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

Structure and Synthesizability of Iron-Sulfur Metal-Organic Frameworks

Sulfur-based metal-organic frameworks (MOFs) and coordination polymers (CPs) are an emerging class of hybrid materials that have received growing attention due to their magnetic, conductive, and catalytic properties with potential applications in electrocatalysis and energy storage. In this work, we report a high-throughput virtual screening protocol to predict the synthesizability of candidate metal-sulfur MOFs/CPs by computing the thermodynamically stable structures resulting from a particular combination of metal cluster, linker, cation, and synthetic conditions. Free energies are computed by using all-atom classical mechanical thermodynamic integration. Low-free-energy structures are refined using ab initio density functional theory, and pair distribution functions and powder X-ray diffraction patterns are calculated to complement and guide experimental structure determination. We validate the computational approach by retrospective predictions of the stable structure produced by experimental syntheses, and a subsequent screen predicts Fe4S4-BDT-TPP as a new thermodynamically stable one-dimensional (1D) CP comprising a redox-active Fe4S4 cluster, a 1,4-benzenedithiolate (BDT) linker, and a tetraphenylphosphonium (TPP) countercation. This material is experimentally synthesized, and the 1D chain structure of the crystal is confirmed using microcrystal electron diffraction. The computational screening pipeline is generically transferable to neutral and ionic MOFs/CPs comprising arbitrary metal clusters, linkers, cations, and synthetic conditions, and we make it freely available as an open source tool to guide and accelerate the discovery and engineering of novel porous materials.

Unveiling non-monotonic deformation of flexible MOFs during gas adsorption: From contraction and softening to expansion and hardening

Flexibility of metal-organic frameworks (MOFs) plays an important role in their applications, particularly in adsorption separations, energy and gas storage, and drug delivery. As an important practical example, we study adsorption of CH4, and CO2 on isoreticular MOF-1 (IRMOF-1) crystal at different temperatures using an original computational scheme of iterative grand canonical Monte Carlo (GCMC) and isothermal-isobaric ensemble molecular dynamics (NPT-MD) simulations. Our findings reveal that thermal fluctuations and flexibility of the host framework affect adsorption of guest molecules, which in turn exert a significant adsorption stress, up to 0.1 GPa, on the framework causing its deformation that occurs in a counterintuitive manner. Contrary to the expected gradual swelling during adsorption, we observe non-monotonic deformation, characterized by sharp contraction during the pore filling, followed by partial expansion. During the pore-filling process, guest molecules engender softening of the host structure to a nearly 100% increase in compressibility. However, upon the pore filling and further densification of the adsorbed phase, the structure hardens and compressibility decreases. These findings are supported by quantitative agreement with adsorption experiments on IRMOF-1 and are expected to be applicable to various degrees, to other MOFs and nanoporous materials.

A Systematic Approach for Incorporating Structural Flexibility in High-Throughput Computational Screening of Metal-Organic Frameworks for Xylene Separation

Separation of xylene isomers poses a significant challenge due to their similar physicochemical properties. Currently, zeolites are utilized as adsorbents for this purpose in the chemical industry despite suboptimal separation performance. With tunable pore size and chemical functionality, metal-organic frameworks (MOFs) are promising adsorbents for separation. By virtue of high-throughput computational screening (HTCS), the adsorption performance of a large collection of MOFs can be evaluated in silico by using Monte Carlo (MC) simulations. Unlike prior studies assuming rigid structures of MOFs during screening, we develop a systematic approach for incorporating flexibility in HTCS for xylene separation. First, MOFs are judiciously classified with external flexibility (volume/shape changes) and internal flexibility (intraframework fluctuations), respectively, based on the nature and extent of structural deformation from molecular dynamics (MD) simulations. Afterward, adsorption in MOFs with external flexibility is simulated by hybrid MC/MD method, the flexible snapshot method is used for MOFs with a sort of internal flexibility, and grand-canonical MC (GCMC) method is employed for MOFs with negligible flexibility. Finally, top-performing MOFs are identified for xylene separation. While substantially reducing computational cost, this study also delivers more reliable results compared to the assumption of rigid structures. The HTCS approach is versatile and can be extended beyond MOFs, offering a robust tool for the virtual screening of other soft-porous materials for a wide range of important applications.

Nonadditive CO2 Uptake of Type II Porous Liquids Based on Imine Cages

Type II porous liquids can potentially exploit the fluidity of liquids and sorption properties of porous sorbents, yet CO2 uptake in porous liquids is still poorly understood. Molecular simulations and experiments are used to examine CO2 uptake by a prototypical porous liquid composed of porous organic cages (CC13) in 2'-hydroxyacetophenone (2'-HAP). The simulations are in reasonable agreement with experimental measurements of CO2 solubility and provide unambiguous information on the partitioning of CO2 within microenvironments in the liquid. Analysis of CO2 dynamics is performed using these simulations, including assessing the self-diffusivity of CO2 in both the neat solvent and porous liquid. This offers insights into the kinetics of CO2 uptake and transport in type II porous liquids based on imine cages. Experiments with type II porous liquids formed by dissolving CC13 in three different size-excluded solvents show nonadditive CO2 absorption relative to predictions based on ideal volume additivity. This nonadditive absorption behavior is also observed in simulations. Nonadditive CO2 uptake is also demonstrated in type II porous liquids based on another imine-based porous cage, CC19.

Modeling Gas Adsorption and Mechanistic Insights into Flexibility in Isoreticular Metal-Organic Frameworks Using High-Dimensional Neural Network Potentials

Metal-organic frameworks (MOFs), known for their remarkable porous and well-organized structures, have found extensive use in various applications, including gas storage. Predicting the bulk properties from atomistic simulations as well as gas uptakes and the adsorption mechanism requires the most accurate definition of MOF systems. The application of ab initio molecular dynamics to these extensive periodic systems exceeds the current computational capabilities. Consequently, alternative strategies need to be devised to decrease computational costs without compromising accuracy. In this work, we construct high-dimensional neural network potentials (HDNNPs) to describe rotationally and translationally invariant energies and forces of isoreticular metal-organic framework (IRMOF) series at the density functional theory level of accuracy using a fragmentation technique to study H2 and CH4 adsorption isotherms by means of an "adsorption-relaxation" model in which molecular dynamics and grand canonical Monte Carlo simulations were performed simultaneously. Herein, for the first time, we report that HDNNPs could be utilized for such simulations with excellent agreement with experimental values. We also report that the UFF4MOF force field may not be suitable for adsorption-relaxation simulations. In addition, we show that the real number of CH4 uptake values of IRMOF-10 under the extreme conditions could be much greater than what the classical force field predicts. Adsorption-relaxation simulations enable us to characterize the behavior of MOF atoms and the distribution of gas molecules during the adsorption process, giving the most detailed mechanistic picture.

Synthesis of Selenized Metal-Organic Framework Hollow Cage under Ambient Condition for Clean Energy Applications

The synthesis of structured metal organic framework (MOF)-derived selenide composites is a vibrantly emerging research area serving clean energy purposes. However, there is no way to convert MOFs into structured selenide composites under ambient conditions for unknown reasons. This work gave mechanistic insights into how the redox properties and release rate of selenium precursors influenced the structural inheritance behavior of MOFs during the selenization process, explaining why maintaining the morphology of MOFs during a room-temperature aqueous selenization process is a tricky task. A novel method of selenizing structured ZIF-67 into CoSex hollow cages with its cubic morphology maintained was developed. The target combination between Co and Se was the primary mechanism accounting for ZIF-67 selenization and its morphology inheritance. The selenized ZIF-67 was used in two typical clean energy areas, i.e., coal combustion detoxification and renewable energy storage. The performances of selenized ZIF-67 surpassed those of unstructured cobalt selenides and other benchmark materials used in these two areas. Following the mechanistic insights into the selenization process of ZIF-67, further work may develop more efficient methods to synthesize MOF-derived metal selenide composites under mild conditions, which is critical to extend the variety of MOF-derived materials and serve their cost-effective uses under practical scenarios.

Leveraging Cross-Diversity Machine Learning to Unveil Metal-Organic Frameworks with Open Copper Sites for Biogas Upgrading

Biogas, primarily composed of methane (CH4) and carbon dioxide (CO2), is considered an alternative renewable energy resource. Efficient CO2/CH4 separation is essential for biogas upgrading to increase energy density, and in this context, metal-organic frameworks (MOFs) have demonstrated significant potential. Here, we integrate multiscale modeling with cross-diversity machine learning (ML) to unveil MOFs with open copper sites (OCS-MOFs) that exhibit exceptional CO2/CH4 separation performance. Our focus on diversity-adaptable ML guarantees that ML models trained in one chemical space are rigorously transferable to unseen MOFs from distinct chemical spaces, assuring their robustness in real-world applications. By leveraging a meticulously curated data set of 27592 OCS-MOFs, we develop ML models with high predictive accuracy, capable of identifying top-performing OCS-MOFs across diverse chemical environments. This work not only elucidates the reticular chemistry that governs optimal CO2/CH4 separation performance in OCS-MOFs but also establishes a new benchmark for scalable and resilient digital MOF discovery, with cross-diversity accuracy as the key determinant of model transferability.

Uncovering the Relationship between Metal Elements and Mechanical Stability for Metal-Organic Frameworks

Assessing the mechanical robustness of metal-organic frameworks (MOFs) is crucial to enhance their applicability in various fields. Although considerable research has been conducted on the relationship between the mechanical properties of MOFs and their structural features (such as pore size, surface area, and topology), the insufficient exploration of metal elements has prevented researchers from fully understanding their mechanical behavior. To plug this knowledge gap, we constructed a database of mechanical properties for 20,342 MOFs included in the QMOF database using molecular simulations to investigate the impact of metal elements on mechanical stability. Through Shapley additive explanations (SHAP) analysis, we found that Co and Ln could enhance the structural stability of MOFs. We validated these findings using newly generated hypothetical MOFs. Notably, we adopted an interpretable machine learning technique to analyze the contribution of remarkably diverse metal elements in the 20,342 MOFs to the mechanical properties of each MOF. We anticipate that this research will serve as a valuable tool for future studies on identifying mechanically robust MOFs suitable for various industrial applications.

Quantifying the Uncertainty of Force Field Selection on Adsorption Predictions in MOFs

Comparisons between simulated and experimental adsorption isotherms in MOFs are fraught with challenges. On the experimental side, there is significant variation between isotherms measured on the same system, with a significant percentage (∼20%) of published data being considered outliers. On the simulation side, force fields are often chosen "off-the-shelf" with little or no validation. The effect of this choice on the reliability of simulated adsorption predictions has not yet been rigorously quantified. In this work, we fill this gap by systematically quantifying the uncertainty arising from force field selection on adsorption isotherm predictions. We choose methane adsorption, where electrostatic interactions are negligible, to independently study the effect of the framework Lennard-Jones parameters on a series of prototypical materials that represent the most widely studied MOF "families". Using this information, we compute an adsorption "consensus isotherm" from simulations, including a quantification of uncertainty, and compare it against a manually curated set of experimental data from the literature. By considering many experimental isotherms measured by different groups and eliminating outliers in the data using statistical analysis, we conduct a rigorous comparison that avoids the pitfalls of the standard approach of comparing simulation predictions to a single experimental data set. Our results show that (1) the uncertainty in simulated isotherms can be as large as 15% and (2) standard force fields can provide reliable predictions for some systems but can fail dramatically for others, highlighting systematic shortcomings in those models. Based on this, we offer recommendations for future simulation studies of adsorption, including high-throughput computational screening of MOFs.

The Open DAC 2023 Dataset and Challenges for Sorbent Discovery in Direct Air Capture

Direct air capture (DAC) of CO2 with porous adsorbents such as metal-organic frameworks (MOFs) has the potential to aid large-scale decarbonization. Previous screening of MOFs for DAC relied on empirical force fields and ignored adsorbed H2O and MOF deformation. We performed quantum chemistry calculations overcoming these restrictions for thousands of MOFs. The resulting data enable efficient descriptions using machine learning.

Does Mixed Linker-Induced Surface Heterogeneity Impact the Accuracy of IAST Predictions in UiO-66-NH2?

To move toward more energy-efficient adsorption-based processes, there is a need for accurate multicomponent data under realistic conditions. While the Ideal Adsorbed Solution Theory (IAST) has been established as the preferred prediction method due to its simplicity, limitations and inaccuracies for less ideal adsorption systems have been reported. Here, we use amine-functionalized derivatives of the UiO-66 structure to change the extent of homogeneity of the internal surface toward the adsorption of the two probe molecules carbon dioxide and ethylene. Although it might seem plausible that more functional groups lead to more heterogeneity and, thus, less accurate predictions by IAST, we find a mixed-linker system with increased heterogeneity in terms of added adsorption sites where IAST predictions and experimental loadings agree exceptionally well. We show that incorporating uncertainty analysis into predictions with IAST is important for assessing the accuracy of these predictions. Energetic investigations combined with Grand Canonical Monte Carlo simulations reveal almost homogeneous carbon dioxide but heterogeneous ethylene adsorption in the mixed-linker material, resulting in local, almost pure phases of the individual components.

Efficient Exploration of Adsorption Space for Separations in Metal-Organic Frameworks Combining the Use of Molecular Simulations, Machine Learning, and Ideal Adsorbed Solution Theory

Adsorption-based separations using metal-organic frameworks (MOFs) are promising candidates for replacing common energy-intensive separation processes. The so-called adsorption space formed by the combination of billions of possible molecules and thousands of reported MOFs is vast. It is very challenging to comprehensively evaluate the performance of MOFs for chemical separation through experiments. Molecular simulations and machine learning (ML) have been widely applied to make predictions for adsorption-based separations. Previous ML approaches to these issues were typically limited to smaller molecules and often had poor accuracy in the dilute limit. To enable exploration of a wider adsorption space, we carefully selected a diverse set of 45 molecules and 335 MOFs and generated single-component isotherms of 15,075 MOF-molecule pairs by grand canonical Monte Carlo. Using this database, we successfully developed accurate (r2 > 0.9) machine learning models predicting adsorption isotherms of diverse molecules in large libraries of MOFs. With this approach, we can efficiently make predictions of large collections of MOFs for arbitrary mixture separations. By combining molecular simulation data and ML predictions with Ideal Adsorbed Solution Theory, we tested the ability of these approaches to make predictions of adsorption selectivity and loading for challenging near-azeotropic mixtures.

Disclosing gate-opening/closing events inside a flexible metal-organic framework loaded with CO2 by reactive and essential dynamics

We have combined reactive molecular dynamics simulations with principal component analysis to provide a clearer view of the interactions and motion of the CO2 molecules inside a metal-organic framework and the movements of the MOF components that regulate storage, adsorption, and diffusion of the guest species. The tens-of-nanometer size of the simulated model, the capability of the reactive force field tuned to reproduce the inorganic-organic material confidently, and the unconventional use of essential dynamics have effectively disclosed the gate-opening/closing phenomenon, possible coordinations of CO2 at the metal centers, all the diffusion steps inside the MOF channels, the primary motions of the linkers, and the effects of their concerted rearrangements on local CO2 relocations.

Metal-Organic Framework/Polyvinyl Alcohol Composite Films for Multiple Applications Prepared by Different Methods

The incorporation of different functional fillers has been widely used to improve the properties of polymeric materials. The polyhydroxy structure of PVA with excellent film-forming ability can be easily combined with organic/inorganic multifunctional compounds, and such an interesting combining phenomenon can create a variety of functional materials in the field of materials science. The composite membrane material obtained by combining MOF material with high porosity, specific surface area, and adjustable structure with PVA, a non-toxic and low-cost polymer material with good solubility and biodegradability, can combine the processability of PVA with the excellent performance of porous filler MOFs, solving the problem that the poor machinability of MOFs and the difficulty of recycling limit the practical application of powdered MOFs and improving the physicochemical properties of PVA, maximizing the advantages of the material to develop a wider range of applications. Firstly, we systematically summarize the preparation of MOF/PVA composite membrane materials using solution casting, electrostatic spinning, and other different methods for such excellent properties, in addition to discussing in detail the various applications of MOF/PVA composite membranes in water treatment, sensing, air purification, separation, antibacterials, and so on. Finally, we conclude with a discussion of the difficulties that need to be overcome during the film formation process to affect the performance of the composite film and offer encouraging solutions.

An amine decorated MOF for direct capture of CO2 from ambient air

A Zn(II)-based metal-organic framework (MOF) was synthesized by the self-assembly of the dicarboxylate ligand terephthalic acid (TPA), 2-aminoterephthalic acid (NH2-TPA) and N-donor auxiliary ligand 1,4-bis(4-pyridinylmethyl)piperazine (bpmp) using Zn(NO3)2·6H2O under hydrothermal conditions. {[Zn(TPA)0.5(NH2TPA)0.5(bpmp)]·DMF·7H2O}n (framework 1) has an sra topology with a BET surface area of 756 m2 g-1. The microporous nature of the framework is apparent from the significant CO2 adsorption capacities observed at various temperatures: 57 cc g-1 at 283 K, 46 cc g-1 at 293 K, 37 cc g-1 at 303 K, and 30 cc g-1 at 313 K. The considerable CO2 adsorption may be caused by the existence of free carboxylate and amine substituents that interact with the gas molecules and micropores. At room temperature, the activated MOF readily converts CO2 into cyclic carbonates when a suspension of the MOF is bubbled with ambient air and different epoxides under solvent-free conditions. The amine groups located within the pores of the MOF interact with CO2 molecules, enhancing their sorption and conversion to cyclic carbonates. However, due to interpenetration within framework 1, only smaller size epoxides can be accommodated and converted to cyclic carbonates in good yields. Additionally, the effectiveness of the catalyst is further confirmed by the positive outcomes obtained from the hot filtration control test. Grand canonical Monte Carlo (GCMC) molecular simulations were utilized to gain a better understanding of molecular interactions. GCMC results are in line with the experiments. The substantial adsorption of CO2 can be ascribed to the strong intermolecular interactions that occur between the amine groups within the framework and the CO2 molecules.

Quantitative Simulations of Siloxane Adsorption in Metal-Organic Frameworks

We present a transferable force field (FF) for simulating the bulk properties of linear and cyclic siloxanes and the adsorption of these species in metal-organic frameworks (MOFs). Unlike previous FFs for siloxanes, our FF accurately reproduces the vapor-liquid equilibria of each species in the bulk phase. The quality of our FF combined with the Universal Force Field using standard Lorentz-Berthelot combining rules for MOF atoms was assessed in a wide range of MOFs without open metal sites, showing good agreement with dispersion-corrected density functional theory calculations. Predictions with this FF show good agreement with the limited experimental data for siloxane adsorption in MOFs that is available. As an example of using the FF to predict adsorption properties in MOFs, we present simulations examining entropy effects in binary linear and cyclic siloxane mixture coadsorption in the large-pore MOF with structure code FOTNIN.

Two-Dimensional Energy Histograms as Features for Machine Learning to Predict Adsorption in Diverse Nanoporous Materials

A major obstacle for machine learning (ML) in chemical science is the lack of physically informed feature representations that provide both accurate prediction and easy interpretability of the ML model. In this work, we describe adsorption systems using novel two-dimensional energy histogram (2D-EH) features, which are obtained from the probe-adsorbent energies and energy gradients at grid points located throughout the adsorbent. The 2D-EH features encode both energetic and structural information of the material and lead to highly accurate ML models (coefficient of determination R2 ∼ 0.94-0.99) for predicting single-component adsorption capacity in metal-organic frameworks (MOFs). We consider the adsorption of spherical molecules (Kr and Xe), linear alkanes with a wide range of aspect ratios (ethane, propane, n-butane, and n-hexane), and a branched alkane (2,2-dimethylbutane) over a wide range of temperatures and pressures. The interpretable 2D-EH features enable the ML model to learn the basic physics of adsorption in pores from the training data. We show that these MOF-data-trained ML models are transferrable to different families of amorphous nanoporous materials. We also identify several adsorption systems where capillary condensation occurs, and ML predictions are more challenging. Nevertheless, our 2D-EH features still outperform structural features including those derived from persistent homology. The novel 2D-EH features may help accelerate the discovery and design of advanced nanoporous materials using ML for gas storage and separation in the future.

Computational investigation of multifunctional MOFs for adsorption and membrane-based separation of CF4/CH4, CH4/H2, CH4/N2, and N2/H2 mixtures

The ease of functionalization of metal-organic frameworks (MOFs) can unlock unprecedented opportunities for gas adsorption and separation applications as the functional groups can impart favorable/unfavorable regions/interactions for the desired/undesired adsorbates. In this study, the effects of the presence of multiple functional groups in MOFs on their CF₄/CH₄, CH₄/H₂, CH₄/N₂, and N₂/H₂ separation performances were computationally investigated combining grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. The most promising adsorbents showing the best combinations of selectivity, working capacity, and regenerability were identified for each gas separation. 15, 13, and 16 out of the top 20 MOFs identified for the CH₄/H₂, CH₄/N₂, and N₂/H₂ adsorption-based separation, respectively, were found to have -OCH₃ groups as one of the functional groups. The biggest improvements in CF₄/CH₄, CH₄/H₂, CH₄/N₂, and N₂/H₂ selectivities were found to be induced by the presence of -OCH₃-OCH₃ groups in MOFs. For CH₄/H₂ separation, MOFs with two and three functionalized linkers were the best adsorbent candidates while for N₂/H₂ separation, all the top 20 materials involve two functional groups. Membrane performances of the MOFs were also studied for CH₄/H₂ and CH₄/N₂ separation and the results showed that MOFs having -F-NH₂ and -F-OCH₃ functional groups present the highest separation performances considering both the membrane selectivity and permeability.

Curated Collection of More than 20,000 Experimentally Reported One-Dimensional Metal-Organic Frameworks

A collection of more than 20,000 experimentally derived crystal structures for metal-organic frameworks (MOFs) that do not have two- or three-dimensional covalently bonded networks has been developed from the materials available at the Cambridge Crystallographic Data Centre. Of these 20,000 1D MOFs, more than 12,000 structures have been verified to be solvent-free and in exact agreement with the stoichiometry of the synthesized materials. More than 10% of the complete data set comprise materials including two or more distinct metals. The band gaps of more than 12,000 1D MOFs have been computed at the density functional theory-generalized gradient approximation level, finding more than 2000 materials that have a zero band gap. Molecular simulations of CH₄ adsorption in a small number of 1D MOFs indicated that adsorbate-induced deformation plays a significant role in determining adsorption isotherms in these materials. As a result, methods that have been used previously for high-throughput predictions of molecular adsorption in 3D MOFs are not suitable for 1D MOFs.

Gate Opening without Volume Change Triggers Cooperative Gas Interactions, Underpins an Isotherm Step in Metal-Organic Frameworks

Three halogenated metal-organic frameworks (MOFs) reported recently exhibited a second step in their CO₂ gas adsorption isotherms. The emergence of halogen-bonding interactions beyond a threshold gas pressure between the framework halogen and the CO₂ guest was conjectured to be the underlying reason for the additional step in the isotherm. Our investigation employing periodic density functional theory calculations did not show significant interactions between the halogen and CO₂ molecules. Further, using a combination of DFT-based ab initio molecular dynamics and grand canonical Monte Carlo simulations, we find that the increased separation of framework nitrate pairs facing each other across the pore channel enables the accommodation of an additional CO₂ molecule which is further stabilized by cooperative interactions─an observation that facilely explains the second isotherm step. The increased separation between the nitrate groups can occur without any lattice expansion, consistent with experiments. The results point to a structural feature to achieve this isotherm step in MOFs that neither possess large pores nor exhibit large-scale structural changes such as breathing.