Multivariable linear models of structural parameters to predict methane uptake in metal–organic frameworks

An XGBoost Algorithm Based on Molecular Structure and Molecular Specificity Parameters for Predicting Gas Adsorption

In this paper, an improved Extreme Gradient Boosting (XGBoost) algorithm based on the Graph Isomorphic Network (GIN) for predicting the adsorption performance of metal-organic frameworks (MOFs) is developed. It is shown that the graph isomorphic layer of this algorithm can directly learn the feature representation of materials from the connection of atoms in MOFs. Then, XGBoost can be used to predict the adsorption performance of MOFs based on feature representation. In this sense, it is not only possible to achieve end-to-end prediction directly from the structure of MOFs to adsorption performance but also to ensure the accuracy of prediction. The comparison between Grand Canonical Monte Carlo (GCMC) simulation and prediction supports the performance and effectiveness of the proposed algorithm.

Development of a High-Accuracy Statistical Model to Identify the Key Parameter for Methane Adsorption in Metal-Organic Frameworks

The geometrical and topological features of metal-organic frameworks (MOFs) play an important role in determining their ability to capture and store methane (CH4). Methane is a greenhouse gas that has been shown to be more dangerous in terms of contributing to global warming than carbon dioxide (CO2), especially in the first 20 years of its release into the atmosphere. Its accelerated emission increases the rate of global temperature increase and needs to be addressed immediately. Adsorption processes have been shown to be effective and efficient in mitigating methane emissions from the atmosphere by providing an enormous surface area for methane storage. Among all the adsorbents, MOFs were shown to be the best adsorbents for methane adsorption due to their higher favorable steric interactions, the presence of binding sites such as open metal sites, and hydrophobic pockets. These features may not necessarily be present in carbonaceous materials and zeolites. Although many studies have suggested that the main reason for the increased storage efficiencies in terms of methane in the MOFs is the high surface area, there was some evidence in certain research works that methane storage performance, as measured by uptakes and deliveries in gravimetric and volumetric units, was higher for certain MOFs with a lower surface area. This prompted us to find out the most significant property of the MOF, whether it be material-based or pore-based, that has the maximum influence on methane uptake and delivery, using a comprehensive statistical approach that has not previously been employed in the methane storage literature. The approach in our study employed various chemometric techniques, including simple and multiple linear regression (SLR and MLR), combined with different types of multicollinearity diagnostics, partial correlations, standardized coefficients, and changes in regression coefficient estimates and their standard errors, applied to both the SLR and MLR models. The main advantages of this statistical approach are that it is quicker, provides a deeper insight into experimental data, and highlights a single, most important, parameter for MOF design and tuning that can predict and maximize the output storage and capture performance. The significance of our approach is that it was modeled purely based on experimental data, which will capture the real system, as opposed to the molecular simulations employed previously in the literature. Our model included data from ~80 MOFs and eight properties related to the material, pore, and thermodynamics (isosteric adsorption energy). Successful attempts to model the methane sorption process have previously been conducted using thermodynamic approaches and by developing adsorption performance indicators, but these are either too complex or time-consuming and their data covers fewer than 10 MOFs and a maximum of three MOF properties. By comparing the statistical metrics between the models, the most important and statistically significant property of the MOF was determined, which will be crucial when designing MOFs for use in storing and delivering methane.

Searching for Mechanically Superior Solid-State Electrolytes in Li-Ion Batteries via Data-Driven Approaches

Li-ion solid-state electrolytes (SSEs) have great potential, but their commercialization is limited due to interfacial contact stability issues and the formation and growth of dendrites. In this study, a machine learning regression algorithm was implemented to screen for mechanically superior SSEs among 17,619 candidates. Elasticity information (14,238 structures) was imported from an available database, and their machine learning descriptors were constructed using physiochemical and structural properties. A surrogate model for predicting the shear and bulk moduli exhibited R² values of 0.819 and 0.863, respectively. The constructed model was applied to predict the elastic properties of potential SSEs, and first-principles calculations were conducted for validation. Furthermore, the application of an active learning process, which reduced the prediction uncertainty, was clearly demonstrated to improve the R² score from approximately 0.6-0.8 by adding only 32-63% of new data sets depending on the type of modulus. We believe that the current model and additional data sets can accelerate the process of finding optimal SSEs to satisfy the mechanical conditions being sought.

MGRNN: Structure Generation of Molecules Based on Graph Recurrent Neural Networks

Molecular structure generation is a critical problem for materials science and has attracted growing attention. The problem is challenging since it requires to generate chemically valid molecular structures. Inspired by the recent work in deep generative models, we propose a graph recurrent neural network model for drug molecular structure generation, briefly called MGRNN (Molecular Graph Recurrent Neural Networks). MGRNN combines the advantages of both iterative molecular generation algorithm and the efficiency of the training strategies. Moreover, MGRNN shows: (i) efficient computation for training; (ii) high model robustness for data; and (iii) an iterative sampling process, which allows to use chemical domain expertise for valency checking. Experimental results show that MGRNN is able to generate 69 % chemically valid molecules even without chemical knowledge and 100 % valid molecules with chemical rules.

In Silico Evolution of High-Performing Metal Organic Frameworks for Methane Adsorption

The increased use of transition fuels, such as natural gas, and the resulting increase in methane emissions have resulted in a need for novel methane storage materials. Metal-organic frameworks (MOFs) have shown promise as efficient storage materials. A virtually limitless number of potential MOFs can be hypothesized, which exhibit a wide variety of different structural and chemical characteristics. Because of the numerous possibilities, identification of the best MOF for methane storage can be a potentially challenging problem. In this work, determination of the best such MOF was cast as an inverse function problem. The function, a random forest (RF) model using 12 structural and chemical descriptors, was trained on 10% of a data set consisting of 130 398 hypothetical MOFs (hMOFs) to predict simulated methane uptake. The RF model was tested on the remaining 90% of the data. After validation, a genetic algorithm (GA) was used to evolve in silico the best MOFs for methane adsorption. The RF model was imbedded into the GA as the fitness function to predict the methane uptake of the evolved MOFs (eMOFs). The best 15 eMOFs matched hMOFs found in the top 1% of the database. Nine of the 15 eMOFs were found in the top 0.1%. More impressively, two of the eMOFs matched the top two hypothetical MOFs with the highest methane uptake values out of the entire database of 130 398 MOFs. Further, by leveraging the ensemble nature of the GA, it was possible to characterize the importance of the different material properties for methane adsorption, providing fundamental insight for future material design strategies.

Machine Learning Meets with Metal Organic Frameworks for Gas Storage and Separation

The acceleration in design of new metal organic frameworks (MOFs) has led scientists to focus on high-throughput computational screening (HTCS) methods to quickly assess the promises of these fascinating materials in various applications. HTCS studies provide a massive amount of structural property and performance data for MOFs, which need to be further analyzed. Recent implementation of machine learning (ML), which is another growing field in research, to HTCS of MOFs has been very fruitful not only for revealing the hidden structure-performance relationships of materials but also for understanding their performance trends in different applications, specifically for gas storage and separation. In this review, we highlight the current state of the art in ML-assisted computational screening of MOFs for gas storage and separation and address both the opportunities and challenges that are emerging in this new field by emphasizing how merging of ML and MOF simulations can be useful.

Accelerating Discovery of Metal-Organic Frameworks for Methane Adsorption with Hierarchical Screening and Deep Learning

In recent years, machine learning (ML) methods have made significant progress, and ML models have been adopted in virtually all aspects of chemistry. In this study, based on the crystal graph convolutional neural networks algorithm, an end-to-end deep learning model was developed for predicting the methane adsorption properties of metal-organic frameworks (MOFs). High-throughput grand canonical Monte Carlo calculations were carried out on the computation-ready, experimental MOF database, which contains approximately 11 000 MOFs, to construct the data set. An area under the curve of 0.930 for the test set proved the reliability of the developed deep learning model. To assess the transferability of the model, we applied it to predict the methane adsorption volume for some randomly selected covalent organic frameworks and zeolitic imidazolate framework materials. The results indicated that the model could also be suitable for other porous materials. We also applied it to the hierarchical screening of a hypothetical MOFs database (∼330 000 MOFs). Four hypothetical MOFs were demonstrated to have the highest performance in methane adsorption. A calculated maximum working capacity of 145 cm³/cm³ at 5-35 bar and 298 K indicated that the hypothetical MOF is close to the Department of Energy's 2015 target of 180 cm³/cm³. Further analyses on all screened out MOFs established correlations between some structural features with the working capacity. The successful incorporation of ML and hierarchical screening can accelerate the discovery of new materials not just for gas adsorption, but also other areas involving interactions in materials and molecules.

Big-Data Science in Porous Materials: Materials Genomics and Machine Learning

By combining metal nodes with organic linkers we can potentially synthesize millions of possible metal-organic frameworks (MOFs). The fact that we have so many materials opens many exciting avenues but also create new challenges. We simply have too many materials to be processed using conventional, brute force, methods. In this review, we show that having so many materials allows us to use big-data methods as a powerful technique to study these materials and to discover complex correlations. The first part of the review gives an introduction to the principles of big-data science. We show how to select appropriate training sets, survey approaches that are used to represent these materials in feature space, and review different learning architectures, as well as evaluation and interpretation strategies. In the second part, we review how the different approaches of machine learning have been applied to porous materials. In particular, we discuss applications in the field of gas storage and separation, the stability of these materials, their electronic properties, and their synthesis. Given the increasing interest of the scientific community in machine learning, we expect this list to rapidly expand in the coming years.

Analysis of CH4 Uptake over Metal-Organic Frameworks Using Data-Mining Tools

A database containing 2224 data points for CH₄ storage or delivery in metal-organic frameworks (MOFs) was analyzed using machine-learning tools to extract knowledge for generalization. The database was first reviewed to observe the basic trends and patterns. It was then analyzed using decision trees and artificial neural networks (ANN) to extract hidden information and develop rules and heuristics for future studies. Five-fold cross validations were used in each analysis to test the validity of the models with data not seen before. Decision-tree analyses were carried out using six user-defined descriptors and two structural properties, separately. The crystal structure and the total degree of unsaturation were found to be the effective user-defined descriptors, whereas the pore volume and maximum pore diameter, as structural properties, were sufficient to determine the MOFs having high CH₄-storage capacity. Moreover, a high pore volume is always required, as expected. In ANN analyses, models were also developed by using user-defined descriptors and structural properties separately. It was observed that the user-defined descriptors were not sufficient to describe the CH₄-storage capacities of MOFs, whereas the structural properties in particular led to accurate CH₄-storage predictions with an RMSE of 26.8 and an R² of 0.92 for testing.

Database for CO2 Separation Performances of MOFs Based on Computational Materials Screening

Metal-organic frameworks (MOFs) are potential adsorbents for CO2 capture. Because thousands of MOFs exist, computational studies become very useful in identifying the top performing materials for target applications in a time-effective manner. In this study, molecular simulations were performed to screen the MOF database to identify the best materials for CO2 separation from flue gas (CO2/N2) and landfill gas (CO2/CH4) under realistic operating conditions. We validated the accuracy of our computational approach by comparing the simulation results for the CO2 uptakes, CO2/N2 and CO2/CH4 selectivities of various types of MOFs with the available experimental data. Binary CO2/N2 and CO2/CH4 mixture adsorption data were then calculated for the entire MOF database. These data were then used to predict selectivity, working capacity, regenerability, and separation potential of MOFs. The top performing MOF adsorbents that can separate CO2/N2 and CO2/CH4 with high performance were identified. Molecular simulations for the adsorption of a ternary CO2/N2/CH4 mixture were performed for these top materials to provide a more realistic performance assessment of MOF adsorbents. The structure-performance analysis showed that MOFs with Δ Qst0 > 30 kJ/mol, 3.8 Å < pore-limiting diameter < 5 Å, 5 Å < largest cavity diameter < 7.5 Å, 0.5 < ϕ < 0.75, surface area < 1000 m2/g, and ρ > 1 g/cm3 are the best candidates for selective separation of CO2 from flue gas and landfill gas. This information will be very useful to design novel MOFs exhibiting high CO2 separation potentials. Finally, an online, freely accessible database https://cosmoserc.ku.edu.tr was established, for the first time in the literature, which reports all of the computed adsorbent metrics of 3816 MOFs for CO2/N2, CO2/CH4, and CO2/N2/CH4 separations in addition to various structural properties of MOFs.

Computer simulations of 4240 MOF membranes for H2/CH4 separations: insights into structure-performance relations

Design of new membranes having high H₂/CH₄ selectivity and high H₂ permeability is strongly desired to reduce the energy demand for H₂ production. Metal organic frameworks (MOFs) offer a great promise for membrane-based gas separations due to their tunable physical and chemical properties. We performed a high-throughput computational screening study to examine membrane-based H₂/CH₄ separation potentials of 4240 MOFs. Grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations were used to compute adsorption and diffusion of H₂ and CH₄ in MOFs. Simulation results were then used to predict adsorption selectivity, diffusion selectivity, gas permeability and membrane selectivity of MOFs. A large number of MOF membranes was found to outperform traditional polymer and zeolite membranes by exceeding the Robeson's upper bound for selective separation of H₂ from CH₄. Structure-performance analysis was carried out to understand the relations between MOF membranes' selectivities and their pore sizes, surface areas, porosities, densities, lattice systems, and metal types. Results showed that MOFs with pore limiting diameters between 3.8 and 6 Å, the largest cavity diameters between 6 and 12 Å, surface areas less than 1000 m² g^-1, porosities between 0.5 and 0.75, and densities between 1 and 1.5 g cm^-3 are the most promising membranes leading to H₂ selectivities >10 and H₂ permeabilities >10⁴ Barrer. Our results suggest that monoclinic MOFs having copper metals are the best membrane candidates for H₂/CH₄ separations. This study represents the first high-throughput computational screening of the most recent MOF database for membrane-based H₂/CH₄ separation and microscopic insight provided from molecular simulations will be highly useful for the future design of new MOFs having extraordinarily high H₂ selectivities.

Computational Screening of MOFs for Acetylene Separation

Efficient separation of acetylene (C₂H₂) from CO₂ and CH₄ is important to meet the requirement of high-purity acetylene in various industrial applications. Metal organic frameworks (MOFs) are great candidates for adsorption-based C₂H₂/CO₂ and C₂H₂/CH₄ separations due to their unique properties such as wide range of pore sizes and tunable chemistries. Experimental studies on the limited number of MOFs revealed that MOFs offer remarkable C₂H₂/CO₂ and C₂H₂/CH₄ selectivities based on single-component adsorption data. We performed the first large-scale molecular simulation study to investigate separation performances of 174 different MOF structures for C₂H₂/CO₂ and C₂H₂/CH₄ mixtures. Using the results of molecular simulations, several adsorbent performance evaluation metrics, such as selectivity, working capacity, adsorbent performance score, sorbent selection parameter, and regenerability were computed for each MOF. Based on these metrics, the best adsorbent candidates were identified for both separations. Results showed that the top three most promising MOF adsorbents exhibit C₂H₂/CO₂ selectivities of 49, 47, 24 and C₂H₂/CH₄ selectivities of 824, 684, 638 at 1 bar, 298 K and these are the highest C₂H₂ selectivities reported to date in the literature. Structure-performance analysis revealed that the best MOF adsorbents have pore sizes between 4 and 11 Å, surface areas in the range of 600–1,200 m²/g and porosities between 0.4 and 0.6 for selective separation of C₂H₂ from CO₂ and CH₄. These results will guide the future studies for the design of new MOFs with high C₂H₂ separation potentials.

High-Throughput Computational Screening of the Metal Organic Framework Database for CH4/H2 Separations

Metal organic frameworks (MOFs) have been considered as one of the most exciting porous materials discovered in the last decade. Large surface areas, high pore volumes, and tailorable pore sizes make MOFs highly promising in a variety of applications, mainly in gas separations. The number of MOFs has been increasing very rapidly, and experimental identification of materials exhibiting high gas separation potential is simply impractical. High-throughput computational screening studies in which thousands of MOFs are evaluated to identify the best candidates for target gas separation is crucial in directing experimental efforts to the most useful materials. In this work, we used molecular simulations to screen the most complete and recent collection of MOFs from the Cambridge Structural Database to unlock their CH₄/H₂ separation performances. This is the first study in the literature, which examines the potential of all existing MOFs for adsorption-based CH₄/H₂ separation. MOFs (4350) were ranked based on several adsorbent evaluation metrics including selectivity, working capacity, adsorbent performance score, sorbent selection parameter, and regenerability. A large number of MOFs were identified to have extraordinarily large CH₄/H₂ selectivities compared to traditional adsorbents such as zeolites and activated carbons. We examined the relations between structural properties of MOFs such as pore sizes, porosities, and surface areas and their selectivities. Correlations between the heat of adsorption, adsorbility, metal type of MOFs, and selectivities were also studied. On the basis of these relations, a simple mathematical model that can predict the CH₄/H₂ selectivity of MOFs was suggested, which will be very useful in guiding the design and development of new MOFs with extraordinarily high CH₄/H₂ separation performances.

Effects of Force Field Selection on the Computational Ranking of MOFs for CO2 Separations

Metal–organic frameworks (MOFs) have been considered as highly promising materials for adsorption-based CO₂ separations. The number of synthesized MOFs has been increasing very rapidly. High-throughput molecular simulations are very useful to screen large numbers of MOFs in order to identify the most promising adsorbents prior to extensive experimental studies. Results of molecular simulations depend on the force field used to define the interactions between gas molecules and MOFs. Choosing the appropriate force field for MOFs is essential to make reliable predictions about the materials’ performance. In this work, we performed two sets of molecular simulations using the two widely used generic force fields, Dreiding and UFF, and obtained adsorption data of CO₂/H₂, CO₂/N₂, and CO₂/CH₄ mixtures in 100 different MOF structures. Using this adsorption data, several adsorbent evaluation metrics including selectivity, working capacity, sorbent selection parameter, and percent regenerability were computed for each MOF. MOFs were then ranked based on these evaluation metrics, and top performing materials were identified. We then examined the sensitivity of the MOF rankings to the force field type. Our results showed that although there are significant quantitative differences between some adsorbent evaluation metrics computed using different force fields, rankings of the top MOF adsorbents for CO₂ separations are generally similar: 8, 8, and 9 out of the top 10 most selective MOFs were found to be identical in the ranking for CO₂/H₂, CO₂/N₂, and CO₂/CH₄ separations using Dreiding and UFF. We finally suggested a force field factor depending on the energy parameters of atoms present in the MOFs to quantify the robustness of the simulation results to the force field selection. This easily computable factor will be highly useful to determine whether the results are sensitive to the force field type or not prior to performing computationally demanding molecular simulations.

Computational design of tetrazolate-based metal–organic frameworks for CH4 storage

Tetrazolate-based metal–organic frameworks are designed and screened for CH₄ storage.

Molecular simulations of MOF membranes for separation of ethane/ethene and ethane/methane mixtures

Metal organic framework (MOF) membranes have been widely investigated for gas separation applications. Several MOFs have been recently examined for selective separation of C2H6. Considering the large number of available MOFs, it is not possible to fabricate and test the C2H6 separation performance of every single MOF membrane using purely experimental methods. In this study, we used molecular simulations to assess the membrane-based C2H6/C2H4 and C2H6/CH4 separation performances of 175 different MOF structures. This is the largest number of MOF membranes studied to date for C2H6 separation. We computed adsorption selectivity, diffusion selectivity, membrane selectivity and gas permeability of MOFs for C2H6/C2H4 and C2H6/CH4 mixtures. Our results show that a significant number of MOF membranes are C2H6 selective for C2H6/C2H4 separation in contrast to traditional nanoporous materials. Selectivity and permeability of MOF membranes were compared with other membrane materials, such as polymers, zeolites, and carbon molecular sieves. Several MOFs were identified to exceed the upper bound established for polymeric membranes and many MOF membranes exhibited higher gas permeabilities than zeolites and carbon molecular sieves. Examining the structure-performance relations of MOF membranes revealed that MOFs with cavity diameters between 6 and 9 Å, porosities lower than 0.50, and surface areas between 500-1000 m2 g-1 have high C2H6 selectivities. The results of this study will be useful to guide the experiments to the most promising MOF membranes for efficient separation of C2H6 and to accelerate the development of new MOFs with high C2H6 selectivities.

Machine Learning Using Combined Structural and Chemical Descriptors for Prediction of Methane Adsorption Performance of Metal Organic Frameworks (MOFs)

Using molecular simulation for adsorbent screening is computationally expensive and thus prohibitive to materials discovery. Machine learning (ML) algorithms trained on fundamental material properties can potentially provide quick and accurate methods for screening purposes. Prior efforts have focused on structural descriptors for use with ML. In this work, the use of chemical descriptors, in addition to structural descriptors, was introduced for adsorption analysis. Evaluation of structural and chemical descriptors coupled with various ML algorithms, including decision tree, Poisson regression, support vector machine and random forest, were carried out to predict methane uptake on hypothetical metal organic frameworks. To highlight their predictive capabilities, ML models were trained on 8% of a data set consisting of 130,398 MOFs and then tested on the remaining 92% to predict methane adsorption capacities. When structural and chemical descriptors were jointly used as ML input, the random forest model with 10-fold cross validation proved to be superior to the other ML approaches, with an R² of 0.98 and a mean absolute percent error of about 7%. The training and prediction using the random forest algorithm for adsorption capacity estimation of all 130,398 MOFs took approximately 2 h on a single personal computer, several orders of magnitude faster than actual molecular simulations on high-performance computing clusters.

Tuning the Gas Separation Performance of CuBTC by Ionic Liquid Incorporation

The efficient separation of gases has industrial, economic, and environmental importance. Here, the gas separation performance of a metal organic framework (MOF) is enhanced by ionic liquid (IL) incorporation. One of the most commonly used ILs, 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]), was incorporated into a commercially available MOF, CuBTC. Detailed characterization by combining spectroscopy with diffraction, electron microscopy, and thermal analysis confirmed that the structures were intact after incorporation. Adsorption isotherms of CH4, H2, N2, and CO2 in IL-incorporated CuBTC were experimentally measured and compared with those of pristine CuBTC. Consequently, ideal selectivities for CO2/CH4, CO2/N2, CO2/H2, CH4/N2, CH4/H2, and N2/H2 separations were calculated. The results showed that the CH4 selectivity of CuBTC over CO2, H2, and N2 gases becomes at least 1.5 times higher than that of pristine CuBTC upon the incorporation of IL. For example, the CH4/H2 selectivity of CuBTC increased from 26 to 56 at 0.2 bar when the IL loading was 30 wt %. These results show that the incorporation of ILs into MOFs can lead to unprecedented improvements in the gas separation performance of MOFs. The tunable physicochemical properties of ILs combined with a large number of possible MOF structures open up opportunities for the rational design of novel materials for meeting future energy challenges.