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.

Probing Structural Defects in MOFs Using Water Stability

Defects in the crystal structures of metal-organic frameworks (MOFs), whether present intrinsically or introduced via so-called defect engineering, can play strong roles in the properties of MOFs for various applications. Unfortunately, direct experimental detection and characterization of defects in MOFs are very challenging. We show that in many cases, the differences between experimentally observed and computationally predicted water stabilities of MOFs can be used to deduce information on the presence of point defects in real materials. Most computational studies of MOFs consider these materials to be defect-free, and in many cases, the resulting structures are predicted to be hydrophobic. Systematic experimental studies, however, have shown that many MOFs are hydrophilic. We show that the existence of chemically plausible point defects can often account for this discrepancy and use this observation in combination with detailed molecular simulations to assess the impact of local defects and flexibility in a variety of MOFs for which defects had not been considered previously.

DFT-Quality Adsorption Simulations in Metal-Organic Frameworks Enabled by Machine Learning Potentials

Nanoporous materials such as metal-organic frameworks (MOFs) have been extensively studied for their potential for adsorption and separation applications. In this respect, grand canonical Monte Carlo (GCMC) simulations have become a well-established tool for computational screenings of the adsorption properties of large sets of MOFs. However, their reliance on empirical force field potentials has limited the accuracy with which this tool can be applied to MOFs with challenging chemical environments such as open-metal sites. On the other hand, density-functional theory (DFT) is too computationally demanding to be routinely employed in GCMC simulations due to the excessive number of required function evaluations. Therefore, we propose in this paper a protocol for training machine learning potentials (MLPs) on a limited set of DFT intermolecular interaction energies (and forces) of CO2 in ZIF-8 and the open-metal site containing Mg-MOF-74, and use the MLPs to derive adsorption isotherms from first principles. We make use of the equivariant NequIP model which has demonstrated excellent data efficiency, and as such an error on the interaction energies below 0.2 kJ mol-1 per adsorbate in ZIF-8 was attained. Its use in GCMC simulations results in highly accurate adsorption isotherms and heats of adsorption. For Mg-MOF-74, a large dependence of the obtained results on the used dispersion correction was observed, where PBE-MBD performs the best. Lastly, to test the transferability of the MLP trained on ZIF-8, it was applied to ZIF-3, ZIF-4, and ZIF-6, which resulted in large deviations in the predicted adsorption isotherms and heats of adsorption. Only when explicitly training on data for all ZIFs, accurate adsorption properties were obtained. As the proposed methodology is widely applicable to guest adsorption in nanoporous materials, it opens up the possibility for training general-purpose MLPs to perform highly accurate investigations of guest adsorption.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Exploring the Potential of a Highly Scalable Metal-Organic Framework CALF-20 for Selective Gas Adsorption at Low Pressure

In this study, the ability of the highly scalable metal-organic framework (MOF) CALF-20 to adsorb polar and non-polar gases at low pressure was investigated using grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. The results from the simulated adsorption isotherms revealed that the highest loading was achieved for SO₂ and Cl₂, while the lowest loading was found for F₂ molecules. The analysis of interaction energies indicated that SO₂ molecules were able to form the strongest adsorbent-adsorbate interactions and had a tight molecular packing due to their polarity and angular structure. Additionally, Cl₂ gas was found to be highly adsorbed due to its large van der Waals surface and strong chemical affinity in CALF-20 pores. MD simulations showed that SO₂ and Cl₂ had the lowest mobility inside CALF-20 pores. The values of the Henry coefficient and isosteric heat of adsorption confirmed that CALF-20 could selectively adsorb SO₂ and Cl₂. Based on the results, it was concluded that CALF-20 is a suitable adsorbent for SO₂ and Cl₂ but not for F₂. This research emphasizes the importance of molecular size, geometry, and polarity in determining the suitability of a porous material as an adsorbent for specific adsorbates.

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.

Eleven NanoHUB Simulation Tools Using RASPA Software To Demonstrate Classical Atomistic Simulations of Fluids and Nanoporous Materials

Eleven interactive simulation tools were created on nanoHUB to help users learn how to perform classical atomistic simulations. These tools enable users to perform classical Monte Carlo and molecular dynamics simulations using RASPA software. These tools use comparatively small numbers of production cycles to keep the runtimes short, so that users will not be discouraged by long wait times to see results. Here, we show that these tools produce results of sufficient accuracy and reproducibility for learning purposes. The 11 tools developed were as follows: (1) calculation of the self-diffusion constant of gas molecules in metal-organic frameworks (MOFs), (2) gas adsorption in MOFs using the grand canonical ensemble, (3) Henry's coefficient calculator for gas molecules in MOFs and a zeolite, (4) adsorption of a gas mixture in a MOF, (5) self-diffusion of a gas mixture in a MOF, (6) void fraction calculation for several MOFs and zeolites, (7) surface area calculation for several MOFs and zeolites, (8) calculation of radial distribution function and self-diffusion constant for several pure gases, (9) energy distribution of adsorption sites using a probe molecule in MOFs, (10) molecular dynamics simulation of pure fluids in the NPT ensemble, and (11) gas adsorption in MOFs using the Gibbs ensemble.

Drug Discovery by Automated Adaptation of Chemical Structure and Identity

Computer-aided drug design offers the potential to dramatically reduce the cost and effort required for drug discovery. While screening-based methods are valuable in the early stages of hit identification, they are frequently succeeded by iterative, hypothesis-driven computations that require recurrent investment of human time and intuition. To increase automation, we introduce a computational method for lead refinement that combines concerted dynamics of the ligand/protein complex via molecular dynamics simulations with integrated Monte Carlo-based changes in the chemical formula of the ligand. This approach, which we refer to as ligand-exchange Monte Carlo molecular dynamics, accounts for solvent- and entropy-based contributions to competitive binding free energies by coupling the energetics of bound and unbound states during the ligand-exchange attempt. Quantitative comparison of relative binding free energies to reference values from free energy perturbation, conducted in vacuum, indicates that ligand-exchange Monte Carlo molecular dynamics simulations sample relevant conformational ensembles and are capable of identifying strongly binding compounds. Additional simulations demonstrate the use of an implicit solvent model. We speculate that the use of chemical graphs in which exchanges are only permitted between ligands with sufficient similarity may enable an automated search to capture some of the benefits provided by human intuition during hypothesis-guided lead refinement.

Incorporating Flexibility Effects into Metal-Organic Framework Adsorption Simulations Using Different Models

High-throughput calculations based on molecular simulations to predict the adsorption of molecules inside metal-organic frameworks (MOFs) have become a useful complement to experimental efforts to identify promising adsorbents for chemical separations and storage. For computational convenience, all existing efforts of this kind have relied on simulations in which the MOF is approximated as rigid. In this paper, we use extensive adsorption-relaxation simulations that fully include MOF flexibility effects to explore the validity of the rigid framework approximation. We also examine the accuracy of several approximate methods to incorporate framework flexibility that are more computationally efficient than adsorption-relaxation calculations. We first benchmark various models of MOF flexibility for four MOFs with well-established CO₂ experimental consensus isotherms. We then consider a range of adsorption properties, including Henry's constants, nondilute loadings, and adsorption selectivity, for seven adsorbates in 15 MOFs randomly selected from the CoRE MOF database. Our results indicate that in many MOFs adsorption-relaxation simulations are necessary to make quantitative predictions of adsorption, particularly for adsorption at dilute concentrations, although more standard calculations based on rigid structures can provide useful information. Finally, we investigate whether a correlation exists between the elastic properties of empty MOFs and the importance of including framework flexibility in making accurate predictions of molecular adsorption. Our results did not identify a simple correlation of this type.

Performance and Nanostructure Simulation of Phosphogypsum Modified by Sodium Carbonate and Alum

This paper presents a new modification of the nanostructure of CaSO₄·2H₂O crystals containing nanopores. This nanoporous structure was achieved in phosphogypsum samples that were modified by sodium carbonate and alum. The effects of sodium carbonate and alum on the properties of phosphogypsum were studied. X-ray diffraction (XRD) and scanning electron microscopy (SEM) methods were used to explore the micro-mechanism of the composite system. Subsequently, molecular dynamics simulations were used to study the nanopore structures of the modified CaSO₄·2H₂O. The results show that the addition of sodium carbonate and alum reduced the absolute dry density by 23.1% compared with the original phosphogypsum sample, with a bending strength of 2.1 MPa and compressive strength of 7.5 MPa. In addition, new hydration products, sodium sulfate and sodium aluminum sulfate, were formed in the sample doped with sodium carbonate and alum. A new nanostructure of CaSO₄·2H₂O crystal containing nanopores was formed. Molecular simulations show that the hydration products were responsible for the surface nanopore formation, which was the main factor leading to an increase in mechanical strength. The presented nanopore structure yields lightweight and high strength properties in the modified phosphogypsum.

Performance-Based Screening of Porous Materials for Carbon Capture

Computational screening methods have changed the way new materials and processes are discovered and designed. For adsorption-based gas separations and carbon capture, recent efforts have been directed toward the development of multiscale and performance-based screening workflows where we can go from the atomistic structure of an adsorbent to its equilibrium and transport properties at different scales, and eventually to its separation performance at the process level. The objective of this work is to review the current status of this new approach, discuss its potential and impact on the field of materials screening, and highlight the challenges that limit its application. We compile and introduce all the elements required for the development, implementation, and operation of multiscale workflows, hence providing a useful practical guide and a comprehensive source of reference to the scientific communities who work in this area. Our review includes information about available materials databases, state-of-the-art molecular simulation and process modeling tools, and a complete catalogue of data and parameters that are required at each stage of the multiscale screening. We thoroughly discuss the challenges associated with data availability, consistency of the models, and reproducibility of the data and, finally, propose new directions for the future of the field.

What Lies beneath a Metal-Organic Framework Crystal Structure? New Design Principles from Unexpected Behaviors

The rational design principles established for metal-organic frameworks (MOFs) allow clear structure-property relationships, fueling expansive growth for energy storage and conversion, catalysis, and beyond. However, these design principles are based on the assumption of compositional and structural rigidity, as measured crystallographically. Such idealization of MOF structures overlooks subtle chemical aspects that can lead to departures from structure-based chemical intuition. In this Perspective, we identify unexpected behavior of MOFs through literature examples. Based on this analysis, we conclude that departures from ideality are not uncommon. Whereas linker topology and metal coordination geometry are useful starting points for understanding MOF properties, we anticipate that deviations from the idealized crystal representation will be necessary to explain important and unexpected behaviors. Although this realization reinforces the notion that MOFs are highly complex materials, it should also stimulate a broader reexamination of the literature to identify corollaries to existing design rules and reveal new structure-property relationships.

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.

Elucidating pore chemistry within metal–organic frameworks via single crystal X-ray diffraction; from fundamental understanding to application

The application of metal–organic frameworks (MOFs) to diverse chemical sectors is aided by their crystallinity, which permits the use of X-ray crystallography to characterise their pore chemistry and provides invaluable insight into their properties.

MOF-Based Membranes for Gas Separations

Metal-organic frameworks (MOFs) represent the largest known class of porous crystalline materials ever synthesized. Their narrow pore windows and nearly unlimited structural and chemical features have made these materials of significant interest for membrane-based gas separations. In this comprehensive review, we discuss opportunities and challenges related to the formation of pure MOF films and mixed-matrix membranes (MMMs). Common and emerging separation applications are identified, and membrane transport theory for MOFs is described and contextualized relative to the governing principles that describe transport in polymers. Additionally, cross-cutting research opportunities using advanced metrologies and computational techniques are reviewed. To quantify membrane performance, we introduce a simple membrane performance score that has been tabulated for all of the literature data compiled in this review. These data are reported on upper bound plots, revealing classes of MOF materials that consistently demonstrate promising separation performance. Recommendations are provided with the intent of identifying the most promising materials and directions for the field in terms of fundamental science and eventual deployment of MOF materials for commercial membrane-based gas separations.

Metal-Organic Framework Nanoparticles Induce Pyroptosis in Cells Controlled by the Extracellular pH

Ion homeostasis is essential for cellular survival, and elevated concentrations of specific ions are used to start distinct forms of programmed cell death. However, investigating the influence of certain ions on cells in a controlled way has been hampered due to the tight regulation of ion import by cells. Here, it is shown that lipid-coated iron-based metal-organic framework nanoparticles are able to deliver and release high amounts of iron ions into cells. While high concentrations of iron often trigger ferroptosis, here, the released iron induces pyroptosis, a form of cell death involving the immune system. The iron release occurs only in slightly acidic extracellular environments restricting cell death to cells in acidic microenvironments and allowing for external control. The release mechanism is based on endocytosis facilitated by the lipid-coating followed by degradation of the nanoparticle in the lysosome via cysteine-mediated reduction, which is enhanced in slightly acidic extracellular environment. Thus, a new functionality of hybrid nanoparticles is demonstrated, which uses their nanoarchitecture to facilitate controlled ion delivery into cells. Based on the selectivity for acidic microenvironments, the described nanoparticles may also be used for immunotherapy: the nanoparticles may directly affect the primary tumor and the induced pyroptosis activates the immune system.

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.

Soft porous crystals hold big promise as functional nanoporous materials due to their stimuli responsive flexibility. Here, molecular dynamics simulations reveal a new type of spatial disorder in mesoscale crystals that helps to understand the size-dependency of their phase transition behavior.

Simulating Enhanced Methane Deliverable Capacity of Guest Responsive Pores in Intrinsically Flexible MOFs

A novel computational procedure, based on the principles of flat-histogram Monte Carlo, is developed for facile prediction of the adsorption thermodynamics of intrinsically flexible adsorbents. We then demonstrate how an accurate prediction of methane deliverable capacity in a metal-organic framework (MOF) with significant intrinsic flexibility requires use of such a method. Dynamic side chains in the framework respond to methane adsorbates and reorganize to exhibit a more conducive pore space at high adsorbate densities while simultaneously providing a less conducive pore space at low adsorbate densities. This "responsive pore" MOF achieves ∼20% higher deliverable capacity than if the framework were rigid and elucidates a strategy for designing high deliverable capacity MOFs in the future.

The role of molecular modelling and simulation in the discovery and deployment of metal-organic frameworks for gas storage and separation

Metal-organic frameworks (MOFs) are highly tuneable, extended-network, crystalline, nanoporous materials with applications in gas storage, separations, and sensing. We review how molecular models and simulations of gas adsorption in MOFs have informed the discovery of performant MOFs for methane, hydrogen, and oxygen storage, xenon, carbon dioxide, and chemical warfare agent capture, and xylene enrichment. Particularly, we highlight how large, open databases of MOF crystal structures, post-processed to enable molecular simulations, are a platform for computational materials discovery. We discuss how to orient research efforts to routinise the computational discovery of MOFs for adsorption-based engineering applications.