Fast and Accurate Machine Learning Strategy for Calculating Partial Atomic Charges in Metal-Organic Frameworks

Recovery of High-Purity SF6 from Humid SF6/N2 Mixture within a Co(II)-Pyrazolate Framework

Sulfur hexafluoride (SF6) is extensively employed in the power industry. However, its emissions significantly contribute to the greenhouse effect. The direct recovery of high purity SF6 from industrial waste gases would benefit its sustainable use, yet this represents a considerable challenge. Herein, we report the enrichment of SF6 from SF6/N2 mixtures via adsorptive separation in a stable Co(II)-pyrazolate MOF BUT-53 (BUT: Beijing University of Technology), which features dynamic molecular traps. BUT-53 exhibits an excellent SF6 adsorption uptake of 2.82 mmol/g at 0.1 bar and 298 K, as well as an unprecedented SF6/N2 (10:90) selectivity of 2485. Besides, the remarkable SF6/N2 selectivity of BUT-53 enables recovery of high purity (>99.9%) SF6 from a low concentration (10%) mixture through a breakthrough experiment. The excellent SF6/N2 separation efficiency was also well maintained under humid conditions (RH = 90%) over multiple cycles. Molecular simulation, single-crystal diffraction, and adsorption kinetics studies elucidate the associated adsorption mechanism and water tolerance.

Engineered Nanoporous Frameworks for Adsorption Cooling Applications

The energy demand for traditional vapor-compressed technology for space cooling continues to soar year after year due to global warming and the increasing human population's need to improve living and working conditions. Thus, there is a growing demand for eco-friendly technologies that use sustainable or waste energy resources. This review discusses the properties of various refrigerants used for adsorption cooling applications followed by a brief discussion on the thermodynamic cycle. Next, sorbents traditionally used for cooling are reviewed to emphasize the need for advanced capture materials with superior properties to improve refrigerant sorption. The remainder of the review focus on studies using engineered nanoporous frameworks (ENFs) with various refrigerants for adsorption cooling applications. The effects of the various factors that play a role in ENF-refrigerant pair selection, including pore structure/dimension/shape, morphology, open-metal sites, pore chemistry and possible presence of defects, are reviewed. Next, in-depth insights into the sorbent-refrigerant interaction, and pore filling mechanism gained through a combination of characterization techniques and computational modeling are discussed. Finally, we outline the challenges and opportunities related to using ENFs for adsorption cooling applications and provide our views on the future of this technology.

PACMAN: A Robust Partial Atomic Charge Predicter for Nanoporous Materials Based on Crystal Graph Convolution Networks

We report a fast and easy method (PACMAN) to assign partial atomic charges on metal-organic framework (MOF) and covalent-organic framework (COF) crystal structures based on graph convolution networks (GCNs) trained on >1.8 million high-fidelity partial atomic charge data obtained from the Quantum Metal-Organic Framework (QMOF) database. The developed model shows outstanding performance, achieving a mean absolute error (MAE) of 0.0055 e (test set performance) while maintaining consistency with DDEC6, Bader, and CM5 charges across diverse chemistry and topologies of MOFs and COFs. We find that the new method accurately assigns partial atomic charges for ion-containing nanoporous materials, which has not been possible in previous machine learning (ML) models. Grand canonical Monte Carlo (GCMC) simulation results for CO2 and N2 uptakes and the Widom particle insertion calculation for Henry's law constant of water results based on PACMAN and the original DDEC6 charges show excellent agreements compared to other ML models reported in the literature. The runtime analysis of the new method demonstrates that the partial atomic charges of MOF and COF structures with up to 500 atoms can be obtained in less than 10 s. An easy-to-use web interface has been developed to facilitate the adoption of the developed model.

Assessment of Embedding Schemes in a Hybrid Machine Learning/Classical Potentials (ML/MM) Approach

Machine learning (ML) methods have reached high accuracy levels for the prediction of in vacuo molecular properties. However, the simulation of large systems solely through ML methods (such as those based on neural network potentials) is still a challenge. In this context, one of the most promising frameworks for integrating ML schemes in the simulation of complex molecular systems are the so-called ML/MM methods. These multiscale approaches combine ML methods with classical force fields (MM), in the same spirit as the successful hybrid quantum mechanics-molecular mechanics methods (QM/MM). The key issue for such ML/MM methods is an adequate description of the coupling between the region of the system described by ML and the region described at the MM level. In the context of QM/MM schemes, the main ingredient of the interaction is electrostatic, and the state of the art is the so-called electrostatic-embedding. In this study, we analyze the quality of simpler mechanical embedding-based approaches, specifically focusing on their application within a ML/MM framework utilizing atomic partial charges derived in vacuo. Taking as reference electrostatic embedding calculations performed at a QM(DFT)/MM level, we explore different atomic charges schemes, as well as a polarization correction computed using atomic polarizabilites. Our benchmark data set comprises a set of about 80k small organic structures from the ANI-1x and ANI-2x databases, solvated in water. The results suggest that the minimal basis iterative stockholder (MBIS) atomic charges yield the best agreement with the reference coupling energy. Remarkable enhancements are achieved by including a simple polarization correction.

A generative artificial intelligence framework based on a molecular diffusion model for the design of metal-organic frameworks for carbon capture

Metal-organic frameworks (MOFs) exhibit great promise for CO2 capture. However, finding the best performing materials poses computational and experimental grand challenges in view of the vast chemical space of potential building blocks. Here, we introduce GHP-MOFassemble, a generative artificial intelligence (AI), high performance framework for the rational and accelerated design of MOFs with high CO2 adsorption capacity and synthesizable linkers. GHP-MOFassemble generates novel linkers, assembled with one of three pre-selected metal nodes (Cu paddlewheel, Zn paddlewheel, Zn tetramer) into MOFs in a primitive cubic topology. GHP-MOFassemble screens and validates AI-generated MOFs for uniqueness, synthesizability, structural validity, uses molecular dynamics simulations to study their stability and chemical consistency, and crystal graph neural networks and Grand Canonical Monte Carlo simulations to quantify their CO2 adsorption capacities. We present the top six AI-generated MOFs with CO2 capacities greater than 2m mol g-1, i.e., higher than 96.9% of structures in the hypothetical MOF dataset.

Gas adsorption meets deep learning: voxelizing the potential energy surface of metal-organic frameworks

Intrinsic properties of metal-organic frameworks (MOFs), such as their ultra porosity and high surface area, deem them promising solutions for problems involving gas adsorption. Nevertheless, due to their combinatorial nature, a huge number of structures is feasible which renders cumbersome the selection of the best candidates with traditional techniques. Recently, machine learning approaches have emerged as efficient tools to deal with this challenge, by allowing researchers to rapidly screen large databases of MOFs via predictive models. The performance of the latter is tightly tied to the mathematical representation of a material, thus necessitating the use of informative descriptors. In this work, a generalized framework to predict gaseous adsorption properties is presented, using as one and only descriptor the capstone of chemical information: the potential energy surface (PES). In order to be machine understandable, the PES is voxelized and subsequently a 3D convolutional neural network (CNN) is exploited to process this 3D energy image. As a proof of concept, the proposed pipeline is applied on predicting [Formula: see text] uptake in MOFs. The resulting model outperforms a conventional model built with geometric descriptors and requires two orders of magnitude less training data to reach a given level of performance. Moreover, the transferability of the approach to different host-guest systems is demonstrated, examining [Formula: see text] uptake in COFs. The generic character of the proposed methodology, inherited from the PES, renders it applicable to fields other than reticular chemistry.

Accelerated Discovery of Metal-Organic Frameworks for CO2 Capture by Artificial Intelligence

The existence of a very large number of porous materials is a great opportunity to develop innovative technologies for carbon dioxide (CO2) capture to address the climate change problem. On the other hand, identifying the most promising adsorbent and membrane candidates using iterative experimental testing and brute-force computer simulations is very challenging due to the enormous number and variety of porous materials. Artificial intelligence (AI) has recently been integrated into molecular modeling of porous materials, specifically metal-organic frameworks (MOFs), to accelerate the design and discovery of high-performing adsorbents and membranes for CO2 adsorption and separation. In this perspective, we highlight the pioneering works in which AI, molecular simulations, and experiments have been combined to produce exceptional MOFs and MOF-based composites that outperform traditional porous materials in CO2 capture. We outline the future directions by discussing the current opportunities and challenges in the field of harnessing experiments, theory, and AI for accelerated discovery of porous materials for CO2 capture.

Leveraging Machine Learning for Metal-Organic Frameworks: A Perspective

Metal-organic frameworks (MOFs) have attracted tremendous interest because of their tunable structures, functionalities, and physiochemical properties. The nearly infinite combinations of metal nodes and organic linkers have led to the synthesis of over 100,000 experimental MOFs and the construction of millions of hypothetical counterparts. It is intractable to identify the best candidates in the immense chemical space of MOFs for applications via conventional trial-to-error experiments or brute-force simulations. Over the past several years, machine learning (ML) has substantially transformed the way of MOF discovery, design, and synthesis. Driven by the abundant data from experiments or simulations, ML can not only efficiently and accurately predict MOF properties but also quantitatively derive structure-property relationships for rational design and screening. In this Perspective, we summarize recent achievements in leveraging ML for MOFs from the aspects of data acquisition, featurization, model training, and applications. Then, current challenges and new opportunities are discussed for the future exploration of ML to accelerate the development of new MOFs in this vibrant field.

Geometry and Chemistry: Influence of Pore Functionalization on Molecular Transport and Diffusion in Solvent-Filled Zirconium Metal-Organic Frameworks

Postsynthetic modification (PSM) of metal-organic frameworks (MOFs) enables incorporation of diverse functionalities in pores for chemical separations, drug delivery, and heterogeneous catalysis. However, the effect of PSM on molecular transport, which is essential for most applications of MOFs, has been rarely studied. In this paper, we used perfluoroalkane-functionalized Zr-MOF NU-1008 as a platform to systematically interrogate transport processes and mechanisms in solvated pores. We anchored perfluoroalkanes onto NU-1008 nodes by solvent-assisted ligand incorporation (SALI-n, with n = 3, 5, 7, and 9 denoting the number of fluorinated carbons). Transport of a luminescent molecule, BODIPY, through individual crystallites of four versions of methanol-filled SALI-n was monitored by confocal fluorescence microscopy as a function of time and location. In comparison with the parent NU-1008, the diffusivity of the probe molecules within SALI-n declined by 2- to 7-fold depending on chain length and loading, presumably due to the reduction in pore diameter or adsorptive interactions with perfluoroalkyl chains. Atomistic simulations were performed to uncover the microscopic behavior of the BODIPY diffusion in SALI-n. The perfluoroalkyl chains are observed to stay close to the pore walls, instead of extending toward the pore center. BODIPY molecules, which preferably interact with linkers, were pushed to the interior of the channels as the chain length increased, resulting in solvated diffusion and minor differences in the short-time mobility of BODIPY in SALI-n. This suggested that the observed decline of transport diffusivity in SALI-n mainly stemmed from the reduction in the pore size when these flexible chains are present. We anticipate that this proof of concept will assist in understanding how pore functionalization can physically and chemically affect mass transport in MOFs and will be useful in further guiding the design of PSM to realize the optimal performance of MOFs for various applications.

Metal-Organic Frameworks for Phthalate Capture

Indoor air contamination by phthalate ester (PAE) derivatives has become a significant concern since traces of PAEs can cause endocrine disruption, among other health issues. PAE abatement from the environment is thus mandatory to further ensure a good quality of indoor air. Herein, we explored the physisorption-based capture of volatile PAEs by metal-organic frameworks (MOFs). A high-throughput computational screening approach was first applied on databases compiling more than 20,000 MOF structures in order to identify the best MOFs for adsorbing traces of dimethyl phthalate (DMP), considered as a representative molecule of the family of PAE contaminants. Among the 20 top candidates, MOF-74(Ni), which combines substantial DMP uptake at the 10 ppm concentration level (∼0.20 g g-1) with high adsorption enthalpy at infinite dilution (-ΔHads(DMP),0 = 109.9 kJ mol-1), was revealed as an excellent porous material to capture airborne DMP. This prediction was validated by further experiments: gravimetric sorption isotherms were carried out on MOF-74(Ni), replacing DMP by dimethyl maleate (DMM), a molecule with a higher vapor pressure and indeed easier to manipulate compared to DMP while mimicking the adsorption behavior of DMP by MOFs, as evidenced by Monte Carlo calculations. Notably, saturation of DMM by MOF-74(Ni) (∼0.35 g g-1 at 343 K) occurs at very low equivalent concentration of the sorbate, i.e., 15 ppm, while half of the DMM molecules remain trapped in the MOF pores, even by heating the system up to 473 K under vacuum. This computational-experimental study reveals for the first time the potential of MOFs for the capture of phthalate ester contaminants as vapors of key importance to address indoor air quality issues.

Accelerating the prediction of CO2 capture at low partial pressures in metal-organic frameworks using new machine learning descriptors

Metal-Organic frameworks (MOFs) have been considered for various gas storage and separation applications. Theoretically, there are an infinite number of MOFs that can be created; however, a finite amount of resources are available to evaluate each one. Computational methods can be adapted to expedite the process of evaluation. In the context of CO2 capture, this paper investigates the method of screening MOFs using machine learning trained on molecular simulation data. New descriptors are introduced to aid this process. Using all descriptors, it is shown that machine learning can predict the CO2 adsorption, with an R2 of above 0.9. The introduced Effective Point Charge (EPoCh) descriptors, which assign values to frameworks' partial charges based on the expected CO2 uptake of an equivalent point charge in isolation, are shown to be the second most important group of descriptors, behind the Henry coefficient. Furthermore, the EPoCh descriptors are hundreds of thousands of times faster to obtain compared with the Henry coefficient, and they achieve similar results when identifying top candidates for CO2 capture using pseudo-classification predictions.

Open-Source Machine Learning in Computational Chemistry

The field of computational chemistry has seen a significant increase in the integration of machine learning concepts and algorithms. In this Perspective, we surveyed 179 open-source software projects, with corresponding peer-reviewed papers published within the last 5 years, to better understand the topics within the field being investigated by machine learning approaches. For each project, we provide a short description, the link to the code, the accompanying license type, and whether the training data and resulting models are made publicly available. Based on those deposited in GitHub repositories, the most popular employed Python libraries are identified. We hope that this survey will serve as a resource to learn about machine learning or specific architectures thereof by identifying accessible codes with accompanying papers on a topic basis. To this end, we also include computational chemistry open-source software for generating training data and fundamental Python libraries for machine learning. Based on our observations and considering the three pillars of collaborative machine learning work, open data, open source (code), and open models, we provide some suggestions to the community.

Water-Accelerated Transport: Vapor-Phase Nerve Agent Simulant Delivery within a Catalytic Zirconium Metal-Organic Framework as a Function of Relative Humidity

Zirconium-based metal-organic frameworks (MOFs) are candidate materials for effective nerve agent detoxification due to their thermo- and water stability as well as high density of catalytic Zr sites. However, as high-porosity materials, most of the active sites of Zr-MOFs can only be accessed by diffusion into the crystal interior. Therefore, the transport of nerve agents in nanopores is an important factor in the catalytic performance of Zr-MOFs. Here, we investigated the transport process and mechanism of a vapor-phase nerve agent simulant, dimethyl methyl phosphonate (DMMP), through a representative Zr-MOF, NU-1008, under practical conditions of varying humidity. Confocal Raman microscopy was used to monitor the transport of DMMP vapor through individual NU-1008 crystallites, where the relative humidity (RH) of the environment was tuned to understand the impact of water. Counterintuitively, water in the MOF channels, instead of blocking DMMP transport, assists DMMP diffusion; indeed, the transport diffusivity (D_t) of DMMP in NU-1008 is one order of magnitude higher at 70% than 0% RH. To understand the mechanism, magic angle spinning NMR and molecular dynamics simulations were performed and suggested that high water content in the channels prevents DMMP from hydrogen-bonding with the nodes, allowing for faster diffusion of DMMP in the channels. The simulated self-diffusivity (D_s) of DMMP is observed to be concentration-dependent. At low loading of DMMP, D_s is higher at 70% RH than 0% RH, while at high loadings the trend reverses due to the DMMP aggregation in water and the reduction of free volume in channels.

High-Throughput Screening of the CoRE-MOF-2019 Database for CO2 Capture from Wet Flue Gas: A Multi-Scale Modeling Strategy

Stabilizing the escalating CO₂ levels in the atmosphere is a grand challenge in view of the increasing global demand for energy, the majority of which currently comes from the burning of fossil fuels. Capturing CO₂ from point source emissions using solid adsorbents may play a part in meeting this challenge, and metal-organic frameworks (MOFs) are considered to be a promising class of materials for this purpose. It is important to consider the co-adsorption of water when designing materials for CO₂ capture from post-combustion flue gases. Computational high-throughput screening (HTS) is a powerful tool to identify top-performing candidates for a particular application from a large material database. Using a multi-scale modeling strategy that includes a machine learning model, density functional theory (DFT) calculations, force field (FF) optimization, and grand canonical Monte Carlo (GCMC) simulations, we carried out a systematic computational HTS of the all-solvent-removed version of the computation-ready experimental metal-organic framework (CoRE-MOF-2019) database for selective adsorption of CO₂ from a wet flue gas mixture. After initial screening based on the pore diameters, a total of 3703 unique MOFs from the database were considered for screening based on the FF interaction energies of CO₂, N₂, and H₂O molecules with the MOFs. MOFs showing stronger interactions with CO₂ compared to that with H₂O and N₂ were considered for the next level of screening based on the interaction energies calculated from DFT. CO₂-selective MOFs from DFT screening were further screened using two-component (CO₂ and N₂) and finally three-component (CO₂, N₂, and H₂O) GCMC simulations to predict the CO₂ capacity and CO₂/N₂ selectivity. Our screening study identified MOFs that show selective CO₂ adsorption under wet flue gas conditions with significant CO₂ uptake capacity and CO₂/N₂ selectivity in the presence of water vapor. We also analyzed the nature of pore confinements responsible for the observed CO₂ selectivity.

Incorporating Polarization and Charge Transfer into a Point-Charge Model for Water Using Machine Learning

Rigid nonpolarizable water models with fixed point charges have been widely employed in molecular dynamics simulations due to their efficiency and reasonable accuracy for the potential energy surface. However, the dipole moment surface of water is not necessarily well-described by the same fixed charges, leading to failure in reproducing dipole-related properties. Here, we developed a machine-learning model trained against electronic structure data to assign point charges for water, and the resulting dipole moment surface significantly improved the predictions of the dielectric constant and the low-frequency IR spectrum of liquid water. Our analysis reveals that within our atom-centered point-charge description of the dipole moment surface, the intermolecular charge transfer is the major source of the peak intensity at 200 cm^-1, whereas the intramolecular polarization controls the enhancement of the dielectric constant. The effects of exact Hartree-Fock exchange in the hybrid density functional on these properties are also discussed.

CRAFTED: An exploratory database of simulated adsorption isotherms of metal-organic frameworks

Grand Canonical Monte Carlo is an important method for performing molecular-level simulations and assisting the study and development of nanoporous materials for gas capture applications. These simulations are based on the use of force fields and partial charges to model the interaction between the adsorbent molecules and the solid framework. The choice of the force field parameters and partial charges can significantly impact the results obtained, however, there are very few databases available to support a comprehensive impact evaluation. Here, we present a database of simulations of CO₂ and N₂ adsorption isotherms on 690 metal-organic frameworks taken from the CoRE MOF 2014 database. We performed simulations with two force fields (UFF and DREIDING), six partial charge schemes (no charges, Qeq, EQeq, MPNN, PACMOF, and DDEC), and three temperatures (273, 298, 323 K). The resulting isotherms compose the Charge-dependent, Reproducible, Accessible, Forcefield-dependent, and Temperature-dependent Exploratory Database (CRAFTED) of adsorption isotherms.

A Theoretical Perspective to Decipher the Origin of High Hydrogen Storage Capacity in Mn(II) Metal-Organic Framework

Herein, we report a detailed periodic DFT investigation of Mn(II)-based [(Mn₄ Cl)₃ (BTT)₈ ]^3- (BTT^3- =1,3,5-benzenetristetrazolate) metal-organic framework (MOF) to explore various hydrogen binding pockets, nature of MOF…H₂ interactions, magnetic coupling and, H₂ uptake capacity. Earlier experiments found an uptake capacity of 6.9 wt % of H_2, with the heat of adsorption estimated to be ∼10 kJ/mol, which is one among the highest for any MOFs reported. Our calculations unveil different binding sites with computed binding energy varying from -6 to -15 kJ/mol. The binding of H₂ at the Mn²⁺ site is found to be the strongest (site I), with H₂ found to bind Mn²⁺ ion in a η² fashion with a distance of 2.27 Å and binding energy of -15.4 kJ/mol. The bonding analysis performed using NBO and AIM reveal a strong donation of σ (H₂ ) to the d_z ² orbital of the Mn²⁺ ion responsible for such large binding energy. The other binding pockets, such as -Cl (site II) and BTT ligands (site III and IV) were found to be weaker, with the binding energy decreasing in the order I>II>III>IV. The average binding energy computed for these four sites put together is 9.6 kJ/mol, which is in excellent agreement with the experimental value of ∼10 kJ/mol. We have expanded our calculations to compute binding energy for multiple sites simultaneously, and in this model, the binding energy per site was found to decrease as we increased the number of H₂ molecules suggesting electronic and steric factors controlling the overall uptake capacity. The calculated adsorption isotherm using the GCMC method reproduces the experimental observations. Further, the magnetic coupling computed for the unbound MOF reveals moderate ferromagnetic and strong antiferromagnetic coupling within the tetrameric {Mn₄ } unit leading to a three-up-one-down spin configuration as the ground state. These were then coupled ferromagnetically to other tetrameric units in the MOF network. The magnetic coupling was found to alter only marginally upon gas binding, suggesting that both exchange interaction and the spin-states are unlikely to play a role in the H₂ uptake. This is contrary to the O₂ uptake studied lately, where strong dependence on exchange-coupling/spin state was witnessed, suggesting exchange-coupling/magnetic field dependent binding as a viable route for gas separation.

Automated Graph Neural Networks Accelerate the Screening of Optoelectronic Properties of Metal-Organic Frameworks

The numerous organic and inorganic components of metal-organic framework (MOF) materials provide intriguing optoelectronic properties. Accurately predicting the electronic structural properties of MOFs has become the main focus. This work establishes two graph neural network models, crystal graph convolutional neural networks and a materials graph network, for predicting the band gaps of more than 10 000 MOF structures and promotes to improve the prediction accuracy through automatic hyperparameter tuning algorithms. Subsequently, for exploring machine learning-assisted screening of MOFs for the broader electronic properties, the screened copper-based MOFs are compared with lead-based MAPbI₃ solar cells with respect to the band gaps, densities of states, and charge density distributions, and the results have demonstrated that the overlap of the wave functions between the initial and final states of MOFs is weakened, which is conducive to the improvement of photoelectric performance. The chlorine doping strategy further enhances the advantage. The tuning of the machine learning model and hyperparameters and the doping strategy of halogen elements furnish empirical rules for the design of MOFs with excellent optoelectronic properties.

Computational Characterization of Zr-Oxide MOFs for Adsorption Applications

Zr-oxide secondary building units construct metal-organic framework (MOF) materials with excellent gas adsorption properties and high mechanical, thermal, and chemical stability. These attributes have led Zr-oxide MOFs to be well-recognized for a wide range of applications, including gas storage and separation, catalysis, as well as healthcare domain. Here, we report structure search methods within the Cambridge Structural Database (CSD) to create a curated subset of 102 Zr-oxide MOFs synthesized to date, bringing a unique record for all researchers working in this area. For the identified structures, we manually corrected the proton topology of hydroxyl and water molecules on the Zr-oxide nodes and characterized their textural properties, Brunauer-Emmett-Teller (BET) area, and topology. Importantly, we performed systematic periodic density functional theory (DFT) calculations comparing 25 different combinations of basis sets and functionals to calculate framework partial atomic charges for use in gas adsorption simulations. Through experimental verification of CO₂ adsorption in selected Zr-oxide MOFs, we demonstrate the sensitivity of CO₂ adsorption predictions at the Henry's regime to the choice of the DFT method for partial charge calculations. We characterized Zr-MOFs for their CO₂ adsorption performance via high-throughput grand canonical Monte Carlo (GCMC) simulations and revealed how the chemistry of the Zr-oxide node could have a significant impact on CO₂ uptake predictions. We found that the maximum CO₂ uptake is obtained for structures with the heat of adsorption values >25 kJ/mol and the largest cavity diameters of ca. 6-7 Å. Finally, we introduced augmented reality (AR) visualizations as a means to bring adsorption phenomena alive in porous adsorbents and to dynamically explore gas adsorption sites in MOFs.

An Amine-Functionalized Ultramicroporous Metal-Organic Framework for Postcombustion CO2 Capture

Among the most promising methods by which to capture CO₂ from flue gas, the emission of which has accelerated global warming, is energy-efficient physisorption using metal-organic framework (MOF) adsorbents. Here, we present a novel cuprous-based ultramicroporous MOF, Cu(adci)-2 (adci^- = 2-amino-4,5-dicyanoimidazolate), which was rationally synthesized by combining two strategies to design MOF physisorbents for enhanced CO₂ capturing, i.e., aromatic amine functionalization and the introduction of ultramicroporosity (pore size <7 Å). Synchrotron powder X-ray diffraction and a Rietveld analysis reveal that the Cu(adci)-2 structure has one-dimensional square-shaped channels, in each of which all affiliated ligands, specifically NH₂ groups at the 2-position of the imidazolate ring, have the same orientation, with a pair of NH₂ groups therefore facing each other on opposite sides of the channel walls. While Cu(adci)-2 exhibits a high CO₂ adsorption capacity (2.01 mmol g^-1 at 298 K and 15 kPa) but a low zero-coverage isosteric heat of adsorption (27.5 kJ mol^-1), breakthrough experiments under dry and 60% relative humidity conditions show that its CO₂ capture ability is retained even in the presence of high amounts of moisture. In a Monte Carlo simulation and a radial distribution analysis, the preferential CO₂ binding site of Cu(adci)-2 was predicted to be between two ligands, forming a sandwich-like structure and implying that its CO₂ adsorption properties originate from the enhancement of Lewis base-acid and London dispersion interactions due to the amino groups and ultramicroporosity, respectively.

Insights and Heuristics for Predicting Diffusion Rates of Chemical Warfare Agents in Zirconium Metal-Organic Frameworks

Designing nanoporous catalysts to destroy chemical warfare agents (CWAs) and environmental contaminants requires consideration of both intrinsic catalytic activity and the mass transfer of molecules in and out of the pores. Polar adsorbates such as CWAs experience a heterogeneous environment in many metal-organic frameworks (MOFs) due to the arrangement of the metal nodes and organic linkers of the MOF. However, quantitative relationships between the pore architecture and the resulting diffusion properties of polar molecules have not been established. We used molecular dynamics simulations to calculate the diffusion coefficients of the CWA simulant dimethyl methyl phosphonate (DMMP) in a diverse set of 776 MOFs with Zr₆ nodes. We developed a 4-parameter machine learning model to predict DMMP diffusivities in Zr₆ MOFs and found the model to be transferable to the CWA sarin. We then developed a simplified heuristic based on the machine learning model that the node-node distance and accessible surface area should be maximized to find MOFs with rapid CWA diffusion.

In Silico Screening of Metal-Organic Frameworks and Zeolites for He/N2 Separation

In silico screening of 10,143 metal-organic frameworks (MOFs) and 218 all-silica zeolites for adsorption-based and membrane-based He and N₂ separation was performed. As a result of geometry-based prescreening, structures having zero accessible surface area (ASA) and pore limiting diameter (PLD) less than 3.75 Å were eliminated. So, both gases can be adsorbed and pass-through MOF and zeolite pores. The Grand canonical Monte Carlo (GCMC) and equilibrium molecular dynamics (EMD) methods were used to estimate the Henry's constants and self-diffusion coefficients at infinite dilution conditions, as well as the adsorption capacity of an equimolar mixture of helium and nitrogen at various pressures. Based on the obtained results, adsorption, diffusion and membrane selectivities as well as membrane permeabilities were calculated. The separation potential of zeolites and MOFs was evaluated in the vacuum and pressure swing adsorption processes. In the case of membrane-based separation, we focused on the screening of nitrogen-selective membranes. MOFs were demonstrated to be more efficient than zeolites for both adsorption-based and membrane-based separation. The analysis of structure-performance relationships for using these materials for adsorption-based and membrane-based separation of He and N₂ made it possible to determine the ranges of structural parameters, such as pore-limiting diameter, largest cavity diameter, surface area, porosity, accessible surface area and pore volume corresponding to the most promising MOFs for each separation model discussed in this study. The top 10 most promising MOFs were determined for membrane-based, vacuum swing adsorption and pressure swing adsorption separation methods. The effect of the electrostatic interaction between the quadrupole moment of nitrogen molecules and MOF atoms on the main adsorption and diffusion characteristics was studied. The obtained results can be used as a guide for selection of frameworks for He/N₂ separation.

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.

High-throughput computational screening of hypothetical metal-organic frameworks with open copper sites for CO2/H2 separation

It is challenging to identify the optimal metal-organic framework (MOF) adsorbents for gas adsorption and membrane-based separation from the large-scale material databases. The high-throughput computational screening (HTCS) method was adopted to discover the optimal materials for CO₂/H₂ separation from thousands of MOFs. First, a hierarchical strategy was used to select 1092 MOFs from 13 512 MOFs, and their adsorption capacity towards the equimolar CO₂/H₂ mixture at 298 K and 10 bar was further calculated using the grand canonical Monte Carlo (GCMC) simulations. The results show that those MOFs with lvtb topology and organic linker 1,2,4,5-tetrazine are conducive to exhibiting high performance CO₂/H₂ adsorption separation among top-100 MOFs with high performance. The MOFs with pore limited diameter (PLD), largest cavity diameter (LCD), gravimetrical surface area (GSA), and void fraction in the range of 4-12 Å, 5-12 Å, 5500-6500 m² g^-1 and 0.80-0.85, respectively, have high adsorption capacity towards CO₂. Second, the dynamic adsorption properties of the top-4 MOFs were simulated by the breakthrough curves of the binary (CO₂/H₂) and quinary (CO₂/H₂/CH₄/CO/N₂) mixtures in the fixed adsorption bed. MOF-4641 exhibits a high breakthrough time of 130 for the quinary mixture. Finally, the adsorption mechanism of CO₂ in the top-4 MOFs was investigated by the radial distribution function (RDF), the mass center probability density distribution, etc. The atomic insights from HTCS and breakthrough curve predictions in this work will be helpful in developing novel porous materials and obtaining superior CO₂ separation performance.

Benchmarking various types of partial atomic charges for classical all-atom simulations of metal-organic frameworks

The density derived electrostatic and chemical (DDEC) approach for calculating the charges of atoms in a metal-organic framework (MOF) is considered to be the most accurate (yet computationally costly) one among many charge-assignment methods. Here, we conducted a comparative study on five different types of atomic partial charges (namely CM5, Mulliken, Qeq, EQeq and PACMOF) prepared for a subset of MOFs with affordable computational costs and benchmarked them with respect to the DDEC charges, which is particularly relevant because currently most databases lack MOFs with pre-calculated DDEC charges. To find a suitable charge type alternative to the DDEC approach, we statistically ranked the five charge types based on two metrics, the relative standard deviation of charges and relative dipole moment difference, based on which we provide general guidance as well as suggestions for specific MOFs according to bond polarity analyses. Finally, we recommend a possible and more accurate parametrization scheme for future studies.

Multi-Level Computational Screening of in Silico Designed MOFs for Efficient SO2 Capture

SO₂ presence in the atmosphere can cause significant harm to the human and environment through acid rain and/or smog formation. Combining the operational advantages of adsorption-based separation and diverse nature of metal-organic frameworks (MOFs), cost-effective separation processes for SO₂ emissions can be developed. Herein, a large database of hypothetical MOFs composed of >300,000 materials is screened for SO₂/CH₄, SO₂/CO₂, and SO₂/N₂ separations using a multi-level computational approach. Based on a combination of separation performance metrics (adsorption selectivity, working capacity, and regenerability), the best materials and the most common functional groups in those most promising materials are identified for each separation. The top bare MOFs and their functionalized variants are determined to attain SO₂/CH₄ selectivities of 62.4-16899.7, SO₂ working capacities of 0.3-20.1 mol/kg, and SO₂ regenerabilities of 5.8-98.5%. Regarding SO₂/CO₂ separation, they possess SO₂/CO₂ selectivities of 13.3-367.2, SO₂ working capacities of 0.1-17.7 mol/kg, and SO₂ regenerabilities of 1.9-98.2%. For the SO₂/N₂ separation, their SO₂/N₂ selectivities, SO₂ working capacities, and SO₂ regenerabilities span the ranges of 137.9-67,338.9, 0.4-20.6 mol/kg, and 7.0-98.6%, respectively. Besides, using breakdowns of gas separation performances of MOFs into functional groups, separation performance limits of MOFs based on functional groups are identified where bare MOFs (MOFs with multiple functional groups) tend to show the smallest (largest) spreads.

Deep Neural Network Model to Predict the Electrostatic Parameters in the Polarizable Classical Drude Oscillator Force Field

The Drude polarizable force field (FF) captures electronic polarization effects via auxiliary Drude particles that are attached to non-hydrogen atoms, distinguishing it from commonly used additive FFs that rely on fixed charges. The Drude FF currently includes parameters for biomolecules such as proteins, nucleic acids, lipids, and carbohydrates and small-molecule representative of those classes of molecules as well as a range of atomic ions. Extension of the Drude FF to novel small druglike molecules is challenging as it requires the assignment of partial charges, atomic polarizabilities, and Thole scaling factors. In the present article, deep neural network (DNN) models are trained on quantum mechanical (QM)-based partial charges and atomic polarizabilities along with Thole scale factors trained to target QM molecular dipole moments and polarizabilities. Training of the DNN model used a collection of 39 421 molecules with molecular weights up to 200 Da and containing H, C, N, O, P, S, F, Cl, Br, or I atoms. The DNN model utilizes bond connectivity, including 1,2, 1,3, 1,4, and 1,5 terms and distances of Drude FF atom types as the feature vector to build the model, allowing it to capture both local and nonlocal effects in the molecules. Novel methods have been developed to determine restrained electrostatic potential (RESP) charges on atoms and external points representing lone pairs and to determine Thole scale factors, which have no QM analogue. A penalty scheme is devised as a performance predictor of the trained model. Validation studies show that these DNN models can precisely predict molecular dipole and polarizabilities of Food and Drug Administration (FDA)-approved drugs compared to reference MP2 calculations. The availability of the DNN model allowing for the rapid estimation of the Drude electrostatic parameters will facilitate its applicability to a wider range of molecular species.

Parametrization of Nonbonded Force Field Terms for Metal-Organic Frameworks Using Machine Learning Approach

The enormous structural and chemical diversity of metal-organic frameworks (MOFs) forces researchers to actively use simulation techniques as often as experiments. MOFs are widely known for their outstanding adsorption properties, so a precise description of the host-guest interactions is essential for high-throughput screening aimed at ranking the most promising candidates. However, highly accurate ab initio calculations cannot be routinely applied to model thousands of structures due to the demanding computational costs. Furthermore, methods based on force field (FF) parametrization suffer from low transferability. To resolve this accuracy-efficiency dilemma, we applied a machine learning (ML) approach: extreme gradient boosting. The trained models reproduced the atom-in-material quantities, including partial charges, polarizabilities, dispersion coefficients, quantum Drude oscillator, and electron cloud parameters, with accuracy similar to the reference data set. The aforementioned FF precursors make it possible to thoroughly describe noncovalent interactions typical for MOF-adsorbate systems: electrostatic, dispersion, polarization, and short-range repulsion. The presented approach can also readily facilitate hybrid atomistic simulation/ML workflows.

Correlation between the Metal and Organic Components, Structure Property, and Gas-Adsorption Capacity of Metal-Organic Frameworks

Metal-organic frameworks (MOFs) are materials in which metals and organic compounds form crystalline and porous structures. Previous studies have investigated the relationships between the structure properties and physical properties of MOFs through molecular simulations, but the overall relationships in MOFs, including the relationships between the metals and organic components and the experimentally measured physical properties, have not been clarified. In this study, we developed two regression models between three elements in MOFs: the components, structure properties, and gas-adsorption capacities as physical properties. Using a nonlinear regression analysis method, we succeeded in predicting the structure properties from the components and the physical properties from the structure properties.

Nanoconfinement and mass transport in metal-organic frameworks

The ubiquity of metal-organic frameworks in recent scientific literature underscores their highly versatile nature. MOFs have been developed for use in a wide array of applications, including: sensors, catalysis, separations, drug delivery, and electrochemical processes. Often overlooked in the discussion of MOF-based materials is the mass transport of guest molecules within the pores and channels. Given the wide distribution of pore sizes, linker functionalization, and crystal sizes, molecular diffusion within MOFs can be highly dependent on the MOF-guest system. In this review, we discuss the major factors that govern the mass transport of molecules through MOFs at both the intracrystalline and intercrystalline scale; provide an overview of the experimental and computational methods used to measure guest diffusivity within MOFs; and highlight the relevance of mass transfer in the applications of MOFs in electrochemical systems, separations, and heterogeneous catalysis.

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.

Zr-MOFs for CF4/CH4, CH4/H2, and CH4/N2 separation: towards the goal of discovering stable and effective adsorbents

Zirconium metal-organic frameworks (MOFs) can be promising adsorbents for various applications as they are highly stable in different chemical environments. In this work, a collection of Zr-MOFs comprised of more than 100 materials is screened for CF₄/CH₄, CH₄/H₂, and CH₄/N₂ separations using atomistic-level simulations. The top three MOFs for the CF₄/CH₄ separation are identified as PCN-700-BPDC-TPDC, LIFM-90, and BUT-67 exhibiting CF₄/CH₄ adsorption selectivities of 4.8, 4.6, and 4.7, CF₄ working capacities of 2.0, 2.0, and 2.1 mol kg^-1, and regenerabilities of 85.1, 84.2, and 75.7%, respectively. For the CH₄/H₂ separation, MOF-812, BUT-67, and BUT-66 are determined to be the top performing MOFs demonstrating CH₄/H₂ selectivities of 61.6, 36.7, and 46.2, CH₄ working capacities of 3.0, 4.1, and 3.4 mol kg^-1, and CH₄ regenerabilities of 70.7, 82.7, and 74.7%, respectively. Regarding the CH₄/N₂ separation, BUT-67, Zr-AbBA, and PCN-702 achieving CH₄/N₂ selectivities of 4.5, 3.4, and 3.8, CH₄ working capacities of 3.6, 3.9, and 3.5 mol kg^-1, and CH₄ regenerabilities of 81.1, 84.0, and 84.5%, in successive order, show the best overall separation performances. To further elucidate the adsorption in top performing adsorbents, the adsorption sites in these materials are analyzed using radial distribution functions and adsorbate density profiles. Finally, the water affinities of Zr-MOFs are explored to comment on their practical use in real gas separation applications. Our findings may inspire future studies probing the adsorption/separation mechanisms and performances of Zr-MOFs for different gases.