Optimizing cross-domain transfer for universal machine learning interatomic potentials.

High-entropy materials are characterized by their complexcompositions,typically comprising five or more elements in near-equiatomic proportions.Applying this concept to metal ions in metal–organic frameworks(MOFs) has paved the way for exploring a new class of high-entropyMOFs. While the compositional strategy of high-entropy materials leveragesconfigurational entropy to aid thermodynamic stability, it also posessignificant analytical challenges due to the vast compositional landscapeand diverse phases that these materials can adopt. We present a computationalstudy of several complexities associated with selecting potentialhigh-entropy versions of a prototype lanthanide-based MOF. We computethe energetics of metal mixing of these heterometallic MOFs usingdensity functional theory (DFT) and machine learning interatomic potential(MLIP) methods. The use of MLIP methods allows a systematic explorationof the convex hull of thermodynamically stable MOF structures containingup to 5 distinct metals.

Machine learning (ML) interatomic potentials (ML-IAPs) are generated for alkane and polyene hydrocarbons using on-the-fly adaptive sampling and a sparse Gaussian process regression (SGPR) algorithm. The ML model is generated based on the PBE+D3 level of density functional theory (DFT) with molecular dynamics (MD) for small alkane and polyene molecules. Intermolecular interactions are also trained with clusters and condensed phases of small molecules. It shows excellent transferability to long alkanes and closely describes the ab inito potential energy surface for polyenes. Simulation of liquid ethane also shows reasonable agreement with experimental reports. This is a promising initiative toward a universal ab initio quality force-field for hydrocarbons and organic molecules.

The development of differentiable invariant descriptors for accurate representations of atomic environments plays a central role in the success of interatomic potentials for chemistry and materials science. We introduce a method to generate fast proper orthogonal descriptors for the construction of many-body interatomic potentials and discuss its relation to exising empirical and machine learning interatomic potentials. A traditional way of implementing the proper orthogonal descriptors has a computational complexity that scales exponentially with the body order in terms of the number of neighbors. We present an algorithm to compute the proper orthogonal descriptors with a computational complexity that scales linearly with the number of neighbors irrespective of the body order. We show that our method can enable a more efficient implementation for a number of existing potentials and provide a scalable systematic framework to construct new many-body potentials. The new potentials are demonstrated on a data set of density functional theory calculations for Tantalum and compared with other interatomic potentials.

A combination of machine learned interatomic potentials (MLIPs) and enhanced sampling simulations is used to investigate the activation of methane on a Ni(111) surface. The work entails the development and iterative refinement of MLIPs, initially trained on a data set constructed via ab initio molecular dynamics simulations, supplemented by adaptive biasing forces, to enrich the sampling of catalytically relevant configurations. Our results reveal that upon incorporation of collective variables that capture the behavior of the reactant molecule, as well as additional frames that describe the dynamic response of the catalytic surface, it is possible to enhance considerably the accuracy of predicted energies and forces. By employing enhanced sampling schemes in the refinement of the MLIP, we systematically explore the potential energy surface, leading to a refined MLIP capable of predicting density functional theory-level energies and forces and replicating key geometric characteristics of the catalytic system. The resulting free energy landscapes at several temperatures provide a detailed view of the thermodynamics and dynamics of methane activation. Specifically, as methane approaches and dissociates on the catalytic surface, the process involves the dynamic interplay of CH4 and the Ni catalyst that includes both enthalpic and entropic contributions. The progression toward the transition state involves a CH4 moiety that is increasingly restrained in its ability to rotate or translate, while the stage following the transition state is characterized by a notable rise of the Ni atom that interacts with the cleaved C-H bond. This leads to an increase in the mobility of the adsorbed species, a feature that becomes more pronounced at higher temperatures.

Dopants can tune the performance of MoS2 in various applications, but the use of molecular dynamics simulations for doped MoS2 materials discovery is limited by the lack of multidopant interatomic potentials. Universal machine learning interatomic potentials (MLIPs) could be a solution, but the accuracy of these potentials must first be evaluated. Here, we evaluate the accuracy of a recently developed MLIP, META's Universal Model for Atoms, for 25 different MoS2 dopants spanning metals, nonmetals, and transition metals in Mo-substitution, S-substitution, and intercalated positions by benchmarking the MLIP-predicted formation energy and the dopant-induced structural change against density functional theory (DFT) calculations. The computational framework for MLIP validation and simulations is described in detail, and the source code is made available online. The MLIP is then demonstrated by performing heating-cooling simulations of MoS2 supercells with all 25 dopants. These simulations capture complex phenomena including dopant clustering, MoS2 layer fracturing, interlayer diffusion, and chemical compound formation at orders-of-magnitude reduced computational cost compared to DFT. This work provides a computational workflow for the application-oriented design of doped-MoS2, enabling high-throughput screening of dopant candidates and optimization of compositions for targeted tribological, electronic, and optoelectronic performance.

The vast combinatorial space of metal-organic frameworks (MOFs) has led to their widespread consideration across diverse application areas. That said, much remains unknown about what factors govern their thermodynamic stability. Herein, we use density functional theory to compute the formation energy and construct convex hull phase diagrams for 20,000+ MOFs and coordination polymers. Using the energy above hull as a measure of stability with respect to decomposition and phase transitions, we validate and expand upon previous hypotheses that all MOFs are thermodynamically metastable and that there is an inherent energetic penalty associated with permanent porosity. We also describe how MOF composition and metal/linker identity influence the degree of metastability, in addition to demonstrating how the energy above hull can be used as a synthesizability metric for newly proposed MOFs. To democratize the knowledge gained from our study, we have released the QMOF-Thermo Database, which is the first database of energy above hull values for MOFs and coordination polymers. We conclude by using the QMOF-Thermo Database to benchmark the ability of pretrained machine learning interatomic potentials to predict the energy above hull of MOFs, and we identify opportunities to correct their performance.

The emergence of Δ-learning models, whereby machine learning (ML) is used to predict a correction to a low-level energy calculation, provides a versatile route to accelerate high-level energy evaluations at a given geometry. However, Δ-learning models are inapplicable to reaction properties like heats of reaction and activation energies that require both a high-level geometry and energy evaluation. Here, a Δ2-learning model is introduced that can predict high-level activation energies based on low-level critical-point geometries. The Δ2 model uses an atom-wise featurization typical of contemporary ML interatomic potentials (MLIPs) and is trained on a dataset of ∼167 000 reactions, using the GFN2-xTB energy and critical-point geometry as a low-level input and the B3LYP-D3/TZVP energy calculated at the B3LYP-D3/TZVP critical point as a high-level target. The excellent performance of the Δ2 model on unseen reactions demonstrates the surprising ease with which the model implicitly learns the geometric deviations between the low-level and high-level geometries that condition the activation energy prediction. The transferability of the Δ2 model is validated on several external testing sets where it shows near chemical accuracy, illustrating the benefits of combining ML models with readily available physical-based information from semi-empirical quantum chemistry calculations. Fine-tuning of the Δ2 model on a small number of Gaussian-4 calculations produced a 35% accuracy improvement over DFT activation energy predictions while retaining xTB-level cost. The Δ2 model approach proves to be an efficient strategy for accelerating chemical reaction characterization with minimal sacrifice in prediction accuracy.

Machine learning interatomic potentials (MLIPs) enable more efficient molecular dynamics (MD) simulations with ab initio accuracy, which have been used in various domains of physical science. However, distribution shift between training and test data causes deterioration of the test performance of MLIPs, and even leads to collapse of MD simulations. In this work, we propose an online Test-time Adaptation Interatomic Potential (TAIP) framework to improve the generalization on test data. Specifically, we design a dual-level self-supervised learning approach that leverages global structure and atomic local environment information to align the model with the test data. Extensive experiments demonstrate TAIP’s capability to bridge the domain gap between training and test dataset without additional data. TAIP enhances the test performance on various benchmarks, from small molecule datasets to complex periodic molecular systems with various types of elements. TAIP also enables stable MD simulations where the corresponding baseline models collapse.

We introduce a new class of machine learning interatomic potentials---fast general two- and three-body potential (GTTP), which is as fast as conventional empirical potentials and require computational time that remains constant with increasing fitting flexibility. GTTP does not contain any assumptions about the functional form of two- and three-body interactions. These interactions can be modeled arbitrarily accurately, potentially by thousands of parameters not affecting resulting computational cost. Time complexity is O(1) per every considered pair or triple of atoms. The fitting procedure is reduced to simple linear regression on ab initio calculated energies and forces and leads to effective two- and three-body potential, reproducing quantum many-body interactions as accurately as possible. Our potential can be made continuously differentiable any number of times at the expense of increased computational time. We made a number of performance tests on one-, two- and three-component systems. The flexibility of the introduced approach makes the potential transferable in terms of size and type of atomic systems as long as they involve the same atomic species. We show that trained on randomly generated structures with just eight atoms in the unit cell, it significantly outperforms common empirical interatomic potentials in the study of large systems, such as grain boundaries in polycrystalline materials.

Efficiently creating a concise but comprehensive data set for training machine-learned interatomic potentials (MLIPs) is an under-explored problem. Active learning, which uses biased or unbiased molecular dynamics (MD) to generate candidate pools, aims to address this objective. Existing biased and unbiased MD-simulation methods, however, are prone to miss either rare events or extrapolative regions—areas of the configurational space where unreliable predictions are made. This work demonstrates that MD, when biased by the MLIP’s energy uncertainty, simultaneously captures extrapolative regions and rare events, which is crucial for developing uniformly accurate MLIPs. Furthermore, exploiting automatic differentiation, we enhance bias-forces-driven MD with the concept of bias stress. We employ calibrated gradient-based uncertainties to yield MLIPs with similar or, sometimes, better accuracy than ensemble-based methods at a lower computational cost. Finally, we apply uncertainty-biased MD to alanine dipeptide and MIL-53(Al), generating MLIPs that represent both configurational spaces more accurately than models trained with conventional MD.

Graph Neural Networks (GNNs) have proven effective and typically benefit from pre-training on accessible graphs to enhance performance on tasks with limited labeled data. However, existing GNNs are constrained by the ``one-domain-one-model'' limitation, which restricts their effectiveness across diverse graph domains. In this paper, we tackle this problem by developing a method called Multi-Domain Pre-training for a Unified GNN Model (MDP-GNN). This method is based on the philosophical notion that everything is interconnected, suggesting that a latent meta-domain exists to encompass the diverse graph domains and their interconnections. MDP-GNN seeks to identify and utilize this meta-domain to train a unified GNN model through three core strategies. Firstly, it integrates node feature semantics from different domains to create unified representations. Secondly, it employs a bi-level learning strategy to build a domain-synthesized network that identifies latent connections to facilitate cross-domain knowledge transfer. Thirdly, it uses Wasserstein distance to map diverse domains into the common meta-domain for graph distribution alignment. We validate the effectiveness of MDP-GNN through theoretical analysis and extensive experiments on four real-world graph datasets, showing its superiority in enhancing GNN performance across diverse domains.

Lithium-based disordered rocksalts (LDRs), which are an important class of positive electrode materials that can increase the energy density of current Li-ion batteries, represent a significantly complex chemical and configurational space for conventional density functional theory (DFT)-based high-throughput screening approaches. Notably, atom-centered machine-learned interatomic potentials (MLIPs) are a promising pathway to accurately model the potential energy surface of highly disordered chemical spaces, such as LDRs, where the performance of such MLIPs has not been rigorously explored yet. Here, we represent a comprehensive evaluation of the accuracy, transferability, and ease of training of five atom-centered MLIPs, including the artificial neural network potentials developed by the atomic energy network (AENET), the Gaussian approximation potential (GAP), the spectral neighbor analysis potential (SNAP) and its quadratic extension (qSNAP), and the moment tensor potential (MTP), in modeling a 11-component LDR chemical space. Specifically, we generate a DFT-calculated data set of 10,842 configurations of disordered LiTMO2 and TMO2 compositions, where TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and/or Cu. To provide a point-of-comparison on the performance of atom-centered MLIPs, we also trained the neural equivariant interatomic potential (NequIP) on a subset of our data. Importantly, we find AENET to be the best potential in terms of accuracy and transferability for energy predictions, while MTP is the best for atomic forces. While AENET is the fastest to train among the MLIPs considered at low number of epochs (300), the training time increases significantly as epochs increase (3300), with a corresponding reduction in training errors (∼60%). Note that AENET and GAP tend to overfit in small data sets, with the extent of overfitting reducing with larger data sets. Finally, we observe AENET to provide reasonable predictions of average Li-intercalation voltages in layered, single-TM LiTMO2 frameworks, compared to DFT (∼10% error on average). Our study should pave the way both for discovering novel disordered rocksalt electrodes and for modeling other configurationally complex systems, such as high-entropy ceramics and alloys.

ConspectusMetal-organic frameworks (MOFs) represent a sophisticated blend of inorganic and organic components, promoting the development of coordination chemistry greatly and offering a versatile platform for tailored functionalities. By combining various metal nodes, organic linkers, and functional guests, MOFs provide numerous pathways for their design, synthesis, and customization. Among these, sequential linker installation (SLI) stands out as a novel and crucial strategy, enabling the precise integration of desired properties and functions at the atomic scale. SLI enhances structural diversity and stability while facilitating the meticulous construction of robust frameworks by leveraging open metal sites and functional organic linkers at targeted locations. Compared to the direct synthesis of MOFs, postsynthetic modification methods allow for precise regulation of their structures and corresponding properties. While unlike conventional postsynthetic modification methods, SLI requires the careful selection of linkers and framework design to ensure precise positioning for installation, which gives rise to the well-designed and ordered positions for the installed linkers, confirmed directly by X-ray diffraction technology.Recent advancements in MOF synthesis have led to the creation of increasingly tailored flexible matrix structures, particularly due to the diverse connection modes of multicore metal clusters, especially for the Zr6 cluster. The spatial hindrance of certain ligands has resulted in the formation of unsaturated metal clusters and various missing linker pockets. Examples of these advanced MOFs include PCN-606, PCN-608, PCN-609, PCN-700, and PCN-808, which feature specific open metal sites and certain framework flexibility conducive to SLI. Strategically positioned open metal sites within these frameworks serve as predetermined anchor points for desired functional molecules, while the frameworks' flexibility can accommodate molecules of varying sizes to a certain extent, enlarging the scopes of application greatly. This precise positioning of functional groups enables the creation of tailored sites for enhanced applications, such as adsorption, catalysis, and recognition.In this Account, we delve into the intricate process of designing and synthesizing MOFs with appropriate missing-linker pockets for the aforementioned applications. We discuss the meticulous selection of functional linkers and the methods used to insert them into the corresponding missing-linker pockets within the MOFs. Additionally, we explore the diverse properties and functionalities of the resulting MOFs, focusing on their adsorptive, catalytic, and recognition performance. Furthermore, we provide insights into the future trajectory of SLI methods, complemented by our recent works. This Account not only reviews the evolution of the SLI method but also underscores its practical applications across various functional domains, paving a rational pathway for the future development of advanced multifunctional MOFs through this method.

The suppression of heat transport in disordered crystals arises from a competition between mass fluctuations and bond disorder, but their relative contributions remain difficult to disentangle. We address this challenge using a machine-learned interatomic potential trained on ab initio data across the PbTe1-xSex alloy series. Molecular dynamics simulations with the trained machine-learned interatomic potential reproduce experimental lattice thermal conductivities and density-functional theory phonon dispersions while enabling frequency-resolved analysis of heat transport from 300 to 800 K. We find a narrow window near 1.7-2.0 THz dominates heat transport across all compositions, where heat is primarily carried by mixed longitudinal acoustic and optical modes. Alloying dramatically reduces spectral diffusivity near 2 THz leading to the deterioration of thermal conductivity. For the parent compounds both the spectral diffusivity and overall thermal conductivity decrease at elevated temperatures. However, the thermal degradation is weaker for the mid-range composition (x = 0.5) due to the greater thermal occupation of vibrational modes and increased heat capacity. Alchemical simulations show that force-constant disorder, not mass contrast, plays the dominant role in this suppression. These results highlight the microscopic mechanisms underlying thermal transport breakdown in alloys and demonstrate how machine-learned interatomic potentials now offer a tractable path toward predictive, physics-rich thermal transport modeling in complex disordered solids.

Photodynamic therapy (PDT), a minimally invasive and effective local treatment, heavily depends on photosensitizer (PS) performance and oxygen availability. Despite the use of PS-based metal-organic frameworks (MOFs) to address the solubility and aggregation issues of PSs, the inherent hypoxic intolerance of mainstream Type II PDT remains challenging. Herein, we report an electron transfer strategy for the fabrication of hypoxia-tolerant Type I MOFs by encapsulating thymoquinone (TQ) into existing Type II MOFs. With TQ serving as an effective electron transfer mediator, it facilitates the electron transfer process from the MOF ligand PS to oxygen, establishing the Type I pathway and attenuating the original Type II pathway. Four representative porphyrin-based MOFs are synthesized to demonstrate the proposed strategy. Our findings reveal that TQ@MOF-1 nanoparticles (NPs) exhibit enhanced anticancer activity under hypoxic conditions and superior in vivo antitumor efficacy compared to parent MOF-1 NPs. This work offers an effective and universal strategy to modulate ROS generation in PS-based MOFs, endowing hypoxic tolerance with improved PDT performance against solid tumors.