From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5

Short-Range Δ-Machine Learning: A Cost-Efficient Strategy to Transfer Chemical Accuracy to Condensed Phase Systems

DFT-based machine-learning potentials (MLPs) are now routinely trained for condensed-phase systems, but surpassing DFT accuracy remains challenging due to the cost or unavailability of periodic reference calculations. Our previous work ( Phys. Rev. Lett. 2022, 129, 226001) demonstrated that high-accuracy periodic MLPs can be trained within the CCMD framework using extended yet finite reference calculations. Here, we introduce short-range Δ-Machine Learning (srΔML), a method that starts from a baseline MLP trained on low-level periodic data and adds a Δ-MLP correction based on high-level cluster calculations at the CC level. Applied to liquid water, srΔML reduces the required cluster size from (H2O)64 to (H2O)15 and significantly lowers the number of clusters needed, resulting in a 50-200× reduction in computational cost. The resulting potential closely reproduces the target CC potential and accurately captures both two- and three-body structural descriptors.

Free energy profiles for chemical reactions in solution from high-dimensional neural network potentials: The case of the Strecker synthesis

Machine learning potentials (MLPs) have become a popular tool in chemistry and materials science as they combine the accuracy of electronic structure calculations with the high computational efficiency of analytic potentials. MLPs are particularly useful for computationally demanding simulations such as the determination of free energy profiles governing chemical reactions in solution, but to date, such applications are still rare. In this work, we show how umbrella sampling simulations can be combined with active learning of high-dimensional neural network potentials (HDNNPs) to construct free energy profiles in a systematic way. For the example of the first step of Strecker synthesis of glycine in aqueous solution, we provide a detailed analysis of the improving quality of HDNNPs for datasets of increasing size. We find that, in addition to the typical quantification of energy and force errors with respect to the underlying density functional theory data, the long-term stability of the simulations and the convergence of physical properties should be rigorously monitored to obtain reliable and converged free energy profiles of chemical reactions in solution.

Modeling Gas Adsorption and Mechanistic Insights into Flexibility in Isoreticular Metal-Organic Frameworks Using High-Dimensional Neural Network Potentials

Metal-organic frameworks (MOFs), known for their remarkable porous and well-organized structures, have found extensive use in various applications, including gas storage. Predicting the bulk properties from atomistic simulations as well as gas uptakes and the adsorption mechanism requires the most accurate definition of MOF systems. The application of ab initio molecular dynamics to these extensive periodic systems exceeds the current computational capabilities. Consequently, alternative strategies need to be devised to decrease computational costs without compromising accuracy. In this work, we construct high-dimensional neural network potentials (HDNNPs) to describe rotationally and translationally invariant energies and forces of isoreticular metal-organic framework (IRMOF) series at the density functional theory level of accuracy using a fragmentation technique to study H2 and CH4 adsorption isotherms by means of an "adsorption-relaxation" model in which molecular dynamics and grand canonical Monte Carlo simulations were performed simultaneously. Herein, for the first time, we report that HDNNPs could be utilized for such simulations with excellent agreement with experimental values. We also report that the UFF4MOF force field may not be suitable for adsorption-relaxation simulations. In addition, we show that the real number of CH4 uptake values of IRMOF-10 under the extreme conditions could be much greater than what the classical force field predicts. Adsorption-relaxation simulations enable us to characterize the behavior of MOF atoms and the distribution of gas molecules during the adsorption process, giving the most detailed mechanistic picture.

Accelerating Global Optimization of Cerium Oxide Nanocluster Structures with High-Dimensional Neural Network Potential

CeO2, characterized by its unique 4f electronic structure and high oxygen storage capacity, is widely recognized as an important catalyst and support material in energy and catalytic applications. Despite its importance, the complexity of CeO2 nanoclusters poses challenges for structural characterization. Herein, we present a machine learning approach to accelerate the global optimization of cerium oxide nanocluster structures using a high-dimensional neural network potential (HDNNP). Our methodology integrates active learning to construct a versatile HDNNP that enables the exploration of the vast configurational space of small to medium cerium oxide clusters (CenO2n+x, n = 2-18, x = -1, 0, +1). The HDNNP, refined through iterative active learning, achieves an accuracy comparable to first-principles calculations. Results indicate that the configuration of the lowest energy structures varies across different intervals. At n = 9 and n = 14, there is a transition from compact structures to multilayered ordered structures, and subsequently to pyramidal structures. When n > 14, almost all structures are derived from the pyramidal structure as the core grows continuously. In addition, the electronic structures of the lowest-energy clusters are analyzed. Our findings provide insights into the size-dependent stability and electronic behavior of cerium oxide nanoclusters.

A machine learned potential for investigating single crystal to single crystal transformations in complex organic molecular systems

The packing of organic molecular crystals is often dominated by weak non-covalent interactions, making their in situ rearrangement under external stimuli challenging to understand. We investigate a pressure-induced single-crystal-to-single-crystal (SCSC) transformation between two polymorphs of 2,4,5-triiodo-1H-imidazole using machine learning potentials. This process involves the rearrangement of halogen and hydrogen bonds combined with proton transfer within a complex solid-state system. We developed a strategy to progressively approach the transition state along the phase transition path from both ends by using both the α and β crystal phases as initial structures for active learning. This method allowed us to develop a DFT-based machine learning potential that faithfully describes both of the stable phases and the transition processes. Our results demonstrate that these anisotropic interactions are represented accurately during molecular dynamic simulations. Bond breaking and reforming during proton transfer is observed and analysed in detail. This approach holds promise for simulating SCSC transitions in organic molecular crystals involving anisotropic interactions and chemical bond changes.

Application of modern artificial intelligence techniques in the development of organic molecular force fields

The molecular force field (FF) determines the accuracy of molecular dynamics (MD) and is one of the major bottlenecks that limits the application of MD in molecular design. Recently, artificial intelligence (AI) techniques, such as machine-learning potentials (MLPs), have been rapidly reshaping the landscape of MD. Meanwhile, organic molecular systems feature unique characteristics, and require more careful treatment in both model construction, optimization, and validation. While an accurate and generic organic molecular force field is still missing, significant progress has been made with the facilitation of AI, warranting a promising future. In this review, we provide an overview of the various types of AI techniques used in molecular FF development and discuss both the advantages and weaknesses of these methodologies. We show how AI methods provide unprecedented capabilities in many tasks such as potential fitting, atom typification, and automatic optimization. Meanwhile, it is also worth noting that more efforts are needed to improve the transferability of the model, develop a more comprehensive database, and establish more standardized validation procedures. With these discussions, we hope to inspire more efforts to solve the existing problems, eventually leading to the birth of next-generation generic organic FFs.

Prediction rigidities for data-driven chemistry

The widespread application of machine learning (ML) to the chemical sciences is making it very important to understand how the ML models learn to correlate chemical structures with their properties, and what can be done to improve the training efficiency whilst guaranteeing interpretability and transferability. In this work, we demonstrate the wide utility of prediction rigidities, a family of metrics derived from the loss function, in understanding the robustness of ML model predictions. We show that the prediction rigidities allow the assessment of the model not only at the global level, but also on the local or the component-wise level at which the intermediate (e.g. atomic, body-ordered, or range-separated) predictions are made. We leverage these metrics to understand the learning behavior of different ML models, and to guide efficient dataset construction for model training. We finally implement the formalism for a ML model targeting a coarse-grained system to demonstrate the applicability of the prediction rigidities to an even broader class of atomistic modeling problems.

Data-Efficient Active Learning for Thermodynamic Integration: Acidity Constants of BiVO4 in Water

The protonation state of molecules and surfaces is pivotal in various disciplines, including (electro-)catalysis, geochemistry, biochemistry, and pharmaceutics. Accurately and efficiently determining acidity constants is critical yet challenging, particularly when explicitly considering the electronic structure, thermal fluctuations, anharmonic vibrations, and solvation effects. In this research, we employ thermodynamic integration accelerated by committee Neural Network potentials, training a single machine learning model that accurately describes the relevant protonated, deprotonated, and intermediate states. We investigate two deprotonation reactions at the BiVO4 (010)-water interface, a promising candidate for efficient photocatalytic water splitting. Our results illustrate the convergence of the required ensemble averages over simulation time and of the final acidity constant as a function of the Kirkwood coupling parameter. We demonstrate that simulation times on the order of nanoseconds are required for statistical convergence. This time scale is currently unachievable with explicit ab-initio molecular dynamics simulations at the hybrid DFT level of theory. In contrast, our machine learning workflow only requires a few hundred DFT single point calculations for training and testing. Exploiting the extended time scales accessible, we furthermore asses the effect of commonly applied bias potentials. Thus, our study significantly advances calculating free energy differences with ab-initio accuracy.

Transferable performance of machine learning potentials across graphene-water systems of different sizes: Insights from numerical metrics and physical characteristics

Machine learning potentials (MLPs) are promising for various chemical systems, but their complexity and lack of physical interpretability challenge their broad applicability. This study evaluates the transferability of the deep potential (DP) and neural equivariant interatomic potential (NequIP) models for graphene-water systems using numerical metrics and physical characteristics. We found that the data quality from density functional theory calculations significantly influences MLP predictive accuracy. Prediction errors in transferring systems reveal the particularities of quantum chemical calculations on the heterogeneous graphene-water systems. Even for supercells with non-planar graphene carbon atoms, k-point mesh is necessary to obtain accurate results. In contrast, gamma-point calculations are sufficiently accurate for water molecules. In addition, we performed molecular dynamics (MD) simulations using these two models and compared the physical features such as atomic density profiles, radial distribution functions, and self-diffusion coefficients. It was found that although the NequIP model has higher accuracy than the DP model, the differences in the above physical features between them were not significant. Considering the stochasticity and complexity inherent in simulations, as well as the statistical averaging of physical characteristics, this motivates us to explore the meaning of accurately predicting atomic force in aligning the physical characteristics evolved by MD simulations with the actual physical features.

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.

Quantum-accurate machine learning potentials for metal-organic frameworks using temperature driven active learning

Understanding structural flexibility of metal-organic frameworks (MOFs) via molecular dynamics simulations is crucial to design better MOFs. Density functional theory (DFT) and quantum-chemistry methods provide highly accurate molecular dynamics, but the computational overheads limit their use in long time-dependent simulations. In contrast, classical force fields struggle with the description of coordination bonds. Here we develop a DFT-accurate machine-learning spectral neighbor analysis potentials for two representative MOFs. Their structural and vibrational properties are then studied and tightly compared with available experimental data. Most importantly, we demonstrate an active-learning algorithm, based on mapping the relevant internal coordinates, which drastically reduces the number of training data to be computed at the DFT level. Thus, the workflow presented here appears as an efficient strategy for the study of flexible MOFs with DFT accuracy, but at a fraction of the DFT computational cost.

Efficient Removal of Greenhouse Gases: Machine Learning-Assisted Exploration of Metal-Organic Framework Space

Global warming is a crisis that humanity must face together. With greenhouse gases (GHGs) as the main factor causing global warming, the adoption of relevant processes to eliminate them is essential. With the advantages of high specific surface area, large pore volume, and tunable synthesis, metal-organic frameworks (MOFs) have attracted much attention in GHG storage, adsorption, separation, and catalysis. However, as the pool of MOFs expands rapidly with new syntheses and discoveries, finding a suitable MOF for a particular application is highly challenging. In this regard, high-throughput computational screening is considered the most effective research method for screening a large number of materials to discover high-performance target MOFs. Typically, high-throughput computational screening generates voluminous and multidimensional data, which is well suited for machine learning (ML) training to improve the screening efficiency and explore the relationships between the multidimensional data in depth. This Review summarizes the general process and common methods for using ML to screen MOFs in the field of GHG removal. It also addresses the challenges faced by ML in exploring the MOF space and potential directions for the future development of ML for MOF screening. This aims to enhance the understanding of the integration of ML and MOFs in various fields and broaden the application and development ideas of MOFs.

In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back

Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.

Understanding Defects in Amorphous Silicon with Million-Atom Simulations and Machine Learning

The structure of amorphous silicon (a-Si) is widely thought of as a fourfold-connected random network, and yet it is defective atoms, with fewer or more than four bonds, that make it particularly interesting. Despite many attempts to explain such "dangling-bond" and "floating-bond" defects, respectively, a unified understanding is still missing. Here, we use advanced computational chemistry methods to reveal the complex structural and energetic landscape of defects in a-Si. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and thousands of individual defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned atomic energies to develop a classification of the different types of defects in a-Si. The results suggest a revision of the established floating-bond model by showing that fivefold-bonded atoms in a-Si exhibit a wide range of local environments-analogous to fivefold centers in coordination chemistry. Furthermore, it is shown that fivefold (but not threefold) coordination defects tend to cluster together. Our study provides new insights into one of the most widely studied amorphous solids, and has general implications for understanding defects in disordered materials beyond silicon alone.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

Deciphering the controlling factors for phase transitions in zeolitic imidazolate frameworks

Zeolitic imidazolate frameworks (ZIFs) feature complex phase transitions, including polymorphism, melting, vitrification, and polyamorphism. Experimentally probing their structural evolution during transitions involving amorphous phases is a significant challenge, especially at the medium-range length scale. To overcome this challenge, here we first train a deep learning-based force field to identify the structural characteristics of both crystalline and non-crystalline ZIF phases. This allows us to reproduce the structural evolution trend during the melting of crystals and formation of ZIF glasses at various length scales with an accuracy comparable to that of ab initio molecular dynamics, yet at a much lower computational cost. Based on this approach, we propose a new structural descriptor, namely, the ring orientation index, to capture the propensity for crystallization of ZIF-4 (Zn(Im)2, Im = C3H3N2-) glasses, as well as for the formation of ZIF-zni (Zn(Im)2) out of the high-density amorphous phase. This crystal formation process is a result of the reorientation of imidazole rings by sacrificing the order of the structure around the zinc-centered tetrahedra. The outcomes of this work are useful for studying phase transitions in other metal-organic frameworks (MOFs) and may thus guide the development of MOF glasses.

Unravelling abnormal in-plane stretchability of two-dimensional metal-organic frameworks by machine learning potential molecular dynamics

Two-dimensional (2D) metal-organic frameworks (MOFs) hold immense potential for various applications due to their distinctive intrinsic properties compared to their 3D analogues. Herein, we designed a highly stable NiF2(pyrazine)2 2D MOF in silico with a two-dimensional periodic wine-rack architecture. Extensive first-principles calculations and molecular dynamics (MD) simulations based on a newly developed machine learning potential (MLP) revealed that this 2D MOF exhibits huge in-plane Poisson's ratio anisotropy. This results in anomalous negative in-plane stretchability, as evidenced by an uncommon decrease in its in-plane area upon the application of uniaxial tensile strain, which makes this 2D MOF particularly attractive for flexible wearable electronics and ultra-thin sensor applications. We further demonstrated the unique capability of MLP to accurately predict the finite-temperature properties of MOFs on a large scale, exemplified by MLP-MD simulations with a dimension of 28.2 × 28.2 nm2, relevant to the length scale experimentally attainable for the fabrication of MOF films.

Robustness of Local Predictions in Atomistic Machine Learning Models

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale ML-driven simulations with a linear-scaling cost and also allows for the identification and posthoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though practical justifications exist for the local decomposition, only the global quantity is rigorously defined. Thus, when the atom-centered contributions are used, their sensitivity to the training strategy or the model architecture should be carefully considered. To this end, we introduce a quantitative metric, which we call the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of the LPR on the aspects of model training, particularly the composition of training data set, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models.

High-Dimensional Neural Network Potentials for Accurate Prediction of Equation of State: A Case Study of Methane

Machine learning-based interatomic potentials, such as those provided by neural networks, are increasingly important in molecular dynamics simulations. In the present work, we consider the applicability and robustness of machine learning molecular dynamics to predict the equation of state properties of methane by using high-dimensional neural network potentials (HDNNPs). We investigate two different strategies for generating training data: one strategy based upon bulk representations using periodic cells and another strategy based upon clusters of molecules. We assess the accuracy of the trained potentials by predicting the equilibrium mass density for a wide range of thermodynamic conditions to characterize the liquid phase, supercritical fluid, and gas phase, as well as the liquid-vapor coexistence curve. Our results show an excellent agreement with reference phase diagrams, with an average error below ∼2% for all studied phases. Moreover, we confirm the applicability of models trained on cluster data sets for producing accurate and reliable results.

Leveraging Machine Learning for Metal-Organic Frameworks: A Perspective

Metal-organic frameworks (MOFs) have attracted tremendous interest because of their tunable structures, functionalities, and physiochemical properties. The nearly infinite combinations of metal nodes and organic linkers have led to the synthesis of over 100,000 experimental MOFs and the construction of millions of hypothetical counterparts. It is intractable to identify the best candidates in the immense chemical space of MOFs for applications via conventional trial-to-error experiments or brute-force simulations. Over the past several years, machine learning (ML) has substantially transformed the way of MOF discovery, design, and synthesis. Driven by the abundant data from experiments or simulations, ML can not only efficiently and accurately predict MOF properties but also quantitatively derive structure-property relationships for rational design and screening. In this Perspective, we summarize recent achievements in leveraging ML for MOFs from the aspects of data acquisition, featurization, model training, and applications. Then, current challenges and new opportunities are discussed for the future exploration of ML to accelerate the development of new MOFs in this vibrant field.

How to train a neural network potential

The introduction of modern Machine Learning Potentials (MLPs) has led to a paradigm change in the development of potential energy surfaces for atomistic simulations. By providing efficient access to energies and forces, they allow us to perform large-scale simulations of extended systems, which are not directly accessible by demanding first-principles methods. In these simulations, MLPs can reach the accuracy of electronic structure calculations, provided that they have been properly trained and validated using a suitable set of reference data. Due to their highly flexible functional form, the construction of MLPs has to be done with great care. In this Tutorial, we describe the necessary key steps for training reliable MLPs, from data generation via training to final validation. The procedure, which is illustrated for the example of a high-dimensional neural network potential, is general and applicable to many types of MLPs.

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

Nanoporous materials such as metal-organic frameworks (MOFs) have been extensively studied for their potential for adsorption and separation applications. In this respect, grand canonical Monte Carlo (GCMC) simulations have become a well-established tool for computational screenings of the adsorption properties of large sets of MOFs. However, their reliance on empirical force field potentials has limited the accuracy with which this tool can be applied to MOFs with challenging chemical environments such as open-metal sites. On the other hand, density-functional theory (DFT) is too computationally demanding to be routinely employed in GCMC simulations due to the excessive number of required function evaluations. Therefore, we propose in this paper a protocol for training machine learning potentials (MLPs) on a limited set of DFT intermolecular interaction energies (and forces) of CO2 in ZIF-8 and the open-metal site containing Mg-MOF-74, and use the MLPs to derive adsorption isotherms from first principles. We make use of the equivariant NequIP model which has demonstrated excellent data efficiency, and as such an error on the interaction energies below 0.2 kJ mol-1 per adsorbate in ZIF-8 was attained. Its use in GCMC simulations results in highly accurate adsorption isotherms and heats of adsorption. For Mg-MOF-74, a large dependence of the obtained results on the used dispersion correction was observed, where PBE-MBD performs the best. Lastly, to test the transferability of the MLP trained on ZIF-8, it was applied to ZIF-3, ZIF-4, and ZIF-6, which resulted in large deviations in the predicted adsorption isotherms and heats of adsorption. Only when explicitly training on data for all ZIFs, accurate adsorption properties were obtained. As the proposed methodology is widely applicable to guest adsorption in nanoporous materials, it opens up the possibility for training general-purpose MLPs to perform highly accurate investigations of guest adsorption.

Transferability evaluation of the deep potential model for simulating water-graphene confined system

Machine learning potentials (MLPs) are poised to combine the accuracy of ab initio predictions with the computational efficiency of classical molecular dynamics (MD) simulation. While great progress has been made over the last two decades in developing MLPs, there is still much to be done to evaluate their model transferability and facilitate their development. In this work, we construct two deep potential (DP) models for liquid water near graphene surfaces, Model S and Model F, with the latter having more training data. A concurrent learning algorithm (DP-GEN) is adopted to explore the configurational space beyond the scope of conventional ab initio MD simulation. By examining the performance of Model S, we find that an accurate prediction of atomic force does not imply an accurate prediction of system energy. The deviation from the relative atomic force alone is insufficient to assess the accuracy of the DP models. Based on the performance of Model F, we propose that the relative magnitude of the model deviation and the corresponding root-mean-square error of the original test dataset, including energy and atomic force, can serve as an indicator for evaluating the accuracy of the model prediction for a given structure, which is particularly applicable for large systems where density functional theory calculations are infeasible. In addition to the prediction accuracy of the model described above, we also briefly discuss simulation stability and its relationship to the former. Both are important aspects in assessing the transferability of the MLP model.

Sub-Micrometer Phonon Mean Free Paths in Metal-Organic Frameworks Revealed by Machine Learning Molecular Dynamics Simulations

Metal-organic frameworks (MOFs) are a family of materials that have high porosity and structural tunability and hold great potential in various applications, many of which require a proper understanding of the thermal transport properties. Molecular dynamics (MD) simulations play an important role in characterizing the thermal transport properties of various materials. However, due to the complexity of the structures, it is difficult to construct accurate empirical interatomic potentials for reliable MD simulations of MOFs. To this end, we develop a set of accurate yet highly efficient machine-learned potentials for three typical MOFs, including MOF-5, HKUST-1, and ZIF-8, using the neuroevolution potential approach as implemented in the GPUMD package, and perform extensive MD simulations to study thermal transport in the three MOFs. Although the lattice thermal conductivity values of the three MOFs are all predicted to be smaller than 1 W/(m K) at room temperature, the phonon mean free paths (MFPs) are found to reach the sub-micrometer scale in the low-frequency region. As a consequence, the apparent thermal conductivity only converges to the diffusive limit for micrometer single crystals, which means that the thermal conductivity is heavily reduced in nanocrystalline MOFs. The sub-micrometer phonon MFPs are also found to be correlated with a moderate temperature dependence of thermal conductivity between those in typical crystalline and amorphous materials. Both the large phonon MFPs and the moderate temperature dependence of thermal conductivity fundamentally change our understanding of thermal transport in MOFs.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Lifelong Machine Learning Potentials

Machine learning potentials (MLPs) trained on accurate quantum chemical data can retain the high accuracy, while inflicting little computational demands. On the downside, they need to be trained for each individual system. In recent years, a vast number of MLPs have been trained from scratch because learning additional data typically requires retraining on all data to not forget previously acquired knowledge. Additionally, most common structural descriptors of MLPs cannot represent efficiently a large number of different chemical elements. In this work, we tackle these problems by introducing element-embracing atom-centered symmetry functions (eeACSFs), which combine structural properties and element information from the periodic table. These eeACSFs are key for our development of a lifelong machine learning potential (lMLP). Uncertainty quantification can be exploited to transgress a fixed, pretrained MLP to arrive at a continuously adapting lMLP, because a predefined level of accuracy can be ensured. To extend the applicability of an lMLP to new systems, we apply continual learning strategies to enable autonomous and on-the-fly training on a continuous stream of new data. For the training of deep neural networks, we propose the continual resilient (CoRe) optimizer and incremental learning strategies relying on rehearsal of data, regularization of parameters, and the architecture of the model.

A first-principles exploration of the conformational space of sodiated pyranose assisted by neural network potentials

Sampling the conformational space of monosaccharides using the first-principles methods is important and as a database of local minima provides a solid base for interpreting experimental measurements such as infrared photo-dissociation (IRPD) spectroscopy or collision-induced dissociation (CID). IRPD emphasizes low-energy conformers and CID can distinguish conformers with distinct reaction pathways. A typical computational approach is to engage empirical or semi-empirical methods to sample the conformational space first, and only selected minima are reoptimized at first-principles levels. In this work, we propose a computational scheme to explore the configurational space of 12 types of sodiated pyranoses with the assistance of a neural network potential (NNP). We demonstrated that it is possible to train an NNP based on the density functional calculations extracted from a previous study on sodiated glucose (Glc), galactose (Gal), and mannose (Man). This NNP yields a better description of the other five types of aldohexoses than the four types of ketohexoses. We further show that such a discrepancy in the accuracy of NNP can be resolved by an active learning scheme where the NNP model is engaged in generating the data and has itself updated. Through this iterative process, we can locate more than 17 000 distinct local minima at the B3LYP/6-311+G(d,p) level and an NNP with an accuracy of 1 kJ mol^-1 was created, which can be used for further studies.

Machine Learning in the Development of Adsorbents for Clean Energy Application and Greenhouse Gas Capture

Addressing climate change challenges by reducing greenhouse gas levels requires innovative adsorbent materials for clean energy applications. Recent progress in machine learning has stimulated technological breakthroughs in the discovery, design, and deployment of materials with potential for high-performance and low-cost clean energy applications. This review summarizes basic machine learning methods-data collection, featurization, model generation, and model evaluation-and reviews their use in the development of robust adsorbent materials. Key case studies are provided where these methods are used to accelerate adsorbent materials design and discovery, optimize synthesis conditions, and understand complex feature-property relationships. The review provides a concise resource for researchers wishing to use machine learning methods to rapidly develop effective adsorbent materials with a positive impact on the environment.

Exploring the configurational space of amorphous graphene with machine-learned atomic energies

Two-dimensionally extended amorphous carbon ("amorphous graphene") is a prototype system for disorder in 2D, showing a rich and complex configurational space that is yet to be fully understood. Here we explore the nature of amorphous graphene with an atomistic machine-learning (ML) model. We create structural models by introducing defects into ordered graphene through Monte-Carlo bond switching, defining acceptance criteria using the machine-learned local, atomic energies associated with a defect, as well as the nearest-neighbor (NN) environments. We find that physically meaningful structural models arise from ML atomic energies in this way, ranging from continuous random networks to paracrystalline structures. Our results show that ML atomic energies can be used to guide Monte-Carlo structural searches in principle, and that their predictions of local stability can be linked to short- and medium-range order in amorphous graphene. We expect that the former point will be relevant more generally to the study of amorphous materials, and that the latter has wider implications for the interpretation of ML potential models.

Metal organic frameworks as advanced functional materials for aptasensor design

BACKGROUND

Advancement in coordination chemistry has achieved an impressive development of metal organic frameworks (MOFs) as the supramolecular hybrid materials, comprising harmonized metal nodes with organic ligands. Scope and approach: MOFs offer the unique properties of easy synthesis, nanoscale structure, adjustable size and morphology, high porosity, large surface area, supreme chemical tunability and stability, and biocompatibility. The features provide an exceptional opportunity for the widely usage of MOFs in the different scientific fields, e.g. biomedicine, electrocatalysis, food safety, energy storage, environmental surveillance, and biosensing platforms. The synergistic incorporation of the aptamer advantages and the superiorities of MOFs attains the novel MOF-based aptasensors. The excellent selectivity and sensitivity of the MOF-based aptasensors nominate them as efficient lab-on-chip tools for cost-effective, label-free, portable, and real-time monitoring of diverse targets.

KEY FINDINGS AND CONCLUSIONS

Here, we review the achievements in the sensor design by cooperation of MOF motifs and aptamers with the conspicuous potential of determining the targets. Finally, some results are expressed that provide a valuable viewpoint for developing the novel MOF-based test strips in the future.

Combined Deep Learning and Classical Potential Approach for Modeling Diffusion in UiO-66

Modeling of diffusion of adsorbates through porous materials with atomistic molecular dynamics (MD) can be a challenging task if the flexibility of the adsorbent needs to be included. This is because potentials need to be developed that accurately account for the motion of the adsorbent in response to the presence of adsorbate molecules. In this work, we show that it is possible to use accurate machine learning atomistic potentials for metal-organic frameworks in concert with classical potentials for adsorbates to accurately compute diffusivities though a hybrid potential approach. As a proof-of-concept, we have developed an accurate deep learning potential (DP) for UiO-66, a metal-organic framework, and used this DP to perform hybrid potential simulations, modeling diffusion of neon and xenon through the crystal. The adsorbate-adsorbate interactions were modeled with Lennard-Jones (LJ) potentials, the adsorbent-adsorbent interactions were described by the DP, and the adsorbent-adsorbate interactions used LJ cross-interactions. Thus, our hybrid potential allows for adsorbent-adsorbate interactions with classical potentials but models the response of the adsorbent to the presence of the adsorbate through near-DFT accuracy DPs. This hybrid approach does not require refitting the DP for new adsorbates. We calculated self-diffusion coefficients for Ne in UiO-66 from DFT-MD, our hybrid DP/LJ approach, and from two different classical potentials for UiO-66. Our DP/LJ results are in excellent agreement with DFT-MD. We modeled diffusion of Xe in UiO-66 with DP/LJ and a classical potential. Diffusion of Xe in UiO-66 is about a factor of 30 slower than that of Ne, so it is not computationally feasible to compute Xe diffusion with DFT-MD. Our hybrid DP-classical potential approach can be applied to other MOFs and other adsorbates, making it possible to use an accurate DP generated from DFT simulations of an empty adsorbent in concert with existing classical potentials for adsorbates to model adsorption and diffusion within the porous material, including adsorbate-induced changes to the framework.

A neural network potential for the IRMOF series and its application for thermal and mechanical behaviors

Metal-organic frameworks (MOFs) with their exceptional porous and organized structures have been the subject of numerous applications. Predicting the bulk properties from atomistic simulations requires the most accurate force fields, which is still a major problem due to MOFs' hybrid structures governed by covalent, ionic and dispersion forces. Application of ab initio molecular dynamics to such large periodic systems is thus beyond the current computational power. Therefore, alternative strategies must be developed to reduce computational cost without losing reliability. In this work, we construct a generic neural network potential (NNP) for the isoreticular metal-organic framework (IRMOF) series trained by PBE-D4/def2-TZVP reference data of MOF fragments. We confirmed the success of the resulting NNP on both fragments and bulk MOF structures by prediction of properties such as equilibrium lattice constants, phonon density of states and linker orientation. The RMSE values of energy and force for the fragments are only 0.0017 eV atom^-1 and 0.15 eV Å^-1, respectively. The NNP predicted equilibrium lattice constants of bulk structures, even though not included in training, are off by only 0.2-2.4% from experimental results. Moreover, our fragment based NNP successfully predicts the phenylene ring torsional energy barrier, equilibrium bond distances and vibrational density of states of bulk MOFs. Furthermore, the NNP enables revealing the odd behaviors of selected MOFs such as the dual thermal expansion properties and the effect of mechanical strain on the adsorption of hydrogen and methane molecules. The NNP based molecular dynamics (MD) simulations suggest IRMOF-4 and IRMOF-7 to have positive-to-negative thermal expansion coefficients while the rest to have only negative thermal expansion at the studied temperatures of 200 K to 400 K. The deformation of the bulk structure by reduction of the unit cell volume has been shown to increase the volumetric methane uptake in IRMOF-1 but decrease the volumetric methane uptake in IRMOF-7 due to the steric hindrance. To the best of our knowledge, this study presents the first pre-trained model publicly available giving the opportunity for the researchers in the field to investigate different aspects of IRMOFs by performing large-scale simulation at the first-principles level of accuracy.

A Hessian-based assessment of atomic forces for training machine learning interatomic potentials

In recent years, many types of machine learning potentials (MLPs) have been introduced, which are able to represent high-dimensional potential-energy surfaces (PESs) with close to first-principles accuracy. Most current MLPs rely on atomic energy contributions given as a function of the local chemical environments. Frequently, in addition to total energies, atomic forces are also used to construct the potentials, as they provide detailed local information about the PES. Since many systems are too large for electronic structure calculations, obtaining reliable reference forces from smaller subsystems, such as molecular fragments or clusters, can substantially simplify the construction of the training sets. Here, we propose a method to determine structurally converged molecular fragments, providing reliable atomic forces based on an analysis of the Hessian. The method, which serves as a locality test and allows us to estimate the importance of long-range interactions, is illustrated for a series of molecular model systems and the metal–organic framework MOF-5 as an example for a complex organic–inorganic hybrid material.

Molecular Simulations to Elucidate Transport Phenomena in Polymeric Membranes

Despite decades of dominance in separation technology, progress in the design and development of high-performance polymer-based membranes has been incremental. Recent advances in materials science and chemical synthesis provide opportunities for molecular-level design of next-generation membrane materials. Such designs necessitate a fundamental understanding of transport and separation mechanisms at the molecular scale. Molecular simulations are important tools that could lead to the development of fundamental structure-property-performance relationships for advancing membrane design. In this Perspective, we assess the application and capability of molecular simulations to understand the mechanisms of ion and water transport across polymeric membranes. Additionally, we discuss the reliability of molecular models in mimicking the structure and chemistry of nanochannels and transport pathways in polymeric membranes. We conclude by providing research directions for resolving key knowledge gaps related to transport phenomena in polymeric membranes and for the construction of structure-property-performance relationships for the design of next-generation membranes.

Insights into lithium manganese oxide-water interfaces using machine learning potentials

Unraveling the atomistic and the electronic structure of solid-liquid interfaces is the key to the design of new materials for many important applications, from heterogeneous catalysis to battery technology. Density functional theory (DFT) calculations can, in principle, provide a reliable description of such interfaces, but the high computational costs severely restrict the accessible time and length scales. Here, we report machine learning-driven simulations of various interfaces between water and lithium manganese oxide (Li_xMn₂O₄), an important electrode material in lithium ion batteries and a catalyst for the oxygen evolution reaction. We employ a high-dimensional neural network potential to compute the energies and forces several orders of magnitude faster than DFT without loss in accuracy. In addition, a high-dimensional neural network for spin prediction is utilized to analyze the electronic structure of the manganese ions. Combining these methods, a series of interfaces is investigated by large-scale molecular dynamics. The simulations allow us to gain insights into a variety of properties, such as the dissociation of water molecules, proton transfer processes, and hydrogen bonds, as well as the geometric and electronic structure of the solid surfaces, including the manganese oxidation state distribution, Jahn-Teller distortions, and electron hopping.

Large-Scale Molecular Dynamics Simulations Reveal New Insights Into the Phase Transition Mechanisms in MIL-53(Al)

Soft porous crystals have the ability to undergo large structural transformations upon exposure to external stimuli while maintaining their long-range structural order, and the size of the crystal plays an important role in this flexible behavior. Computational modeling has the potential to unravel mechanistic details of these phase transitions, provided that the models are representative for experimental crystal sizes and allow for spatially disordered phenomena to occur. Here, we take a major step forward and enable simulations of metal-organic frameworks containing more than a million atoms. This is achieved by exploiting the massive parallelism of state-of-the-art GPUs using the OpenMM software package, for which we developed a new pressure control algorithm that allows for fully anisotropic unit cell fluctuations. As a proof of concept, we study the transition mechanism in MIL-53(Al) under various external pressures. In the lower pressure regime, a layer-by-layer mechanism is observed, while at higher pressures, the transition is initiated at discrete nucleation points and temporarily induces various domains in both the open and closed pore phases. The presented workflow opens the possibility to deduce transition mechanism diagrams for soft porous crystals in terms of the crystal size and the strength of the external stimulus.

Gaussian Process Regression for Materials and Molecules

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

Machine-learned potentials for next-generation matter simulations

The choice of simulation methods in computational materials science is driven by a fundamental trade-off: bridging large time- and length-scales with highly accurate simulations at an affordable computational cost. Venturing the investigation of complex phenomena on large scales requires fast yet accurate computational methods. We review the emerging field of machine-learned potentials, which promises to reach the accuracy of quantum mechanical computations at a substantially reduced computational cost. This Review will summarize the basic principles of the underlying machine learning methods, the data acquisition process and active learning procedures. We highlight multiple recent applications of machine-learned potentials in various fields, ranging from organic chemistry and biomolecules to inorganic crystal structure predictions and surface science. We furthermore discuss the developments required to promote a broader use of ML potentials, and the possibility of using them to help solve open questions in materials science and facilitate fully computational materials design.

Machine Learning Meets with Metal Organic Frameworks for Gas Storage and Separation

The acceleration in design of new metal organic frameworks (MOFs) has led scientists to focus on high-throughput computational screening (HTCS) methods to quickly assess the promises of these fascinating materials in various applications. HTCS studies provide a massive amount of structural property and performance data for MOFs, which need to be further analyzed. Recent implementation of machine learning (ML), which is another growing field in research, to HTCS of MOFs has been very fruitful not only for revealing the hidden structure-performance relationships of materials but also for understanding their performance trends in different applications, specifically for gas storage and separation. In this review, we highlight the current state of the art in ML-assisted computational screening of MOFs for gas storage and separation and address both the opportunities and challenges that are emerging in this new field by emphasizing how merging of ML and MOF simulations can be useful.

Deep Eutectic Solvents: A Review of Fundamentals and Applications

Deep eutectic solvents (DESs) are an emerging class of mixtures characterized by significant depressions in melting points compared to those of the neat constituent components. These materials are promising for applications as inexpensive "designer" solvents exhibiting a host of tunable physicochemical properties. A detailed review of the current literature reveals the lack of predictive understanding of the microscopic mechanisms that govern the structure-property relationships in this class of solvents. Complex hydrogen bonding is postulated as the root cause of their melting point depressions and physicochemical properties; to understand these hydrogen bonded networks, it is imperative to study these systems as dynamic entities using both simulations and experiments. This review emphasizes recent research efforts in order to elucidate the next steps needed to develop a fundamental framework needed for a deeper understanding of DESs. It covers recent developments in DES research, frames outstanding scientific questions, and identifies promising research thrusts aligned with the advancement of the field toward predictive models and fundamental understanding of these solvents.

Mean-field density matrix decompositions

We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.

The Role of Machine Learning in the Understanding and Design of Materials

Developing algorithmic approaches for the rational design and discovery of materials can enable us to systematically find novel materials, which can have huge technological and social impact. However, such rational design requires a holistic perspective over the full multistage design process, which involves exploring immense materials spaces, their properties, and process design and engineering as well as a techno-economic assessment. The complexity of exploring all of these options using conventional scientific approaches seems intractable. Instead, novel tools from the field of machine learning can potentially solve some of our challenges on the way to rational materials design. Here we review some of the chief advancements of these methods and their applications in rational materials design, followed by a discussion on some of the main challenges and opportunities we currently face together with our perspective on the future of rational materials design and discovery.