Force-Field Development from Electronic Structure Calculations with Periodic Boundary Conditions: Applications to Gaseous Adsorption and Transport in Metal-Organic Frameworks

Computational Simulations of Metal-Organic Frameworks to Enhance Adsorption Applications

Metal-organic frameworks (MOFs), renowned for their exceptional porosity and crystalline structure, stand at the forefront of gas adsorption and separation applications. Shortly after their discovery through experimental synthesis, computational simulations quickly become an important method in broadening the use of MOFs by offering deep insights into their structural, functional, and performance properties. This review specifically addresses the pivotal role of molecular simulations in enlarging the molecular understanding of MOFs and enhancing their applications, particularly for gas adsorption. After reviewing the historical development and implementation of molecular simulation methods in the field of MOFs, high-throughput computational screening (HTCS) studies used to unlock the potential of MOFs in CO2 capture, CH4 storage, H2 storage, and water harvesting are visited and recent advancements in these adsorption applications are highlighted. The transformative impact of integrating artificial intelligence with HTCS on the prediction of MOFs' performance and directing the experimental efforts on promising materials is addressed. An outlook on current opportunities and challenges in the field to accelerate the adsorption applications of MOFs is finally provided.

Multiscale Modeling of Physical Properties of Nanoporous Frameworks: Predicting Mechanical, Thermal, and Adsorption Behavior

ConspectusNanoporous frameworks are a large and diverse family of supramolecular materials, whose chemical building units (organic, inorganic, or both) are assembled into a 3D architecture with well-defined connectivity and topology, featuring intrinsic porosity. These materials play a key role in various industrial processes and applications, such as energy production and conversion, fluid separation, gas storage, water harvesting, and many more. The performance and suitability of nanoporous materials for each specific application are directly related to both their physical and chemical properties, and their determination is crucial for process engineering and optimization of performances. In this Account, we focus on some recent developments in the multiscale modeling of physical properties of nanoporous frameworks, highlighting the latest advances in three specific areas: mechanical properties, thermal properties, and adsorption.In the study of the mechanical behavior of nanoporous materials, the past few years have seen a rapid acceleration of research. For example, computational resources have been pooled to create a public large-scale database of elastic constants as part of the Materials Project initiative to accelerate innovation in materials research: those can serve as a basis for data-based discovery of materials with targeted properties, as well as the training of machine learning predictor models.The large-scale prediction of thermal behavior, in comparison, is not yet routinely performed at such a large scale. Tentative databases have been assembled at the DFT level on specific families of materials, such as zeolites, but prediction at larger scale currently requires the use of transferable classical force fields, whose accuracy can be limited.Finally, adsorption is naturally one of the most studied physical properties of nanoporous frameworks, as fluid separation or storage is often the primary target for these materials. We highlight the recent achievements and open challenges for adsorption prediction at a large scale, focusing in particular on the accuracy of computational models and the reliability of comparisons with experimental data available. We detail some recent methodological improvements in the prediction of adsorption-related properties: in particular, we describe the recent research efforts to go beyond the study of thermodynamic quantities (uptake, adsorption enthalpy, and thermodynamic selectivity) and predict transport properties using data-based methods and high-throughput computational schemes. Finally, we stress the importance of data-based methods of addressing all sources of uncertainty.The Account concludes with some perspectives about the latest developments and open questions in data-based approaches and the integration of computational and experimental data together in the materials discovery loop.

Influence of Pressure and Temperature on the Flexible Behavior of Iron-Based MIL-53 with the CO2 Host: A Comprehensive Experimental and DFT Study

This research focuses on developing MIL-53-type compounds with Fe obtained with ligands derived from PET waste, followed by the controlled addition of hydrofluoric acid (HF). Incorporating HF into the MOF structure induced substantial changes in the material textural properties, resulting in a significant change in CO2 adsorption. Furthermore, a distinctive structural alteration (breathing effect) was observed in the CO2 isotherms at different temperatures; these structural changes have not been observed by X-ray diffraction (XRD) because this characterization has been performed at room temperature, whereas the adsorption experiments were conducted at 260, 273, and 303 K and different pressures. Subsequently, DFT studies were performed to investigate the CO2-filling mechanisms and elucidate the material respiration effect. This approach offers promising opportunities for sustainable materials with improved gas adsorption properties.

Machine learning potential for modelling H2 adsorption/diffusion in MOFs with open metal sites

Metal-organic frameworks (MOFs) incorporating open metal sites (OMS) have been identified as promising sorbents for many societally relevant-adsorption applications including CO2 capture, natural gas purification and H2 storage. This has been ascribed to strong specific interactions between OMS and the guest molecules that enable the MOF to achieve an effective capture even under low gas pressure conditions. In particular, the presence of OMS in MOFs was demonstrated to substantially boost the H2 binding energy for achieving high adsorbed hydrogen densities and large usable hydrogen capacities. So far, there is a critical bottleneck to computationally attain a full understanding of the thermodynamics and dynamics of H2 in this sub-class of MOFs since the generic classical force fields (FFs) are known to fail to accurately describe the interactions between OMS and any guest molecules, in particular H2. This clearly hampers the computational-assisted identification of MOFs containing OMS for a target adsorption-related application since the standard high-throughput screening approach based on these generic FFs is not applicable. Therefore, there is a need to derive novel FFs to achieve accurate and effective evaluation of MOFs for H2 adsorption. On this path, as a proof-of-concept, the soc-MOF-1d containing OMS, previously envisaged as a potential platform for H2 adsorption, was selected as a benchmark material and a machine learning potential (MLP) was derived for the Al-soc-MOF-1d from a dataset initially generated by ab initio molecular dynamics (AIMD) simulations. This MLP was further implemented in MD simulations to explore the H2 binding modes as well as the temperature dependence distribution of H2 in the MOF pores from 10 K to 80 K. MLP-Grand Canonical Monte Carlo (GCMC) simulations were then performed to predict the H2 sorption isotherm of Al-soc-MOF-1d at 77 K that was further confirmed using sorption data we collected on this sample. As a further step, MLP-based molecular dynamics (MD) simulations were conducted to anticipate the kinetics of H2 in this MOF. This work delivers the first MLP able to describe accurately the interactions between the challenging H2 guest molecule and MOFs containing OMS. This innovative strategy applied to one of the most complex molecules owing to its highly polarizable nature, paves the way towards a more systematic accurate and efficient in silico assessment of MOFs containing OMS for H2 adsorption and beyond to the low-pressure capture of diverse molecules.

Understanding Carbon Monoxide Binding and Interactions in M-MOF-74 (M = Mg, Mn, Ni, Zn)

Small molecules may adsorb strongly in metal-organic frameworks (MOFs) through interactions with under-coordinated open metal sites (OMS) that often exist within these structures. Among adsorbates, CO is attractive to study both for its relevance in energy-related applications and for its ability to engage in both σ-donation and π-backbonding interactions with the OMS in MOFs. Concomitant with strong adsorption, structural changes arise due to modifications of the electronic structure of both the adsorbate and adsorbent. These structural changes affect the separation performance of materials, and accurately capturing these changes and the resulting energetics is critical for accurate predictive modeling of adsorption. Traditional approaches to modeling using classical force fields typically do not capture or account for changes at the electronic level. To characterize the structural and energetic effects of the local structural changes, we employed density functional theory (DFT) to study CO adsorption in M-MOF-74s. M-MOF-74s feature OMS at which CO is known to adsorb strongly and can be synthesized with a variety of divalent metal cations with distinct performance in adsorption. We considered M-MOF-74s with a range of metals of varied d-band occupations (Mg (3d0), Mn (3d5), Ni (3d8), and Zn (3d10)) with various structural constraints ranging from geometrically constrained adsorbent and adsorbate ions to fully optimized geometries to deconvolute the relative contributions of various structural effects to the adsorption energetics and binding distances observed. Our data indicate that the most significant structural changes during adsorption correlate with the greatest π-backbonding behaviors and commensurately result in a sizable binding energy change observed for CO adsorption. The insights built from this work are relevant to two longstanding research challenges within the MOF community: rational design of materials for separations and the design of force fields capable of accurately modeling adsorption.

Development of a Transferable Force Field between Metal-Organic Framework and Its Polymorph

Conventionally, force fields for specific metal-organic frameworks (MOFs) are derived from quantum chemical simulations, but this method can be computationally intensive, especially in cases for large MOF structures. In this work, we devise a methodology to reduce the force field derivation costs by replacing the original MOF with a smaller polymorphic structure, with the hypothesis that the force field parameters will be transferrable among chemically identical, polymorphic MOF structures. Specifically, we demonstrate this transferability in MOF-177 structure for H2O and NH3 gas molecules and show that the force field parameters derived from a smaller polymorphic MOF-177 can be used accurately to the original MOF-177 structure. This methodology can accelerate the development of force field parameters for large porous materials, in which computational costs for conventional methods are expensive.

Storage and Diffusion of Carbon Dioxide in the Metal Organic Framework MOF-5─A Semi-empirical Molecular Dynamics Study

Metal-organic frameworks (MOFs) have attracted increasing attention due to their high porosity for exceptional gas storage applications. MOF-5 belongs to the family of isoreticular MOFs (IRMOFs) and consists of Zn4O6+ clusters linked by 1,4-benzenedicarboxylate. Due to the large number of atoms in the unit cell, molecular dynamics simulation based on density functional theory has proved to be too demanding, while force field models are often inadequate to model complex host-guest interactions. To overcome this limitation, an alternative semi-empirical approach using a set of approximations and extensive parametrization of interactions called density functional tight binding (DFTB) was applied in this work to study CO2 in the MOF-5 host. Calculations of pristine MOF-5 yield very good agreement with experimental data in terms of X-ray diffraction patterns as well as mechanical properties, such as the negative thermal expansion coefficient and the bulk modulus. In addition, different loadings of CO2 were introduced, and the associated self-diffusion coefficients and activation energies were investigated. The results show very good agreement with those of other experimental and theoretical investigations. This study provides detailed insights into the capability of semi-empirical DFTB-based molecular dynamics simulations of these challenging guest@host systems. Based on the comparison of the guest-guest pair distributions observed inside the MOF host and the corresponding gas-phase reference, a liquid-like structure of CO2 can be deduced upon storage in the host material.

Solvent-derived defects suppress adsorption in MOF-74

Defects in metal-organic frameworks (MOFs) have great impact on their nano-scale structure and physiochemical properties. However, isolated defects are easily concealed when the frameworks are interrogated by typical characterization methods. In this work, we unveil the presence of solvent-derived formate defects in MOF-74, an important class of MOFs with open metal sites. With multi-dimensional solid-state nuclear magnetic resonance (NMR) investigations, we uncover the ligand substitution role of formate and its chemical origin from decomposed N,N-dimethylformamide (DMF) solvent. The placement and coordination structure of formate defects are determined by ¹³C NMR and density functional theory (DFT) calculations. The extra metal-oxygen bonds with formates partially eliminate open metal sites and lead to a quantitative decrease of N₂ and CO₂ adsorption with respect to the defect concentration. In-situ NMR analysis and molecular simulations of CO₂ dynamics elaborate the adsorption mechanisms in defective MOF-74. Our study establishes comprehensive strategies to search, elucidate and manipulate defects in MOFs.

Interaction energy and isosteric heat of adsorption between hydrogen and magnesium diboride

Hydrogen storage materials form a crucial research topic for future energy utilization employing hydrogen and among those of interest magnesium diboride (MgB₂) has shown its prevalence. In this study, a first-principles analytical adsorption model of one hydrogen molecule in the vicinity of various magnesium diboride crystal surfaces was developed in order to obtain surface thermodynamic properties as a function of molecular and lattice properties. Henry's law constant (K_H) and isosteric heat of adsorption (ΔH_ads) indicators of the affinity between a gaseous molecule and a solid surface are thus calculated. The results in this paper not only address questions pertaining to the first stage of hydrogen storage processes but also advance the understanding of physisorption thermodynamics of a neutral molecule (H₂) coming in contact with a layered metallic-like surface (MgB₂). Although the model is built from a framework of classical calculations, quantum effects are incorporated as the fractional charge of the ions on the free surfaces, which is essential for the calculation of analytic thermodynamic values that approximate calculations from other methods. To benchmark our theoretical models, periodic density functional calculations were performed to determine the interactions between H₂ and different MgB₂ surfaces from first-principles. By considering both the top and sublayers of MgB₂ in calculating interaction energy, we have analytically and computationally calculated the interaction energies of H₂ molecules and MgB₂'s terminated planes, and witnessed the strong dependence of interaction energies on surface charges. We have also observed a dipole flipping phenomenon which explains the discontinuity seen in the interaction energy graph of Mg(0001). Both analytical and computational results showed heat of adsorption at zero coverage varying at a very low range (<7 kJ mol^-1).

Structural Properties of Metal-Organic Frameworks at Elevated Thermal Conditions via a Combined Density Functional Tight Binding Molecular Dynamics (DFTB MD) Approach

The performance of different density functional tight binding (DFTB) methods for the description of six increasingly complex metal-organic framework (MOF) compounds have been assessed. In particular the self-consistent charge density functional tight binding (SCC DFTB) approach utilizing the 3ob and matsci parameter sets have been considered for a set of four Zn-based and two Al-based MOF systems. Moreover, the extended tight binding for geometries, frequencies, and noncovalent interactions (GFN2-xTB) approach has been considered as well. In addition to the application of energy minimizations of the respective unit cells, molecular dynamics (MD) simulations at constant temperature and pressure conditions (298.15 K, 1.013 bar) have been carried out to assess the performance of the different DFTB methods at nonzero thermal conditions. In order to obtain the XRD patterns from the MD simulations, a flexible workflow to obtain time-averaged XRD patterns from (in this study 5000) individual snapshots taken at regular intervals over the simulation trajectory has been applied. In addition, the comparison of pair-distribution functions (PDFs) directly accessible from the simulation data shows very good agreement with experimental reference data obtained via measurements employing synchrotron radiation in case of MOF-5. The comparison of the lattice constants and the associated X-ray diffraction (XRD) patterns with the experimental reference data demonstrate, that the SCC DFTB approach provides a highly efficient and accurate description of the target systems.

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

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

Multilayer Graphtriyne Membranes for Separation and Storage of CO2: Molecular Dynamics Simulations of Post-Combustion Model Mixtures

The ability to remove carbon dioxide from gaseous mixtures is a necessary step toward the reduction of greenhouse gas emissions. As a contribution to this field of research, we performed a molecular dynamics study assessing the separation and adsorption properties of multi-layered graphtriyne membranes on gaseous mixtures of CO₂, N₂, and H₂O. These mixtures closely resemble post-combustion gaseous products and are, therefore, suitable prototypes with which to model possible technological applications in the field of CO₂ removal methodologies. The molecular dynamics simulations rely on a fairly accurate description of involved force fields, providing reliable predictions of selectivity and adsorption coefficients. The characterization of the interplay between molecules and membrane structure also permitted us to elucidate the adsorption and crossing processes at an atomistic level of detail. The work is intended as a continuation and a strong enhancement of the modeling research and characterization of such materials as molecular sieves for CO₂ storage and removal.

Computational Investigations of Metal-Organic Frameworks as Sorbents for BTEX Removal

Sequestration of aromatic volatile organic compounds (VOCs) via metal-organic frameworks (MOFs) as sorbents is a viable means of environmental preservation. In this investigation, we shed light on the key features associated with MOFs that govern the selective uptake of a subclass of VOCs containing benzene, toluene, ethylbenzene, and xylenes (BTEX). We investigate, through a multistep computational framework including ab initio electronic structure and classical molecular dynamics simulations, the energetic and dynamical properties associated with BTEX capture in three MOFs: HKUST-1, ZIF-8, and MIL-53. Our work demonstrates the importance of considering both static and dynamical properties upon introduction of guest molecules in such computational investigations. We elucidate the key geometric factors associated with efficient capture of BTEX compounds and highlight possible postsynthetic modifications that can be used to produce next generation sorbents for BTEX capture.

Computational Study of Alkane Adsorption in Brønsted Acid Zeolites for More Efficient Alkane Cracking

Alkane cracking using Brønsted acid zeolites, catalytically converting long-chain molecules into smaller ones, is critical to fuel and chemical production. To enable more energy-efficient cracking processes, developing zeolite catalysts with enhanced performance (i.e., a faster reaction rate with reduced methane formation) plays a substantial role. Given the adsorption thermodynamics of alkanes onto the protons of Brønsted acid zeolites is a key step in the overall cracking reactions; therefore, catalysts possessing a more negative Gibbs free energy of adsorption for alkanes with a larger central-to-terminal bond adsorption selectivity to promote central cracking are of particular interest. This Feature Article discusses recent computational developments and discoveries by Lin and co-workers in studying the adsorption of alkanes in Brønsted acid zeolites. Their developed approach, employing configurational bias Monte Carlo with domain decomposition, with a newly parametrized molecular potential to compute the adsorption properties is first introduced. With these developments, the roles of the Si/Al ratio and Al sitting are explored and discussed. Subsequently, the Feature Article discusses the key findings obtained from a large-scale computational screening of studying more than 100 000 possible zeolite structures. The performance of identified top candidates and associated key structural features leading to desirable adsorption properties are highlighted.

Understanding the Effect of Water on CO2 Adsorption

Carbon capture from large sources and ambient air is one of the most promising strategies to curb the deleterious effect of greenhouse gases. Among different technologies, CO₂ adsorption has drawn widespread attention mostly because of its low energy requirements. Considering that water vapor is a ubiquitous component in air and almost all CO₂-rich industrial gas streams, understanding its impact on CO₂ adsorption is of critical importance. Owing to the large diversity of adsorbents, water plays many different roles from a severe inhibitor of CO₂ adsorption to an excellent promoter. Water may also increase the rate of CO₂ capture or have the opposite effect. In the presence of amine-containing adsorbents, water is even necessary for their long-term stability. The current contribution is a comprehensive review of the effects of water whether in the gas feed or as adsorbent moisture on CO₂ adsorption. For convenience, we discuss the effect of water vapor on CO₂ adsorption over four broadly defined groups of materials separately, namely (i) physical adsorbents, including carbons, zeolites and MOFs, (ii) amine-functionalized adsorbents, and (iii) reactive adsorbents, including metal carbonates and oxides. For each category, the effects of humidity level on CO₂ uptake, selectivity, and adsorption kinetics under different operational conditions are discussed. Whenever possible, findings from different sources are compared, paying particular attention to both similarities and inconsistencies. For completeness, the effect of water on membrane CO₂ separation is also discussed, albeit briefly.

Next-Generation Accurate, Transferable, and Polarizable Potentials for Material Simulations

PHAHST (potentials with high accuracy, high speed, and transferability) intermolecular potential energy functions have been developed from first principles for H₂, N₂, the noble gases, and a metal-organic material, HKUST-1. The potentials are designed from the outset to be transferable to heterogeneous environments including porous materials, interfaces, and material simulations. This is accomplished by theoretically justified choices for all functional forms, parameters, and mixing rules, including explicit polarization in every environment and fitting to high quality electronic structure calculations using methods that are tractable for real systems. The models have been validated in neat systems by comparison to second virial coefficients and bulk pressure-density isotherms. For inhomogeneous applications, our main target, comparisons are presented to previously published experimental studies on the metal-organic material HKUST-1 including adsorption, isosteric heats of adsorption, binding site locations, and binding site energies. A systematic prescription is provided for developing compatible potentials for additional small molecules and materials. The resulting models are recommended for use in complex heterogeneous simulations where existing potentials may be inadequate.

Adsorption Isotherm Predictions for Multiple Molecules in MOFs Using the Same Deep Learning Model

Tailoring the structure and chemistry of metal-organic frameworks (MOFs) enables the manipulation of their adsorption properties to suit specific energy and environmental applications. As there are millions of possible MOFs (with tens of thousands already synthesized), molecular simulation has frequently been used to rapidly evaluate the adsorption performance of a large set of MOFs. This allows subsequent experiments to focus only on a small subset of the most promising MOFs. In many instances, however, even molecular simulation becomes prohibitively time-consuming, underscoring the need for alternative screening methods, such as machine learning, to precede molecular simulation efforts. In this study, as a proof of concept, we trained a neural network-specifically, a multilayer perceptron (MLP)-as the first example of a machine learning model capable of predicting full adsorption isotherms of different molecules not included in the training of the model. To achieve this, we trained our MLP on "alchemical" species, represented only by variables derived from their force-field parameters, to predict the loadings of real adsorbates. Alchemical species used for training were small, near-spherical, and nonpolar, enabling the prediction of analogous real molecules relevant for chemical separations such as argon, krypton, xenon, methane, ethane, and nitrogen. MOFs were also represented by simple descriptors (e.g., geometric properties and chemical moieties). The trained model was shown to make accurate adsorption predictions for these six adsorbates in both hypothetical and existing MOFs. The MLP presented here is not expected to be applied "as is" to more complex adsorbates with properties not considered during its training. However, our results illustrate a new philosophy of training that can be built upon with the goal of predicting adsorption isotherms in not only a database of MOFs but also a database of adsorbates and over a range of relevant operating conditions.

A Strong Test of Atomically Detailed Models of Molecular Adsorption in Zeolites Using Multilaboratory Experimental Data for CO2 Adsorption in Ammonium ZSM-5

A recent international interlaboratory study led by the U.S. National Institute of Standards (NIST) reported CO₂ adsorption isotherms measured independently by 11 groups on reference material RM 8852, an ammonium ZSM-5 zeolite. Good reproducibility and high reliability of this experimental data provide a strong test for the ability of atomically detailed models to predict adsorption of CO₂ in zeolites. We developed force fields for CO₂ in ammonium zeolites based on first-principles calculations and also independently performed experiments with RM 8852 by microcalorimetry. At low pressures good agreement was obtained between predictions and experiments. At high pressures, however, deviations were observed. We show that the charge-balancing cations in the experimental material are the predominant source of the discrepancy between simulation and experiment at high pressures; the experimental sample treatment causes deammoniation. In addition, accounting for a small amount of noncrystalline mesoporosity in the zeolite brings predictions into much better agreement with experiments.

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.

Computational prediction of promising pyrazine and bipyridine analogues of a fluorinated MOF platform, MFN-Ni-L (M = SI/AL; N = SIX/FIVE; L = pyr/bipyr), for CO2 capture under pre-humidified conditions

The CO2 separation performance has been explored under dry and pre-humidified conditions for the fluorinated metal organic frameworks SIFSIX-Ni-pyr, ALFFIVE-Ni-pyr, SIFSIX-Ni-bipyr and ALFFIVE-Ni-bipyr, which are incorporated with/without a coordinatively unsaturated site (CUS), Al, and organic linkers 1,4-pyrazine and 4,4'-bipyridine. The ultra-small pore size (∼4 Å) of the pyrazine analogues of fluorinated-MOFs, i.e. SIFSIX-Ni-pyr and ALFFIVE-Ni-pyr, showed infinite selectivity towards CO2 with low uptake capability under dry conditions, which drastically reduced to 0 wt% under very low pre-humidification conditions (∼10-15 wt% adsorbed moisture). In marked contrast, the bipyridine analogues SIFSIX-Ni-bipyr and ALFFIVE-Ni-bipyr showed significant CO2 capture performance of up to 30-40 wt% with pre-humidification. Further, both SIFSIX-Ni-bipyr and ALFFIVE-Ni-bipyr showed high CO2 selectivity as well as good working capacity at 1-10 bar while poor selectivity is observed for the pyrazine analogues with pre-humidification. The incorporation of Al as a CUS provides stability to the ALFFIVE-Ni-bipyr fluorinated-MOF under pre-humidified conditions due to the ability of Al to co-ordinate with water molecules in hydrogen bonded networks. Therefore, to develop physisorption-based CO2 capturing processes under pre-humidified conditions, the use of Al incorporated ALFFIVE-Ni-bipyr is highly suitable, which may outperform most of the fluorinated-MOFs and other classes of porous solids reported so far.

Ab Initio Flexible Force Field for Metal-Organic Frameworks Using Dummy Model Coordination Bonds

We present force fields developed from periodic density functional theory (DFT) calculations that can be used in classical molecular simulations to model M-MOF-74 (M = Co, Fe, Mg, Mn, Ni, Zn) and its extended linker analogs. Our force fields are based on cationic dummy models (CDMs). These dummy models simplify the methodology required to tune the parameters and improve the accuracy of the force fields. We used our force fields to compare mechanical properties across the M-MOF-74 series and determine that increasing the size of the linker decreases the framework rigidity. In addition, we applied our force fields to an extended linker analog of Mg-MOF-74 and characterized the free energy of a previously reported deformation pattern in which the one-dimensional hexagonal channels of the framework become irregular. The free energy profiles confirm that the deformation is adsorbate induced and impossible to access solely by a pressure stimulus. On the basis of our results, we conclude that the force fields presented here and others that may be developed using our methodology are transferable across metal-organic framework series that share a metal center topology. Finally, we believe that these force fields have the potential to be adapted for the study of complex problems in MOF chemistry, including defects and crystal growth, that have thus far been beyond the scope of classical molecular simulations.

Challenges and opportunities for adsorption-based CO2 capture from natural gas combined cycle emissions

In recent years, the power sector has shown a growing reliance on natural gas, a cleaner-burning fuel than coal that emits approximately half as much CO2 per kWh of energy produced. This rapid growth in the consumption of natural gas has led to increased CO2 emissions from gas-fired power plants. To limit the contribution of fossil fuel combustion to atmospheric CO2 levels, carbon capture and sequestration has been proposed as a potential emission mitigation strategy. However, despite extensive exploration of solid adsorbents for CO2 capture, few studies have examined the performance of adsorbents in post-combustion capture processes specific to natural gas flue emissions. In this perspective, we emphasize the importance of considering gas-fired power plants alongside coal-fired plants in future analyses of carbon capture materials. We address specific challenges and opportunities related to adsorptive carbon capture from the emissions of gas-fired plants and discuss several promising candidate materials. Finally, we suggest experiments to determine the viability of new CO2 capture materials for this separation. This broadening in the scope of current carbon capture research is urgently needed to accelerate the deployment of transformational carbon capture technologies.

A generalized van der Waals model for light gas adsorption prediction in IRMOFs

A generalized van der Waals model for predicting the adsorption isotherms in IRMOFs by defining different attractive regions.

Polarizable Force Field for CO2 in M-MOF-74 Derived from Quantum Mechanics

On the short term, carbon capture is a viable solution to reduce human-induced CO₂ emissions, which requires an energy efficient separation of CO₂. Metal-organic frameworks (MOFs) may offer opportunities for carbon capture and other industrially relevant separations. Especially, MOFs with embedded open metal sites have been shown to be promising. Molecular simulation is a useful tool to predict the performance of MOFs even before the synthesis of the material. This reduces the experimental effort, and the selection process of the most suitable MOF for a particular application can be accelerated. To describe the interactions between open metal sites and guest molecules in molecular simulation is challenging. Polarizable force fields have potential to improve the description of such specific interactions. Previously, we tested the applicability of polarizable force fields for CO₂ in M-MOF-74 by verifying the ability to reproduce experimental measurements. Here, we develop a predictive polarizable force field for CO₂ in M-MOF-74 (M = Co, Fe, Mg, Mn, Ni, Zn) without the requirement of experimental data. The force field is derived from energies predicted from quantum mechanics. The procedure is easily transferable to other MOFs. To incorporate explicit polarization, the induced dipole method is applied between the framework and the guest molecule. Atomic polarizabilities are assigned according to the literature. Only the Lennard-Jones parameters of the open metal sites are parameterized to reproduce energies from quantum mechanics. The created polarizable force field for CO₂ in M-MOF-74 can describe the adsorption well and even better than that in our previous work.

DFT studies on storage and adsorption capacities of gases on MOFs

Metal-organic frameworks (MOFs) are highly porous crystalline materials, consisting of metal ions linked together with organic bridging ligands, exhibiting high surface areas. Lately, they have been utilized for gas sorption, storage, sensing, drug delivery, etc. The chemistry of MOFs is expanding with an extraordinary speed, constituting both theoretical and experimental research, and MOFs have proved to be promising candidates so far. In this work, we have reviewed the density functional theory studies of MOFs in the adsorption and separation of the greenhouse gas, CO2, as well as the storage efficiencies for fuel gases like H2, CH4 and C2H2. The role of organic ligands, doping with other metal ions and functional groups, open metal sites and hybrid MOFs have been reviewed in brief.

Covalent and Ionic Capacity of MOFs To Sorb Small Gas Molecules

In this work, the aim is to characterize how an Fe-based metal-organic framework (MOF) behaves when gases, like carbon dioxide, are inserted through their channels and to characterize the nature and strength of those interactions. Despite the computational nature of the project, it is based on the experimental results obtained in 2016 by Mı́nguez-Espallargas and co-workers ( J. Am. Chem. Soc. 2013, 135, 15986 - 15989 ). Those MOFs were found to selectively allocate/adsorb CO₂, having as a drawback that apparently each cavity allocates only one CO₂ molecule. Despite truncating the MOF to its unitary cell, the whole cavity of the MOF can be described in detail by precise ab initio calculations. Another computational goal is to unravel why experimentally CO₂ was preferred with respect to N₂, and for the sake of consistency, a list of common gases will be further studied, such as H₂, O₂, H₂O, CH₄, C₂H₆, N₂O, or NO.

Unexpected Diffusion Anisotropy of Carbon Dioxide in the Metal-Organic Framework Zn2(dobpdc)

Metal-organic frameworks are promising materials for energy-efficient gas separations, but little is known about the diffusion of adsorbates in materials featuring one-dimensional porosity at the nanoscale. An understanding of the interplay between framework structure and gas diffusion is crucial for the practical application of these materials as adsorbents or in mixed-matrix membranes, since the rate of gas diffusion within the adsorbent pores impacts the required size (and therefore cost) of the adsorbent column or membrane. Here, we investigate the diffusion of CO2 within the pores of Zn2(dobpdc) (dobpdc4- = 4,4'-dioxidobiphenyl-3,3'-dicarboxylate) using pulsed field gradient (PFG) nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations. The residual chemical shift anisotropy for pore-confined CO2 allows PFG NMR measurements of self-diffusion in different crystallographic directions, and our analysis of the entire NMR line shape as a function of the applied field gradient provides a precise determination of the self-diffusion coefficients. In addition to observing CO2 diffusion through the channels parallel to the crystallographic c axis (self-diffusion coefficient D∥ = (5.8 ± 0.1) × 10-9 m2 s-1 at a pressure of 625 mbar CO2), we unexpectedly find that CO2 is also able to diffuse between the hexagonal channels in the crystallographic ab plane (D⊥ = (1.9 ± 0.2) × 10-10 m2 s-1), despite the walls of these channels appearing impermeable by single-crystal X-ray crystallography and flexible lattice MD simulations. Observation of such unexpected diffusion in the ab plane suggests the presence of defects that enable effective multidimensional CO2 transport in a metal-organic framework with nominally one-dimensional porosity.

Joint Experimental and Computational Investigation of the Flexibility of a Diacetylene-Based Mixed-Linker MOF: Revealing the Existence of Two Low-Temperature Phase Transitions and the Presence of Colossal Positive and Giant Negative Thermal Expansions

Solvothermal reaction in N,N-dimethylformamide (DMF) between 1,6-bis(1-imidazolyl)-2,4-hexadiyne monohydrate (L1⋅H₂ O), isophthalic acid (H₂ L2), and Zn(NO₃ )₂ ⋅6 H₂ O gives the diacetylene-based mixed-ligand coordination polymer {[Zn(L1)(L2)](DMF)₂ }_n (UMON-44) in 38 % yield. Combination of DSC with variable-temperature single-crystal X-ray diffraction revealed the occurrence of two phase transitions spanning the ranges 129-144 K and 158-188 K. Furthermore, the three structurally similar phases of UMON-44 show giant negative and/or colossal positive thermal expansions. These unusual phenomena exist without any change in the contents of the unit cell. DFT calculations using the PBE+D3 dispersion scheme were able to distinguish between these polymorphs by accurately reproducing their salient structural features, although corrections in the size of the unit cell turned out to be necessary for the high-temperature phase to account for its large thermal expansion. In addition, the infrared spectra (vibration frequencies and peak intensities) of these theoretical models were calculated, allowing for univocal identification of the corresponding polymorphs. Last, the limits of our computational method were tested by calculating the phase transition temperatures and their associated enthalpies, and the derived figures compare favorably with the values determined experimentally.

Potential of polarizable force fields for predicting the separation performance of small hydrocarbons in M-MOF-74

Including explicit polarization significantly improves the description of the adsorption in comparison to non-polarizable generic force fields.

Origin of the Strong Interaction between Polar Molecules and Copper(II) Paddle-Wheels in Metal Organic Frameworks

The copper paddle-wheel is the building unit of many metal organic frameworks. Because of the ability of the copper cations to attract polar molecules, copper paddle-wheels are promising for carbon dioxide adsorption and separation. They have therefore been studied extensively, both experimentally and computationally. In this work we investigate the copper-CO2 interaction in HKUST-1 and in two different cluster models of HKUST-1: monocopper Cu(formate)2 and dicopper Cu2(formate)4. We show that density functional theory methods severely underestimate the interaction energy between copper paddle-wheels and CO2, even including corrections for the dispersion forces. In contrast, a multireference wave function followed by perturbation theory to second order using the CASPT2 method correctly describes this interaction. The restricted open-shell Møller-Plesset 2 method (ROS-MP2, equivalent to (2,2) CASPT2) was also found to be adequate in describing the system and used to develop a novel force field. Our parametrization is able to predict the experimental CO2 adsorption isotherms in HKUST-1, and it is shown to be transferable to other copper paddle-wheel systems.

Ab Initio Prediction of Adsorption Isotherms for Gas Mixtures by Grand Canonical Monte Carlo Simulations on a Lattice of Sites

Gibbs free energies of adsorption on individual sites and the lateral (adsorbate-adsorbate) interaction energies are obtained from quantum chemical ab initio methods and molecular statistics. They define a Grand Canonical Monte Carlo (GCMC) Hamiltonian for simulations of gas mixtures on a lattice of adsorption sites. Coadsorption of CO₂ and CH₄ at Mg²⁺ sites in the pores of the metal-organic framework CPO-27-Mg (Mg-MOF-74) is studied as an example. Simulations with different approximations as made in widely used coadsorption models such as the ideal adsorbed solution theory (IAST) show their limitations in describing adsorption selectivities for binary mixtures.

Structural characterization of framework-gas interactions in the metal-organic framework Co2(dobdc) by in situ single-crystal X-ray diffraction

The crystallographic characterization of framework-guest interactions in metal-organic frameworks allows the location of guest binding sites and provides meaningful information on the nature of these interactions, enabling the correlation of structure with adsorption behavior. Here, techniques developed for in situ single-crystal X-ray diffraction experiments on porous crystals have enabled the direct observation of CO, CH4, N2, O2, Ar, and P4 adsorption in Co2(dobdc) (dobdc4- = 2,5-dioxido-1,4-benzenedicarboxylate), a metal-organic framework bearing coordinatively unsaturated cobalt(ii) sites. All these molecules exhibit such weak interactions with the high-spin cobalt(ii) sites in the framework that no analogous molecular structures exist, demonstrating the utility of metal-organic frameworks as crystalline matrices for the isolation and structural determination of unstable species. Notably, the Co-CH4 and Co-Ar interactions observed in Co2(dobdc) represent, to the best of our knowledge, the first single-crystal structure determination of a metal-CH4 interaction and the first crystallographically characterized metal-Ar interaction. Analysis of low-pressure gas adsorption isotherms confirms that these gases exhibit mainly physisorptive interactions with the cobalt(ii) sites in Co2(dobdc), with differential enthalpies of adsorption as weak as -17(1) kJ mol-1 (for Ar). Moreover, the structures of Co2(dobdc)·3.8N2, Co2(dobdc)·5.9O2, and Co2(dobdc)·2.0Ar reveal the location of secondary (N2, O2, and Ar) and tertiary (O2) binding sites in Co2(dobdc), while high-pressure CO2, CO, CH4, N2, and Ar adsorption isotherms show that these binding sites become more relevant at elevated pressures.

Materials Genome in Action: Identifying the Performance Limits of Physical Hydrogen Storage

The Materials Genome is in action: the molecular codes for millions of materials have been sequenced, predictive models have been developed, and now the challenge of hydrogen storage is targeted. Renewably generated hydrogen is an attractive transportation fuel with zero carbon emissions, but its storage remains a significant challenge. Nanoporous adsorbents have shown promising physical adsorption of hydrogen approaching targeted capacities, but the scope of studies has remained limited. Here the Nanoporous Materials Genome, containing over 850 000 materials, is analyzed with a variety of computational tools to explore the limits of hydrogen storage. Optimal features that maximize net capacity at room temperature include pore sizes of around 6 Å and void fractions of 0.1, while at cryogenic temperatures pore sizes of 10 Å and void fractions of 0.5 are optimal. Our top candidates are found to be commercially attractive as "cryo-adsorbents", with promising storage capacities at 77 K and 100 bar with 30% enhancement to 40 g/L, a promising alternative to liquefaction at 20 K and compression at 700 bar.

CO2 Capture and Separations Using MOFs: Computational and Experimental Studies

This Review focuses on research oriented toward elucidation of the various aspects that determine adsorption of CO₂ in metal-organic frameworks and its separation from gas mixtures found in industrial processes. It includes theoretical, experimental, and combined approaches able to characterize the materials, investigate the adsorption/desorption/reaction properties of the adsorbates inside such environments, screen and design new materials, and analyze additional factors such as material regenerability, stability, effects of impurities, and cost among several factors that influence the effectiveness of the separations. CO₂ adsorption, separations, and membranes are reviewed followed by an analysis of the effects of stability, impurities, and process operation conditions on practical applications.

Polarizable Force Fields for CO2 and CH4 Adsorption in M-MOF-74

The family of M-MOF-74, with M = Co, Cr, Cu, Fe, Mg, Mn, Ni, Ti, V, and Zn, provides opportunities for numerous energy related gas separation applications. The pore structure of M-MOF-74 exhibits a high internal surface area and an exceptionally large adsorption capacity. The chemical environment of the adsorbate molecule in M-MOF-74 can be tuned by exchanging the metal ion incorporated in the structure. To optimize materials for a given separation process, insights into how the choice of the metal ion affects the interaction strength with adsorbate molecules and how to model these interactions are essential. Here, we quantitatively highlight the importance of polarization by comparing the proposed polarizable force field to orbital interaction energies from DFT calculations. Adsorption isotherms and heats of adsorption are computed for CO2, CH4, and their mixtures in M-MOF-74 with all 10 metal ions. The results are compared to experimental data, and to previous simulation results using nonpolarizable force fields derived from quantum mechanics. To the best of our knowledge, the developed polarizable force field is the only one so far trying to cover such a large set of possible metal ions. For the majority of metal ions, our simulations are in good agreement with experiments, demonstrating the effectiveness of our polarizable potential and the transferability of the adopted approach.

Rational Design of a Low-Cost, High-Performance Metal-Organic Framework for Hydrogen Storage and Carbon Capture

We present the in silico design of a MOF-74 analogue, hereon known as M2(DHFUMA) [M = Mg, Fe, Co, Ni, Zn], with enhanced small-molecule adsorption properties over the original M2(DOBDC) series. Constructed from 2,3-dihydroxyfumarate (DHFUMA), an aliphatic ligand which is smaller than the aromatic 2,5-dioxidobenzene-1,4-dicarboxylate (DOBDC), the M2(DHFUMA) framework has a reduced channel diameter, resulting in higher volumetric density of open metal sites and significantly improved volumetric hydrogen (H2) storage potential. Furthermore, the reduced distance between two adjacent open metal sites in the pore channel leads to a CO2 binding mode of one molecule per two adjacent metals with markedly stronger binding energetics. Through dispersion-corrected density functional theory (DFT) calculations of guest-framework interactions and classical simulation of the adsorption behavior of binary CO2:H2O mixtures, we theoretically predict the M2(DHFUMA) series as an improved alternative for carbon capture over the M2(DOBDC) series when adsorbing from wet flue gas streams. The improved CO2 uptake and humidity tolerance in our simulations is tunable based upon metal selection and adsorption temperature which, combined with the significantly reduced ligand expense, elevates this material's potential for CO2 capture and H2 storage. The dynamical and elastic stabilities of Mg2(DHFUMA) were verified by hybrid DFT calculations, demonstrating its significant potential for experimental synthesis.

Computational prediction of high methane storage capacity in V-MOF-74

The methane adsorption properties in M-MOF-74 (M = Mg, Ti, V, Cr, Mn, Co, Ni, Cu, and Zn) were investigated for potential adsorbed natural gas (ANG) vehicle applications.

Probing gas adsorption in MOFs using an efficient ab initio widom insertion Monte Carlo method

We propose a novel biased Widom insertion method that can efficiently compute the Henry coefficient, K_H , of gas molecules inside porous materials exhibiting strong adsorption sites by employing purely DFT calculations. This is achieved by partitioning the simulation volume into strongly and weakly adsorbing regions and selectively biasing the Widom insertion moves into the former region. We show that only few thousands of single point energy calculations are necessary to achieve accurate statistics compared to many hundreds of thousands or millions of such calculations in conventional random insertions. The methodology is used to compute the Henry coefficient for CO₂ , N₂ , CH₄ , and C₂ H₂ in M-MOF-74(M = Zn and Mg), yielding good agreement with published experimental data. Our results demonstrate that the DFT binding energy and the heat of adsorption are not accurate enough indicators to rank the guest adsorption properties at the Henry regime. © 2016 Wiley Periodicals, Inc.