Data-Driven Imputation of Miscibility of Aqueous Solutions via Graph-Regularized Logistic Matrix Factorization.

Aqueous, two-phase systems (ATPSs) may form upon mixing two solutions of independently water-soluble compounds. Many separation, purification, and extraction processes rely on ATPSs. Predicting the miscibility of solutions can accelerate and reduce the cost of the discovery of new ATPSs for these applications. Whereas previous machine learning approaches to ATPS prediction used physicochemical properties of each solute as a descriptor, in this work, we show how to impute missing miscibility outcomes directly from an incomplete collection of pairwise miscibility experiments. We use graph-regularized logistic matrix factorization (GR-LMF) to learn a latent vector of each solution from (i) the observed entries in the pairwise miscibility matrix and (ii) a graph where each node is a solution and edges are relationships indicating the general category of the solute (i.e., polymer, surfactant, salt, protein). For an experimental data set of the pairwise miscibility of 68 solutions from Peacock et al. [ACS Appl. Mater. Interfaces 2021, 13, 11449-11460], we find that GR-LMF more accurately predicts missing (im)miscibility outcomes of pairs of solutions than ordinary logistic matrix factorization and random forest classifiers that use physicochemical features of the solutes. GR-LMF obviates the need for features of the solutions and solutions to impute missing miscibility outcomes, but it cannot predict the miscibility of a new solution without some observations of its miscibility with other solutions in the training data set.

Classifying the toxicity of pesticides to honey bees via support vector machines with random walk graph kernels.

Pesticides benefit agriculture by increasing crop yield, quality, and security. However, pesticides may inadvertently harm bees, which are valuable as pollinators. Thus, candidate pesticides in development pipelines must be assessed for toxicity to bees. Leveraging a dataset of 382 molecules with toxicity labels from honey bee exposure experiments, we train a support vector machine (SVM) to predict the toxicity of pesticides to honey bees. We compare two representations of the pesticide molecules: (i) a random walk feature vector listing counts of length-L walks on the molecular graph with each vertex- and edge-label sequence and (ii) the Molecular ACCess System (MACCS) structural key fingerprint (FP), a bit vector indicating the presence/absence of a list of pre-defined subgraph patterns in the molecular graph. We explicitly construct the MACCS FPs but rely on the fixed-length-L random walk graph kernel (RWGK) in place of the dot product for the random walk representation. The L-RWGK-SVM achieves an accuracy, precision, recall, and F1 score (mean over 2000 runs) of 0.81, 0.68, 0.71, and 0.69, respectively, on the test data set-with L = 4 being the mode optimal walk length. The MACCS-FP-SVM performs on par/marginally better than the L-RWGK-SVM, lends more interpretability, but varies more in performance. We interpret the MACCS-FP-SVM by illuminating which subgraph patterns in the molecules tend to strongly push them toward the toxic/non-toxic side of the separating hyperplane.

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.

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.

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.

Statistical Mechanical Model of Gas Adsorption in a Metal-Organic Framework Harboring a Rotaxane Molecular Shuttle.

Metal-organic frameworks (MOFs) are modular and tunable nanoporous materials with applications in gas storage, separations, and sensing. Integrating flexible/dynamic, gas-responsive components into MOFs can give them unique or enhanced adsorption properties. Here, we explore the adsorption properties that could be imparted to a MOF by a rotaxane molecular shuttle (RMS) in its pores. In the unit cell of an RMS-MOF, a macrocyclic wheel is mechanically interlocked with a strut of the MOF scaffold. The wheel shuttles between stations on the strut that are also gas adsorption sites. At a level of abstraction similar to the seminal Langmuir adsorption model, we pose and analyze a simple statistical mechanical model of gas adsorption in an RMS-MOF that accounts for (i) wheel/gas competition for sites on the strut and (ii) gas-induced changes in the configurational entropy of the shuttling wheel. We determine how the amount of gas adsorbed, the position of the wheel, and the differential energy of adsorption depend on temperature, pressure, and the interactions of the gas and wheel with the stations on the strut. Our model reveals that, compared to a rigid, Langmuir material, the chemistry of the RMS-MOF can be tuned to render gas adsorption more or less temperature sensitive and to release more or less heat upon adsorption. The model also uncovers that, if gas-wheel competition for a station is fierce, temperature influences the position of the wheel differently depending on the amount of gas adsorbed.

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.

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

Metal-organic frameworks (MOFs) are highly tuneable, extended-network, crystalline, nanoporous materials with applications in gas storage, separations, and sensing. We review how molecular models and simulations of gas adsorption in MOFs have informed the discovery of performant MOFs for methane, hydrogen, and oxygen storage, xenon, carbon dioxide, and chemical warfare agent capture, and xylene enrichment. Particularly, we highlight how large, open databases of MOF crystal structures, post-processed to enable molecular simulations, are a platform for computational materials discovery. We discuss how to orient research efforts to routinise the computational discovery of MOFs for adsorption-based engineering applications.

Understanding Gas Storage in Cuboctahedral Porous Coordination Cages.

Porous molecular solids are promising materials for gas storage and gas separation applications. However, given the relative dearth of structural information concerning these materials, additional studies are vital for further understanding their properties and developing design parameters for their optimization. Here, we examine a series of isostructural cuboctahedral, paddlewheel-based coordination cages, M24(tBu-bdc)24 (M = Cr, Mo, Ru; tBu-bdc2- = 5-tert-butylisophthalate), for high-pressure methane storage. As the decrease in crystallinity upon activation of these porous molecular materials precludes diffraction studies, we turn to a related class of pillared coordination cage-based metal-organic frameworks, M24(Me-bdc)24(dabco)6 (M = Fe, Co; Me-bdc2- = 5-methylisophthalate; dabco = 1,4-diazabicyclo[2.2.2]octane) for neutron diffraction studies. The five porous materials display BET surface areas from 1057-1937 m2/g and total methane uptake capacities of up to 143 cm3(STP)/cm3. Both the porous cages and cage-based frameworks display methane adsorption enthalpies of -15 to -22 kJ/mol. Also supported by molecular modeling, neutron diffraction studies indicate that the triangular windows of the cage are favorable methane adsorption sites with CD4-arene interactions between 3.7 and 4.1 Å. At both low and high loadings, two additional methane adsorption sites on the exterior surface of the cage are apparent for a total of 56 adsorption sites per cage. These results show that M24L24 cages are competent gas storage materials and further adsorption sites may be optimized by judicious ligand functionalization to control extracage pore space.

Multi- and instabilities in gas partitioning between nanoporous materials and rubber balloons.

In the two-balloon experiment, two rubber balloons are connected and allowed to exchange gas. Owing to the non-monotonic relationship between the radius of the balloon and the pressure of gas inside it, the two-balloon system presents multi- and in-stabilities. Herein, we consider a two-adsorbent system, where two different adsorbents are allowed to exchange gas. We show that, for rigid adsorbents, the thermodynamic equilibrium state is unique. Then, we consider an adsorbent-balloon system, where an adsorbent exchanges gas with a rubber balloon. This system can exhibit multiple states at thermodynamic equilibrium- two (meta)stable and one unstable. The size of the balloon, pressure of gas in the balloon, and partitioning of gas between the adsorbent and the balloon differ among the equilibrium states. Temperature changes and the addition/removal of gas into/from the adsorbent-balloon system can induce catastrophe bifurcations and show hysteresis. Furthermore, the adsorbent-balloon system exhibits a critical temperature where, when approached from below, the discrepancy of balloon size between the two (meta)stable states decreases and, beyond, bistability is impossible. Practically, our findings preclude multiple partitions of adsorbed gas in rigid, mixed-linker or stratified metal-organic frameworks and may inspire new soft actuator and sensor designs.

Eigencages: Learning a Latent Space of Porous Cage Molecules.

Porous organic cage molecules harbor nanosized cavities that can selectively adsorb gas molecules, lending them applications in separations and sensing. The geometry of the cavity strongly influences their adsorptive selectivity. For comparing cages and predicting their adsorption properties, we embed/encode a set of 74 porous organic cage molecules into a low-dimensional, latent "cage space" on the basis of their intrinsic porosity. We first computationally scan each cage to generate a three-dimensional (3D) image of its porosity. Leveraging the singular value decomposition, in an unsupervised manner, we then learn across all cages an approximate, lower-dimensional subspace in which the 3D porosity images congregate. The "eigencages" are the set of orthogonal, characteristic 3D porosity images that span this lower-dimensional subspace, ordered in terms of importance. A latent representation/encoding of each cage follows by approximately expressing it as a combination of the eigencages. We show that the learned encoding captures salient features of the cavities of porous cages and is predictive of properties of the cages that arise from cavity shape. Our methods could be applied to learn latent representations of cavities within other classes of porous materials and of shapes of molecules in general.

High-Throughput Computational Screening of Multivariate Metal-Organic Frameworks (MTV-MOFs) for CO2 Capture.

Multivariate metal-organic frameworks (MTV-MOFs) contain multiple linker types within a single structure. Arrangements of linkers containing different functional groups confer structural diversity and surface heterogeneity and result in a combinatorial explosion in the number of possible structures. In this work, we carried out high-throughput computational screening of a large number of computer-generated MTV-MOFs to assess their CO2 capture properties using grand canonical Monte Carlo simulations. The results demonstrate that functionalization enhances CO2 capture performance of MTV-MOFs when compared to their parent (unfunctionalized) counterparts, and the pore size plays a dominant role in determining the CO2 adsorption capabilities of MTV-MOFs irrespective of the combinations of the three functional groups (-F, -NH2, and -OCH3) that we investigated. We also found that the functionalization of parent MOFs with small pores led to larger enhancements in CO2 uptake and CO2/N2 selectivity than functionalization in larger-pore MOFs. Free energy contour maps are presented to visually compare the influence of linker functionalization between frameworks with large and small pores.

Effect of ring rotation upon gas adsorption in SIFSIX-3-M (M = Fe, Ni) pillared square grid networks.

Dynamic and flexible metal-organic frameworks (MOFs) that respond to external stimuli, such as stress, light, heat, and the presence of guest molecules, hold promise for applications in chemical sensing, drug delivery, gas separations, and catalysis. A greater understanding of the relationship between flexible constituents in MOFs and gas adsorption may enable the rational design of MOFs with dynamic moieties and stimuli-responsive behavior. Here, we detail the effect of subtle structural changes upon the gas sorption behavior of two "SIFSIX" pillared square grid frameworks, namely SIFSIX-3-M (M = Ni, Fe). We observe a pronounced inflection in the Xe adsorption isotherm in the Ni variant. With evidence from X-ray diffraction studies, density functional theory, and molecular simulations, we attribute the inflection to a disordered to ordered transition of the rotational configurations of the pyrazine rings induced by sorbate-sorbent interactions. We also address the effect of cage size, temperature, and sorbate on the guest-induced ring rotation and the adsorption isotherms. The absence of an inflection in the Xe adsorption isotherm in SIFSIX-3-Fe and in the Kr, N2, and CO2 adsorption isotherms in SIFSIX-3-Ni suggest that the inflection is highly sensitive to the match between the size of the cage and the guest molecule.

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

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

Statistical mechanical model of gas adsorption in porous crystals with dynamic moieties.

Some nanoporous, crystalline materials possess dynamic constituents, for example, rotatable moieties. These moieties can undergo a conformation change in response to the adsorption of guest molecules, which qualitatively impacts adsorption behavior. We pose and solve a statistical mechanical model of gas adsorption in a porous crystal whose cages share a common ligand that can adopt two distinct rotational conformations. Guest molecules incentivize the ligands to adopt a different rotational configuration than maintained in the empty host. Our model captures inflections, steps, and hysteresis that can arise in the adsorption isotherm as a signature of the rotating ligands. The insights disclosed by our simple model contribute a more intimate understanding of the response and consequence of rotating ligands integrated into porous materials to harness them for gas storage and separations, chemical sensing, drug delivery, catalysis, and nanoscale devices. Particularly, our model reveals design strategies to exploit these moving constituents and engineer improved adsorbents with intrinsic thermal management for pressure-swing adsorption processes.

Adsorbate-induced lattice deformation in IRMOF-74 series.

IRMOF-74 analogues are among the most widely studied metal-organic frameworks (MOFs) for adsorption applications because of their one-dimensional channels and high metal density. Most studies involving the IRMOF-74 series assume that the crystal lattice is rigid. This assumption guides the interpretation of experimental data, as changes in the crystal symmetry have so far been ignored as a possibility in the literature. Here, we report a deformation pattern, induced by the adsorption of argon, for IRMOF-74-V. This work has two main implications. First, we use molecular simulations to demonstrate that the IRMOF-74 series undergoes a deformation that is similar to the mechanism behind breathing MOFs, but is unique because the deformation pattern extends beyond a single unit cell of the original structure. Second, we provide an alternative interpretation of experimental small-angle X-ray scattering profiles of these systems, which changes how we view the fundamentals of adsorption in this MOF series.

Noria: A Highly Xe-Selective Nanoporous Organic Solid.

Separation of xenon and krypton is of industrial and environmental concern; the existing technologies use cryogenic distillation. Thus, a cost-effective, alternative technology for the separation of Xe and Kr and their capture from air is of significant importance. Herein, we report the selective Xe uptake in a crystalline porous organic oligomeric molecule, noria, and its structural analogue, PgC-noria, under ambient conditions. The selectivity of noria towards Xe arises from its tailored pore size and small cavities, which allows a directed non-bonding interaction of Xe atoms with a large number of carbon atoms of the noria molecular wheel in a confined space.

Metal-organic framework with optimally selective xenon adsorption and separation.

Nuclear energy is among the most viable alternatives to our current fossil fuel-based energy economy. The mass deployment of nuclear energy as a low-emissions source requires the reprocessing of used nuclear fuel to recover fissile materials and mitigate radioactive waste. A major concern with reprocessing used nuclear fuel is the release of volatile radionuclides such as xenon and krypton that evolve into reprocessing facility off-gas in parts per million concentrations. The existing technology to remove these radioactive noble gases is a costly cryogenic distillation; alternatively, porous materials such as metal-organic frameworks have demonstrated the ability to selectively adsorb xenon and krypton at ambient conditions. Here we carry out a high-throughput computational screening of large databases of metal-organic frameworks and identify SBMOF-1 as the most selective for xenon. We affirm this prediction and report that SBMOF-1 exhibits by far the highest reported xenon adsorption capacity and a remarkable Xe/Kr selectivity under conditions pertinent to nuclear fuel reprocessing.