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

The use of collective variables and enhanced sampling in the simulations of existing and emerging microporous materials

Microporous materials, including zeolites, metal-organic frameworks, and cage compounds, offer diverse functionalities due to their unique dynamics and guest confinement properties. These materials play a significant role in separation, catalysis, and sensing, but their complexity hinders exploration using traditional atomistic simulations. This review explores collective variables (CVs) paired with enhanced sampling as a powerful approach to enable efficient investigation of key features in microporous materials. We highlight successful applications of CVs in studying adsorption, diffusion, phase transitions, and mechanical properties, demonstrating their crucial role in guiding material design and optimisation. The future of CVs lies in integration with techniques like machine learning, allowing for enhanced efficiency and accuracy. By tailoring CVs to specific materials and developing multi-scale approaches we can further unlock the intricacies of these fascinating materials. Simulations are a cornerstone in unravelling the complexities of microporous materials and are crucial for our future understanding.

Cutting-edge molecular modelling to unveil new microscopic insights into the guest-controlled flexibility of metal-organic frameworks

Metal-organic frameworks are a class of porous solids that exhibit intriguing flexibility under stimuli, leading often to reversible giant structural changes upon guest adsorption. DUT-49(Cu) and MIL-53(Cr) are fascinating flexible MOFs owing to their guest-induced breathing and negative gas adsorption behaviors respectively. Molecular simulation is one of the most relevant tools to examine these phenomena at the atomistic scale and gain a unique understanding of the physics behind them. Although molecular dynamics and Monte Carlo simulations are widely used in the field of porous materials, these methods hardly consider the structural deformation of a soft material upon guest adsorption. In this work, a cutting-edge osmotic molecular dynamics approach is developed to consider simultaneously the fluid adsorption process and material flexibility. We demonstrate that this newly developed computational strategy offers a unique opportunity to gain unprecedented molecular insights into the flexibility of this class of materials.

ResponZIF Structures: Zeolitic Imidazolate Frameworks as Stimuli-Responsive Materials

Zeolitic imidazolate frameworks (ZIFs) have long been recognized as a prominent subset of the metal-organic framework (MOF) family, in part because of their ease of synthesis and good thermal and chemical stability, alongside attractive properties for diverse potential applications. Prototypical ZIFs like ZIF-8 have become embodiments of the significant promise held by porous coordination polymers as next-generation designer materials. At the same time, their intriguing property of experiencing significant structural changes upon the application of external stimuli such as temperature, mechanical pressure, guest adsorption, or electromagnetic fields, among others, has placed this family of MOFs squarely under the umbrella of stimuli-responsive materials. In this review, we provide an overview of the current understanding of the triggered structural and electronic responses observed in ZIFs (linker and bond dynamics, crystalline and amorphous phase changes, luminescence, etc.). We then describe the state-of-the-art experimental and computational methodology capable of shedding light on these complex phenomena, followed by a comprehensive summary of the stimuli-responsive nature of four prototypical ZIFs: ZIF-8, ZIF-7, ZIF-4, and ZIF-zni. We further expose the relevant challenges for the characterization and fundamental understanding of responsive ZIFs, including how to take advantage of their flexible properties for new application avenues.

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.

Charting the Complete Thermodynamic Landscape of Gas Adsorption for a Responsive Metal–Organic Framework

New nanoporous materials have the ability to revolutionize adsorption and separation processes. In particular, materials with adaptive cavities have high selectivity and may display previously undiscovered phenomena, such as negative gas adsorption (NGA), in which gas is released from the framework upon an increase in pressure. Although the thermodynamic driving force behind this and many other counterintuitive adsorption phenomena have been thoroughly investigated in recent years, several experimental observations remain difficult to explain. This necessitates a comprehensive analysis of gas adsorption akin to the conformational free energy landscapes used to understand the function of proteins. We have constructed the complete thermodynamic landscape of methane adsorption on DUT-49. Traversing this complex landscape reproduces the experimentally observed structural transitions, temperature dependence, and the hysteresis between adsorption and desorption. The complete thermodynamic description presented here provides unparalleled insight into adsorption and provides a framework to understand other adsorbents that challenge our preconceptions.

Low Temperature Calorimetry Coupled with Molecular Simulations for an In-Depth Characterization of the Guest-Dependent Compliant Behavior of MOFs

In this study adsorption microcalorimetry is employed to monitor the adsorption of four probes (argon, oxygen, nitrogen, and carbon monoxide) on a highly flexible mesoporous metal-organic framework (DUT-49, DUT = Dresden University of Technology), precisely measuring the differential enthalpy of adsorption alongside high-resolution isotherms. This experimental approach combined with force field Monte Carlo simulations reveals distinct pore filling adsorption behaviors for the selected probes, with argon and oxygen showing abrupt adsorption in the open pore form of DUT-49, in contrast with the gradual filling for nitrogen and carbon monoxide. A complex structural transition behavior of DUT-49 observed upon nitrogen adsorption is elucidated through an isotherm deconvolution in order to quantify the fractions of the open pore, contracted pore, and intermediate pore forms that coexist at a given gas pressure. Finally, the heat flow measured during the guest-induced structural contraction of DUT-49 allowed an exploration of complex open-contracted pore transition energetics, leading to a first assessment of the energy required to induce this spectacular structural change.

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.