PHAHST Potential: Modeling Sorption in a Dispersion-Dominated Environment

PHAHST (potentials with high accuracy, high speed, and transferability) is a recently developed force field that utilizes exponential repulsion, multiple dispersion terms, explicit many-body polarization, and many-body van der Waals interactions. The result is a systematic approach to force field development that is computationally practical. Here, PHAHST is employed in the simulation for rare gas uptake of krypton and xenon in the metal-organic material, HKUST-1. This material has shown promise in use as an adsorptive separating agent and presents a challenge to model due to the presence of heterogeneous interaction sorption surfaces, which include pores with readily accessible, open-metal sites that compete with dispersion-dominated pores. Such environments are difficult to simulate with commonly used empirical force fields, such as the Lennard-Jones (LJ) potential, which perform better when electrostatics are dominant in determining the nature of sorption and alone are incapable of modeling interactions with open-metal sites. The effectiveness of PHAHST is compared to the LJ potential in a series of mixed Kr-Xe gas simulations. It has been demonstrated that PHAHST compares favorably with experimental results, and the LJ potential is inadequate. Overall, we establish that force fields with physically grounded repulsion/dispersion terms are required in order to accurately model sorption, as these interactions are an important component of the energy. Furthermore, it is shown that the simple mixing rules work nearly quantitatively for the true pair potentials, while they are not transferable for effective potentials like LJ.

Prediction of Xe/Kr Separation in Metal-Organic Frameworks by a Precursor-Based Neural Network Synergistic with a Polarizable Adsorbate Model

Adsorption and separation of Xe/Kr are significant for making high-density nuclear energy environmentally friendly and for meeting the requirements of the gas industry. Enhancing the accuracy of the adsorbate model for describing the adsorption behaviors of Xe and Kr in MOFs and the efficiency of the model for predicting the separation potential (SP) value of Xe/Kr separation in MOFs helps in searching for promising MOFs for Xe/Kr adsorption and separation within a short time and at a low cost. In this work, polarizable and transferable models for mimic Xe and Kr adsorption behaviors in MOFs were constructed. Using these models, SP values of 38 MOFs at various temperatures and pressures were calculated. An optimal neural network model called BPNN-SP was designed to predict SP value based on physical parameters of metal center (electronegativity and radius) and organic linker (three-dimensional size and polarizability) combined with temperature and pressure. The regression coefficient value of the BPNN-SP model for each data set is higher than 0.995. MAE, MBE, and RMSE of BPNN-SP are only 0.331, -0.002, and 0.505 mmol/g, respectively. Finally, BPNN-SP was validated by experiment data from six MOFs. The transferable adsorbate model combined with the BPNN-SP model would highly improve the efficiency for designing MOFs with high performance for Xe/Kr adsorption and separation.

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.

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

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

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.

Investigation on the catalytic behavior of a novel thulium-organic framework with a planar tetranuclear {Tm4} cluster as the active center for chemical CO2 fixation

Herein, the exquisite combination of coplanar [Tm₄(CO₂)₁₀(μ₃-OH)₂(μ₂-HCO₂)(OH₂)₂] clusters ({Tm₄}) and structure-oriented functional BDCP^5- leads to the highly robust nanoporous {Tm₄}-organic framework {(Me₂NH₂)[Tm₄(BDCP)₂(μ₃-OH)₂(μ₂-HCO₂)(H₂O)₂]·7DMF·5H₂O}_n (NUC-37, H₅BDCP = 2,6-bis(2,4-dicarboxylphenyl)-4-(4-carboxylphenyl)pyridine). To the best of our knowledge, NUC-37 is the first anionic {Ln₄}-based three-dimensional framework with embedded hierarchical microporous and nanoporous channels, among which each larger one is shaped by six rows of coplanar {Tm₄} clusters and characterized by plentiful coexisting Lewis acid-base sites on the inner wall including open Tm^III sites, N_pyridine atoms, μ₃-OH and μ₂-HCO₂. Catalytic experimental studies exhibit that NUC-37 possesses highly selective catalytic activity on the cycloaddition of epoxides with CO₂ as well as high recyclability under gentle conditions, which should be ascribed to its nanoscale channels, rich bifunctional active sites, and stable physicochemical properties. This work offers an effective means for synthesizing productive cluster-based Ln-MOF catalysts by employing structure-oriented ligands and controlling the solvothermal reaction conditions.

Competitive Adsorption of Xylenes at Chemical Equilibrium in Zeolites

The separation of xylenes is one of the most important processes in the petrochemical industry. In this article, the competitive adsorption from a fluid-phase mixture of xylenes in zeolites is studied. Adsorption from both vapor and liquid phases is considered. Computations of adsorption of pure xylenes and a mixture of xylenes at chemical equilibrium in several zeolite types at 250 °C are performed by Monte Carlo simulations. It is observed that shape and size selectivity entropic effects are predominant for small one-dimensional systems. Entropic effects due to the efficient arrangement of xylenes become relevant for large one-dimensional systems. For zeolites with two intersecting channels, the selectivity is determined by a competition between enthalpic and entropic effects. Such effects are related to the orientation of the methyl groups of the xylenes. m-Xylene is preferentially adsorbed if xylenes fit tightly in the intersection of the channels. If the intersection is much larger than the adsorbed molecules, p-xylene is preferentially adsorbed. This study provides insight into how the zeolite topology can influence the competitive adsorption and selectivity of xylenes at reaction conditions. Different selectivities are observed when a vapor phase is adsorbed compared to the adsorption from a liquid phase. These insight have a direct impact on the design criteria for future applications of zeolites in the industry. MRE-type and AFI-type zeolites exclusively adsorb p-xylene and o-xylene from the mixture of xylenes in the liquid phase, respectively. These zeolite types show potential to be used as high-performing molecular sieves for xylene separation and catalysis.

Insights into the Gas Adsorption Mechanisms in Metal-Organic Frameworks from Classical Molecular Simulations

Classical molecular simulations can provide significant insights into the gas adsorption mechanisms and binding sites in various metal-organic frameworks (MOFs). These simulations involve assessing the interactions between the MOF and an adsorbate molecule by calculating the potential energy of the MOF-adsorbate system using a functional form that generally includes nonbonded interaction terms, such as the repulsion/dispersion and permanent electrostatic energies. Grand canonical Monte Carlo (GCMC) is the most widely used classical method that is carried out to simulate gas adsorption and separation in MOFs and identify the favorable adsorbate binding sites. In this review, we provide an overview of the GCMC methods that are normally utilized to perform these simulations. We also describe how a typical force field is developed for the MOF, which is required to compute the classical potential energy of the system. Furthermore, we highlight some of the common analysis techniques that have been used to determine the locations of the preferential binding sites in these materials. We also review some of the early classical molecular simulation studies that have contributed to our working understanding of the gas adsorption mechanisms in MOFs. Finally, we show that the implementation of classical polarization for simulations in MOFs can be necessary for the accurate modeling of an adsorbate in these materials, particularly those that contain open-metal sites. In general, molecular simulations can provide a great complement to experimental studies by helping to rationalize the favorable MOF-adsorbate interactions and the mechanism of gas adsorption.

Electrostatic Potential Optimized Molecular Models for Molecular Simulations: CO, CO2, COS, H2S, N2, N2O, and SO2

Molecular simulations have been widely employed in the discovery of nanoporous materials, such as metal-organic frameworks (MOFs) and zeolite, for energy- and environment-related applications. To achieve simulation predictions with better accuracy, we herein present a collection of molecular models, including carbon monoxide (CO), carbon dioxide (CO₂), carbonyl sulfide (COS), hydrogen sulfide (H₂S), nitrogen (N₂), nitrous oxide (N₂O), and sulfur dioxide (SO₂). These models, denoted as electrostatic potential optimized molecular models (ESP-MMs), are systematically developed to not only reproduce experimental vapor-liquid equilibrium but also have accurate electrostatic potential representation surrounding the molecules. Our results show that, with accurate electrostatic potential representations, ESP-MMs can offer improved predictions in a variety of adsorption properties for porous materials, including MOFs with open-metal sites and all-silica zeolites. Specifically, by using ESP-MMs, the binding geometry and adsorption energy landscape can be well captured. This enables these models to be employed to unravel the fundamental mechanism of gaseous adsorption in materials of interest as well as to facilitate the parametrization of adsorbent-adsorbate interactions. We also demonstrate that, combined with generic force fields for adsorbents, ESP-MMs can offer reasonable predictions in adsorption isotherms. Although these ESP-MMs use a relatively simple and nonpolarizable potential form for the sake of efficiency and applicability, their accuracy has been extensively validated in this study. Furthermore, the set of Lennard-Jones potentials with static point charges adopted for ESP-MMs can be readily implemented in all available simulation packages. We anticipate that these ESP-MMs can largely facilitate future computational studies of porous materials for gas separation and removal.

Acetylene Storage and Separation Using Metal-Organic Frameworks with Open Metal Sites

Efficient separation and storage of gas streams involving light hydrocarbons is essential for industrial applications. These hydrocarbons are widely used as energy resources and/or chemical raw materials in various chemical reactions. Here, we focus on the separation of acetylene from methane and carbon dioxide. The separation of acetylene from carbon dioxide is, in particular, challenging due to the similar kinetic diameters and boiling points of the molecules. In recent years, considerable progress has been made in adsorption-based separations using porous metal-organic frameworks (MOFs). Most reported studies are experimental. We present a computational study on these gas separations using a variety of MOFs. This allows investigation of the competitive gas adsorption, which is experimentally challenging, as well as understanding the adsorption mechanisms at the molecular level, which in turn allows further experimental MOF design for this application. MOFs with open metal sites, and particularly Fe-MOF-74, seem to be good for this separation, with a trade-off between physical adsorption capacity and selectivity. Based on experimental single-adsorption isotherms at various temperatures, we developed and validated a specific parameterization to account for the interactions of the olefin with the open metal sites. In addition to volumetric and calorimetric adsorption, we comprehensively investigate the characteristics of the interaction between the MOFs and the guest molecules in terms of binding sites and density profiles. The overall agreement of our simulated results with experimental data for pure components points to the reliability of the models and methods to successfully predict the separation of mixtures.