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

Computational Modeling of Reticular Materials: The Past, the Present, and the Future

Reticular materials rely on a unique building concept where inorganic and organic building units are stitched together giving access to an almost limitless number of structured ordered porous materials. Given the versatility of chemical elements, underlying nets, and topologies, reticular materials provide a unique platform to design materials for timely technological applications. Reticular materials have now found their way in important societal applications, like carbon capture to address climate change, water harvesting to extract atmospheric moisture in arid environments, and clean energy applications. Combining predictions from computational materials chemistry with advanced experimental characterization and synthesis procedures unlocks a design strategy to synthesize new materials with the desired properties and functions. Within this review, the current status of modeling reticular materials is addressed and supplemented with topical examples highlighting the necessity of advanced molecular modeling to design materials for technological applications. This review is structured as a templated molecular modeling study starting from the molecular structure of a realistic material towards the prediction of properties and functions of the materials. At the end, the authors provide their perspective on the past, present of future in modeling reticular materials and formulate open challenges to inspire future model and method developments.

Efficient Implementation of Monte Carlo Algorithms on Graphical Processing Units for Simulation of Adsorption in Porous Materials

We present enhancements in Monte Carlo simulation speed and functionality within an open-source code, gRASPA, which uses graphical processing units (GPUs) to achieve significant performance improvements compared to serial, CPU implementations of Monte Carlo. The code supports a wide range of Monte Carlo simulations, including canonical ensemble (NVT), grand canonical, NVT Gibbs, Widom test particle insertions, and continuous-fractional component Monte Carlo. Implementation of grand canonical transition matrix Monte Carlo (GC-TMMC) and a novel feature to allow different moves for the different components of metal-organic framework (MOF) structures exemplify the capabilities of gRASPA for precise free energy calculations and enhanced adsorption studies, respectively. The introduction of a High-Throughput Computing (HTC) mode permits many Monte Carlo simulations on a single GPU device for accelerated materials discovery. The code can incorporate machine learning (ML) potentials, and this is illustrated with grand canonical Monte Carlo simulations of CO2 adsorption in Mg-MOF-74 that show much better agreement with experiment than simulations using a traditional force field. The open-source nature of gRASPA promotes reproducibility and openness in science, and users may add features to the code and optimize it for their own purposes. The code is written in CUDA/C++ and SYCL/C++ to support different GPU vendors. The gRASPA code is publicly available at https://github.com/snurr-group/gRASPA.

Fine-Tuning Microporosity of Crystalline Vanadomolybdate Frameworks for Selective Adsorptive Separation of Kr from Xe

Selective adsorptive capture and separation of chemically inert krypton (Kr) and xenon (Xe) noble gases with very low ppmv concentrations in air and industrial off-gases constitute an important technological challenge. Here, using a synergistic combination of experiment and theory, the microporous crystalline vanadomolybdates (MoVOx) as highly selective Kr sorbents are studied in detail. By varying the Mo/V ratios, we show for the first time that their one-dimensional (1D) pores can be fine-tuned for the size-selective adsorption of Kr over the larger Xe with selectivities reaching >100. Using extensive electronic structure calculations and grand canonical Monte Carlo simulations, the competition between Kr uptake with CO2 and N2 was also investigated. As most materials reported so far are selective toward the larger, more polarizable Xe than Kr, this work constitutes an important step toward robust Kr-selective sorbent materials. This work highlights the potential use of porous crystalline transition metal oxides as energy-efficient and selective noble gas capture sorbents for industrial applications.

From Data to Discovery: Recent Trends of Machine Learning in Metal-Organic Frameworks

Renowned for their high porosity and structural diversity, metal-organic frameworks (MOFs) are a promising class of materials for a wide range of applications. In recent decades, with the development of large-scale databases, the MOF community has witnessed innovations brought by data-driven machine learning methods, which have enabled a deeper understanding of the chemical nature of MOFs and led to the development of novel structures. Notably, machine learning is continuously and rapidly advancing as new methodologies, architectures, and data representations are actively being investigated, and their implementation in materials discovery is vigorously pursued. Under these circumstances, it is important to closely monitor recent research trends and identify the technologies that are being introduced. In this Perspective, we focus on emerging trends of machine learning within the field of MOFs, the challenges they face, and the future directions of their development.

Understanding the Selective Removal of Perfluoroalkyl and Polyfluoroalkyl Substances via Fluorine-Fluorine Interactions: A Critical Review

As regulatory standards for per- and polyfluoroalkyl substances (PFAS) become increasingly stringent, innovative water treatment technologies are urgently demanded for effective PFAS removal. Reported sorbents often exhibit limited affinity for PFAS and are frequently hindered by competitive background substances. Recently, fluorinated sorbents (abbreviated as fluorosorbents) have emerged as a potent solution by leveraging fluorine-fluorine (F···F) interactions to enhance selectivity and efficiency in PFAS removal. This review delves into the designs and applications of fluorosorbents, emphasizing how F···F interactions improve PFAS binding affinity. Specifically, the existence of F···F interactions results in removal efficiencies orders of magnitude higher than other counterpart sorbents, particularly under competitive conditions. Furthermore, we provide a detailed analysis of the fundamental principles underlying F···F interactions and elucidate their synergistic effects with other sorption forces, which contribute to the enhanced efficacy and selectivity. Subsequently, we examine various fluorosorbents and their synthesis and fluorination techniques, underscore the importance of accurately characterizing F···F interactions through advanced analytical methods, and emphasize the significance of this interaction in developing selective sorbents. Finally, we discuss challenges and opportunities associated with employing advanced techniques to guide the design of selective sorbents and advocate for further research in the development of sustainable and cost-effective treatment technologies leveraging F···F interactions.

Improving Machine Learned Force Fields for Complex Fluids through Enhanced Sampling: A Liquid Crystal Case Study

Machine learned force fields offer the potential for faster execution times while retaining the accuracy of traditional DFT calculations, making them promising candidates for molecular simulations in cases where reliable classical force fields are not available. Some of the challenges associated with machine learned force fields include simulation stability over extended periods of time and ensuring that the statistical and dynamical properties of the underlying simulated systems are correctly captured. In this work, we propose a systematic training pipeline for such force fields that leads to improved model quality, compared to that achieved by traditional data generation and training approaches. That pipeline relies on the use of enhanced sampling techniques, and it is demonstrated here in the context of a liquid crystal, which exemplifies many of the challenges that are encountered in fluids and materials with complex free energy landscapes. Our results indicate that, whereas the majority of traditional machine learned force field training approaches lead to molecular dynamics simulations that are only stable over hundred-picosecond trajectories, our approach allows for stable simulations over tens of nanoseconds for organic molecular systems comprising thousands of atoms.

Computational Simulations of Metal-Organic Frameworks to Enhance Adsorption Applications

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

Reaching Quantum Accuracy in Predicting Adsorption Properties for Ethane/Ethene in Zeolitic Imidazolate Framework-8 at Low Pressure Regime

Nanoporous materials in the form of metal-organic frameworks such as zeolitic imidazolate framework-8 (ZIF-8) are promising membrane materials for the separation of hydrocarbon mixtures. To compute the adsorption isotherms in such adsorbents, grand canonical Monte Carlo simulations have proven to be very useful. The quality of these isotherms depends on the accuracy of adsorbate-adsorbent interactions, which are mostly described using force fields owing to their low computational cost. However, force field predictions of adsorption uptake often show discrepancies from experiments at low pressures, providing the need for methods that are more accurate. Hence, in this work, we propose and validate two novel methodologies for the ZIF-8/ethane and ethene systems; a benchmarking methodology to evaluate the performance of any given force field in describing adsorption in the low-pressure regime and a refinement procedure to rescale the parameters of a force field to better describe the host-guest interactions and provide for simulation isotherms with close agreement to experimental isotherms. Both methodologies were developed based on a reference Henry coefficient, computed with the PBE-MBD functional using the importance sampling technique. The force field rankings predicted by the benchmarking methodology involve the comparison of force field derived Henry coefficients with the reference Henry coefficients and ranking the force fields based on the disparities between these Henry coefficients. The ranking from this methodology matches the rankings made based on uptake disparities by comparing force field derived simulation isotherms to experimental isotherms in the low-pressure regime. The force field rescaling methodology was proven to refine even the worst performing force field in UFF/TraPPE. The uptake disparities of UFF/TraPPE improved from 197% and 194% to 11% and 21% for ethane and ethene, respectively. The proposed methodology is applicable to predict adsorption across nanoporous materials and allows for rescaled force fields to reach quantum accuracy without the need for experimental input.

Molecular Recognition between Carbon Dioxide and Biodegradable Hydrogel Models: A Density Functional Theory (DFT) Investigation

In this research, we explore the potential of employing density functional theory (DFT) for the design of biodegradable hydrogels aimed at capturing carbon dioxide (CO2) and mitigating greenhouse gas emissions. We employed biodegradable hydrogel models, including polyethylene glycol, polyvinylpyrrolidone, chitosan, and poly-2-hydroxymethacrylate. The complexation process between the hydrogel and CO2 was thoroughly investigated at the ωB97X-D/6-311G(2d,p) theoretical level. Our findings reveal a strong affinity between the hydrogel models and CO2, with binding energies ranging from -4.5 to -6.5 kcal/mol, indicative of physisorption processes. The absorption order observed was as follows: chitosan > PVP > HEAC > PEG. Additionally, thermodynamic parameters substantiated this sequence and even suggested that these complexes remain stable up to 160 °C. Consequently, these polymers present a promising avenue for crafting novel materials for CO2 capture applications. Nonetheless, further research is warranted to optimize the design of these materials and assess their performance across various environmental conditions.

Transferable Water Potentials Using Equivariant Neural Networks

Machine learning interatomic potentials (MLIPs) have emerged as a technique that promises quantum theory accuracy for reduced cost. It has been proposed [J. Chem. Phys. 2023, 158, 084111] that MLIPs trained on solely liquid water data cannot accurately transfer to the vapor-liquid equilibrium while recovering the many-body decomposition (MBD) analysis of gas-phase water clusters. This suggests that MLIPs do not directly learn the physically correct interactions of water molecules, limiting transferability. In this work, we show that MLIPs using equivariant architecture and trained on 3200 liquid water structures reproduces liquid-phase water properties (e.g., density within 0.003 g/cm3 between 230 and 365 K), vapor-liquid equilibrium properties up to 550 K, the MBD analysis of gas-phase water cluster up to six-body interactions, and the relative energy and the vibrational density of states of ice phases. We show that potentials developed using equivariant MLIPs allow transferability for arbitrary phases of water that remain stable in nanosecond long simulations.

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

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

Predicting Spin-Dependent Phonon Band Structures of HKUST-1 Using Density Functional Theory and Machine-Learned Interatomic Potentials

The present study focuses on the spin-dependent vibrational properties of HKUST-1, a metal-organic framework with potential applications in gas storage and separation. Employing density functional theory (DFT), we explore the consequences of spin couplings in the copper paddle wheels (as the secondary building units of HKUST-1) on the material's vibrational properties. By systematically screening the impact of the spin state on the phonon bands and densities of states in the various frequency regions, we identify asymmetric -COO- stretching vibrations as being most affected by different types of magnetic couplings. Notably, we also show that the DFT-derived insights can be quantitatively reproduced employing suitably parametrized, state-of-the-art machine-learned classical potentials with root-mean-square deviations from the DFT results between 3 cm-1 and 7 cm-1. This demonstrates the potential of machine-learned classical force fields for predicting the spin-dependent properties of complex materials, even when explicitly considering spins only for the generation of the reference data used in the force-field parametrization process.

Screening Cu-Zeolites for Methane Activation Using Curriculum-Based Training

Machine learning (ML), when used synergistically with atomistic simulations, has recently emerged as a powerful tool for accelerated catalyst discovery. However, the application of these techniques has been limited by the lack of interpretable and transferable ML models. In this work, we propose a curriculum-based training (CBT) philosophy to systematically develop reactive machine learning potentials (rMLPs) for high-throughput screening of zeolite catalysts. Our CBT approach combines several different types of calculations to gradually teach the ML model about the relevant regions of the reactive potential energy surface. The resulting rMLPs are accurate, transferable, and interpretable. We further demonstrate the effectiveness of this approach by exhaustively screening thousands of [CuOCu]2+ sites across hundreds of Cu-zeolites for the industrially relevant methane activation reaction. Specifically, this large-scale analysis of the entire International Zeolite Association (IZA) database identifies a set of previously unexplored zeolites (i.e., MEI, ATN, EWO, and CAS) that show the highest ensemble-averaged rates for [CuOCu]2+-catalyzed methane activation. We believe that this CBT philosophy can be generally applied to other zeolite-catalyzed reactions and, subsequently, to other types of heterogeneous catalysts. Thus, this represents an important step toward overcoming the long-standing barriers within the computational heterogeneous catalysis community.