The role of molecular modelling and simulation in the discovery and deployment of metal-organic frameworks for gas storage and separation

Synthesis, structure elucidation, SC-XRD/DFT, molecular modelling simulations and DNA binding studies of 3,5-diphenyl-4,5-dihydro-1H-pyrazole chalcones

Deoxyribonucleic acid (DNA) acts as the most important intracellular target for various drugs. Exploring the DNA binding interactions of small bioactive molecules offers a structural guideline for designing new drugs with higher clinical efficacy and enhanced selectivity. This study presents the facile synthesis of pyrazoline-derived compounds (4a)-(4f) by reacting substituted chalcones with hydrazine hydrate using formic acid. The structure elucidation of substituted pyrazoline compounds was carried out using 1H-NMR, FT-IR and elemental analyses. While the crystal structures of two compounds (4a) and (4b) have been resolved by single-crystal X-ray diffraction (SC-XRD) analysis. Hirshfeld surface analysis also endorsed their greater molecular stability. Computational calculations at DFT/B3LYP/6-311++G(d,p) were executed to compare the structural properties (bond angle and bond length) and explore reactivity descriptors, frontier molecular orbitals (FMO), Mulliken atomic charges (MAC), molecular electrostatic potential (MEP) and electronic properties. All the compounds were evaluated for DNA binding interactions by UV-Vis spectrophotometric analysis. The results revealed that compounds (4a)-(4f) bind to DNA via non-covalent binding mode having binding constant values ranging from 1.22 × 103 to 6.81 × 104 M-1. The negative values of Gibbs free energy also proved the interaction of studied compounds with DNA as a spontaneous process. The findings of molecular docking simulations depicted that these studied compounds showed significant binding interactions with DNA and these results were consistent with experimental findings. Compound (4b) was concluded as the most potent compound of the series with the highest binding constant (4.95 × 104) and strongest binding affinity (-8.48 kcal/mol).Communicated by Ramaswamy H. Sarma.

Accelerated convergence via adiabatic sampling for adsorption and desorption processes

Under isothermal conditions, phase transitions occur through a nucleation event when conditions are sufficiently close to coexistence. The formation of a nucleus of the new phase requires the system to overcome a free energy barrier of formation, whose height rapidly rises as supersaturation decreases. This phenomenon occurs both in the bulk and under confinement and leads to a very slow kinetics for the transition, ultimately resulting in hysteresis, where the system can remain in a metastable state for a long time. This has broad implications, for instance, when using simulations to predict phase diagrams or screen porous materials for gas storage applications. Here, we leverage simulations in an adiabatic statistical ensemble, known as adiabatic grand-isochoric ensemble (μ, V, L) ensemble, to reach equilibrium states with a greater efficiency than its isothermal counterpart, i.e., simulations in the grand-canonical ensemble. For the bulk, we show that at low supersaturation, isothermal simulations converge slowly, while adiabatic simulations exhibit a fast convergence over a wide range of supersaturation. We then focus on adsorption and desorption processes in nanoporous materials, assess the reliability of (μ, V, L) simulations on the adsorption of argon in IRMOF-1, and demonstrate the efficiency of adiabatic simulations to predict efficiently the equilibrium loading during the adsorption and desorption of argon in MCM-41, a system that exhibits significant hysteresis. We provide quantitative measures of the increased rate of convergence when using adiabatic simulations. Adiabatic simulations explore a wide temperature range, leading to a more efficient exploration of the configuration space.

An automated protocol to construct flexibility parameters for classical forcefields: applications to metal-organic frameworks

In this work, forcefield flexibility parameters were constructed and validated for more than 100 metal-organic frameworks (MOFs). We used atom typing to identify bond types, angle types, and dihedral types associated with bond stretches, angle bends, dihedral torsions, and other flexibility interactions. Our work used Manz's angle-bending and dihedral-torsion model potentials. For a crystal structure containing N atoms in its unit cell, the number of independent flexibility interactions is 3(N atoms - 1). Because the number of bonds, angles, and dihedrals is normally much larger than 3(N atoms - 1), these internal coordinates are redundant. To reduce (but not eliminate) this redundancy, our protocol prunes dihedral types in a way that preserves symmetry equivalency. Next, each dihedral type is classified as non-rotatable, hindered, rotatable, or linear. We introduce a smart selection method that identifies which particular torsion modes are important for each rotatable dihedral type. Then, we computed the force constants for all flexibility interactions together via LASSO regression (i.e., regularized linear least-squares fitting) of the training dataset. LASSO automatically identifies and removes unimportant forcefield interactions. For each MOF, the reference dataset was quantum-mechanically-computed in VASP via DFT with dispersion and included: (i) finite-displacement calculations along every independent atom translation mode, (ii) geometries randomly sampled via ab initio molecular dynamics (AIMD), (iii) the optimized ground-state geometry using experimental lattice parameters, and (iv) rigid torsion scans for each rotatable dihedral type. After training, the flexibility model was validated across geometries that were not part of the training dataset. For each MOF, we computed the goodness of fit (R-squared value) and the root-mean-squared error (RMSE) separately for the training and validation datasets. We compared flexibility models with and without bond-bond cross terms. Even without cross terms, the model yielded R-squared values of 0.910 (avg across all MOFs) ± 0.018 (st. dev.) for atom-in-material forces in the validation datasets. Our SAVESTEPS protocol should find widespread applications to parameterize flexible forcefields for material datasets. We performed molecular dynamics simulations using these flexibility parameters to compute heat capacities and thermal expansion coefficients for two MOFs.

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.

Flat-Histogram Monte Carlo Simulation of Water Adsorption in Metal-Organic Frameworks

Molecular simulations of water adsorption in porous materials often converge slowly due to sampling bottlenecks that follow from hydrogen bonding and, in many cases, the formation of water clusters. These effects may be exacerbated in metal-organic framework (MOF) adsorbents, due to the presence of pore spaces (cages) that promote the formation of discrete-size clusters and hydrophobic effects (if present), among other reasons. In Grand Canonical Monte Carlo (MC) simulations, these sampling challenges are typically manifested by low MC acceptance ratios, a tendency for the simulation to become stuck in a particular loading state (i.e., macrostates), and the persistence of specific clusters for long periods of the simulation. We present simulation strategies to address these sampling challenges, by applying flat-histogram MC (FHMC) methods and specialized MC move types to simulations of water adsorption. FHMC, in both Transition-matrix and Wang-Landau forms, drives the simulation to sample relevant macrostates by incorporating weights that are self-consistently adjusted throughout the simulation and generate the macrostate probability distribution (MPD). Specialized MC moves, based on aggregation-volume bias and configurational bias methods, separately address low acceptance ratios for basic MC trial moves and specifically target water molecules in clusters; in turn, the specialized MC moves improve the efficiency of generating new configurations which is ultimately reflected in improved statistics collected by FHMC. The combined strategies are applied to study the adsorption of water in CuBTC and ZIF-8 at 300 K, through examination of the MPD and the adsorption isotherm generated by histogram reweighting. A key result is the appearance of nontrivial oscillations in the MPD, which we show to be associated with water clusters in the adsorption system. Additionally, we show that the probabilities of certain clusters become similar in value near the boundaries of the isotherm hysteresis loop, indicating a strong connection between cluster formation/destruction and the thermodynamic limits of stability. For a hydrophobic MOF, the FHMC results show that the phase transition from low density to high density is suppressed to water pressure far above the bulk-fluid saturation pressure; this is consistent with results presented elsewhere. We also compare our FHMC simulation isotherm to one measured by a different technique but with ostensibly the same molecular interactions and comment on observed differences and the need for follow-up work. The simulation strategies presented here can be applied to the simulation of water in other MOFs using heuristic guidelines laid out in our text, which should facilitate the more consistent and efficient simulation of water adsorption in porous materials in future applications.

Gas adsorption and framework flexibility of CALF-20 explored via experiments and simulations

In 2021, Svante, in collaboration with BASF, reported successful scale up of CALF-20 production, a stable MOF with high capacity for post-combustion CO2 capture which exhibits remarkable stability towards water. CALF-20's success story in the MOF commercialisation space provides new thinking about appropriate structural and adsorptive metrics important for CO2 capture. Here, we combine atomistic-level simulations with experiments to study adsorptive properties of CALF-20 and shed light on its flexible crystal structure. We compare measured and predicted CO2 and water adsorption isotherms and explain the role of water-framework interactions and hydrogen bonding networks in CALF-20's hydrophobic behaviour. Furthermore, regular and enhanced sampling molecular dynamics simulations are performed with both density-functional theory (DFT) and machine learning potentials (MLPs) trained to DFT energies and forces. From these simulations, the effects of adsorption-induced flexibility in CALF-20 are uncovered. We envisage this work would encourage development of other MOF materials useful for CO2 capture applications in humid conditions.

Temperature Extrapolation of Henry's Law Constants and the Isosteric Heat of Adsorption

Computational screening of adsorbent materials often uses the Henry's law constant (K_H) (at a particular temperature) as a first discriminator metric due to its relative ease of calculation. The isosteric heat of adsorption in the limit of zero pressure (q_st^∞) is often calculated along with the Henry's law constant, and both properties are informative metrics of adsorbent material performance at low-pressure conditions. In this article, we introduce a method for extrapolating K_H as a function of temperature, using series-expansion coefficients that are easily computed at the same time as K_H itself; the extrapolation function also yields q_st^∞. The extrapolation is highly accurate over a wide range of temperatures when the basis temperature is sufficiently high, for a wide range of adsorbent materials and adsorbate gases. Various results suggest that the extrapolation is accurate when the extrapolation range in inverse-temperature space is limited to |β - β₀ | < 0.5 mol/kJ. Application of the extrapolation to a large set of materials is shown to be successful provided that K_H is not extremely large and/or the extrapolation coefficients converge satisfactorily. The extrapolation is also able to predict q_st^∞ for a system that shows an unusually large temperature dependence. The work provides a robust method for predicting K_H and q_st^∞ over a wide range of industrially relevant temperatures with minimal effort beyond that necessary to compute those properties at a single temperature, which facilitates the addition of practical operating (or processing) conditions to computational screening exercises.

Rational Design of Smart Metal-Organic Frameworks for Light-Modulated Gas Transport

Smart metal-organic frameworks (MOFs) are constructed by introducing stimuli-responsive functional groups into MOF platforms. Through membrane systems containing smart MOFs, external field-modulated gas transport can be achieved, which finds potential applications in chemical engineering. In this work, we design a series of Mg-MOF-74-III-based frameworks functionalized by arylazopyrazole groups. Methyleneamine chains with various lengths are attached to the photoresponsive azopyrazole moiety. Molecular dynamics simulations show that CO₂ diffusion can be remarkably changed by controlling the cis-to-trans isomerization of the functional unit due to the tunable adsorbate-adsorbent and adsorbate-adsorbate interactions of the two states. With the optimal length of the functional chain, the spatial hindrance and adsorbate-adsorbent interaction exhibit a synergetic effect to maximize the stimuli-responsive kinetic separation of N₂ over CO₂. This work provides a promising strategy for elevating smart MOFs' potential in gas separation.

Discovery of High-Performing Metal-Organic Frameworks for On-Board Methane Storage and Delivery via LNG-ANG Coupling: High-Throughput Screening, Machine Learning, and Experimental Validation

Liquefied natural gas (LNG) gasification coupled with adsorbed natural gas (ANG) charging (LNG-ANG coupling) is an emerging strategy for efficient delivery of natural gas. However, the potential of LNG-ANG to attain the advanced research projects agency-energy (ARPA-E) target for onboard methane storage has not been fully investigated. In this work, large-scale computational screening is performed for 5446 metal-organic frameworks (MOFs), and over 193 MOFs whose methane working capacities exceed the target (315 cm3 (STP) cm-3 ) are identified. Furthermore, structure-performance relationships are realized under the LNG-ANG condition using a machine learning method. Additional molecular dynamics simulations are conducted to investigate the effects of the structural changes during temperature and pressure swings, further narrowing down the materials, and two synthetic targets are identified. The synthesized DUT-23(Cu) and DUT-23(Co) show higher working capacities (≈373 cm3 (STP) cm-3 ) than that of any other porous material under ANG or LNG-ANG conditions, and excellent stability during cyclic LNG-ANG operation.

Gas sensing based on metal-organic frameworks: Concepts, functions, and developments

Effective detection of pollutant gases is vital for protection of natural environment and human health. There is an increasing demand for sensing devices that are equipped with high sensitivity, fast response/recovery speed, and remarkable selectivity. Particularly, attention is given to the designability of sensing materials with porous structures. Among diverse kinds of porous materials, metal-organic frameworks (MOFs) exhibit high porosity, high degree of crystallinity and exceptional chemical activity. Their strong host-guest interactions with guest molecules facilitate the application of MOFs in adsorption, catalysis and sensing systems. In particular, the tailorable framework/composition and potential for post-synthetic modification of MOFs endow them with widely promising application in gas sensing devices. In this review, we outlined the fundamental aspects and applications of MOFs for gas sensors, and discussed various techniques of monitoring gases based on MOFs as functional materials. Insights and perspectives for further challenges faced by MOFs are discussed in the end.

Unlocking the computational design of metal-organic cages

Metal-organic cages are macrocyclic structures that can possess an intrinsic void that can hold molecules for encapsulation, adsorption, sensing, and catalysis applications. As metal-organic cages may be comprised from nearly any combination of organic and metal-containing components, cages can form with diverse shapes and sizes, allowing for tuning toward targeted properties. Therefore, their near-infinite design space is almost impossible to explore through experimentation alone and computational design can play a crucial role in exploring new systems. Although high-throughput computational design and screening workflows have long been known as powerful tools in drug and materials discovery, their application in exploring metal-organic cages is more recent. We show examples of structure prediction and host-guest/catalytic property evaluation of metal-organic cages. These examples are facilitated by advances in methods that handle metal-containing systems with improved accuracy and are the beginning of the development of automated cage design workflows. We finally outline a scope for how high-throughput computational methods can assist and drive experimental decisions as the field pushes toward functional and complex metal-organic cages. In particular, we highlight the importance of considering realistic, flexible systems.

PoreMatMod.jl: Julia Package for in Silico Postsynthetic Modification of Crystal Structure Models

PoreMatMod.jl is a free, open-source, user-friendly, and documented Julia package for modifying crystal structure models of porous materials such as metal-organic frameworks (MOFs). PoreMatMod.jl functions as a find-and-replace algorithm on crystal structures by leveraging (i) Ullmann's algorithm to search for subgraphs of the crystal structure graph that are isomorphic to the graph of a query fragment and (ii) the orthogonal Procrustes algorithm to align a replacement fragment with a targeted substructure of the crystal structure for installation. The prominent application of PoreMatMod.jl is to generate libraries of hypothetical structures for virtual screenings. For example, one can install functional groups on the linkers of a parent MOF, mimicking postsynthetic modification. Other applications of PoreMatMod.jl to modify crystal structure models include introducing defects with precision and correcting artifacts of X-ray structure determination (adding missing hydrogen atoms, resolving disorder, and removing guest molecules). The find-and-replace operations implemented by PoreMatMod.jl can be applied broadly to diverse atomistic systems for various in silico structural modification tasks.

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

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

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

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

Computational Design of MOF-Based Electronic Noses for Dilute Gas Species Detection: Application to Kidney Disease Detection

The diverse chemical composition of exhaled human breath contains a vast amount of information about the health of the body, and yet this is seldom taken advantage of for diagnostic purposes due to the lack of appropriate gas-sensing technologies. In this work, we apply computational methods to design mass-based gas sensor arrays, often called electronic noses, that are optimized for detecting kidney disease from breath, for which ammonia is a known biomarker. We define combined linear adsorption coefficients (CLACs), which are closely related to Henry's law coefficients, for calculating gas adsorption in metal-organic frameworks (MOFs) of gases commonly found in breath (i.e., carbon dioxide, argon, and ammonia). These CLACs were determined computationally using classical atomistic molecular simulation techniques and subsequently used to design and evaluate gas sensor arrays. We also describe a novel numerical algorithm for determining the composition of a breath sample given a set of sensor outputs and a library of CLACs. After identifying an optimal array of five MOFs, we screened a set of 100 simplified computer-generated, water-free breath samples for kidney disease and were able to successfully quantify the amount of ammonia in all samples within the tolerances needed to classify them as either healthy or diseased, demonstrating the promise of such devices for disease detection applications.

Data-Centric Architecture for Self-Driving Laboratories with Autonomous Discovery of New Nanomaterials

Artificial intelligence (AI) approaches continue to spread in almost every research and technology branch. However, a simple adaptation of AI methods and algorithms successfully exploited in one area to another field may face unexpected problems. Accelerating the discovery of new functional materials in chemical self-driving laboratories has an essential dependence on previous experimenters' experience. Self-driving laboratories help automate and intellectualize processes involved in discovering nanomaterials with required parameters that are difficult to transfer to AI-driven systems straightforwardly. It is not easy to find a suitable design method for self-driving laboratory implementation. In this case, the most appropriate way to implement is by creating and customizing a specific adaptive digital-centric automated laboratory with a data fusion approach that can reproduce a real experimenter's behavior. This paper analyzes the workflow of autonomous experimentation in the self-driving laboratory and distinguishes the core structure of such a laboratory, including sensing technologies. We propose a novel data-centric research strategy and multilevel data flow architecture for self-driving laboratories with the autonomous discovery of new functional nanomaterials.

Thermodynamic exploration of xenon/krypton separation based on a high-throughput screening

Nanoporous framework materials are a promising class of materials for energy-efficient technology of xenon/krypton separation by physisorption. Many studies on Xe/Kr separation by adsorption have focused on the determination of structure/property relationships, the description of theoretical limits of performance, and the identification of top-performing materials. Here, we provide a study based on a high-throughput screening of the adsorption of Xe, Kr, and Xe/Kr mixtures in 12 020 experimental MOF materials, to provide a better comprehension of the thermodynamics behind Xe/Kr separation in nanoporous materials and the microscopic origins of Xe/Kr selectivity at both low and ambient pressure.

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.

Predicting hydrogen storage in MOFs via machine learning

The H2 capacities of a diverse set of 918,734 metal-organic frameworks (MOFs) sourced from 19 databases is predicted via machine learning (ML). Using only 7 structural features as input, ML identifies 8,282 MOFs with the potential to exceed the capacities of state-of-the-art materials. The identified MOFs are predominantly hypothetical compounds having low densities (<0.31 g cm-3) in combination with high surface areas (>5,300 m2 g-1), void fractions (∼0.90), and pore volumes (>3.3 cm3 g-1). The relative importance of the input features are characterized, and dependencies on the ML algorithm and training set size are quantified. The most important features for predicting H2 uptake are pore volume (for gravimetric capacity) and void fraction (for volumetric capacity). The ML models are available on the web, allowing for rapid and accurate predictions of the hydrogen capacities of MOFs from limited structural data; the simplest models require only a single crystallographic feature.

Nanoporous Material Recognition via 3D Convolutional Neural Networks: Prediction of Adsorption Properties

Nanoporous materials can be effective adsorbents for various energy applications. Because of their abundant number, brute-force-based material discovery can, however, be challenging. Data-driven approaches can be advantageous for such purposes. In this study, we demonstrate for the first time the applicability of a 3D convolutional neural network (CNN) in material recognition for predicting adsorption properties. 2D CNNs have been widely applied to image recognition, where the CNN self-learns important features of images, without the need of handcrafting features that are subject to human bias. This study explores methane adsorption in zeolites as a case study, where ∼6500 hypothetical zeolites are utilized to train/validate our designed CNN model. The CNN model offers highly accurate predictions, and the self-learned features resemble the channel and pore-like geometry of structures. This study demonstrates the extension of computer vision to materials science and paves the way for future studies such as carbon capture.

Gas Storage in Porous Molecular Materials

Molecules with permanent porosity in the solid state have been studied for decades. Porosity in these systems is governed by intrinsic pore space, as in cages or macrocycles, and extrinsic void space, created through loose, intermolecular solid-state packing. The development of permanently porous molecular materials, especially cages with organic or metal-organic composition, has seen increased interest over the past decade, and as such, incredibly high surface areas have been reported for these solids. Despite this, examples of these materials being explored for gas storage applications are relatively limited. This minireview outlines existing molecular systems that have been investigated for gas storage and highlights strategies that have been used to understand adsorption mechanisms in porous molecular materials.

Engineering entangled photon pairs with metal-organic frameworks

The discovery and design of new materials with competitive optical frequency conversion efficiencies can accelerate the development of scalable photonic quantum technologies. Metal-organic framework (MOF) crystals without inversion symmetry have shown potential for these applications, given their nonlinear optical properties and the combinatorial number of possibilities for MOF self-assembly. In order to accelerate the discovery of MOF materials for quantum optical technologies, scalable computational assessment tools are needed. We develop a multi-scale methodology to study the wavefunction of entangled photon pairs generated by selected non-centrosymmetric MOF crystals via spontaneous parametric down-conversion (SPDC). Starting from an optimized crystal structure, we predict the shape of the G (2) intensity correlation function for coincidence detection of the entangled pairs, produced under conditions of collinear type-I phase matching. The effective nonlinearities and photon pair correlation times obtained are comparable to those available with inorganic crystal standards. Our work thus provides fundamental insights into the structure-property relationships for entangled photon generation with metal-organic frameworks, paving the way for the automated discovery of molecular materials for optical quantum technology.

The crystalline sponge method: quantum chemical in silico derivation and analysis of guest binding energies

Computational techniques combined with single-crystal structural data provide a means to further analyse MOF-based crystalline sponge complexes.

Evaluating the Fitness of Combinations of Adsorbents for Quantitative Gas Sensor Arrays

Robust, high-performance gas-sensing technology has applications in industrial process monitoring and control, air quality monitoring, food quality assessment, medical diagnosis, and security threat detection. Nanoporous materials (NPMs) could be utilized as recognition elements in a gas sensor because they selectively adsorb gas. Imitating mammalian olfaction, sensor arrays of NPMs use measurements of the adsorbed mass of gas in a set of distinct NPMs to infer the gas composition. Modular and adjustable NPMs, such as metal-organic frameworks (MOFs), offer a vast material space to sample for combinations to comprise a sensor array that produces a response pattern rich with information about the gas composition. Herein, we frame quantitative gas sensing, using arrays of NPMs, as an inverse problem, which equips us with a method to evaluate the fitness of a proposed combination of NPMs in a sensor array. While the (routine) forward problem is to use an adsorption model to predict the mass of gas adsorbed in each NPM when immersed in a gas mixture of a given composition, the inverse problem is to predict the gas composition from the observed masses of adsorbed gas in the NPMs of the array. The fitness of a given combination of NPMs for gas sensing is then determined by the conditioning of its inverse problem: the prediction of the gas composition provided by a fit (unfit) combination of NPMs is insensitive (sensitive) to inevitable errors in the measurements of the mass of gas adsorbed in the NPMs. For illustration, we use experimentally measured adsorption data to analyze the conditioning of the inverse problem associated with a (IRMOF-1 and HKUST-1) CH₄/CO₂ sensor array.

Too Many Materials and Too Many Applications: An Experimental Problem Waiting for a Computational Solution

Finding the best material for a specific application is the ultimate goal of materials discovery. However, there is also the reverse problem: when experimental groups discover a new material, they would like to know all the possible applications this material would be promising for. Computational modeling can aim to fulfill this expectation, thanks to the sustained growth of computing power and the collective engagement of the scientific community in developing more efficient and accurate workflows for predicting materials' performances. We discuss the impact that reproducibility and automation of the modeling protocols have on the field of gas adsorption in nanoporous crystals. We envision a platform that combines these tools and enables effective matching between promising materials and industrial applications.

Influence of flexible side-chains on the breathing phase transition of pillared layer MOFs: a force field investigation

The prototypical pillared layer MOFs, formed by a square lattice of paddle-wheel units and connected by dinitrogen pillars, can undergo a breathing phase transition by a "wine-rack" type motion of the square lattice. We studied this behavior, which is not yet fully understood, using an accurate first principles parameterized force field (MOF-FF) for larger nanocrystallites on the example of Zn₂(bdc)₂(dabco) [bdc: benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)], and found clear indications for an interface between a closed and an open pore phase traveling through the system during the phase transformation [J. Keupp and R. Schmid, Adv. Theory Simul., 2019, 2, 1900117]. In conventional simulations in small supercells this mechanism is prevented by periodic boundary conditions (PBCs), enforcing a synchronous transformation of the entire crystal. Here, we extend this investigation to pillared layer MOFs with flexible side-chains, attached to the linker. Such functionalized (fu-)MOFs are experimentally known to have different properties with the side-chains acting as fixed guest molecules. First, in order to extend the parameterization for such flexible groups, a new parameterization strategy for MOF-FF had to be developed, using a multi-structure force based fit method. The resulting parameterization for a library of fu-MOFs is then validated with respect to a set of reference systems and shows very good accuracy. In the second step, a series of fu-MOFs with increasing side-chain length is studied with respect to the influence of the side-chains on the breathing behavior. For small supercells in PBCs a systematic trend of the closed pore volume with the chain length is observed. However, for a nanocrystallite model a distinct interface between a closed and an open pore phase is visible only for the short chain length, whereas for longer chains the interface broadens and a nearly concerted transformation is observed. Only by molecular dynamics simulations using accurate force fields can such complex phenomena can be studied on a molecular level.

Transfer Learning Study of Gas Adsorption in Metal-Organic Frameworks

Metal-organic frameworks (MOFs) are a class of materials promising for gas adsorption due to their highly tunable nanoporous structures and host-guest interactions. While machine learning (ML) has been leveraged to aid the design or screen of MOFs for different purposes, the needs of big data are not always met, limiting the applicability of ML models trained against small data sets. In this work, we introduce an inductive transfer learning technique to improve the accuracy and applicability of ML models trained with a small amount of MOF adsorption data. This technique leverages potentially shareable knowledge from a source task to improve the models on the target tasks. As demonstrations, a deep neural networks (DNNs) trained on H₂ adsorption data with 13 506 MOF structures at 100 bar and 243 K is used as the source task. When transferring knowledge from the source task to H₂ adsorption at 100 bar and 130 K (one target task), the average predictive accuracy on target tasks was improved from 0.960 (direct training) to 0.991 (transfer learning), and transfer learning works in 89.3% of the cases. We also tested transfer learning across different gas species (i.e., from H₂ to CH₄), with an average predictive accuracy of CH₄ adsorption being improved from 0.935 (direct training) to 0.980 (transfer learning), and transfer learning works in 82.0% of the cases. More importantly, transfer learning is shown to effectively improve the models on the target tasks with low accuracy from direct training. However, when transferring the knowledge from the source task to Xe/Kr adsorption, the transfer learning does not improve the predictive accuracy significantly and even makes it worse in ∼50.0% of the cases, which is attributed to the lack of common descriptors that is key to the underlying knowledge.

Beyond the BET Analysis: The Surface Area Prediction of Nanoporous Materials Using a Machine Learning Method

Surface areas of porous materials such as metal-organic frameworks (MOFs) are commonly characterized using the Brunauer-Emmett-Teller (BET) method. However, it has been shown that the BET method does not always provide an accurate surface area estimation, especially for large-surface area MOFs. In this work, we propose, for the first time, a data-driven approach to accurately predict the surface area of MOFs. Machine learning is employed to train models based on adsorption isotherm features of more than 300 diverse structures to predict a benchmark measure of the surface area known as the true monolayer area. We demonstrate that the ML-based methods can predict true monolayer areas significantly better than the BET method, showing great promise for their potential as a more accurate alternative to the BET method in the structural characterization of porous materials.

Identifying misbonded atoms in the 2019 CoRE metal-organic framework database

Databases of experimentally-derived metal-organic framework (MOF) crystal structures are useful for large-scale computational screening to identify which MOFs are best-suited for particular applications. However, these crystal structures must be cleaned to identify and/or correct various artifacts. The recently published 2019 CoRE MOF database (Chung et al., J. Chem. Eng. Data, 2019, 64, 5985-5998) reported thousands of experimentally-derived crystal structures that were partially cleaned to remove solvent molecules, to identify hundreds of disordered structures (approximately thirty of those were corrected), and to manually correct approximately 100 structures (e.g., adding missing hydrogen atoms). Herein, further cleaning of the 2019 CoRE MOF database is performed to identify structures with misbonded or isolated atoms: (i) structures containing an isolated atom, (ii) structures containing atoms too close together (i.e., overlapping atoms), (iii) structures containing a misplaced hydrogen atom, (iv) structures containing an under-bonded carbon atom (which might be caused by missing hydrogen atoms), and (v) structures containing an over-bonded carbon atom. This study should not be viewed as the final cleaning of this database, but rather as progress along the way towards the goal of someday achieving a completely cleaned set of experimentally-derived MOF crystal structures. We performed atom typing for all of the accepted structures to identify those structures that can be parameterized by previously reported forcefield precursors (Chen and Manz, RSC Adv., 2019, 9, 36492-36507). We report several forcefield precursors (e.g., net atomic charges, atom-in-material polarizabilities, atom-in-material dispersion coefficients, electron cloud parameters, etc.) for more than five thousand MOFs in the 2019 CoRE MOF database.

Coupling Structural and Adsorption Properties of Metal-Organic Frameworks: From Pore Size Distribution to Pore Type Distribution

Metal-organic frameworks (MOFs) attract a rapidly growing attention across the disciplines due to their multifarious pore structures and unique ability to selectively adsorb, store, and release various guest molecules. Pore structure characterization and coupling of adsorption and structural properties are imperative for rational design of advanced MOF materials and their applications. The pore structure of MOFs represents a three-dimensional network comprised of several types of pore compartments: interconnected cages and channels distinguished by their size, shape, and chemistry. Here, we propose a novel methodology for pore structure characterization of MOF materials based on matching of the experimental adsorption isotherms to in silico-generated fingerprint isotherms of adsorption in individual pore compartments of the ideal crystal. The proposed approach couples structural and adsorption properties, determines the contributions of different types of pores into the total adsorption, and estimates to what extent the pore structure of the sample under investigation is different from the ideal crystal. The MOF pore structure is characterized by the pore type distribution (PTD), which is more informative than the traditional pore size distribution that is based on oversimplistic pore models. The method is illustrated on the example of Ar adsorption at 87 K on hydrated and dehydrated structures of Cu-BTC, one of the most well-known MOF materials. The PTD determined from the experimental isotherm provides an estimate of the crystal fraction in the sample and the accessibility and degree of hydration of different types of pore compartments. In addition, the PTD determined from the experimental adsorption isotherm is used to predict the isosteric heat of adsorption that provides important information on the specifics of adsorption interactions. The results are found to be in excellent agreement with experimental data. Such detailed information about the pore structure and adsorption properties of practical MOF samples cannot be obtained with currently available methods of adsorption characterization.

Curating Metal-Organic Frameworks To Compose Robust Gas Sensor Arrays in Dilute Conditions

Metal-organic frameworks (MOFs), tunable, nanoporous materials, are alluring recognition elements for gas sensing. Mimicking human olfaction, an array of cross-sensitive, MOF-based sensors could enable analyte detection in complex, variable gas mixtures containing confounding gas species. Herein, we address the question: given a set of MOF candidates and their adsorption properties, how do we select the optimal subset to compose a sensor array that accurately and robustly predicts the gas composition via monitoring the adsorbed mass in each MOF? We first mathematically formulate the MOF-based sensor array problem under dilute conditions. Instructively, the sensor array can be viewed as a linear map from gas composition space to sensor array response space defined by the matrix H of Henry coefficients of the gases in the MOFs. Characterizing this mapping, the singular value decomposition of H is a useful tool for evaluating MOF subsets for sensor arrays, as it determines the sensitivity of the predicted gas composition to measurement error, quantifies the magnitude of the response to changes in composition, and recovers which direction in gas composition space elicits the largest/smallest response. To illustrate, on the basis of experimental adsorption data, we curate MOFs for a sensor array with the objective of determining the concentration of CO₂ and SO₂ in the gas phase.

A collection of forcefield precursors for metal-organic frameworks

A host of important performance properties for metal-organic frameworks (MOFs) and other complex materials can be calculated by modeling statistical ensembles. The principle challenge is to develop accurate and computationally efficient interaction models for these simulations. Two major approaches are (i) ab initio molecular dynamics in which the interaction model is provided by an exchange-correlation theory (e.g., DFT + dispersion functional) and (ii) molecular mechanics in which the interaction model is a parameterized classical force field. The first approach requires further development to improve computational speed. The second approach requires further development to automate accurate forcefield parameterization. Because of the extreme chemical diversity across thousands of MOF structures, this problem is still mostly unsolved today. For example, here we show structures in the 2014 CoRE MOF database contain more than 8 thousand different atom types based on first and second neighbors. Our results showed that atom types based on both first and second neighbors adequately capture the chemical environment, but atom types based on only first neighbors do not. For 3056 MOFs, we used density functional theory (DFT) followed by DDEC6 atomic population analysis to extract a host of important forcefield precursors: partial atomic charges; atom-in-material (AIM) C6, C8, and C10 dispersion coefficients; AIM dipole and quadrupole moments; various AIM polarizabilities; quantum Drude oscillator parameters; AIM electron cloud parameters; etc. Electrostatic parameters were validated through comparisons to the DFT-computed electrostatic potential. These forcefield precursors should find widespread applications to developing MOF force fields.