On the inner workings of Monte Carlo codes

The Impact of Metal Centers in the M-MOF-74 Series on Formic Acid Production

The confinement effect of porous materials on the thermodynamical equilibrium of the CO2 hydrogenation reaction presents a cost-effective alternative to transition metal catalysts. In metal-organic frameworks, the type of metal center has a greater impact on the enhancement of formic acid production than the scale of confinement resulting from the pore size. The M-MOF-74 series enables a comprehensive study of how different metal centers affect HCOOH production, minimizing the effect of pore size. In this work, molecular simulations were used to analyze the adsorption of HCOOH and the CO2 hydrogenation reaction in M-MOF-74, where M = Ni, Cu, Co, Fe, Mn, Zn. We combine classical simulations and density functional theory calculations to gain insights into the mechanisms that govern the low coverage adsorption of HCOOH in the surrounding of the metal centers of M-MOF-74. The impact of metal centers on the HCOOH yield was assessed by Monte Carlo simulations in the grand-canonical ensemble, using gas-phase compositions of CO2, H2, and HCOOH at chemical equilibrium at 298.15-800 K, 1-60 bar. The performance of M-MOF-74 in HCOOH production follows the same order as the uptake and the heat of HCOOH adsorption: Ni > Co > Fe > Mn > Zn > Cu. Ni-MOF-74 increases the mole fraction of HCOOH by ca. 105 times compared to the gas phase at 298.15 K, 60 bar. Ni-MOF-74 has the potential to be more economically attractive for CO2 conversion than transition metal catalysts, achieving HCOOH production at concentrations comparable to the highest formate levels reported for transition metal catalysts and offering a more valuable molecular form of the product.

Competitive Adsorptive Mechanism of H2/N2 in LTA/FAU Zeolites by Molecular Simulations and Experiments

For industrial tail gas to be converted into high-purity hydrogen, the H2-N2 mixture needs to be separated efficiently. This work examined the adsorption characteristics and competitive mechanisms of H2 and N2 on LTA- and FAU-type zeolites, at 77 K, 298 K, and 0.1-10 bar by thoroughly analyzing results of adsorption capacity experiments and molecular simulations. In the Grand Canonical Monte Carlo (GCMC) simulations, the force field causing a molecular dipole of H2 and the polarization force field of N2 are first applied. The accuracy of the force field was experimentally verified. The findings indicate that N2 and H2 loading on Ca-FAU (Ca-LTA) are higher than Na-FAU (Na-LTA). On NaX at 77 K, the highest adsorption selectivity (N2/H2) is observed; on NaA at 298 K, it is the opposite. The GCMC data findings demonstrate that H2 and N2 have remarkably similar adsorption sites, with framework oxygen atoms and non-framework cations serving as the main adsorption sites for adsorbate molecules. Furthermore, the rate at which H2 diffuses is higher than that of N2. The study of redistribution charge before and after adsorption demonstrated that N2 has a greater affinity for the framework oxygen atoms than H2. This study provides a molecular theoretical foundation for the adsorption behavior of H2-N2 mixture in zeolites.

Equilibration of linear polyethylene melts with pre-defined molecular weight distributions employing united atom Monte Carlo simulations

Possessing control over the molecular size (molecular weight/chain length/degree of polymerization) distribution of a polymeric material is extremely important in applications. This is manifested de facto by the extensive contemporary scientific literature on processes for controlling this distribution experimentally. Yet, the literature on computational techniques for achieving prescribed molecular size distributions in simulations and exploring their impact on properties is much less abundant than its experimental/technical counterpart. Here, we develop-on the basis of united atom melt simulations employing connectivity-altering Monte Carlo moves-a new Metropolis selection criterion that drives the multichain system to a prescribed but otherwise arbitrary distribution of molecular sizes. The new formulation is a generalization of that originally proposed [P. V. K. Pant and D. N. Theodorou, Macromolecules 28, 7224 (1995)], but simpler and more computationally efficient. It requires knowledge solely of the target distribution, which need not be normalized. We have implemented the new formulation on long-chain linear polyethylene melts, obtaining excellent results. The target molecular size distribution can be provided in tabulated form, allowing absolute freedom as to the types of chain size profiles that can be simulated. Distributions for which equilibration has been achieved here for linear polyethylene include a truncated most probable, a truncated Schulz-Zimm, an arbitrary one defined in tabulated form, a broad truncated Gaussian, and a bimodal Gaussian. The last two are comparable to those encountered in industrial applications. The impact of the molecular size distribution on the properties of the simulated melts, such as density, chain dimensions, and mixing thermodynamics, is explored.

Monte Carlo Simulations of Water Pollutant Adsorption at Parts-per-Billion Concentration: A Study on 1,4-Dioxane

1,4-dioxane, an emerging water pollutant with high production volumes, is a probable human carcinogen. The inadequacy of conventional treatment processes demonstrates the need for an effective remediation strategy. Crystalline nanoporous materials are cost-effective adsorbents due to their high capacity and selective separation in mixtures. This study explores the potential of all-silica zeolites for the separation of 1,4-dioxane from water. These zeolites are highly hydrophobic and can preferentially adsorb nonpolar molecules from mixtures. We investigated six zeolite frameworks (BEA, EUO, FER, IFR, MFI, and MOR) using Monte Carlo simulations in the Gibbs ensemble. The simulations indicate high selectivity by FER and EUO, especially at low pressures, which we attribute to pore sizes and shapes with a greater affinity to 1,4-dioxane. We also demonstrate a Monte Carlo simulation workflow using gauge cells to model the adsorption of an aqueous solution of 1,4-dioxane at a 0.35 ppb concentration. We quantify 1,4-dioxane and water coadsorption and observe selectivities ranging from 1.1 × 105 in MOR to 8.7 × 106 in FER. We also demonstrate that 1,4-dioxane is in the infinite dilution regime in the aqueous phase at this concentration. This simulation technique can be extended to model other emerging water contaminants such as perfluoroalkyl and polyfluoroalkyl substances (PFAS), chlorofluorocarbons, and others, which are also found in extremely low concentrations.

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.

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

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

Avoiding pitfalls in molecular simulation of vapor sorption: Example of propane and isobutane in metal-organic frameworks for adsorption cooling applications

This study introduces recommendations for conducting molecular simulations of vapor adsorption, with an emphasis on enhancing the accuracy, reproducibility, and comparability of results. The first aspect we address is consistency in the implementation of some details of typical molecular models, including tail corrections and cutoff distances, due to their significant influence on generated data. We highlight the importance of explicitly calculating the saturation pressures at relevant temperatures using methods such as Gibbs ensemble Monte Carlo simulations and illustrate some pitfalls in extrapolating saturation pressures using this method. For grand canonical Monte Carlo (GCMC) simulations, the input fugacity is usually calculated using an equation of state, which often requires the critical parameters of the fluid. We show the importance of using critical parameters derived from the simulation with the same model to ensure internal consistency between the simulated explicit adsorbate phase and the implicit bulk phase in GCMC. We show the advantages of presenting isotherms on a relative pressure scale to facilitate easier comparison among models and with experiment. Extending these guidelines to a practical case study, we evaluate the performance of various isoreticular metal-organic frameworks (MOFs) in adsorption cooling applications. This includes examining the advantages of using propane and isobutane as working fluids and identifying MOFs with a superior performance.

pyCOFBuilder: A Python Package for Automated Creation of Covalent Organic Framework Models Based on the Reticular Approach

Covalent organic frameworks (COFs) have gained significant popularity in recent years due to their unique ability to provide a high surface area and customizable pore geometry and chemistry, making them an ideal choice for a wide range of applications. However, exploring COFs experimentally can be arduous and time-consuming due to their immense number of potential structures. As a result, computational high-throughput studies have become an attractive option. Nevertheless, generating COF structures can also be a challenging and time-consuming task. To address this challenge, here, we introduce the pyCOFBuilder, an open-source Python package designed to facilitate the generation of COF structures for computational studies. The pyCOFBuilder software provides an easy-to-use set of functionalities to generate COF structures following the reticular approach. In this paper, we describe the implementation, main features, and capabilities of the pyCOFBuilder, demonstrating its utility for generating COF structures with varying topologies and chemical properties. pyCOFBuilder is freely available on GitHub at https://github.com/lipelopesoliveira/pyCOFBuilder.

High throughput screening of pure silica zeolites for CF4 capture from electronics industry gas

The capture and separation of CF4 from CF4/N2 mixture gas is a crucial issue in the electronics industry, as CF4 is a commonly used etching gas and the ratio of CF4 to N2 directly affects process efficiency. Utilizing high-throughput computational screening techniques and grand canonical Monte Carlo (GCMC) simulations, we comprehensively screened and assessed 247 types of pure silicon zeolite materials to determine their adsorption and separation performance for CF4/N2 mixtures. Based on screening, the relationships between the structural parameters and adsorption and separation properties were meticulously investigated. Four indicators including adsorption selectivity, working capacity, adsorbent performance score (APS), and regenerability (R%) were used to evaluate the performance of adsorbents. Based on the evaluation, we selected the top three best-performing zeolite structures for vacuum swing adsorption (LEV, AWW and ESV) and pressure swing adsorption (AVL, ZON, and ERI) processes respectively. Also, we studied the preferable adsorption sites of CF4 and N2 in the selected zeolite structures through centroid density distributions at the molecule level. We expect the study may provide some valuable guidance for subsequent experimental investigations on adsorption and separation of CF4/N2.

Constrained and Open Mesoporosity in Polypropylene Cracking: Insight From Spectroscopic Investigations of Acidity, Diffusion, and Activity

The outcome of the demetalation process of zeolites depends on applied treatment conditions and can lead to the formation of either open or constrained mesopores. The quaternary ammonium cations as pore-directing agents during desilication are responsible for developing constrained mesoporosity with bottleneck entrances. However, higher mesopore surface area and higher accessibility of acid sites are often found for the hierarchical zeolites with constrained mesopores. This is followed by better catalytic activity in the cracking of vacuum gas oil and polymers. For desilication with pure NaOH, a realumination process is observed and an additional acid-wash step is required to reach their full catalytic potential. Thus, this study aims to analyze the acidic and catalytic properties of hierarchical ZSM-5 zeolites of different mesoporosity types employing in situ and operando FT-IR spectroscopic evaluation of polypropylene cracking. The suitability of constrained mesoporosity is studied by assessing the neopentane diffusion in kinetic adsorption, Monte Carlo calculations, and rapid scan FT-IR spectroscopic measurement analyzed by Crank solution for diffusion. The FT-IR spectroscopic results of in situ and operando studies are supported by two-dimensional correlation analysis, allowing to establish the direction of changes seen on spectra and their order.

Hierarchical Computational Screening of Quantum Metal-Organic Framework Database to Identify Metal-Organic Frameworks for Volatile Organic-Compound Capture from Air

The design and discovery of novel porous materials that can efficiently capture volatile organic compounds (VOCs) from air are critical to address one of the most important challenges of our world, air pollution. In this work, we studied a recently introduced metal-organic framework (MOF) database, namely, quantum MOF (QMOF) database, to unlock the potential of both experimentally synthesized and hypothetically generated structures for adsorption-based n-butane (C4H10) capture from air. Configurational Bias Monte Carlo (CBMC) simulations were used to study the adsorption of a quaternary gas mixture of N2, O2, Ar, and C4H10 in QMOFs for two different processes, pressure swing adsorption (PSA) and vacuum-swing adsorption (VSA). Several adsorbent performance evaluation metrics, such as C4H10 selectivity, working capacity, the adsorbent performance score, and percent regenerability, were used to identify the best adsorbent candidates, which were then further studied by molecular simulations for C4H10 capture from a more realistic seven-component air mixture consisting of N2, O2, Ar, C4H10, C3H8, C3H6, and C2H6. Results showed that the top five QMOFs have C4H10 selectivities between 6.3 × 103 and 9 × 103 (3.8 × 103 and 5 × 103) at 1 bar (10 bar). Detailed analysis of the structure-performance relations showed that low/mediocre porosity (0.4-0.6) and narrow pore sizes (6-9 Å) of QMOFs lead to high C4H10 selectivities. Radial distribution function analyses of the top materials revealed that C4H10 molecules tend to confine close to the organic parts of MOFs. Our results provided the first information in the literature about the VOC capture potential of a large variety and number of MOFs, which will be useful to direct the experimental efforts to the most promising adsorbent materials for C4H10 capture from air.

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

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

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

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

Cooperative Catalytic Alkyne Hydrosilylation by a Porphyrinic Metal-Organic Framework Composite

Vinylsilanes are valuable building blocks and important structural units in organic chemistry. Herein, catalytic alkyne hydrosilylation was reported to be promoted by a porphyrin metal-organic framework with the incorporation of Pd nanoparticles (Pd@Ir-PCN-222). Catalytic results showed that Pd@Ir-PCN-222 displayed high catalytic efficiency, giving rise to the E isomer vinylsilane with an excellent turnover frequency (TOF) of 2564 h-1. The mechanism studies revealed that the enhancement of the catalytic activity originated from the cooperation between iridium porphyrin and the Pd nanoparticle in confined spaces. The iridium porphyrin was prone to absorb and condense the hydrosilane and alkyne in the inner cavities of Ir-PCN-222, not only accelerating the reaction but also promoting the Pd nanoparticle to activate the Si-H and C≡C bonds of hydrosilane and alkyne, respectively.

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations

Within this Perspective, we critically reflect on the role of first-principles molecular dynamics (MD) simulations in unraveling the catalytic function within zeolites under operating conditions. First-principles MD simulations refer to methods where the dynamics of the nuclei is followed in time by integrating the Newtonian equations of motion on a potential energy surface that is determined by solving the quantum-mechanical many-body problem for the electrons. Catalytic solids used in industrial applications show an intriguing high degree of complexity, with phenomena taking place at a broad range of length and time scales. Additionally, the state and function of a catalyst critically depend on the operating conditions, such as temperature, moisture, presence of water, etc. Herein we show by means of a series of exemplary cases how first-principles MD simulations are instrumental to unravel the catalyst complexity at the molecular scale. Examples show how the nature of reactive species at higher catalytic temperatures may drastically change compared to species at lower temperatures and how the nature of active sites may dynamically change upon exposure to water. To simulate rare events, first-principles MD simulations need to be used in combination with enhanced sampling techniques to efficiently sample low-probability regions of phase space. Using these techniques, it is shown how competitive pathways at operating conditions can be discovered and how broad transition state regions can be explored. Interestingly, such simulations can also be used to study hindered diffusion under operating conditions. The cases shown clearly illustrate how first-principles MD simulations reveal insights into the catalytic function at operating conditions, which could not be discovered using static or local approaches where only a few points are considered on the potential energy surface (PES). Despite these advantages, some major hurdles still exist to fully integrate first-principles MD methods in a standard computational catalytic workflow or to use the output of MD simulations as input for multiple length/time scale methods that aim to bridge to the reactor scale. First of all, methods are needed that allow us to evaluate the interatomic forces with quantum-mechanical accuracy, albeit at a much lower computational cost compared to currently used density functional theory (DFT) methods. The use of DFT limits the currently attainable length/time scales to hundreds of picoseconds and a few nanometers, which are much smaller than realistic catalyst particle dimensions and time scales encountered in the catalysis process. One solution could be to construct machine learning potentials (MLPs), where a numerical potential is derived from underlying quantum-mechanical data, which could be used in subsequent MD simulations. As such, much longer length and time scales could be reached; however, quite some research is still necessary to construct MLPs for the complex systems encountered in industrially used catalysts. Second, most currently used enhanced sampling techniques in catalysis make use of collective variables (CVs), which are mostly determined based on chemical intuition. To explore complex reactive networks with MD simulations, methods are needed that allow the automatic discovery of CVs or methods that do not rely on a priori definition of CVs. Recently, various data-driven methods have been proposed, which could be explored for complex catalytic systems. Lastly, first-principles MD methods are currently mostly used to investigate local reactive events. We hope that with the rise of data-driven methods and more efficient methods to describe the PES, first-principles MD methods will in the future also be able to describe longer length/time scale processes in catalysis. This might lead to a consistent dynamic description of all steps-diffusion, adsorption, and reaction-as they take place at the catalyst particle level.

An Efficient Strategy for Electroreduction Reactor Outlet Fractioning into Valuable Products

In this work, two industrial dual-step pressure swing adsorption (PSA) processes were designed and simulated to obtain high-purity methane, CO₂, and syngas from a gas effluent of a CO₂ electroreduction reactor using different design configurations. Among the set of zeolites that was investigated using Monte Carlo and molecular dynamics simulations, NaX and MFI were the ones selected. The dual-PSA process for case study 1 is only capable of achieving a 90.5% methane purity with a 95.2% recovery. As for case study 2, methane is obtained with a 97.5% purity and 95.3% recovery. Both case studies can produce CO₂ with high purity and recovery (>97 and 95%, respectively) and syngas with a H₂/CO ratio above 4. Although case study 2 allows methane to be used as domestic gas, a much higher value for its energy consumption is observed compared to case study 1 (64.9 vs 29.8 W h mol_CH4^-1).

Computational investigation of hysteresis and phase equilibria of n-alkanes in a metal-organic framework with both micropores and mesopores

Adsorption hysteresis is a phenomenon related to phase transitions that can impact applications such as gas storage and separations in porous materials. Computational approaches can greatly facilitate the understanding of phase transitions and phase equilibria in porous materials. In this work, adsorption isotherms for methane, ethane, propane, and n-hexane were calculated from atomistic grand canonical Monte Carlo (GCMC) simulations in a metal-organic framework having both micropores and mesopores to better understand hysteresis and phase equilibria between connected pores of different size and the external bulk fluid. At low temperatures, the calculated isotherms exhibit sharp steps accompanied by hysteresis. As a complementary simulation method, canonical (NVT) ensemble simulations with Widom test particle insertions are demonstrated to provide additional information about these systems. The NVT+Widom simulations provide the full van der Waals loop associated with the sharp steps and hysteresis, including the locations of the spinodal points and points within the metastable and unstable regions that are inaccessible to GCMC simulations. The simulations provide molecular-level insight into pore filling and equilibria between high- and low-density states within individual pores. The effect of framework flexibility on adsorption hysteresis is also investigated for methane in IRMOF-1.

Molecular modelling of the thermophysical properties of fluids: expectations, limitations, gaps and opportunities

This manuscript provides an overview of the current state of the art in terms of the molecular modelling of the thermophysical properties of fluids. It is intended to manage the expectations and serve as guidance to practising physical chemists, chemical physicists and engineers in terms of the scope and accuracy of the more commonly available intermolecular potentials along with the peculiarities of the software and methods employed in molecular simulations while providing insights on the gaps and opportunities available in this field. The discussion is focused around case studies which showcase both the precision and the limitations of frequently used workflows.

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

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

Screening of Alkali Metal-Exchanged Zeolites for Nitrogen/Methane Separation

Methane (CH4) is the primary component of natural gas and must be purified to a certain level before it can be used as pipeline gas or liquified natural gas (LNG). In particular, nitrogen (N2), a common contaminant in natural gas needs to be rejected to increase the heating value of the gas and meet the LNG product specifications. The development of energy-efficient N2 removal technologies is hampered by N2's inertness and its resemblance to CH4 in terms of kinetic size and polarizability. N2-selective materials are so rare. Here, for the first time, we screened 1425 alkali metal cation exchange zeolites to identify the candidates with the best potential for the separation of N2 from CH4. We discovered a few extraordinary zeolite frameworks capable of achieving equilibrium selectivity toward N2. Particularly, Li+-RRO-3 zeolite with a specific two-dimensional structure demonstrated a selective N2 adsorption capacity of 2.94 mmol/g at 283 K and 1 bar, outperforming the capacity of all known zeolites. Through an ab initio density functional theory study, we found that the five-membered ring of the RRO framework is the most stable cationic site for Li+, and this Li+ can interact with multiple N2 molecules but only one CH4, revealing the mechanism for the high capacity and selectivity of N2. This work suggests promising adsorbents to enable N2 rejection from CH4 in the gas industry without going for energy-intensive cryogenic distillations.

Selective adsorption of sulphur dioxide and hydrogen sulphide by metal-organic frameworks

The removal of highly toxic gasses such as SO₂ and H₂S is important in various industrial and environmental applications. Metal organic frameworks (MOFs) are promising candidates for the capture of toxic gases owing to their favorable properties such as high selectivity, moisture stability, thermostability, acid gas resistance, high sorption capacity, and low-cost regenerability. In this study, we perform first principles density functional theory (DFT) and grand-canonical Monte Carlo (GCMC) simulations to investigate the capture of highly toxic gases, SO₂ and H₂S, by the recently designed ZTF and MAF-66 MOFs. Our results indicate that ZTF and MAF-66 show good adsorption performances for SO₂ and H₂S capture. The nature of the interactions between H₂S or SO₂ and the pore surface cavities was examined at the microscopic level. SO₂ is adsorbed on the pore surface through two types of hydrogen bonds, either between O of SO₂ with the closest H of the triazole 5-membred ring or between O of SO₂ with the hydrogen of the amino group. For H₂S inside the pores, the principal interactions between H₂S and surface pores are due to a relatively strong hydrogen bonds established between the nitrogens of the organic part of MOFs and H₂S. Also, we found that these interactions depend on the orientation of SO₂/H₂S inside the pores. Moreover, we have studied the influence of the presence of water and CO₂ on H₂S and SO₂ capture by the ZTF MOF. The present GCMC simulations reveal that the addition of H₂O molecules at low pressure leads to an enhancement of the H₂S adsorption, in agreement with experimental findings. However, the presence of water molecules decreases the adsorption of SO₂ irrespective of the pressure used. Besides, SO₂ adsorption is increased in the presence of a small number of CO₂ molecules, whereas the presence of carbon dioxide in ZTF pores has an unfavorable effect on the capture of H₂S.

Mechanical and gas adsorption properties of graphene and graphynes under biaxial strain

The exceptional properties of two-dimensional (2D) solids have motivated extensive research, which revealed the possibility of controlling many characteristics of these materials through strain. For instance, previous investigations demonstrated that compressive deformation could be used to direct the chemisorption of atomic hydrogen and oxygen. Still, to our knowledge, there is no work detailing how strain affects the adsorption isotherms of 2D materials and the adsorption properties of materials such as the graphynes, which are monolayers composed of sp and sp[Formula: see text] carbon atoms. In the present work, we analyze how biaxial tensile deformation changes the adsorption properties of four 2D materials (graphene, [Formula: see text]-graphyne, [Formula: see text]-graphyne, and [Formula: see text]-graphyne). To achieve this, we perform Monte Carlo Grand Canonical calculations to obtain the adsorption isotherms of H[Formula: see text], CO[Formula: see text], and CH[Formula: see text] on the monolayers with and without strain. And, to apply the deformation, we carry out Molecular Dynamics simulations. We find a substantial reduction in the amount of gas adsorbed on the monolayers for nearly all gas-solid combinations. This is particularly true for graphene, where 14.5% strain reduces the quantity of H[Formula: see text]/CO[Formula: see text]/CH[Formula: see text] by 44.7/64.1/41.7% at P [Formula: see text] 1 atm. To understand the results, we calculate adsorption enthalpies and analyze the gas distribution above the monolayers. We also characterize the mechanical properties of the considered solids under biaxial deformation. Finally, a comparison of pore sizes with the kinetic diameters of various gases suggests applications for the graphynes, with and without strain, in gas separation.

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.

Exceptionally high selectivity in the separation of light hydrocarbons by adsorption on MIL-127(Fe) and on a (9,9) carbon nanotube

Porous solids with channel sizes that are not much above the size of small hydrocarbons can yield extremely large adsorption selectivity. Our Grand Canonical Monte-Carlo simulations indicate exceptionally high selectivity for the separation of methane, ethane and propane from natural gas. At 250 K the C₃H₈/CH₄ separation on MIL-127 at low pressure has a selectivity of more than 1000 and the C₃H₈/CH₄ separation on CNT (9,9) is even above 2000. This is due to the strong molecule lattice interaction in narrow channels which leads to large enthalpies of adsorption. The Arrhenius law for the Henry coefficients is analysed in order to show that the effect is due to this enthalpy rather than to steric reasons.

Spatial disposition of square-planar mononuclear nodes in metal-organic frameworks for C2H2/CO2 separation

The efficient separation of acetylene (C2H2) from its mixture with carbon dioxide (CO2) remains a challenging industrial process due to their close molecular sizes/shapes and similar physical properties. Herein, we report a microporous metal-organic framework (JNU-4) with square-planar mononuclear copper(ii) centers as nodes and tetrahedral organic linkers as spacers, allowing for two accessible binding sites per metal center for C2H2 molecules. Consequently, JNU-4 exhibits excellent C2H2 adsorption capacity, particularly at 298 K and 0.5 bar (200 cm3 g-1). Detailed computational studies confirm that C2H2 molecules are indeed predominantly located in close proximity to the square-planar copper centers on both sides. Breakthrough experiments demonstrate that JNU-4 is capable of efficiently separating C2H2 from a 50 : 50 C2H2/CO2 mixture over a broad range of flow rates, affording by far the largest C2H2 capture capacity (160 cm3 g-1) and fuel-grade C2H2 production (105 cm3 g-1, ≥98% purity) upon desorption. Simply by maximizing accessible open metal sites on mononuclear metal centers, this work presents a promising strategy to improve the C2H2 adsorption capacity and address the challenging C2H2/CO2 separation.

Defect-induced tuning of polarity-dependent adsorption in hydrophobic-hydrophilic UiO-66

Structural defects in metal-organic frameworks can be exploited to tune material properties. In the case of UiO-66 material, they may change its nature from hydrophobic to hydrophilic and therefore affect the mechanism of adsorption of polar and non-polar molecules. In this work, we focused on understanding this mechanism during adsorption of molecules with different dipole moments, using the standard volumetric adsorption measurements, IR spectroscopy, DFT + D calculations, and Monte Carlo calculations. Average occupation profiles showed that polar and nonpolar molecules change their preferences for adsorption sites. Hence, defects in the structure can be used to tune the adsorption properties of the MOF as well as to control the position of the adsorbates within the micropores of UiO-66.

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

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

Atomic-Scale Quantum Sensing of Ensembles of Guest Molecules in a Metal-Organic Framework with Intrinsic Electron Spin Centers

One of the exciting applications of electron-spin-based quantum sensing is the detection of distant nuclear spins of external molecular species. Here, we explore the application of a metal-organic framework (MOF) material as a host matrix for sensing spin centers. As a sensor, we employ inherent Cu²⁺ ions in the structure of a Zn-doped HKUST-1 framework. As a target molecular species, we use butane gas that exhibits no specific chemical reactivity toward the inner surface of HKUST-1 and is thus randomly distributed inside the MOF pore network. By employing a conventional double-resonance pulse sequence, we can effectively detect the coupling of the distant ¹H nuclear spins of butane to the electron spin of the sensor and gain atomic-scale insight into their spatial distribution. Thus, our proof-of-the-concept experiment demonstrates that MOFs, the materials featuring extremely large surface area and great tunability, are perfectly suited as a key element for emerging magnetic quantum sensing solutions.

Interlayer Expansion in a Layered Metal-Organic Framework Enhances CO2 Capture and CO2/N2 Separation

Developing efficient CO 2 adsorbent materials and technologies is significant to reduce the increasing greenhouse gases concentration in the atmosphere. Herein, a layered MOF with a porous kagomé lattice (kgm), which owned three phases (kgm-1, kgm-2, and kgm-3) via interlayer expansion, was evaluated as a promising CO 2 capture and separation material by using grand canonical Monte Carlo simulations. Results showed that the interlayer expansion provided additional pore volume, which played a considerable role in CO 2 adsorption and separation. The CO 2 adsorption capacity and CO 2 /N 2 selectivity followed the sequence kgm-3 > kgm-2 > kgm-1, and kgm-3 exhibited an excellent CO 2 adsorption capacity of 8.7 mmol g -1 at 1 bar with a CO 2 /N 2 selectivity of 130.3 at 20 bar and 298 K. Gas distribution analysis showed that CO 2 and N 2 are adsorbed only in the channels in kgm-1, whereas they could be adsorbed between layers in kgm-2 and kgm-3 due to the interlayer expansion. The adsorption heat and interactions between CO 2 and frameworks were analyzed to elucidate the effect of interlayer expansion. Results of this work highlighted that appropriate interlayer expansion can be an effective approach for framework adsorbents to improve CO 2 capture ability and separation performance at the same time.

Anion Regulates Topological Porous Coordination Polymers into the Acetylene Trap

The development of efficient porous absorbents with high uptake and selectivity remains a great challenge, especially for the recovery of acetylene (C₂H₂) from its carbon dioxide (CO₂)-containing mixtures. Here, we propose and report an anion-planting strategy for regulating the scu topological porous coordination polymers (PCPs) into the C₂H₂ trap. The three electronegative anions SiF₆^2-, TiF₆^2-, and ZrF₆^2-, in addition to the ligand of 3,5-di(1H-imidazol-1-yl)benzoic acid (HL) and Cu²⁺ ion, were employed to construct highly porous PCPs (NTU-60, NTU-61, and NTU-62) with varied window aperture. Especially, due to a matching distance (d_F-F) of 5.7 Å along the c-axis, the limited space that can be assigned as a single C₂H₂ trap enables NTU-61 to show optimal ability for C₂H₂ (van der Waals (vdW) parameters of the two H atoms: ∼5.72 Å) recognition, validated by Grand Canonical Monte Carlo (GCMC) calculations and Raman spectra. These characteristics allow the NTU-series to show higher C₂H₂ uptake, as well as excellent C₂H₂/CO₂ separation performance under dynamic conditions. The molecular insight and strategy here not only permit balanced adsorption and separation in a single domain but also exhibit an opportunity to develop advanced adsorbents in nearly all frameworks with lattice or coordinated ions, which may act as the platforms for various selective guest trappings with on-demand time and/or spatial resolution.

MOF-VR: A Virtual Reality Program for Performing and Visualizing Immersive Molecular Dynamics Simulations of Guest Molecules in Metal-Organic Frameworks

Molecular dynamics simulations are useful to study diffusion of guest molecules in metal-organic frameworks. The interpretation of the generated three-dimensional trajectories is often difficult, because most visualization tools only allow two-dimensional projections. To facilitate interpretation, we present MOF-VR: a virtual reality program for performing interactive molecular dynamics simulations in metal-organic frameworks and visualizing atomic or molecular trajectories. MOF-VR consists of three subroutines: a construction routine to create hypothetical metal-organic frameworks by hand, a molecular dynamics suite, and a trajectory visualizer. To the best of our knowledge, MOF-VR is the first virtual reality program that allows hypothetical metal-organic frameworks to be constructed and tested in molecular dynamics simulations of guest molecules. We further show that MOF-VR is capable of performing state-of-the-art molecular dynamics simulations of guest molecules in rigid metal-organic frameworks in virtual reality and provides reliable simulation results.

Influence of the extent of hydrophobicity on water organization and dynamics on 2D graphene oxide surfaces

Graphene oxide (GO) nanomaterials are being extensively explored for a wide spectrum of applications, ranging from water desalination to fuel cell applications due to their tunable mechanical, thermal, and electrical...

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

High-throughput calculations based on molecular simulations to predict the adsorption of molecules inside metal-organic frameworks (MOFs) have become a useful complement to experimental efforts to identify promising adsorbents for chemical separations and storage. For computational convenience, all existing efforts of this kind have relied on simulations in which the MOF is approximated as rigid. In this paper, we use extensive adsorption-relaxation simulations that fully include MOF flexibility effects to explore the validity of the rigid framework approximation. We also examine the accuracy of several approximate methods to incorporate framework flexibility that are more computationally efficient than adsorption-relaxation calculations. We first benchmark various models of MOF flexibility for four MOFs with well-established CO₂ experimental consensus isotherms. We then consider a range of adsorption properties, including Henry's constants, nondilute loadings, and adsorption selectivity, for seven adsorbates in 15 MOFs randomly selected from the CoRE MOF database. Our results indicate that in many MOFs adsorption-relaxation simulations are necessary to make quantitative predictions of adsorption, particularly for adsorption at dilute concentrations, although more standard calculations based on rigid structures can provide useful information. Finally, we investigate whether a correlation exists between the elastic properties of empty MOFs and the importance of including framework flexibility in making accurate predictions of molecular adsorption. Our results did not identify a simple correlation of this type.

Reactive Grand-Canonical Monte Carlo Simulations for Modeling Hydration of MgCl2

Thermochemical heat-storage applications, based on the reversible endo-/exothermic hydration reaction of salts, are intensively investigated to search for compact heat-storage devices. To achieve a truly valuable storage system, progressively complex salts are investigated. For these salts, the equilibrium temperature and pressure conditions are not always easy to predict. However, these conditions are crucial for the design of thermochemical heat-storage systems. A biased grand-canonical Monte Carlo (GCMC) tool is developed, enabling the study of equilibrium conditions at the molecular level. The GCMC algorithm is combined with reactive force field molecular dynamics (ReaxFF), which allows bond formation within the simulation. The Weeks-Chandler-Andersen (WCA) potential is used to scan multiple trial positions for the GCMC algorithm at a small cost. The most promising trial positions can be selected for recomputation with the more expensive ReaxFF. The developed WCA-ReaxFF-GCMC tool was used to study the hydration of MgCl2·nH2O. The simulation results show a good agreement with experimental and thermodynamic equilibriums for multiple hydration levels. The hydration shows that water, present at the surface of crystalline salt, deforms the surface layers and promotes further hydration of these deformed layers. Additionally, the WCA-ReaxFF-GCMC algorithm can be used to study other, non-TCM-related, reactive sorption processes.

Performance-Based Screening of Porous Materials for Carbon Capture

Computational screening methods have changed the way new materials and processes are discovered and designed. For adsorption-based gas separations and carbon capture, recent efforts have been directed toward the development of multiscale and performance-based screening workflows where we can go from the atomistic structure of an adsorbent to its equilibrium and transport properties at different scales, and eventually to its separation performance at the process level. The objective of this work is to review the current status of this new approach, discuss its potential and impact on the field of materials screening, and highlight the challenges that limit its application. We compile and introduce all the elements required for the development, implementation, and operation of multiscale workflows, hence providing a useful practical guide and a comprehensive source of reference to the scientific communities who work in this area. Our review includes information about available materials databases, state-of-the-art molecular simulation and process modeling tools, and a complete catalogue of data and parameters that are required at each stage of the multiscale screening. We thoroughly discuss the challenges associated with data availability, consistency of the models, and reproducibility of the data and, finally, propose new directions for the future of the field.

Non-injective gas sensor arrays: identifying undetectable composition changes

Metal-organic frameworks (MOFs) are nanoporous materials with good prospects as recognition elements for gas sensors owing to their adsorptive sensitivity and selectivity. A gravimetric, MOF-based sensor functions by measuring the mass of gas adsorbed in a MOF. Changes in the gas composition are expected to produce detectable changes in the mass of gas adsorbed in the MOF. In practical settings, multiple components of the gas adsorb into the MOF and contribute to the sensor response. As a result, there are typically many distinct gas compositions that produce the same single-sensor response. The response vector of a gas sensor array places multiple constraints on the gas composition. Still, if the number of degrees of freedom in the gas composition is greater than the number of MOFs in the sensor array, the map from gas compositions to response vectors will be non-injective (many-to-one). Here, we outline a mathematical method to determine undetectable changes in gas composition to which non-injective gas sensor arrays are unresponsive. This is important for understanding their limitations and vulnerabilities. We focus on gravimetric, MOF-based gas sensor arrays. Our method relies on a mixed-gas adsorption model in the MOFs comprising the sensor array, which gives the mass of gas adsorbed in each MOF as a function of the gas composition. The singular value decomposition of the Jacobian matrix of the adsorption model uncovers (i) the unresponsive directions and (ii) the responsive directions, ranked by sensitivity, in gas composition space. We illustrate the identification of unresponsive subspaces and ranked responsive directions for gas sensor arrays based on Co-MOF-74 and HKUST-1 aimed at quantitative sensing of CH₄/N₂/CO₂/C₂H₆mixtures relevant to natural gas sensing.

Classical statistical mechanics in the grand canonical ensemble

The methodology developed by Lustig for calculating thermodynamic properties in the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994)JCPSA60021-960610.1063/1.466446; Mol. Phys. 110, 3041 (2012)MOPHAM0026-897610.1080/00268976.2012.695032] is applied to derive rigorous expressions for thermodynamic properties of fluids in the grand canonical ensemble. All properties are expressed by phase-space functions, which are related to derivatives of the grand canonical potential with respect to the three independent variables of the ensemble: temperature, volume, and chemical potential. The phase-space functions contain ensemble averages of combinations of the number of particles, potential energy, and derivatives of the potential energy with respect to volume. In addition, expressions for the phase-space functions for temperature-dependent potentials are provided, which are required to account for quantum corrections semiclassically in classical simulations. Using the Lennard-Jones model fluid as a test case, the derived expressions are validated by Monte Carlo simulations. In contrast to expressions for the thermal expansion coefficient, the isothermal compressibility, and the thermal pressure coefficient from the literature, our expressions yield more reliable results for these properties, which agree well with a recent accurate equation of state for the Lennard-Jones model fluid. Moreover, they become equivalent to the corresponding expressions in the canonical ensemble in the thermodynamic limit.

Carbon dioxide capture enhanced by pre-adsorption of water and methanol in UiO-66

The rapidly rising level of carbon dioxide in the atmosphere resulting from human activity is one of the greatest environmental problems facing our civilization today. Most technologies are not yet sufficiently developed to move existing infrastructure to cleaner alternatives. Therefore, techniques for capturing carbon dioxide from emission sources may play a key role at the moment. The structure of the UiO‐66 material not only meets the requirement of high stability in contact with water vapor but through the water pre‐adsorbed in the pores, the selectivity of carbon dioxide adsorption is increased. We successfully applied the recently developed methodology for water adsorption modelling. It allowed to elucidate the influence of water on CO₂ adsorption and study the mechanism of this effect. We showed that water is adsorbed in octahedral cage and stands for promotor for CO₂ adsorption in less favorable space than tetrahedral cages. Water plays a role of a mediator of adsorption, what is a general idea of improving affinity of adsorbate. On the basis of pre‐adsorption of methanol as another polar solvent, we have shown that the adsorption sites play a key role here, and not, as previously thought, only the interaction between the solvent and quadrupole carbon dioxide. Overall, we explained the mechanism of increased CO₂ adsorption in the presence of water and methanol, as polar solvents, in the UiO‐66 pores for a potential post‐combustion carbon dioxide capture application.

Adsorption and the Chemical Reaction N2O4 ↔ 2NO2 in the Presence of N2 in a Gas Phase Connected with a Carbon Nanotube

The paper shows, by molecular simulations, that a CNT (9,9) carbon nanotube allows very efficient separation of nitrogen oxides (NO _x ) from N₂, that has in good approximation properties of the complete air mixture. Gibbs ensemble Monte Carlo simulations are used to describe the adsorption. The permanent chemical reaction between N₂O₄ and NO₂, which occurs simultaneously to adsorption, is treated by the reactive Monte Carlo simulation. A very high selectivity has been found. For a low pressure and at T = 298 K, an adsorption/reaction selectivity between NO _x and N₂ can reach values up to 3 × 10³.