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.

How Reproducible are Surface Areas Calculated from the BET Equation?

Porosity and surface area analysis play a prominent role in modern materials science. At the heart of this sits the Brunauer-Emmett-Teller (BET) theory, which has been a remarkably successful contribution to the field of materials science. The BET method was developed in the 1930s for open surfaces but is now the most widely used metric for the estimation of surface areas of micro- and mesoporous materials. Despite its widespread use, the calculation of BET surface areas causes a spread in reported areas, resulting in reproducibility problems in both academia and industry. To prove this, for this analysis, 18 already-measured raw adsorption isotherms were provided to sixty-one labs, who were asked to calculate the corresponding BET areas. This round-robin exercise resulted in a wide range of values. Here, the reproducibility of BET area determination from identical isotherms is demonstrated to be a largely ignored issue, raising critical concerns over the reliability of reported BET areas. To solve this major issue, a new computational approach to accurately and systematically determine the BET area of nanoporous materials is developed. The software, called "BET surface identification" (BETSI), expands on the well-known Rouquerol criteria and makes an unambiguous BET area assignment possible.

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.

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.

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 CsPbI_2.85 Br_0.15 powders as they cool from a high-temperature cubic perovskite (α-phase) is reported. Tetragonal distortions (β-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) CsPbI_{3- x} Br_x 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-CsPbI_{3- x} Br_x 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.

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.

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.

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.

Metal-organic and covalent organic frameworks as single-site catalysts

Heterogeneous single-site catalysts consist of isolated, well-defined, active sites that are spatially separated in a given solid and, ideally, structurally identical. In this review, the potential of metal-organic frameworks (MOFs) and covalent organic frameworks (COFs) as platforms for the development of heterogeneous single-site catalysts is reviewed thoroughly. In the first part of this article, synthetic strategies and progress in the implementation of such sites in these two classes of materials are discussed. Because these solids are excellent playgrounds to allow a better understanding of catalytic functions, we highlight the most important recent advances in the modelling and spectroscopic characterization of single-site catalysts based on these materials. Finally, we discuss the potential of MOFs as materials in which several single-site catalytic functions can be combined within one framework along with their potential as powerful enzyme-mimicking materials. The review is wrapped up with our personal vision on future research directions.

Influence of a Confined Methanol Solvent on the Reactivity of Active Sites in UiO-66

UiO-66, composed of Zr-oxide bricks and terephthalate linkers, is currently one of the most studied metal-organic frameworks due to its exceptional stability. Defects can be introduced in the structure, creating undercoordinated Zr atoms which are Lewis acid sites. Here, additional Brønsted sites can be generated by coordinated protic species from the solvent. In this Article, a multilevel modeling approach was applied to unravel the effect of a confined methanol solvent on the active sites in UiO-66. First, active sites were explored with static periodic density functional theory calculations to investigate adsorption of water and methanol. Solvent was then introduced in the pores with grand canonical Monte Carlo simulations, followed by a series of molecular dynamics simulations at operating conditions. A hydrogen-bonded network of methanol molecules is formed, allowing the protons to shuttle between solvent methanol, adsorbed water, and the inorganic brick. Upon deprotonation of an active site, the methanol solvent aids the transfer of protons and stabilizes charged configurations via hydrogen bonding, which could be crucial in stabilizing reactive intermediates. The multilevel modeling approach adopted here sheds light on the important role of a confined solvent on the active sites in the UiO-66 material, introducing dynamic acidity in the system at finite temperatures by which protons may be easily shuttled from various positions at the active sites.

Elucidating the Vibrational Fingerprint of the Flexible Metal-Organic Framework MIL-53(Al) Using a Combined Experimental/Computational Approach

In this work, mid-infrared (mid-IR), far-IR, and Raman spectra are presented for the distinct (meta)stable phases of the flexible metal-organic framework MIL-53(Al). Static density functional theory (DFT) simulations are performed, allowing for the identification of all IR-active modes, which is unprecedented in the low-frequency region. A unique vibrational fingerprint is revealed, resulting from aluminum-oxide backbone stretching modes, which can be used to clearly distinguish the IR spectra of the closed- and large-pore phases. Furthermore, molecular dynamics simulations based on a DFT description of the potential energy surface enable determination of the theoretical Raman spectrum of the closed- and large-pore phases for the first time. An excellent correspondence between theory and experiment is observed. Both the low-frequency IR and Raman spectra show major differences in vibrational modes between the closed- and large-pore phases, indicating changes in lattice dynamics between the two structures. In addition, several collective modes related to the breathing mechanism in MIL-53(Al) are identified. In particular, we rationalize the importance of the trampoline-like motion of the linker for the phase transition.

Reliably Modeling the Mechanical Stability of Rigid and Flexible Metal-Organic Frameworks

Over the past two decades, metal-organic frameworks (MOFs) have matured from interesting academic peculiarities toward a continuously expanding class of hybrid, nanoporous materials tuned for targeted technological applications such as gas storage and heterogeneous catalysis. These oft-times crystalline materials, composed of inorganic moieties interconnected by organic ligands, can be endowed with desired structural and chemical features by judiciously functionalizing or substituting these building blocks. As a result of this reticular synthesis, MOF research is situated at the intriguing intersection between chemistry and physics, and the building block approach could pave the way toward the construction of an almost infinite number of possible crystalline structures, provided that they exhibit stability under the desired operational conditions. However, this enormous potential is largely untapped to date, as MOFs have not yet found a major breakthrough in technological applications. One of the remaining challenges for this scale-up is the densification of MOF powders, which is generally achieved by subjecting the material to a pressurization step. However, application of an external pressure may substantially alter the chemical and physical properties of the material. A reliable theoretical guidance that can presynthetically identify the most stable materials could help overcome this technological challenge. In this Account, we describe the recent research the progress on computational characterization of the mechanical stability of MOFs. So far, three complementary approaches have been proposed, focusing on different aspects of mechanical stability: (i) the Born stability criteria, (ii) the anisotropy in mechanical moduli such as the Young and shear moduli, and (iii) the pressure-versus-volume equations of state. As these three methods are grounded in distinct computational approaches, it is expected that their accuracy and efficiency will vary. To date, however, it is unclear which set of properties are suited and reliable for a given application, as a comprehensive comparison for a broad variety of MOFs is absent, impeding the widespread use of these theoretical frameworks. Herein, we fill this gap by critically assessing the performance of the three computational models on a broad set of MOFs that are representative for current applications. These materials encompass the mechanically rigid UiO-66(Zr) and MOF-5(Zn) as well as the flexible MIL-47(V) and MIL-53(Al), which undergo pressure-induced phase transitions. It is observed that the Born stability criteria and pressure-versus-volume equations of state give complementary insight into the macroscopic and microscopic origins of instability, respectively. However, interpretation of the Born stability criteria becomes increasingly difficult when less symmetric materials are considered. Moreover, pressure fluctuations during the simulations hamper their accuracy for flexible materials. In contrast, the pressure-versus-volume equations of state are determined in a thermodynamic ensemble specifically targeted to mitigate the effects of these instantaneous fluctuations, yielding more accurate results. The critical Account presented here paves the way toward a solid computational framework for an extensive presynthetic screening of MOFs to select those that are mechanically stable and can be postsynthetically densified before their use in targeted applications.

Thermodynamic insight into stimuli-responsive behaviour of soft porous crystals

Knowledge of the thermodynamic potential in terms of the independent variables allows to characterize the macroscopic state of the system. However, in practice, it is difficult to access this potential experimentally due to irreversible transitions that occur between equilibrium states. A showcase example of sudden transitions between (meta)stable equilibrium states is observed for soft porous crystals possessing a network with long-range structural order, which can transform between various states upon external stimuli such as pressure, temperature and guest adsorption. Such phase transformations are typically characterized by large volume changes and may be followed experimentally by monitoring the volume change in terms of certain external triggers. Herein, we present a generalized thermodynamic approach to construct the underlying Helmholtz free energy as a function of the state variables that governs the observed behaviour based on microscopic simulations. This concept allows a unique identification of the conditions under which a material becomes flexible.

Efficient Construction of Free Energy Profiles of Breathing Metal-Organic Frameworks Using Advanced Molecular Dynamics Simulations

In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials.

Acidity Constant (pKa ) Calculation of Large Solvated Dye Molecules: Evaluation of Two Advanced Molecular Dynamics Methods

pH‐Sensitive dyes are increasingly applied on polymer substrates for the creation of novel sensor materials. Recently, these dye molecules were modified to form a covalent bond with the polymer host. This had a large influence on the pH‐sensitive properties, in particular on the acidity constant (pK_a). Obtaining molecular control over the factors that influence the pK_a value is mandatory for the future intelligent design of sensor materials. Herein, we show that advanced molecular dynamics (MD) methods have reached the level at which the pK_a values of large solvated dye molecules can be predicted with high accuracy. Two MD methods were used in this work: steered or restrained MD and the insertion/deletion scheme. Both were first calibrated on a set of phenol derivatives and afterwards applied to the dye molecule bromothymol blue. Excellent agreement with experimental values was obtained, which opens perspectives for using these methods for designing dye molecules.