocks and topologies, which is submitted to operando structural characterization. The dynamic averaging in the latter accounts for the operando conditions and inherent temporal character of experimental measurements, yielding unparalleled agreement with experimental powder XRD patterns. The proposed concept can hence unquestionably identify the structure of experimentally synthesized materials, a crucial step to design next generation functional materials.

The micromechanical model to computationally investigate cooperative and correlated phenomena in metal-organic frameworks.

Computational insight into the impact of cooperative phenomena and correlated spatial disorder on the macroscopic behaviour of metal-organic frameworks (MOFs) is essential in order to consciously engineer these phenomena for targeted applications. However, the spatial extent of these effects, ranging over hundreds of nanometres, limits the applicability of current state-of-the-art computational tools in this field. To obtain a fundamental understanding of these long-range effects, the micromechanical model is introduced here. This model overcomes the challenges associated with conventional coarse-graining techniques by exploiting the natural partitioning of a MOF material into unit cells. By adopting the elastic deformation energy as the central quantity, the micromechanical model hierarchically builds on experimentally accessible input parameters that are obtained from atomistic quantum mechanical or force field simulations. As a result, the here derived micromechanical equations of motion can be adopted to shed light on the effect of long-range cooperative phenomena and correlated spatial disorder on the performance of mesoscale MOF materials.

Strongly Reducing (Diarylamino)benzene-Based Covalent Organic Framework for Metal-Free Visible Light Photocatalytic H2O2 Generation.

Photocatalytic reduction of molecular oxygen is a promising route toward sustainable production of hydrogen peroxide (H2O2). This challenging process requires photoactive semiconductors enabling solar energy driven generation and separation of electrons and holes with high charge transfer kinetics. Covalent organic frameworks (COFs) are an emerging class of photoactive semiconductors, tunable at a molecular level for high charge carrier generation and transfer. Herein, we report two newly designed two-dimensional COFs based on a (diarylamino)benzene linker that form a Kagome (kgm) lattice and show strong visible light absorption. Their high crystallinity and large surface areas (up to 1165 m2·g-1) allow efficient charge transfer and diffusion. The diarylamine (donor) unit promotes strong reduction properties, enabling these COFs to efficiently reduce oxygen to form H2O2. Overall, the use of a metal-free, recyclable photocatalytic system allows efficient photocatalytic solar transformations.

Charting the Metal-Dependent High-Pressure Stability of Bimetallic UiO-66 Materials.

In theory, bimetallic UiO-66(Zr:Ce) and UiO-66(Zr:Hf) metal-organic frameworks (MOFs) are extremely versatile and attractive nanoporous materials as they combine the high catalytic activity of UiO-66(Ce) or UiO-66(Hf) with the outstanding stability of UiO-66(Zr). Using in situ high-pressure powder X-ray diffraction, however, we observe that this expected mechanical stability is not achieved when incorporating cerium or hafnium in UiO-66(Zr). This observation is akin to the earlier observed reduced thermal stability of UiO-66(Zr:Ce) compounds. To elucidate the atomic origin of this phenomenon, we chart the loss-of-crystallinity pressures of 22 monometallic and bimetallic UiO-66 materials and systematically isolate their intrinsic mechanical stability from their defect-induced weakening. This complementary experimental/computational approach reveals that the intrinsic mechanical stability of these bimetallic MOFs decreases nonlinearly upon cerium incorporation but remains unaffected by the zirconium: hafnium ratio. Additionally, all experimental samples suffer from defect-induced weakening, a synthesis-controlled effect that is observed to be independent of their intrinsic stability.

Unraveling the thermodynamic criteria for size-dependent spontaneous phase separation in soft porous crystals.

Soft porous crystals (SPCs) harbor a great potential as functional nanoporous materials owing to their stimuli-induced and tuneable morphing between different crystalline phases. These large-amplitude phase transitions are often assumed to occur cooperatively throughout the whole material, which thereby retains its perfect crystalline order. Here, we disprove this paradigm through mesoscale first-principles based molecular dynamics simulations, demonstrating that morphological transitions do induce spatial disorder under the form of interfacial defects and give rise to yet unidentified phase coexistence within a given sample. We hypothesize that this phase coexistence can be stabilized by carefully tuning the experimental control variables through, e.g., temperature or pressure quenching. The observed spatial disorder helps to rationalize yet elusive phenomena in SPCs, such as the impact of crystal downsizing on their flexible nature, thereby identifying the crystal size as a crucial design parameter for stimuli-responsive devices based on SPC nanoparticles and thin films.

Thermal unequilibrium of strained black CsPbI3 thin films.

The high-temperature, all-inorganic CsPbI3 perovskite black phase is metastable relative to its yellow, nonperovskite phase at room temperature. Because only the black phase is optically active, this represents an impediment for the use of CsPbI3 in optoelectronic devices. We report the use of substrate clamping and biaxial strain to render black-phase CsPbI3 thin films stable at room temperature. We used synchrotron-based, grazing incidence, wide-angle x-ray scattering to track the introduction of crystal distortions and strain-driven texture formation within black CsPbI3 thin films when they were cooled after annealing at 330°C. The thermal stability of black CsPbI3 thin films is vastly improved by the strained interface, a response verified by ab initio thermodynamic modeling.

On the importance of anharmonicities and nuclear quantum effects in modelling the structural properties and thermal expansion of MOF-5.

In this article, we investigate the influence of anharmonicities and nuclear quantum effects (NQEs) in modelling the structural properties and thermal expansion of the empty MOF-5 metal-organic framework. To introduce NQEs in classical molecular dynamics simulations, two different methodologies are considered, comparing the approximate, but computationally cheap, method of generalised Langevin equation thermostatting to the more advanced, computationally demanding path integral molecular dynamics technique. For both methodologies, similar results were obtained for all the properties under investigation. The structural properties of MOF-5, probed by means of radial distribution functions (RDFs), show some distinct differences with respect to a classical description. Besides a broadening of the RDF peaks under the influence of quantum fluctuations, a different temperature dependence is also observed due to a dominant zero-point energy (ZPE) contribution. For the thermal expansion of MOF-5, by contrast, NQEs appear to be only of secondary importance with respect to an adequate modelling of the anharmonicities of the potential energy surface (PES), as demonstrated by the use of two differently parametrised force fields. Despite the small effect in the temperature dependence of the volume of MOF-5, NQEs do however significantly affect the absolute volume of MOF-5, in which the ZPE resulting from the intertwining of NQEs and anharmonicities plays a crucial role. A sufficiently accurate description of the PES is therefore prerequisite when modelling NQEs.

Protocol for Identifying Accurate Collective Variables in Enhanced Molecular Dynamics Simulations for the Description of Structural Transformations in Flexible Metal-Organic Frameworks.

Various kinds of flexibility have been observed in metal-organic frameworks, which may originate from the topology of the material or the presence of flexible ligands. The construction of free energy profiles describing the full dynamical behavior along the phase transition path is challenging since it is not trivial to identify collective variables able to identify all metastable states along the reaction path. In this work, a systematic three-step protocol to uniquely identify the dominant order parameters for structural transformations in flexible metal-organic frameworks and subsequently construct accurate free energy profiles is presented. Methodologically, this protocol is rooted in the time-structure based independent component analysis (tICA), a well-established statistical modeling technique embedded in the Markov state model methodology and often employed to study protein folding, that allows for the identification of the slowest order parameters characterizing the structural transformation. To ensure an unbiased and systematic identification of these order parameters, the tICA decomposition is performed based on information from a prior replica exchange (RE) simulation, as this technique enhances the sampling along all degrees of freedom of the system simultaneously. From this simulation, the tICA procedure extracts the order parameters-often structural parameters-that characterize the slowest transformations in the material. Subsequently, these order parameters are adopted in traditional enhanced sampling methods such as umbrella sampling, thermodynamic integration, and variationally enhanced sampling to construct accurate free energy profiles capturing the flexibility in these nanoporous materials. In this work, the applicability of this tICA-RE protocol is demonstrated by determining the slowest order parameters in both MIL-53(Al) and CAU-13, which exhibit a strongly different type of flexibility. The obtained free energy profiles as a function of this extracted order parameter are furthermore compared to the profiles obtained when adopting less-suited collective variables, indicating the importance of systematically selecting the relevant order parameters to construct accurate free energy profiles for flexible metal-organic frameworks, which is in correspondence with experimental findings. The method succeeds in mapping the full free energy surface in terms of appropriate collective variables for MOFs exhibiting linker flexibility. For CAU-13, we show the decreased stability of the closed pore phase by systematically adding adsorbed xylene molecules in the framework.

The Importance of Cell Shape Sampling To Accurately Predict Flexibility in Metal-Organic Frameworks.

In this work, the influence of cell shape sampling on the predicted stability of the different metastable phases in flexible metal-organic frameworks at finite temperatures is investigated. The influence on the free energy by neglecting cell shape sampling is quantified for the prototypical MIL-53(Al) and the topical DUT-49(Cu). This goal is achieved by constructing free energy profiles in ensembles either in which the phase space associated with the cell shape is sampled explicitly or in which the cell shape is kept fixed. When neglecting cell shape sampling, thermodynamic integration of the hydrostatic pressure yields unreliable free energy profiles that depend on the choice of the fixed cell shape. In this work, we extend the thermodynamic integration procedure via the introduction of a generalized pressure, derived from the Lagrangian strain tensor and the second Piola-Kirchhoff tensor. Using this generalized procedure, the dependence on the unit cell shape can be eliminated, and the inaccuracy in free energy stemming from the lack of cell shape sampling can be uniquely quantified. Finally, it is shown that the inaccuracy in free energy when fixing the cell shape at room temperature stems mainly from entropic contributions for both MIL-53(Al) and DUT-49(Cu).