Daily Papers

We present two new interatomic potentials for platinum (Pt) in angular-dependent potential (ADP) and modified Tersoff (MT) formats. Both potentials have been trained on a reference database of first-principles calculations without using experimental data. The properties of Pt predicted by the ADP and MT potentials agree better with DFT calculations and experimental data than the potentials available in the literature. Future applications of the MT model to mixed-bonding metal-covalent systems are discussed.

Foundational machine learning interatomic potentials that can accurately and efficiently model a vast range of materials are critical for accelerating atomistic discovery. We introduce universal potentials based on the graph atomic cluster expansion (GRACE) framework, trained on several of the largest available materials datasets. Through comprehensive benchmarks, we demonstrate that the GRACE models establish a new Pareto front for accuracy versus efficiency among foundational interatomic potentials. We further showcase their exceptional versatility by adapting them to specialized tasks and simpler architectures via fine-tuning and knowledge distillation, achieving high accuracy while preventing catastrophic forgetting. This work establishes GRACE as a robust and adaptable foundation for the next generation of atomistic modeling, enabling high-fidelity simulations across the periodic table.

Machine learning potentials (MLPs) have become essential for large-scale atomistic simulations, enabling ab initio-level accuracy with computational efficiency. However, current MLPs struggle with uncertainty quantification, limiting their reliability for active learning, calibration, and out-of-distribution (OOD) detection. We address these challenges by developing Bayesian E(3) equivariant MLPs with iterative restratification of many-body message passing. Our approach introduces the joint energy-force negative log-likelihood (NLL_JEF) loss function, which explicitly models uncertainty in both energies and interatomic forces, yielding superior accuracy compared to conventional NLL losses. We systematically benchmark multiple Bayesian approaches, including deep ensembles with mean-variance estimation, stochastic weight averaging Gaussian, improved variational online Newton, and laplace approximation by evaluating their performance on uncertainty prediction, OOD detection, calibration, and active learning tasks. We further demonstrate that NLL_JEF facilitates efficient active learning by quantifying energy and force uncertainties. Using Bayesian active learning by disagreement (BALD), our framework outperforms random sampling and energy-uncertainty-based sampling. Our results demonstrate that Bayesian MLPs achieve competitive accuracy with state-of-the-art models while enabling uncertainty-guided active learning, OOD detection, and energy/forces calibration. This work establishes Bayesian equivariant neural networks as a powerful framework for developing uncertainty-aware MLPs for atomistic simulations at scale.

Molecular dynamics simulation of plasma-surface interactions requires an interatomic potential that is simultaneously accurate, computationally efficient, and able to describe many elements and bonding types in reactive systems. In principle, a foundation model for machine-learned interatomic potential (MLIP) can meet these demands. We explore the use of the Universal Models for Atoms (UMA) model, developed by Meta FAIR, for the interactions of oxygen plasma species on a multilayer of WS_2, a promising 2D material. Starting from the pretrained uma-s-1p1 model under the Open Catalyst 2020 (OC20) task, we apply an iterative fine-tuning loop with maximally diverse configuration sampling using Smooth Overlap of Atomic Positions (SOAP) and Farthest Point Sampling (FPS); DFT labeling at the PBE+D3+U+spin level; and fine-tuning on energy, force, and stress labels. Even in the absence of fine-tuning, the pretrained model reproduces the production-scale observables of interest, namely, chemisorbed S and O coverage under 15eV O^+ and O_2^+ bombardment. These results were obtained without spin polarization and Hubbard U correction. Nonetheless, fine-tuning reduces the energy and force mean absolute error (MAE) to 4.5times10^{-3}eV/atom and 0.076eV/angstrom, respectively.

Most machine-learning interatomic potentials (MLIPs) are trained on gas-phase data, which limits their use for chemistry in solution. Here, we introduce AnySolv, a transferable implicit solvation potential that provides solvent-dependent energy and force corrections to existing gas-phase potentials without retraining them. It is trained on 1.4 million solvation energies and forces computed with density functional theory (DFT) and SMD in 36 solvents, spanning charged, open-shell, and transition-state structures. Because solvents are represented by continuous physical descriptors, AnySolv supports 179 solvents, including those absent from training. On external benchmarks, AnySolv reproduces DFT-SMD solvation energies to 2-4 meV mean absolute error at more than three orders of magnitude lower cost, and it matches the accuracy of DFT-SMD against experimental solvation free energies. This enables screening of the mechanisms of 120 nucleophilic aromatic substitution reactions in six phases as well as molecular dynamics simulations that reproduce the experimentally observed solvent-dependent conformational preferences of alanine dipeptide. By providing transferable solvation corrections to existing MLIPs, AnySolv enables scalable simulations of solvent-dependent chemical reactivity and molecular dynamics.

Machine learning interatomic potentials (MLIPs) have become increasingly effective at approximating quantum mechanical calculations at a fraction of the computational cost. However, lower errors on held out test sets do not always translate to improved results on downstream physical property prediction tasks. In this paper, we propose testing MLIPs on their practical ability to conserve energy during molecular dynamic simulations. If passed, improved correlations are found between test errors and their performance on physical property prediction tasks. We identify choices which may lead to models failing this test, and use these observations to improve upon highly-expressive models. The resulting model, eSEN, provides state-of-the-art results on a range of physical property prediction tasks, including materials stability prediction, thermal conductivity prediction, and phonon calculations.

Computational quantum chemistry plays a critical role in drug discovery, chemical synthesis, and materials science. While first-principles methods, such as density functional theory (DFT), provide high accuracy in modeling electronic structures and predicting molecular properties, they are computationally expensive. Machine learning interatomic potentials (MLIPs) have emerged as promising surrogate models that aim to achieve DFT-level accuracy while enabling efficient large-scale atomistic simulations. The development of accurate and transferable MLIPs requires large-scale, high-quality datasets with both energy and force labels. Critically, MLIPs must generalize not only to stable geometries but also to intermediate, non-equilibrium conformations encountered during atomistic simulations. In this work, we introduce PubChemQCR, a large-scale dataset of molecular relaxation trajectories curated from the raw geometry optimization outputs of the PubChemQC project. PubChemQCR is the largest publicly available dataset of DFT-based relaxation trajectories for small organic molecules, comprising approximately 3.5 million trajectories and over 300 million molecular conformations computed at various levels of theory. Each conformation is labeled with both total energy and atomic forces, making the dataset suitable for training and evaluating MLIPs. To provide baselines for future developments, we benchmark nine representative MLIP models on the dataset. Our resources are publicly available at https://huggingface.co/divelab

Machine learning interatomic potentials (MLIPs) have revolutionized molecular and materials modeling, but existing benchmarks suffer from data leakage, limited transferability, and an over-reliance on error-based metrics tied to specific density functional theory (DFT) references. We introduce MLIP Arena, a benchmark platform that evaluates force field performance based on physics awareness, chemical reactivity, stability under extreme conditions, and predictive capabilities for thermodynamic properties and physical phenomena. By moving beyond static DFT references and revealing the important failure modes of current foundation MLIPs in real-world settings, MLIP Arena provides a reproducible framework to guide the next-generation MLIP development toward improved predictive accuracy and runtime efficiency while maintaining physical consistency. The Python package and online leaderboard are available at https://github.com/atomind-ai/mlip-arena.

Machine Learning Interatomic Potentials (MLIP) are a novel in silico approach for molecular property prediction, creating an alternative to disrupt the accuracy/speed trade-off of empirical force fields and density functional theory (DFT). In this white paper, we present our MLIP library which was created with two core aims: (1) provide to industry experts without machine learning background a user-friendly and computationally efficient set of tools to experiment with MLIP models, (2) provide machine learning developers a framework to develop novel approaches fully integrated with molecular dynamics tools. The library includes in this release three model architectures (MACE, NequIP, and ViSNet), and two molecular dynamics (MD) wrappers (ASE, and JAX-MD), along with a set of pre-trained organics models. The seamless integration with JAX-MD, in particular, facilitates highly efficient MD simulations, bringing MLIP models significantly closer to industrial application. The library is available on GitHub and on PyPI under the Apache license 2.0.

Machine learning interatomic potentials (MLIPs) enable large-scale atomistic simulations but remain challenged in describing mixed-valence materials where charge ordering strongly influences thermodynamic stability. Here we investigate the role of electronic entropy in MLIP structural optimization of the battery cathode material NaFePO4. We show that conventional MLIPs fail to reproduce the correct stability of intermediate Na concentrations because structural optimization leads to incorrect Fe^{2+}/Fe^{3+} charge assignments, resulting in erroneous energy ordering and convex-hull predictions. Analysis of magnetic moments during structural optimization reveals that MLIPs are unable to capture electronic entropy associated with charge ordering. To address this limitation, we introduce an approach that embeds charge-state information directly into the MLIP representation by distinguishing between Fe^{2+} and Fe^{3+} environments during training. Retraining CHGNet, cPaiNN, and MACE with this representation enables accurate structural optimization, correct identification of charge ordering, and improved agreement with density functional theory convex hulls. Our results demonstrate that incorporating electronic entropy into MLIP representations is essential for modeling charge-disordered materials and provide a practical framework for extending MLIP simulations to mixed-valence transition-metal systems.

Machine-learning interatomic potentials now approach quantum-mechanical accuracy on standard benchmarks, but the training cost of the most expressive equivariant architectures has become a serious bottleneck. We introduce DPA4, an SE(3)-equivariant interatomic-potential architecture with an EMFA (Edge-conditioned, Multi-Focus, Attention) SO(2)-equivariant convolution that combines a low-rank edge-node SO(2)-equivariant product, a multi-focus design for message nonlinearity, and envelope-gated attention for message aggregation. A Lebedev-grid projection further preserves SO(3)-equivariance in the nonlinearity to machine precision. A compiler-friendly conservative energy-gradient training path provides up to sim3 times wall-clock speedup under torch compile. On the compliant Matbench Discovery benchmark, DPA4-Pro attains the best Combined Performance Score (CPS) on the leaderboard, while the 2.76M-parameter DPA4-Air exceeds the accuracy of the 30.1M-parameter eSEN-30M-MP baseline with 10.9times fewer parameters and 42.9times less training compute. On SPICE-MACE-OFF, the 5.4M-parameter DPA4-Plus lowers the aggregate molecular energy and force errors of the 6.5M-parameter eSEN baseline by 29% and 30%, while the 2.7M-parameter DPA4-Air still surpasses that baseline with sim2.4times fewer parameters. Together these results place DPA4 on a new accuracy-cost Pareto frontier on Matbench Discovery and position it as a strong candidate backbone for future multi-task large atomistic model (LAM) pretraining.

Machine-learned interatomic potentials are revolutionising atomistic materials simulations by providing accurate and scalable predictions within the scope covered by the training data. However, generation of an accurate and robust training data set remains a challenge, often requiring thousands of first-principles calculations to achieve high accuracy. Foundation models have started to emerge with the ambition to create universally applicable potentials across a wide range of materials. While foundation models can be robust and transferable, they do not yet achieve the accuracy required to predict reaction barriers, phase transitions, and material stability. This work demonstrates that foundation model potentials can reach chemical accuracy when fine-tuned using transfer learning with partially frozen weights and biases. For two challenging datasets on reactive chemistry at surfaces and stability and elastic properties of tertiary alloys, we show that frozen transfer learning with 10-20% of the data (hundreds of datapoints) achieves similar accuracies to models trained from scratch (on thousands of datapoints). Moreover, we show that an equally accurate, but significantly more efficient surrogate model can be built using the transfer learned potential as the ground truth. In combination, we present a simulation workflow for machine learning potentials that improves data efficiency and computational efficiency.

The rapid development of universal machine learning interatomic potentials (uMLIPs) has demonstrated the possibility for generalizable learning of the universal potential energy surface. In principle, the accuracy of uMLIPs can be further improved by bridging the model from lower-fidelity datasets to high-fidelity ones. In this work, we analyze the challenge of this transfer learning problem within the CHGNet framework. We show that significant energy scale shifts and poor correlations between GGA and r^2SCAN pose challenges to cross-functional data transferability in uMLIPs. By benchmarking different transfer learning approaches on the MP-r^2SCAN dataset of 0.24 million structures, we demonstrate the importance of elemental energy referencing in the transfer learning of uMLIPs. By comparing the scaling law with and without the pre-training on a low-fidelity dataset, we show that significant data efficiency can still be achieved through transfer learning, even with a target dataset of sub-million structures. We highlight the importance of proper transfer learning and multi-fidelity learning in creating next-generation uMLIPs on high-fidelity data.

Fundamental tasks in computational chemistry, from transition state search to vibrational analysis, rely on molecular Hessians, which are the second derivatives of the potential energy. Yet, Hessians are computationally expensive to calculate and scale poorly with system size, with both quantum mechanical methods and neural networks. In this work, we demonstrate that Hessians can be predicted directly from a deep learning model, without relying on automatic differentiation or finite differences. We observe that one can construct SE(3)-equivariant, symmetric Hessians from irreducible representations (irrep) features up to degree l=2 computed during message passing in graph neural networks. This makes HIP Hessians one to two orders of magnitude faster, more accurate, more memory efficient, easier to train, and enables more favorable scaling with system size. We validate our predictions across a wide range of downstream tasks, demonstrating consistently superior performance for transition state search, accelerated geometry optimization, zero-point energy corrections, and vibrational analysis benchmarks. We open-source the HIP codebase and model weights to enable further development of the direct prediction of Hessians at https://github.com/BurgerAndreas/hip

SO(3)-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks in which CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of SO(3)-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the O(L^3) CG paths into a single shared parameter set without compromising equivariance, where L is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from O(L^6) to O(L^4). We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS/tree/main/OpenMol/TDN{https://github.com/divelab/AIRS/}).

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries -- permutation, rotation, and translation -- for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions must be modified, and each layer must handle multiple data types for different harmonic orders. We present Facet, a GNN architecture for efficient ML potentials, developed through systematic analysis of steerable GNNs. Our innovations include replacing expensive multi-layer perceptrons (MLPs) for interatomic distances with splines, which match performance while cutting computational and memory demands. We also introduce a general-purpose equivariant layer that mixes node information via spherical grid projection followed by standard MLPs -- faster than tensor products and more expressive than linear or gate layers. On the MPTrj dataset, Facet matches leading models with far fewer parameters and under 10% of their training compute. On a crystal relaxation task, it runs twice as fast as MACE models. We further show SevenNet-0's parameters can be reduced by over 25% with no accuracy loss. These techniques enable more than 10x faster training of large-scale foundation models for ML potentials, potentially reshaping computational materials discovery.

Atomistic modeling of solid-solid battery interfaces is essential for understanding electro-chemo-mechanical coupling, but the complex interfacial chemistry and heterogeneous environments pose major challenges for quantum-accurate, data-efficient modeling. Herein, we propose an approach of fine-tuning with integrated replay and efficiency (FIRE), a general framework for universal machine-learning interatomic potentials by combining efficient configurational sampling with a replay-argumented continual strategy, achieving quantum-level accuracy at moderate cost. Across six solid-solid battery interface systems, FIRE consistently achieves root-mean-square errors in energy below 1 meV/atom and in force near 20 meV/angstrom, marking an order-of-magnitude improvement over existing models while requiring only 10% of the original datasets. In addition, the fine-tuned model successfully reproduces key mechanical and electrochemical properties of the materials, in close agreement with experimental data. The FIRE offers a generalizable and data-efficient approach for developing accurate interatomic potentials across diverse materials, enabling predictive simulations beyond the reach of first-principles methods.

Scaling has been critical in improving model performance and generalization in machine learning. It involves how a model's performance changes with increases in model size or input data, as well as how efficiently computational resources are utilized to support this growth. Despite successes in other areas, the study of scaling in Neural Network Interatomic Potentials (NNIPs) remains limited. NNIPs act as surrogate models for ab initio quantum mechanical calculations. The dominant paradigm here is to incorporate many physical domain constraints into the model, such as rotational equivariance. We contend that these complex constraints inhibit the scaling ability of NNIPs, and are likely to lead to performance plateaus in the long run. In this work, we take an alternative approach and start by systematically studying NNIP scaling strategies. Our findings indicate that scaling the model through attention mechanisms is efficient and improves model expressivity. These insights motivate us to develop an NNIP architecture designed for scalability: the Efficiently Scaled Attention Interatomic Potential (EScAIP). EScAIP leverages a multi-head self-attention formulation within graph neural networks, applying attention at the neighbor-level representations. Implemented with highly-optimized attention GPU kernels, EScAIP achieves substantial gains in efficiency--at least 10x faster inference, 5x less memory usage--compared to existing NNIPs. EScAIP also achieves state-of-the-art performance on a wide range of datasets including catalysts (OC20 and OC22), molecules (SPICE), and materials (MPTrj). We emphasize that our approach should be thought of as a philosophy rather than a specific model, representing a proof-of-concept for developing general-purpose NNIPs that achieve better expressivity through scaling, and continue to scale efficiently with increased computational resources and training data.

No interatomic potential has offered universality across chemistry, near-first-principles accuracy and the speed of empirical potentials at once. Here we introduce DPA4C, an equivariant potential whose architecture and compressed CUDA operators are co-designed under deployment constraints to pursue accuracy and efficiency together. Five variants spanning a 49-fold parameter range form the high-throughput end of the measured accuracy--throughput frontier. The largest variant approaches the accuracy of the MACE-Omat models at about two orders of magnitude higher measured throughput. The most compact reduces the energy, force and stress errors of the fastest existing universal MLIP by 61.4%, 48.1% and 34.3% at 1.92 times its saturated throughput. All five variants complete multimillion-atom simulations on a single GPU and run molecular dynamics for 2.048 billion atoms on 1,024 16-GB NVIDIA V100 GPUs at 83.3--91.2% weak-scaling efficiency. Compared with the MEAM empirical potential, DPA4C-Nano reaches 1.8 and 2.5 times the saturated throughput in single-GPU scans on the same V100 hardware for diamond carbon and FCC copper, respectively. DPA4C therefore brings quantum-trained universal accuracy into a regime of speed and system size previously associated with empirical potentials.

Accurate potential energy surface (PES) descriptions are essential for atomistic simulations of materials. Universal machine learning interatomic potentials (UMLIPs)^{1-3} offer a computationally efficient alternative to density functional theory (DFT)^4 for PES modeling across the periodic table. However, their accuracy today is fundamentally constrained due to a reliance on DFT relaxation data.^{5,6} Here, we introduce MatPES, a foundational PES dataset comprising sim 400,000 structures carefully sampled from 281 million molecular dynamics snapshots that span 16 billion atomic environments. We demonstrate that UMLIPs trained on the modestly sized MatPES dataset can rival, or even outperform, prior models trained on much larger datasets across a broad range of equilibrium, near-equilibrium, and molecular dynamics property benchmarks. We also introduce the first high-fidelity PES dataset based on the revised regularized strongly constrained and appropriately normed (r^2SCAN) functional^7 with greatly improved descriptions of interatomic bonding. The open source MatPES initiative emphasizes the importance of data quality over quantity in materials science and enables broad community-driven advancements toward more reliable, generalizable, and efficient UMLIPs for large-scale materials discovery and design.

Machine-learned interatomic potentials trained across the periodic table have made atomistic simulation broadly accessible, and specializing them to a single compound class is widely expected to improve accuracy. Yet examples remain scarce, and fewer still surpass universal models in speed or reach a higher level of electronic-structure theory. Here we present a potential that is universal within the class of water-free solid-state hydrogen-bond network mediated proton conductors rather than across chemistry and a database of 4.4 million first-principles configurations spanning 55 materials. It surpasses leading general-purpose potentials across this domain, recovering measured activation energies and the ordering of anion rotational dynamics that those models miss; agreement on static structure does not imply agreement on transport. Accuracy falls for compositions far from the training set but stays competitive for close structural relatives, and a higher level of electronic-structure theory is reached with a few hundred additional configurations per material. We further introduce a compact variant carrying a fifth of the parameters, faster still and yet more accurate than every general-purpose model tested. It sustains more than a quarter of a million atoms on a single graphics processor, placing grain boundaries and the transition into the highly conducting phase within reach, and making a quantum treatment of the protons affordable. Reference accuracy and accessible system size thus become largely independent, offering a template for other compound classes.

Machine learning interatomic potentials (MLIPs) balance high accuracy and lower costs compared to density functional theory calculations, but their performance often depends on the size and diversity of training datasets. Large datasets improve model accuracy and generalization but are computationally expensive to produce and train on, while smaller datasets risk discarding rare but important atomic environments and compromising MLIP accuracy/reliability. Here, we develop an information-theoretical framework to quantify the efficiency of dataset compression methods and propose an algorithm that maximizes this efficiency. By framing atomistic dataset compression as an instance of the minimum set cover (MSC) problem over atom-centered environments, our method identifies the smallest subset of structures that contains as much information as possible from the original dataset while pruning redundant information. The approach is extensively demonstrated on the GAP-20 and TM23 datasets, and validated on 64 varied datasets from the ColabFit repository. Across all cases, MSC consistently retains outliers, preserves dataset diversity, and reproduces the long-tail distributions of forces even at high compression rates, outperforming other subsampling methods. Furthermore, MLIPs trained on MSC-compressed datasets exhibit reduced error for out-of-distribution data even in low-data regimes. We explain these results using an outlier analysis and show that such quantitative conclusions could not be achieved with conventional dimensionality reduction methods. The algorithm is implemented in the open-source QUESTS package and can be used for several tasks in atomistic modeling, from data subsampling, outlier detection, and training improved MLIPs at a lower cost.

Machine-learning interatomic potentials have become indispensable tools in atomistic simulations. The most popular models rely heavily on physical priors, such as locality, smoothness and symmetry, that are assumed to improve the accuracy and transferability of the trained models. However, recent evidence suggests that, in the data-rich regime, unconstrained models that learn symmetry from the data can achieve very competitive accuracy and computational efficiency, without sacrificing stability and generalization power. Many equivariant symmetric architectures historically rely on the assumption that the interatomic potential can be approximated well by a convergentcluster expansion, i.e., a decomposition in terms associated to atomic pairs, triplets, quadruplets, and higher-order tuples. We describe an architecture that incorporates locality, smoothness, and symmetry priors, but that -- thanks to a computationally efficient tensor product formulation -- does not assume low-order truncation of the body-ordered series.

Machine-learned interatomic potentials distilled from foundation models enable fast large-scale molecular dynamics (MD), but they can fail locally in chemical environments that their training data did not sample. System-averaged error metrics and small random audits often miss such sparse or isolated failures. Here we use an exact equivariant foundation model, MACE-MPA-0, to check every atom of million-atom production simulations. Reorganizing two-layer MACE inference into a receiver-chunked three-pass schedule that keeps no per-edge intermediates resident reduces the marginal memory per atom 340-fold, evaluates up to 2.86times10^{7} atoms on a single H200 GPU, and supervises 10^{6}-atom trajectories in LAMMPS at 1.3% of the run time. Distilled MACE students run four to nine times slower than NEP89 with 0.95-1.28 times the teacher's force error against density functional theory (DFT). In molten SiO_2, whole-system checks uncover a persistent tail of under-coordinated atoms hidden by the system-averaged error and an isolated, unphysical O-O contact that a 1% random audit misses 94% of the time. On-the-fly retraining on teacher-labelled 13-Å clusters, with the force loss restricted to their inner 6 Å, removes three quarters of the failure tail and the kilobar-level pressure biases in SiO_2 and compressed water; the repair converges to the teacher, not to DFT.

Accurately modeling chemical reactions at the atomistic level requires high-level electronic structure theory due to the presence of unpaired electrons and the need to properly describe bond breaking and making energetics. Commonly used approaches such as Density Functional Theory (DFT) frequently fail for this task due to deficiencies that are well recognized. However, for high-fidelity approaches, creating large datasets of energies and forces for reactive processes to train machine learning interatomic potentials or force fields is daunting. For example, the use of the unrestricted coupled cluster level of theory has previously been seen as unfeasible due to high computational costs, the lack of analytical gradients in many computational codes, and additional challenges such as constructing suitable basis set corrections for forces. In this work, we develop new methods and workflows to overcome the challenges inherent to automating unrestricted coupled cluster calculations. Using these advancements, we create a dataset of gas-phase reactions containing energies and forces for 3119 different organic molecules configurations calculated at the gold-standard level of unrestricted CCSD(T) (coupled cluster singles doubles and perturbative triples). With this dataset, we provide an analysis of the differences between the density functional and unrestricted CCSD(T) descriptions. We develop a transferable machine learning interatomic potential for gas-phase reactions, trained on unrestricted CCSD(T) data, and demonstrate the advantages of transitioning away from DFT data. Transitioning from training to DFT to training to UCCSD(T) datasets yields an improvement of more than 0.1 eV/Å in force accuracy and over 0.1 eV in activation energy reproduction.

We introduce AceFF, a pre-trained machine learning interatomic potential (MLIP) optimized for small molecule drug discovery. While MLIPs have emerged as efficient alternatives to Density Functional Theory (DFT), generalizability across diverse chemical spaces remains difficult. AceFF addresses this via a refined TensorNet2 architecture trained on a comprehensive dataset of drug-like compounds. This approach yields a force field that balances high-throughput inference speed with DFT-level accuracy. AceFF fully supports the essential medicinal chemistry elements (H, B, C, N, O, F, Si, P, S, Cl, Br, I) and is explicitly trained to handle charged states. Validation against rigorous benchmarks, including complex torsional energy scans, molecular dynamics trajectories, batched minimizations, and forces and anergy accuracy demonstrates that AceFF establishes a new state-of-the-art for organic molecules. The AceFF-2 model weights and inference code are available at https://huggingface.co/Acellera/AceFF-2.0.

Large-scale datasets have enabled highly accurate machine learning interatomic potentials (MLIPs) for general-purpose heterogeneous catalysis modeling. There are, however, some limitations in what can be treated with these potentials because of gaps in the underlying training data. To extend these capabilities, we introduce AQCat25, a complementary dataset of 13.5 million density functional theory (DFT) single point calculations designed to improve the treatment of systems where spin polarization and/or higher fidelity are critical. We also investigate methodologies for integrating new datasets, such as AQCat25, with the broader Open Catalyst 2020 (OC20) dataset to create spin-aware models without sacrificing generalizability. We find that directly tuning a general model on AQCat25 leads to catastrophic forgetting of the original dataset's knowledge. Conversely, joint training strategies prove effective for improving accuracy on the new data without sacrificing general performance. This joint approach introduces a challenge, as the model must learn from a dataset containing both mixed-fidelity calculations and mixed-physics (spin-polarized vs. unpolarized). We show that explicitly conditioning the model on this system-specific metadata, for example by using Feature-wise Linear Modulation (FiLM), successfully addresses this challenge and further enhances model accuracy. Ultimately, our work establishes an effective protocol for bridging DFT fidelity domains to advance the predictive power of foundational models in catalysis.

The simulation of large-scale systems with complex electron interactions remains one of the greatest challenges for the atomistic modeling of materials. Although classical force fields often fail to describe the coupling between electronic states and ionic rearrangements, the more accurate ab-initio molecular dynamics suffers from computational complexity that prevents long-time and large-scale simulations, which are essential to study many technologically relevant phenomena, such as reactions, ion migrations, phase transformations, and degradation. In this work, we present the Crystal Hamiltonian Graph neural Network (CHGNet) as a novel machine-learning interatomic potential (MLIP), using a graph-neural-network-based force field to model a universal potential energy surface. CHGNet is pretrained on the energies, forces, stresses, and magnetic moments from the Materials Project Trajectory Dataset, which consists of over 10 years of density functional theory static and relaxation trajectories of sim 1.5 million inorganic structures. The explicit inclusion of magnetic moments enables CHGNet to learn and accurately represent the orbital occupancy of electrons, enhancing its capability to describe both atomic and electronic degrees of freedom. We demonstrate several applications of CHGNet in solid-state materials, including charge-informed molecular dynamics in Li_xMnO_2, the finite temperature phase diagram for Li_xFePO_4 and Li diffusion in garnet conductors. We critically analyze the significance of including charge information for capturing appropriate chemistry, and we provide new insights into ionic systems with additional electronic degrees of freedom that can not be observed by previous MLIPs.

Accurate and scalable machine-learned inter-atomic potentials (MLIPs) are essential for molecular simulations ranging from drug discovery to new material design. Current state-of-the-art models enforce roto-translational symmetries through equivariant neural network architectures, a hard-wired inductive bias that can often lead to reduced flexibility, computational efficiency, and scalability. In this work, we introduce TransIP: Transformer-based Inter-Atomic Potentials, a novel training paradigm for interatomic potentials achieving symmetry compliance without explicit architectural constraints. Our approach guides a generic non-equivariant Transformer-based model to learn SO(3)-equivariance by optimizing its representations in the embedding space. Trained on the recent Open Molecules (OMol25) collection, a large and diverse molecular dataset built specifically for MLIPs and covering different types of molecules (including small organics, biomolecular fragments, and electrolyte-like species), TransIP attains comparable performance in machine-learning force fields versus state-of-the-art equivariant baselines. Further, compared to a data augmentation baseline, TransIP achieves 40% to 60% improvement in performance across varying OMol25 dataset sizes. More broadly, our work shows that learned equivariance can be a powerful and efficient alternative to equivariant or augmentation-based MLIP models.

We introduce Orb, a family of universal interatomic potentials for atomistic modelling of materials. Orb models are 3-6 times faster than existing universal potentials, stable under simulation for a range of out of distribution materials and, upon release, represented a 31% reduction in error over other methods on the Matbench Discovery benchmark. We explore several aspects of foundation model development for materials, with a focus on diffusion pretraining. We evaluate Orb as a model for geometry optimization, Monte Carlo and molecular dynamics simulations.

Chemical potential of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot satisfy a constant chemical potential condition as solute species can migrate to the interface and deplete the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative constant chemical potential molecular dynamics (iCuMD) simulation, which helps simulate targeted molar concentrations of species in solution. iCuMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target concentration (chemical potential). We demonstrate our approach using solid-liquid and liquid-air interfacial systems as case studies. Specifically, we perform classical force field-based MD simulations of NaCl(aq)-air and NaCl(aq)-graphite interfaces and machine learning interatomic potential (MLIP)-based MD simulations of the Na2SO4(aq)-graphene interface. Our results show that the iCuMD approach efficiently achieves the desired bulk ion concentration within two iterations and can also be integrated with MLIP-driven simulations which enable constant potential simulations with DFT-level accuracy. We show that iCuMD offers a robust and simple computational framework for constant chemical potential simulations as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

The demand for safe, high-energy-density batteries has spotlighted halide solid-state electrolytes, which offer the potential for enhanced ionic mobility, electrochemical stability, and interfacial deformability. Accelerating their discovery requires extensive molecular dynamics, which has been increasingly enabled by universal machine learning interatomic potentials trained on foundational datasets. However, the dynamic softness of halides poses a stringent test of whether general-purpose models can reliably replace first-principles calculations under the highly distorted, elevated-temperature regimes necessary to probe ion transport. Here, we present AQVolt26, a dataset of 322,656 r^2SCAN single-point calculations for lithium halides, generated via high-temperature configurational sampling across sim5K structures. We demonstrate that foundational datasets provide a strong baseline for stable halide chemistries and transfer local forces well, however absolute energy predictions degrade in distorted higher-temperature regimes. Co-training with AQVolt26 resolves this blind spot. Furthermore, incorporating Materials Project relaxation data improves near-equilibrium performance but degrades extreme-strain robustness without enhancing high-temperature force accuracy. These results demonstrate that domain-specific configurational sampling is essential for the reliable dynamic screening of halide electrolytes. Furthermore, our findings suggest that while foundational models provide a robust base, they are most effective for dynamically soft solid-state chemistries when augmented with targeted, high-temperature data. Finally, we show that near-equilibrium relaxation data serves as a task-specific complement rather than a universally beneficial addition.

Creating a single unified interatomic potential capable of attaining ab initio accuracy across all chemistry remains a long-standing challenge in computational chemistry and materials science. This work introduces a training protocol for foundation machine-learning interatomic potentials (MLIPs) that bridge molecular, surface, and materials chemistry through cross-domain learning. First, we introduce enhancements to the MACE architecture that improve its performance on chemically diverse databases by increasing weight sharing across chemical elements and introducing non-linear factors into the tensor decomposition of the product basis. Second, we develop a multi-head replay post-training methodology that enables efficient knowledge transfer across diverse chemical domains. By fine-tuning on datasets at different levels of electronic structure theory, including inorganic crystals, molecular systems, surface chemistry, and reactive organic chemistry, we demonstrate that a single unified model achieves state-of-the-art performance across several chemical domains. Comprehensive benchmarking reveals superior cross-domain transferability compared with existing specialised and multi-task models, with notable improvements in molecular and surface properties while maintaining state-of-the-art performance in materials-property prediction.

Adapting machine-learned interatomic potential (MLIP) foundation models to specialised tasks through fine-tuning is an increasingly important practice, yet systematic guidance on when and how to fine-tune is currently limited. We evaluate seven fine-tuning strategies -- naive full-parameter updates, two layer-freezing variants, Low-Rank Adaptation (LoRA), multihead replay, pseudolabelled replay, and replay combined with LoRA -- across five chemically diverse benchmarks (aqueous NaCl, ice polymorphs, S_N2 reactions, SPICE biomolecules, and lithium electrolytes), three generations of foundation models, and training sets spanning five orders of magnitude. To support this evaluation we implement three capabilities in the MACE codebase: LoRA adapted for equivariant message-passing architectures, including both scalar and equivariant linear layers; pseudolabelled replay, which decouples the replay data source from the original pretraining corpus; and model-aware atomic reference energy (E0) reestimation for fine-tuning workflows. We find that foundation model quality, correct E0 initialisation, and well-chosen hyperparameters are prerequisites whose impact routinely exceeds that of the fine-tuning strategy itself. Once these prerequisites are met, most strategies achieve strong target-task accuracy, consistently surpassing models trained from scratch. The practical distinction depends on deployment scope: naive fine-tuning offers the best convergence for single-system applications, while multihead replay -- with either original or pseudolabelled data -- is the only approach tested that consistently preserves out-of-distribution robustness, maintaining both pretraining-distribution accuracy for broader deployment and many-body short-range repulsion.

Alchemical relative binding free energy (RBFE) calculations are limited by the fixed-charge approximation of classical force fields. Hybrid machine learning interatomic potential/molecular mechanics (MLIP/MM) schemes correct ligand strain, but under mechanical embedding still describe ligand--environment electrostatics with static point charges. Electrostatic embedding schemes coupling machine-learned charges to the MM environment have been proposed and validated against QM/MM for simple systems, but not tested in a production alchemical workflow. We take the electrostatic embedding scheme of Semelak et al.\ and evaluate it on protein--ligand RBFE. We trained a TensorNet2 model, AceFF-2-RESP-1, on 10^{6} conformations from the AceFF dataset, jointly predicting energies, forces and Restrained Electrostatic Potential (RESP) charges. We chose RESP over MBIS for commensurability with the AMBER-family force field it couples to. The predicted charges enter the short-range direct-space part of the particle mesh Ewald sum, with Thole damping to prevent polarization catastrophes during alchemical transformations. We tested the scheme across five targets from the Wang et al.\ benchmark set, fixed in advance by a prior study, with three replicates per edge and matched protocols. Electrostatic embedding improved every accuracy and correlation metric for TYK2 (ΔΔG RMSE 0.86 rightarrow 0.45~kcal/mol against GAFF2), but performed comparably to the classical and mechanical-embedding baselines for CDK2, thrombin, p38 and JNK1. Standard single-molecule energy and charge benchmarks were not good predictors of this target-dependent outcome. TYK2 combined good ΔΔG accuracy with the lowest force error on the Schrödinger benchmark, but this pattern did not hold for the other targets.

Machine learning-based interatomic potentials and force fields depend critically on accurate atomic structures, yet such data are scarce due to the limited availability of experimentally resolved crystals. Although atomic-resolution electron microscopy offers a potential source of structural data, converting these images into simulation-ready formats remains labor-intensive and error-prone, creating a bottleneck for model training and validation. We introduce AutoMat, an end-to-end, agent-assisted pipeline that automatically transforms scanning transmission electron microscopy (STEM) images into atomic crystal structures and predicts their physical properties. AutoMat combines pattern-adaptive denoising, physics-guided template retrieval, symmetry-aware atomic reconstruction, fast relaxation and property prediction via MatterSim, and coordinated orchestration across all stages. We propose the first dedicated STEM2Mat-Bench for this task and evaluate performance using lattice RMSD, formation energy MAE, and structure-matching success rate. By orchestrating external tool calls, AutoMat enables a text-only LLM to outperform vision-language models in this domain, achieving closed-loop reasoning throughout the pipeline. In large-scale experiments over 450 structure samples, AutoMat substantially outperforms existing multimodal large language models and tools. These results validate both AutoMat and STEM2Mat-Bench, marking a key step toward bridging microscopy and atomistic simulation in materials science.The code and dataset are publicly available at https://github.com/yyt-2378/AutoMat and https://huggingface.co/datasets/yaotianvector/STEM2Mat.

Machine-learned interatomic potentials (MLIPs) have shown significant promise in predicting infrared spectra with high fidelity. However, the absence of general-purpose MLIPs capable of handling a wide range of elements and their combinations has limited their broader applicability. In this work, we introduce MACE4IR, a machine learning foundation model built on the MACE architecture and trained on 10 million geometries and corresponding density-functional theory (DFT) energies, forces and dipole moments from the QCML dataset. The training data encompasses approximately 80 elements and a diverse set of molecules, including organic compounds, inorganic species, and metal complexes. MACE4IR accurately predicts energies, forces, dipole moments, and infrared spectra at significantly reduced computational cost compared to DFT. By combining generality, accuracy, and efficiency, MACE4IR opens the door to rapid and reliable infrared spectra prediction for complex systems across chemistry, biology, and materials science.

The groundbreaking advance in materials and chemical research has been driven by the development of atomistic simulations. However, the broader applicability of the atomistic simulations remains restricted, as they inherently depend on energy models that are either inaccurate or computationally prohibitive. Machine learning interatomic potentials (MLIPs) have recently emerged as a promising class of energy models, but their deployment remains challenging due to the lack of systematic protocols for generating diverse training data. Here we automate the construction of training datasets to enable the development of general-purpose MLIPs, by introducing GAIA, an end-to-end framework to build a wide range of atomic arrangements. By employing systematic evaluation of metadynamics for effective structural exploration, GAIA overcomes the heuristic nature of conventional dataset generation. Using GAIA, we constructed Titan25, a benchmark-scale dataset, and trained MLIPs that closely match both static and dynamic density functional theory results. The models further reproduce experimental observations across reactive regimes, including detonation, coalescence, and catalytic activity. GAIA narrows the gap between experiment and simulation, and paves the way for the development of universal MLIPs that can reliably describe a wide spectrum of materials and chemical processes.

Machine-learning interatomic potentials (MLIPs) have advanced rapidly, with many top models relying on strong physics-based inductive biases. However, as models scale to larger systems like biomolecules and electrolytes, they struggle to accurately capture long-range (LR) interactions, leading current approaches to rely on explicit physics-based terms or components. In this work, we propose AllScAIP, a straightforward, attention-based, and energy-conserving MLIP model that scales to O(100 million) training samples. It addresses the long-range challenge using an all-to-all node attention component that is data-driven. Extensive ablations reveal that in low-data/small-model regimes, inductive biases improve sample efficiency. However, as data and model size scale, these benefits diminish or even reverse, while all-to-all attention remains critical for capturing LR interactions. Our model achieves state-of-the-art energy/force accuracy on molecular systems, as well as a number of physics-based evaluations (OMol25), while being competitive on materials (OMat24) and catalysts (OC20). Furthermore, it enables stable, long-timescale MD simulations that accurately recover experimental observables, including density and heat of vaporization predictions.

Foundation machine-learned interatomic potentials (MLIPs) are trained on large quantum-mechanical datasets and generalise across broad regions of chemical and configurational space. Beyond their usual role in accelerating sampling-based simulations, their internal representations encode chemically rich local atomic environments. Here, we introduce Rem3Di, a representation-learning framework that repurposes latent features from atomistic foundation models as transferable molecular descriptors for property prediction and virtual screening. Rem3Di combines a potential's per-atom features into a single fixed-length descriptor of the whole molecule that varies smoothly with three-dimensional structure and is invariant to the ordering of the atoms. The descriptor can be used directly or fine-tuned for specific prediction tasks. To capture molecular handedness, Rem3Di constructs pseudoscalar features, which are unchanged by rotation but reverse sign under mirror reflection. This lets the descriptor distinguish enantiomers, which can differ in activity and toxicity. The transformer is pretrained on large molecular datasets by reconstructing corrupted atom features, so no experimental labels are required. Across public drug-property benchmarks, Rem3Di matches or exceeds published baselines without relying on classical 2D fingerprints. Additionally, the same descriptor yields chemically meaningful differentiation of transition-metal complexes without predefined bonding rules or handcrafted representations. Rem3Di therefore provides a route from simulation-trained atomistic representations to transferable, chirality-aware molecular representations for chemical machine learning.

Machine learning interatomic potentials trained on first-principles reference data are becoming valuable tools for computational physics, biology, and chemistry. Equivariant message-passing neural networks, including transformers, achieve state-of-the-art accuracy but rely on cutoff-based graphs, limiting their ability to capture long-range effects such as electrostatics or dispersion, as well as electron delocalization. While long-range correction schemes based on inverse power laws of interatomic distances have been proposed, they are unable to communicate higher-order geometric information and are thus limited in applicability. To address this shortcoming, we propose the use of equivariant, rather than scalar, charges for long-range interactions, and design a graph neural network architecture, LOREM, around this long-range message passing mechanism. We consider several datasets specifically designed to highlight non-local physical effects, and compare short-range message passing with different receptive fields to invariant and equivariant long-range message passing. Even though most approaches work for careful dataset-specific choices of their model hyperparameters, LOREM works consistently without such changes, with excellent benchmark performance.

In this work, we introduce PhononBench, the first large-scale benchmark for dynamical stability in AI-generated crystals. Leveraging the recently developed MatterSim interatomic potential, which achieves DFT-level accuracy in phonon predictions across more than 10,000 materials, PhononBench enables efficient large-scale phonon calculations and dynamical-stability analysis for 108,843 crystal structures generated by six leading crystal generation models. PhononBench reveals a widespread limitation of current generative models in ensuring dynamical stability: the average dynamical-stability rate across all generated structures is only 25.83%, with the top-performing model, MatterGen, reaching just 41.0%. Further case studies show that in property-targeted generation-illustrated here by band-gap conditioning with MatterGen--the dynamical-stability rate remains as low as 23.5% even at the optimal band-gap condition of 0.5 eV. In space-group-controlled generation, higher-symmetry crystals exhibit better stability (e.g., cubic systems achieve rates up to 49.2%), yet the average stability across all controlled generations is still only 34.4%. An important additional outcome of this study is the identification of 28,119 crystal structures that are phonon-stable across the entire Brillouin zone, providing a substantial pool of reliable candidates for future materials exploration. By establishing the first large-scale dynamical-stability benchmark, this work systematically highlights the current limitations of crystal generation models and offers essential evaluation criteria and guidance for their future development toward the design and discovery of physically viable materials. All model-generated crystal structures, phonon calculation results, and the high-throughput evaluation workflows developed in PhononBench will be openly released at https://github.com/xqh19970407/PhononBench

We introduce Orb-v3, the next generation of the Orb family of universal interatomic potentials. Models in this family expand the performance-speed-memory Pareto frontier, offering near SoTA performance across a range of evaluations with a >10x reduction in latency and > 8x reduction in memory. Our experiments systematically traverse this frontier, charting the trade-off induced by roto-equivariance, conservatism and graph sparsity. Contrary to recent literature, we find that non-equivariant, non-conservative architectures can accurately model physical properties, including those which require higher-order derivatives of the potential energy surface. This model release is guided by the principle that the most valuable foundation models for atomic simulation will excel on all fronts: accuracy, latency and system size scalability. The reward for doing so is a new era of computational chemistry driven by high-throughput and mesoscale all-atom simulations.

Merging first-principles calculations with machine learning (ML), we aim to accelerate the exploration of catalytic behaviour in novel materials. We focus on two-dimensional (2D) Ti_2CT_y MXenes, whose versatile surface chemistry makes them particularly compelling candidates for catalysis. Resolving their composition and structure under realistic conditions exceeds the reach of standard density functional theory (DFT) due to computational cost. To address this challenge, we generate a comprehensive dataset of 50,000 DFT calculations for training and 10,000 for testing, encompassing both Ti_2CT_y MXene configurations and molecular systems, along with an additional test dataset with 1000 genuinely new, larger systems to investigate how well models generalise. We train and validate widely used and competitive machine learning interatomic potential (MLIP) models, including EquiformerV2, MACE, MatRIS, and UPET, that accurately predict atomic forces and formation energies -- quantities that DFT must repeatedly compute for structural and catalytic investigations -- for these 2D materials. This combined DFT-ML framework achieves computational acceleration on the order of approximately 1-4 cdot 10^3 (on a CPU) while maintaining desired-level accuracy (approximately +/- 10 meV/A for forces and approximately +/- 1 meV for per-atom energies), paving the way for more efficient investigations of MXene catalytic behaviour. Moreover, we perform an extensive qualitative evaluation of the trained models, showcasing the importance of comprehensive simulation-based comparison beyond benchmark metrics. The dataset and the trained models with the code are available at https://huggingface.co/datasets/CatalystAnonymous/catalyst_mxenes.

Crystal generative models mainly learn what stable crystals look like, with little explicit supervision for what makes them stable. We reveal a substantial representation gap between state-of-the-art crystal generative models and pretrained universal machine learning interatomic potentials (MLIPs) via energy probing, and show this gap can be closed by a simple training-time alignment. We propose Crystal REPresentation Alignment (CrystalREPA), a plug-and-play framework that aligns the atom-wise hidden states of generative encoders with frozen MLIP representations through an element-aware contrastive objective, transferring stability-aware atomistic priors with marginal training overhead and no additional inference cost. Across three generative frameworks, ten MLIP teachers, and two benchmark datasets, CrystalREPA consistently improves the thermodynamic stability, structural validity, and structural fidelity of generated crystals. Equally important, we find that an MLIP's transfer effectiveness is poorly predicted by its accuracy on standard leaderboards (e.g., Matbench Discovery) but strongly predicted by the distinguishability of its atom-wise representation space, yielding a practical, accuracy-independent criterion for selecting MLIP teachers for generative transfer.

We propose a machine learning method to model molecular tensorial quantities, namely the magnetic anisotropy tensor, based on the Gaussian-moment neural-network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3--0.4 cm^{-1} and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.

Modern materials science has historically been founded on combining restricted subsets of the periodic table, favoring high-purity, few-element systems. However, the demands of an emerging circular economy, together with the need to understand materials behavior under planetary and industrial extremes, increasingly require mastering Mendeleev materials - chemically and structurally complex systems that span large portions of the periodic table. In these regimes, current universal machine-learning interatomic potentials often fail, largely due to systematic gaps in traditional training datasets that heavily emphasize low-energy, near-equilibrium structures. We address this limitation by introducing a chemistry-agnostic, information-entropy-maximization protocol for data generation. By decoupling structural sampling from thermodynamic bias, our approach provides a robust physical prior for atomic interactions across the entire periodic table, including regimes far from equilibrium and under extreme conditions. Training a Graph Atomic Cluster Expansion (GRACE) model on the resulting statistically maximized entropy (SMAX) dataset yields markedly improved robustness across a range of stringent benchmarks. These include large-strain phase transformations in tin, defect evolution in tungsten-based alloys, and catalytic reaction barrier prediction. More broadly, our approach establishes a scalable and principled methodology for navigating the vast chemical and configurational space relevant to future materials design. It enables a paradigm of discovery by simulation in which unbiased sampling protocols autonomously resolve emergent structures in multi-elemental mixtures-such as systems containing the nine most abundant elements in the Earth's crust-without reliance on a priori chemical assumptions.

We explore the integration of Kolmogorov Networks (KANs) into molecular dynamics (MD) simulations to improve interatomic potentials. We propose that widely used potentials, such as the Lennard-Jones (LJ) potential, the embedded atom model (EAM), and artificial neural network (ANN) potentials, can be interpreted within the KAN framework. Specifically, we demonstrate that the descriptors for ANN potentials, typically constructed using polynomials, can be redefined using KAN's non-linear functions. By employing linear or cubic spline interpolations for these KAN functions, we show that the computational cost of evaluating ANN potentials and their derivatives is reduced.

E(3)-equivariant neural networks have demonstrated success across a wide range of 3D modelling tasks. A fundamental operation in these networks is the tensor product, which interacts two geometric features in an equivariant manner to create new features. Due to the high computational complexity of the tensor product, significant effort has been invested to optimize the runtime of this operation. For example, Luo et al. (2024) recently proposed the Gaunt tensor product (GTP) which promises a significant speedup. In this work, we provide a careful, systematic analysis of a number of tensor product operations. In particular, we emphasize that different tensor products are not performing the same operation. The reported speedups typically come at the cost of expressivity. We introduce measures of expressivity and interactability to characterize these differences. In addition, we realized the original implementation of GTP can be greatly simplified by directly using a spherical grid at no cost in asymptotic runtime. This spherical grid approach is faster on our benchmarks and in actual training of the MACE interatomic potential by 30%. Finally, we provide the first systematic microbenchmarks of the various tensor product operations. We find that the theoretical runtime guarantees can differ wildly from empirical performance, demonstrating the need for careful application-specific benchmarking. Code is available at https://github.com/atomicarchitects/PriceofFreedom.

The emergence of spin-polarized electrons from nonmagnetic chiral molecules and crystals is called Chirality-induced spin selectivity (CISS). A chiral phonon of definite wavevector q can strongly enhance it, but near equilibrium the two helicities +q and -q are equally populated: they are time-reversal partners and their contributions cancel. We show that in a biased chiral conductor the current causes the phonon of one helicity to damp less than the other. The damping asymmetry is odd in the current, odd under qrightarrow-q, invariant under a mirror that reverses the structural handedness, and equal, mode for mode, to the current-induced nonconservative Berry force on the phonon coordinate. Closing the phonon kinetics with a rate equation turns the asymmetry into a net lattice helicity: at any finite bias one helicity is preferentially populated, with no threshold, growing linearly with the current as Vrightarrow0; above a threshold that helicity becomes a self-sustained coherent travelling wave. We demonstrate this effect in elemental tellurium, treated as an open quantum system (electronic Hamiltonian, phonon bath, and electron-phonon coupling) within a quasi-ab initio framework. The electronic Hamiltonian is supplied by a vertex-corrected quasiparticle self-consistent GW (QSGW) potential with spin-orbit coupling; nuclear displacements are modeled with a machine-learned interatomic potential, which yields chiral phonon modes at finite pm q_z on the Γ-A line. The perturbation to the electronic Hamiltonian from a nuclear displacement is approximated by a frozen-phonon deformation potential. No optical pump is needed: a bias alone drives the current and selects the phonon helicity; reversing the current reverses the selection.

Matbench Discovery simulates the deployment of machine learning (ML) energy models in a high-throughput search for stable inorganic crystals. We address the disconnect between (i) thermodynamic stability and formation energy and (ii) in-domain vs out-of-distribution performance. Alongside this paper, we publish a Python package to aid with future model submissions and a growing online leaderboard with further insights into trade-offs between various performance metrics. To answer the question which ML methodology performs best at materials discovery, our initial release explores a variety of models including random forests, graph neural networks (GNN), one-shot predictors, iterative Bayesian optimizers and universal interatomic potentials (UIP). Ranked best-to-worst by their test set F1 score on thermodynamic stability prediction, we find CHGNet > M3GNet > MACE > ALIGNN > MEGNet > CGCNN > CGCNN+P > Wrenformer > BOWSR > Voronoi tessellation fingerprints with random forest. The top 3 models are UIPs, the winning methodology for ML-guided materials discovery, achieving F1 scores of ~0.6 for crystal stability classification and discovery acceleration factors (DAF) of up to 5x on the first 10k most stable predictions compared to dummy selection from our test set. We also highlight a sharp disconnect between commonly used global regression metrics and more task-relevant classification metrics. Accurate regressors are susceptible to unexpectedly high false-positive rates if those accurate predictions lie close to the decision boundary at 0 eV/atom above the convex hull where most materials are. Our results highlight the need to focus on classification metrics that actually correlate with improved stability hit rate.

Molecular dynamics (MD) simulations play a crucial role in scientific research. Yet their computational cost often limits the timescales and system sizes that can be explored. Most data-driven efforts have been focused on reducing the computational cost of accurate interatomic forces required for solving the equations of motion. Despite their success, however, these machine learning interatomic potentials (MLIPs) are still bound to small time-steps. In this work, we introduce TrajCast, a transferable and data-efficient framework based on autoregressive equivariant message passing networks that directly updates atomic positions and velocities lifting the constraints imposed by traditional numerical integration. We benchmark our framework across various systems, including a small molecule, crystalline material, and bulk liquid, demonstrating excellent agreement with reference MD simulations for structural, dynamical, and energetic properties. Depending on the system, TrajCast allows for forecast intervals up to 30times larger than traditional MD time-steps, generating over 15 ns of trajectory data per day for a solid with more than 4,000 atoms. By enabling efficient large-scale simulations over extended timescales, TrajCast can accelerate materials discovery and explore physical phenomena beyond the reach of traditional simulations and experiments. An open-source implementation of TrajCast is accessible under https://github.com/IBM/trajcast.

Identifying useful sorbent materials for direct air capture (DAC) from humid air remains a challenge. We present the Open DAC 2025 (ODAC25) dataset, a significant expansion and improvement upon ODAC23 (Sriram et al., ACS Central Science, 10 (2024) 923), comprising nearly 70 million DFT single-point calculations for CO_2, H_2O, N_2, and O_2 adsorption in 15,000 MOFs. ODAC25 introduces chemical and configurational diversity through functionalized MOFs, high-energy GCMC-derived placements, and synthetically generated frameworks. ODAC25 also significantly improves upon the accuracy of DFT calculations and the treatment of flexible MOFs in ODAC23. Along with the dataset, we release new state-of-the-art machine-learned interatomic potentials trained on ODAC25 and evaluate them on adsorption energy and Henry's law coefficient predictions.

Atomic-scale simulations have been transformed by machine-learning models that predict the properties of atomistic structures with the accuracy of quantum calculations, but at a small fraction of the cost. These models have increased dramatically in generality, thanks to the availability of synthetic datasets of ever-increasing size and scope. The proliferation of datasets, with properties often computed using different levels of electronic-structure approximation, is problematic, as there is often overlap between different datasets, and strong correlations between structures obtained with short molecular dynamics trajectories or geometry optimization. To address these problems, we introduce a protocol to stratify a dataset into a hierarchy of nested subsets, subsampling from the coarsest to the finest resolution based on an "ecumetric" built to reflect the latent space representation of several popular universal machine-learning interatomic potentials. We then use this approach to combine most of the open structural datasets currently available, consolidating them into MAD-COSMO, a well-organized collection of almost 1.7 billion structures, whose 2^{24} most diverse members form the MAD-CORE stratified coreset, which can be easily used for all sorts of tasks, from exploratory experiments to the training of foundation models at scale. We envision that this collection will guide and help coordinate future efforts, focusing them on the most relevant and/or undersampled regions of chemical and structural space, and that it will be further extended to incorporate the outcomes of the collective work of this community.

The quality, consistency, and information content of training data is often what determines the practical value of machine-learning models for atomistic simulations. Yet, many widely used electronic-structure databases are assembled having materials screening as primary goal rather than robust force-field learning, are limited in their scope to a specific class of chemical compounds, and/or employ inconsistent DFT functionals and settings. Here we introduce MAD-1.6, a highly curated dataset designed explicitly for training broadly applicable atomistic models across the periodic table at high levels of theory. MAD-1.6 extends the MAD dataset with targeted enrichment strategies that improve the coverage of chemical space to 102 elements while keeping the total number of configurations compact. All structures are computed with a single, standardized all-electron DFT workflow using the r^2SCAN meta-GGA functional and consistent convergence settings, ensuring uniformity across chemically heterogeneous systems. The dataset encompasses molecules, clusters, bulk crystals, surfaces, and low-dimensional structures, and its quality and consistency are further enhanced by outlier removal using uncertainty quantification. We demonstrate the high accuracy that can be achieved with the proposed dataset by training PET-MAD-1.6, a generally applicable r^2SCAN interatomic potential that covers 102 elements in the periodic table and achieves exceptional levels of benchmark accuracy and stability in challenging simulation protocols.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Predicting physical properties of materials from their crystal structures is a fundamental problem in materials science. In peripheral areas such as the prediction of molecular properties, fully connected attention networks have been shown to be successful. However, unlike these finite atom arrangements, crystal structures are infinitely repeating, periodic arrangements of atoms, whose fully connected attention results in infinitely connected attention. In this work, we show that this infinitely connected attention can lead to a computationally tractable formulation, interpreted as neural potential summation, that performs infinite interatomic potential summations in a deeply learned feature space. We then propose a simple yet effective Transformer-based encoder architecture for crystal structures called Crystalformer. Compared to an existing Transformer-based model, the proposed model requires only 29.4% of the number of parameters, with minimal modifications to the original Transformer architecture. Despite the architectural simplicity, the proposed method outperforms state-of-the-art methods for various property regression tasks on the Materials Project and JARVIS-DFT datasets.

Organic molecular crystals underpin technologies ranging from pharmaceuticals to organic electronics, yet predicting solid-state packing of molecules remains challenging because candidate generation is combinatorial and stability is only resolved after costly energy evaluations. Here we introduce PackFlow, a flow matching framework for molecular crystal structure prediction (CSP) that generates heavy-atom crystal proposals by jointly sampling Cartesian coordinates and unit-cell lattice parameters given a molecular graph. This lattice-aware generation interfaces directly with downstream relaxation and lattice-energy ranking, positioning PackFlow as a scalable proposal engine within standard CSP pipelines. To explicitly steer generation toward physically favourable regions, we propose physics alignment, a reinforcement learning post-training stage that uses machine-learned interatomic potential energies and forces as stability proxies. Physics alignment improves physical validity without altering inference-time sampling. We validate PackFlow's performance against heuristic baselines through two distinct evaluations. First, on a broad unseen set of molecular systems, we demonstrate superior candidate generation capability, with proposals exhibiting greater structural similarity to experimental polymorphs. Second, we assess the full end-to-end workflow on two unseen CSP blind-test case studies, including relaxation and lattice-energy analysis. In both settings, PackFlow outperforms heuristics-based methods by concentrating probability mass in low-energy basins, yielding candidates that relax into lower-energy minima and offering a practical route to amortize the relax-and-rank bottleneck.

The development of accurate and efficient machine learning models for predicting the structure and properties of molecular crystals has been hindered by the scarcity of publicly available datasets of structures with property labels. To address this challenge, we introduce the Open Molecular Crystals 2025 (OMC25) dataset, a collection of over 27 million molecular crystal structures containing 12 elements and up to 300 atoms in the unit cell. The dataset was generated from dispersion-inclusive density functional theory (DFT) relaxation trajectories of over 230,000 randomly generated molecular crystal structures of around 50,000 organic molecules. OMC25 comprises diverse chemical compounds capable of forming different intermolecular interactions and a wide range of crystal packing motifs. We provide detailed information on the dataset's construction, composition, structure, and properties. To demonstrate the quality and use cases of OMC25, we further trained and evaluated state-of-the-art open-source machine learning interatomic potentials. By making this dataset publicly available, we aim to accelerate the development of more accurate and efficient machine learning models for molecular crystals.

Graph Neural Networks (GNNs) are the dominant architecture for molecular machine learning, particularly for molecular property prediction and machine learning interatomic potentials (MLIPs). GNNs perform message passing on predefined graphs often induced by a fixed radius cutoff or k-nearest neighbor scheme. While this design aligns with the locality present in many molecular tasks, a hard-coded graph can limit expressivity due to the fixed receptive field and slows down inference with sparse graph operations. In this work, we investigate whether pure, unmodified Transformers trained directly on Cartesian coordinatesx2013without predefined graphs or physical priorsx2013can approximate molecular energies and forces. As a starting point for our analysis, we demonstrate how to train a Transformer to competitive energy and force mean absolute errors under a matched training compute budget, relative to a state-of-the-art equivariant GNN on the OMol25 dataset. We discover that the Transformer learns physically consistent patternsx2013such as attention weights that decay inversely with interatomic distancex2013and flexibly adapts them across different molecular environments due to the absence of hard-coded biases. The use of a standard Transformer also unlocks predictable improvements with respect to scaling training resources, consistent with empirical scaling laws observed in other domains. Our results demonstrate that many favorable properties of GNNs can emerge adaptively in Transformers, challenging the necessity of hard-coded graph inductive biases and pointing toward standardized, scalable architectures for molecular modeling.

Diffusion-based samplers learn to sample complex, high-dimensional distributions using energies or log densities alone, without training data. Yet, they remain impractical for molecular sampling because they are often slower than molecular dynamics and miss thermodynamically relevant modes. Inspired by enhanced sampling, we encourage exploration by introducing a sequential bias along bespoke, information-rich, low-dimensional projections of atomic coordinates known as collective variables (CVs). We introduce a repulsive potential centered on the CVs from recent samples, which pushes future samples towards novel CV regions and effectively increases the temperature in the projected space. Our resulting method improves efficiency, mode discovery, enables the estimation of free energy differences, and retains independent sampling from the approximate Boltzmann distribution via reweighting by the bias. On standard peptide conformational sampling benchmarks, the method recovers diverse conformational states and accurate free energy profiles. We are the first to demonstrate reactive sampling using a diffusion-based sampler, capturing bond breaking and formation with universal interatomic potentials at near-first-principles accuracy. The approach resolves reactive energy landscapes at a fraction of the wall-clock time of standard sampling methods, advancing diffusion-based sampling towards practical use in molecular sciences.

We present FreeBird, an extensible Julia-based platform for computational studies of phase equilibria at generic interfaces. The package supports a range of system configurations, from atomistic solid surfaces to coarse-grained lattice-gas models, with energies evaluated using classical interatomic potentials or lattice Hamiltonians. Both atomistic and lattice systems accommodate single- or multi-component mixtures with flexibly definable surface and lattice geometries. Implemented sampling algorithms include nested sampling, Wang-Landau sampling, Metropolis Monte Carlo, and, for tractable lattice systems, exact enumeration. Leveraging Julia's type hierarchies and multiple dispatch, FreeBird provides a modular interface that allows seamless integration of system definitions, energy evaluators, and sampling schemes. Designed for flexibility, extensibility, and performance, FreeBird offers a versatile framework for exploring the thermodynamics of interfacial phenomena.

Deep generative models have shown promise for modeling metal-organic frameworks (MOFs), but existing approaches (1) rely on coarse-grained representations that assume fixed bond lengths and angles, and (2) neglect the MOF-adsorbate interactions, which are critical for downstream applications. We introduce AtomMOF, a scalable flow-based model built on an all-atom Diffusion Transformer that maps 2D molecular graphs of building blocks and adsorbates directly to equilibrium 3D structures without imposing structural constraints. We further present scaling laws for porous crystal generation, indicating predictable performance gains with increased model capacity, and introduce Feynman-Kac steering guided by machine-learned interatomic potentials to improve geometric validity and sampling stability. On the (MOF-only) BW dataset, AtomMOF increases the match rate by 35.00% and reduces RMSD by 32.64%. On the ODAC25 dataset (MOF-adsorbate), AtomMOF is substantially more sample-efficient than grand canonical Monte Carlo in recovering adsorption configurations and can identify candidates with lower adsorption energies than the reference dataset. Code is available at https://github.com/nayoung10/AtomMOF.

Accurate modelling of electrostatic interactions and charge transfer is fundamental to computational chemistry, yet most machine learning interatomic potentials (MLIPs) rely on local atomic descriptors that cannot capture long-range electrostatic effects. We present a new electrostatic foundation model for molecular chemistry that extends the MACE architecture with explicit treatment of long-range interactions and electrostatic induction. Our approach combines local many-body geometric features with a non-self-consistent field formalism that updates learnable charge and spin densities through polarisable iterations to model induction, followed by global charge equilibration via learnable Fukui functions to control total charge and total spin. This design enables an accurate and physical description of systems with varying charge and spin states while maintaining computational efficiency. Trained on the OMol25 dataset of 100 million hybrid DFT calculations, our models achieve chemical accuracy across diverse benchmarks, with accuracy competitive with hybrid DFT on thermochemistry, reaction barriers, conformational energies, and transition metal complexes. Notably, we demonstrate that the inclusion of long-range electrostatics leads to a large improvement in the description of non-covalent interactions and supramolecular complexes over non-electrostatic models, including sub-kcal/mol prediction of molecular crystal formation energy in the X23-DMC dataset and a fourfold improvement over short-ranged models on protein-ligand interactions. The model's ability to handle variable charge and spin states, respond to external fields, provide interpretable spin-resolved charge densities, and maintain accuracy from small molecules to protein-ligand complexes positions it as a versatile tool for computational molecular chemistry and drug discovery.

We present a method for computing free-energy differences using thermodynamic integration with a neural network potential that interpolates between two target Hamiltonians. The interpolation is defined at the sample distribution level, and the neural network potential is optimized to match the corresponding equilibrium potential at every intermediate time-step. Once the interpolating potentials and samples are well-aligned, the free-energy difference can be estimated using (neural) thermodynamic integration. To target molecular systems, we simultaneously couple Lennard-Jones and electrostatic interactions and model the rigid-body rotation of molecules. We report accurate results for several benchmark systems: a Lennard-Jones particle in a Lennard-Jones fluid, as well as the insertion of both water and methane solutes in a water solvent at atomistic resolution using a simple three-body neural-network potential.

Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model -- and its qualitative and at times quantitative accuracy -- on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, and chemical reactions. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry.

Thermodynamic integration (TI) offers a rigorous method for estimating free-energy differences by integrating over a sequence of interpolating conformational ensembles. However, TI calculations are computationally expensive and typically limited to coupling a small number of degrees of freedom due to the need to sample numerous intermediate ensembles with sufficient conformational-space overlap. In this work, we propose to perform TI along an alchemical pathway represented by a trainable neural network, which we term Neural TI. Critically, we parametrize a time-dependent Hamiltonian interpolating between the interacting and non-interacting systems, and optimize its gradient using a score matching objective. The ability of the resulting energy-based diffusion model to sample all intermediate ensembles allows us to perform TI from a single reference calculation. We apply our method to Lennard-Jones fluids, where we report accurate calculations of the excess chemical potential, demonstrating that Neural TI reproduces the underlying changes in free energy without the need for simulations at interpolating Hamiltonians.

When hydrogen atoms occupy interstitial sites in metal lattices, they form metal hydrides (MHx), whose structural and electronic properties can differ significantly from the host metals. Owing to the small size of hydrogen atom and its unique interactions with the host metal, MHx is of broad interest in both fundamental science and technological applications. Determining where the hydrogen is located within the MHx, and whether it orders on the partially occupied interstitial sites is crucial for predicting and understanding the resultant physical and electronic properties of the hydride. Directly imaging hydrogen within a host material remains a major challenge due to its weak interaction with X-rays and electrons in conventional imaging techniques. Here, we employ electron ptychography, a scanning transmission electron microscopy technique, to image the three-dimensional (3D) distribution of H atoms in Palladium hydrides (PdHx) nanocubes, one of the most studied and industrially relevant MHx materials. We observe an unexpected one-dimensional superlattice ordering of hydrogen within the PdHx nanocubes and 3D hydrogen clustering in localized regions within PdHx nanocubes, revealing spatial heterogeneity in metal hydride nanoparticles previously inaccessible by other methods.

We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models are trained on and compared to atomization energies computed with hybrid density-functional theory. Cross-validation over more than seven thousand small organic molecules yields a mean absolute error of ~10 kcal/mol. Applicability is demonstrated for the prediction of molecular atomization potential energy curves.

One of the distinguishing aspects of CP2K is its seamless integration of diverse structural and transition-state optimization techniques with advanced sampling approaches including Monte Carlo, molecular dynamics, and metadynamics, enabling the efficient exploration of complex potential- and free-energy landscapes, including rare events. These capabilities are combined with a broad hierarchy of energy and force evaluation methods, ranging from classical and machine-learned interaction potentials and mixed quantum-classical multiscale and semiempirical schemes, to highly accurate quantum-mechanical electronic-structure approaches. At the heart of the latter lies the Gaussian and plane-wave framework, along with its augmented all-electron generalization, which have been described in detail in our previous code review [T. D. Kühne et al., J. Chem. Phys. 152, 194103 (2020)]. Building on this foundation, the present work revisits the methods within CP2K that turn electronic structure into dynamics, transport, and spectroscopic response. Particular emphasis is placed on the coupling between static response calculations and nuclear motion: spectra may be evaluated at optimized structures, averaged over thermally sampled configurations, obtained from time-correlation functions along ab-initio or path integral molecular trajectories, or followed in real time together with electronic and nuclear dynamics. The same modular structure also enables equilibrium and biased transport simulations, from Kubo-type linear response to open-boundary approaches under external potentials, highlighting CP2K's unique capability to unify quantum chemistry with quantum and statistical mechanics within a versatile, holistic simulation environment.

Colloids play an important role in fundamental science as well as in nature and technology. They have had a strong impact on the fundamental understanding of statistical physics. For example, colloids have helped to obtain a better understanding of collective phenomena, ranging from phase transitions and glass formation to the swarming of active Brownian particles. Yet the success of colloidal systems hinges crucially on the specific physical and chemical properties of the colloidal particles, i.e. particles with the appropriate characteristics must be available. Here we present an idea to create particles with freely selectable properties. The properties might depend, for example, on the presence of other particles (hence mimicking specific pair or many-body interactions), previous configurations (hence introducing some memory or feedback), or a directional bias (hence changing the dynamics). Without directly interfering with the sample, each particle is fully controlled and can receive external commands through a predefined algorithm that can take into account any input parameters. This is realized with computer-controlled colloids, which we term cybloids - short for cybernetic colloids. The potential of cybloids is illustrated by programming a time-delayed external potential acting on a single colloid and interaction potentials for many colloids. Both an attractive harmonic potential and an annular potential are implemented. For a single particle, this programming can cause subdiffusive behavior or lend activity. For many colloids, the programmed interaction potential allows to select a crystal structure at wish. Beyond these examples, we discuss further opportunities which cybloids offer.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

Phase stability in multicomponent solid solutions depends on configurational entropy beyond the ideal mixing limit, but capturing it together with vibrational entropy within the same atomistic framework remains challenging. Here, we extend non-equilibrium thermodynamic integration to composition-dependent transformations through an alchemical interpolation of the interactions, combined with Monte Carlo identity exchange moves and molecular dynamics that sample the vibrational and non-ideal configurational entropy along the integration path. We apply the framework to the Au-Cu binary alloy using Atomic Cluster Expansion potentials trained on density functional theory data using the LDA, PBE, and r2SCAN functionals, and construct composition-temperature phase diagrams directly from atomistic free energies. We find that explicit configurational sampling lowers the AuCu order-disorder transition temperature predicted by the ACE potential trained on LDA data from approximately 810 K to 710 K, closer to the experimental value of 683 K, and substantially widens the stability range of the solid solution. At the same time, the much larger sensitivity to the exchange-correlation functional shows that this level of agreement should not be interpreted as general predictive accuracy. Non-ideal configurational entropy must therefore be sampled explicitly, alongside a careful choice of functional, for a reliable atomistic description of binary phase diagrams.

Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations and proton disorder. This is made possible by combining advanced free energy methods and state-of-the-art machine learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments, and reliable estimates of the melting points of light and heavy water. We observe that nuclear quantum effects contribute a crucial 0.2 meV/H_2O to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine learning potentials as an intermediate step.

Molecular dynamics (MD) provides insights into atomic-scale processes by integrating over time the equations that describe the motion of atoms under the action of interatomic forces. Machine learning models have substantially accelerated MD by providing inexpensive predictions of the forces, but they remain constrained to minuscule time integration steps, which are required by the fast time scale of atomic motion. In this work, we propose FlashMD, a method to predict the evolution of positions and momenta over strides that are between one and two orders of magnitude longer than typical MD time steps. We incorporate considerations on the mathematical and physical properties of Hamiltonian dynamics in the architecture, generalize the approach to allow the simulation of any thermodynamic ensemble, and carefully assess the possible failure modes of such a long-stride MD approach. We validate FlashMD's accuracy in reproducing equilibrium and time-dependent properties, using both system-specific and general-purpose models, extending the ability of MD simulation to reach the long time scales needed to model microscopic processes of high scientific and technological relevance.

Many chemical concepts can be well defined in the context of quantum chemical theories. Examples are the electronegativity scale of Mulliken and Jaffe and the hard and soft acids and bases concept of Pearson. The sound theoretical basis allows for a systematic definition of such concepts. However, while they are often used to describe and compare chemical processes in terms of reactivity, their predictive power remains unclear. In this work, we elaborate on the predictive potential of chemical reactivity concepts, which can be crucial for autonomous reaction exploration protocols to guide them by first-principles heuristics that expoit these concepts.

The interstellar medium (ISM) is all but empty. To date, more than 300 molecules have already been discovered. Because of the extremely low temperature, the gas-phase chemistry is dominated by barrierless exothermic reactions of radicals and ions. However, several abundant molecules and organic molecules cannot be produced efficiently by gas-phase reactions. To explain the existence of such molecules in the ISM, gas-surface interactions between small molecules and dust particles covered with amorphous solid water (ASW) mantles must be considered. In general, surface processes such as adsorption, diffusion, desorption, and chemical reactions can be linked to the binding energy of molecules to the surface. Hence, a lot of studies have been performed to identify the binding energies of interstellar molecules on ASW surfaces. Cosmic radiation and free electrons may induce a negative charge on the dust particles, and the binding energies may be affected by this charge. In this study, we calculate the binding energies of CO, CH4, and NH3, on neutral and charged ASW surfaces using DFT calculations. Our results indicate that CO can interact with the surface charge, increasing its binding energy. In contrast, the binding energy of CH4 remains unchanged in the presence of surface charge, and that of NH3 typically decreases.

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.

A physically motivated equation that determines the number of electrons of a molecule is proposed based on chemical common sense. It shows that all molecules are entangled in the number of electrons and results in the fundamental assumption of molecular energy convexity that underpins molecular quantum mechanics. The proposed physical principle includes the molecular size consistency principle as a special case. Application of wavefunction theory to the principle shows that an individual molecule with a noninteger number of electrons is locally physical albeit locally unreal. The energy of a molecule is piecewise linear with respect to its continuous number of electrons. The continuity of the number of electrons allows the definition of an electronic chemical potential of a single molecule. A state function equivalent to the energy of a molecule can be defined using the chemical potential as a variable. The aforementioned physical principle can alternatively be expressed as a simple additivity with the new state function. The latter also shows that the quantum entanglement in the number of electrons can be viewed as all molecules sharing the same chemical potential.

Catalysis at solid-liquid interfaces plays a central role in the advancement of energy storage and sustainable chemical production technologies. By enabling accurate, long-time scale simulations, machine learning (ML) models have the potential to accelerate the discovery of (electro)catalysts. While prior Open Catalyst datasets (OC20 and OC22) have advanced the field by providing large-scale density functional theory (DFT) data of adsorbates on surfaces at solid-gas interfaces, they do not capture the critical role of solvent and electrolyte effects at solid-liquid interfaces. To bridge this gap, we introduce the Open Catalyst 2025 (OC25) dataset, consisting of 7,801,261 calculations across 1,511,270 unique explicit solvent environments. OC25 constitutes the largest and most diverse solid-liquid interface dataset that is currently available and provides configurational and elemental diversity: spanning 88 elements, commonly used solvents/ions, varying solvent layers, and off-equilibrium sampling. State-of-the-art models trained on the OC25 dataset exhibit energy, force, and solvation energy errors as low as 0.1 eV, 0.015 eV/A, and 0.04 eV, respectively; significantly lower than than the recently released Universal Models for Atoms (UMA-OC20). Additionally, we discuss the impact of the quality of DFT-calculated forces on model training and performance. The dataset and accompanying baseline models are made openly available for the community. We anticipate the dataset to facilitate large length-scale and long-timescale simulations of catalytic transformations at solid-liquid interfaces, advancing molecular-level insights into functional interfaces and enabling the discovery of next-generation energy storage and conversion technologies.

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data. rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange-correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principle PIMC and DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions.

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 has been trained from scratch because learning additional data typically requires to train again 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 a key for our development of a lifelong machine learning potential (lMLP). Uncertainty quantification can be exploited to transgress a fixed, pre-trained 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.

The key challenge in advancing multivalent-ion batteries lies in finding suitable intercalation hosts. Open-tunnel oxides, featuring one-dimensional channels or nanopores, show promise for enabling effective ion transport. However, the vast range of compositional possibilities renders traditional experimental and quantum-based methods impractical for large-scale studies. This work presents a generative AI framework that uses the Crystal Diffusion Variational Autoencoder (CDVAE) and a fine-tuned Large Language Model (LLM) to expedite the discovery of stable open-tunneled oxide materials for multivalent-ion batteries. By combining machine learning with data mining techniques, five promising transition metal oxide (TMO) structures are generated. These structures, known for forming open-tunnel oxide frameworks, are structurally validated through Density Functional Theory (DFT). The results show that the generated structures have lower formation energies compared to similar compositions in the Materials Project (MP) database, indicating improved thermodynamic stability. Additionally, the graph-based M3GNet model is employed to relax further generated structures, providing a more computationally efficient alternative to DFT. Machine learning-based predictions of formation energy, band gap, and energy above the hull refine the selection process, leading to the identification of materials with significant potential for real-world battery applications. This research demonstrates the power of generative AI in rapidly exploring the vast chemical space of TMOs, offering a new approach to discovering stable open-tunnel oxides for multivalent-ion batteries. The results highlight the potential of this approach to contribute to more sustainable energy storage technologies, addressing the growing concerns surrounding the scarcity of lithium.

Accurate and fast prediction of materials properties is central to the digital transformation of materials design. However, the vast design space and diverse operating conditions pose significant challenges for accurately modeling arbitrary material candidates and forecasting their properties. We present MatterSim, a deep learning model actively learned from large-scale first-principles computations, for efficient atomistic simulations at first-principles level and accurate prediction of broad material properties across the periodic table, spanning temperatures from 0 to 5000 K and pressures up to 1000 GPa. Out-of-the-box, the model serves as a machine learning force field, and shows remarkable capabilities not only in predicting ground-state material structures and energetics, but also in simulating their behavior under realistic temperatures and pressures, signifying an up to ten-fold enhancement in precision compared to the prior best-in-class. This enables MatterSim to compute materials' lattice dynamics, mechanical and thermodynamic properties, and beyond, to an accuracy comparable with first-principles methods. Specifically, MatterSim predicts Gibbs free energies for a wide range of inorganic solids with near-first-principles accuracy and achieves a 15 meV/atom resolution for temperatures up to 1000K compared with experiments. This opens an opportunity to predict experimental phase diagrams of materials at minimal computational cost. Moreover, MatterSim also serves as a platform for continuous learning and customization by integrating domain-specific data. The model can be fine-tuned for atomistic simulations at a desired level of theory or for direct structure-to-property predictions, achieving high data efficiency with a reduction in data requirements by up to 97%.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms H_c, {He_c}^+ and {Li_c}^{2+} confined by an impenetrable spherical box. Novel expressions for entropic uncertainty relation and Shannon entropies S_r and S_p are proposed to ensure their physical dimensionless characteristic. The electronic ground state energy and the quantities S_r, S_p and S_t are calculated for the hydrogenic-like atoms to different confinement radii by using a variational method. The global behavior of these quantities and different conjectures are analyzed. The results are compared, when available, with those previously published.

The combination of modern scientific computing with electronic structure theory can lead to an unprecedented amount of data amenable to intelligent data analysis for the identification of meaningful, novel, and predictive structure-property relationships. Such relationships enable high-throughput screening for relevant properties in an exponentially growing pool of virtual compounds that are synthetically accessible. Here, we present a machine learning (ML) model, trained on a data base of ab initio calculation results for thousands of organic molecules, that simultaneously predicts multiple electronic ground- and excited-state properties. The properties include atomization energy, polarizability, frontier orbital eigenvalues, ionization potential, electron affinity, and excitation energies. The ML model is based on a deep multi-task artificial neural network, exploiting underlying correlations between various molecular properties. The input is identical to ab initio methods, i.e. nuclear charges and Cartesian coordinates of all atoms. For small organic molecules the accuracy of such a "Quantum Machine" is similar, and sometimes superior, to modern quantum-chemical methods---at negligible computational cost.

We developed a multiscale approach (MultiSCAAL) that integrates the potential of mean force (PMF) obtained from all-atomistic molecular dynamics simulations with a knowledge-based energy function for coarse-grained molecular simulations in better exploring the energy landscape of a small protein under chemical interference such as chemical denaturation. An excessive amount of water molecules in all-atomistic molecular dynamics simulations often negatively impacts the sampling efficiency of some advanced sampling techniques such as the replica exchange method and it makes the investigation of chemical interferences on protein dynamics difficult. Thus, there is a need to develop an effective strategy that focuses on sampling structural changes in protein conformations rather than solvent molecule fluctuations. In this work, we address this issue by devising a multiscale simulation scheme (MultiSCAAL) that bridges the gap between all-atomistic molecular dynamics simulation and coarse-grained molecular simulation. The two key features of this scheme are the Boltzmann inversion and a protein atomistic reconstruction method we previously developed (SCAAL). Using MultiSCAAL, we were able to enhance the sampling efficiency of proteins solvated by explicit water molecules. Our method has been tested on the folding energy landscape of a small protein Trp-cage with explicit solvent under 8M urea using both the all-atomistic replica exchange molecular dynamics (AA-REMD) and MultiSCAAL. We compared computational analyses on ensemble conformations of Trp-cage with its available experimental NOE distances. The analysis demonstrated that conformations explored by MultiSCAAL better agree with the ones probed in the experiments because it can effectively capture the changes in side chain orientations that can flip out of the hydrophobic pocket in the presence of urea and water molecules.

Point defects play a central role in driving the properties of materials. First-principles methods are widely used to compute defect energetics and structures, including at scale for high-throughput defect databases. However, these methods are computationally expensive, making machine-learning force fields (MLFFs) an attractive alternative for accelerating structural relaxations. Most existing MLFFs are based on graph neural networks (GNNs), which can suffer from oversmoothing and poor representation of long-range interactions. Both of these issues are especially of concern when modeling point defects. To address these challenges, we introduce the Accelerated Deep Atomic Potential Transformer (ADAPT), an MLFF that replaces graph representations with a direct coordinates-in-space formulation and explicitly considers all pairwise atomic interactions. Atoms are treated as tokens, with a Transformer encoder modeling their interactions. Applied to a dataset of silicon point defects, ADAPT achieves a roughly 33 percent reduction in both force and energy prediction errors relative to a state-of-the-art GNN-based model, while requiring only a fraction of the computational cost.

Machine learning potentials are an important tool for molecular simulation, but their development is held back by a shortage of high quality datasets to train them on. We describe the SPICE dataset, a new quantum chemistry dataset for training potentials relevant to simulating drug-like small molecules interacting with proteins. It contains over 1.1 million conformations for a diverse set of small molecules, dimers, dipeptides, and solvated amino acids. It includes 15 elements, charged and uncharged molecules, and a wide range of covalent and non-covalent interactions. It provides both forces and energies calculated at the ωB97M-D3(BJ)/def2-TZVPPD level of theory, along with other useful quantities such as multipole moments and bond orders. We train a set of machine learning potentials on it and demonstrate that they can achieve chemical accuracy across a broad region of chemical space. It can serve as a valuable resource for the creation of transferable, ready to use potential functions for use in molecular simulations.

In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields an implicit solvent method identical in form to the Molecular Density Functional theory of Borgis et. al., but with an explicit formula for the 'ideal' free energy term. This new expression for the ideal free energy term can be computed from all-atom molecular dynamics of a solvent with only short-range interactions. The key hypothesis required to make the theory valid is that all smooth (and hence long-range) energy functions obey Gaussian statistics. This is essentially a random phase approximation for perturbations from a short-range only, 'reference,' fluid. This single hypothesis is enough to prove that the self-consistent LMF procedure minimizes a novel density functional whose 'ideal' free energy is the molecular system under a specific, reference Hamiltonian, as opposed to the non-interacting gas of conventional density functionals. Implementation of this new functional into existing software should be straightforward and robust.

Machine-learned exchange--correlation (XC) functionals offer a route to improve Kohn--Sham density-functional theory without incurring the cost of explicitly correlated electronic-structure methods. Their use in production simulation codes, however, requires a well-defined mapping between the learned model and the host-code density representation. We formulate and implement a Skala-1.1 interface in CP2K through the external GauXC library. CP2K supplies the geometry, Gaussian basis, spin-resolved atomic-orbital density matrix, and communicator, while GauXC evaluates the XC energy, atomic-orbital potential matrix, and available nuclear derivatives. The interface accepts both all-electron and valence-only density matrices. The latter may arise from separable dual-space pseudopotentials or molecular effective-core potentials. Implementation errors are isolated from functional differences by comparing the Perdew--Burke--Ernzerhof (PBE) functional evaluated through GauXC with native CP2K PBE. The resulting interface gives consistent energies, forces validated against finite-difference total-energy checks, and force-based molecular-virial diagnostics for representative molecular cases. The dietGMTKN55 benchmark suite is evaluated with an all-electron Gaussian augmented plane-wave treatment for elements up to bromine and def2 effective-core potentials for the heavier elements. The resulting aggregate mean absolute deviation of 1.255 kcal/mol is within 0.020 kcal/mol of the corresponding Skala reference value of 1.235 kcal/mol. This work establishes a validated molecular implementation of Skala in CP2K through GauXC.

Generating the periodic structure of stable materials is a long-standing challenge for the material design community. This task is difficult because stable materials only exist in a low-dimensional subspace of all possible periodic arrangements of atoms: 1) the coordinates must lie in the local energy minimum defined by quantum mechanics, and 2) global stability also requires the structure to follow the complex, yet specific bonding preferences between different atom types. Existing methods fail to incorporate these factors and often lack proper invariances. We propose a Crystal Diffusion Variational Autoencoder (CDVAE) that captures the physical inductive bias of material stability. By learning from the data distribution of stable materials, the decoder generates materials in a diffusion process that moves atomic coordinates towards a lower energy state and updates atom types to satisfy bonding preferences between neighbors. Our model also explicitly encodes interactions across periodic boundaries and respects permutation, translation, rotation, and periodic invariances. We significantly outperform past methods in three tasks: 1) reconstructing the input structure, 2) generating valid, diverse, and realistic materials, and 3) generating materials that optimize a specific property. We also provide several standard datasets and evaluation metrics for the broader machine learning community.

The one-dimensional J_1-J_2 q-state Potts model is solved exactly for arbitrary q, based on using OpenAI's latest reasoning model o3-mini-high to exactly solve the q=3 case. The exact results provide insights to outstanding physical problems such as the stacking of atomic or electronic orders in layered materials and the formation of a T_c-dome-shaped phase often seen in unconventional superconductors. The work is anticipated to fuel both the research in one-dimensional frustrated magnets for recently discovered finite-temperature application potentials and the fast moving topic area of AI for sciences.

The gradual insertion method for direct calculation of the chemical potential by molecular simulation is applied in the NpT ensemble to different quadrupolar two-centre Lennard-Jones fluids at high density state points. The results agree well with Widom's test particle insertion but show at very high densities significantly smaller statistical uncertainties. The gradual insertion method, which is coupled here with preferential sampling, extends the density range where reliable information on the chemical potential can be obtained. Application details are reported.

The origin of a chemical reaction between two reactant atoms is associated to the activation energy, with the assumption that, high-energy collisions between these atoms, are the ones that overcome the activation energy. Here, we (i) show that a stronger attractive van der Waals (vdW) and electron-ion Coulomb interactions between two polarized atoms are responsible to initiate a chemical reaction, either before or after the collision. We derive this stronger vdW attraction formula exactly using the quasi one-dimensional Drude model within the ionization energy theory and the energy-level spacing renormalization group method. Along the way, we (ii) expose the precise physical mechanism responsible for the existence of a stronger vdW interaction for both long and short distances, and also show how to technically avoid the electron-electron Coulomb repulsion between polarized electrons from these two reactant atoms. Finally, we properly and correctly associate the existence of this stronger attraction to Ramachandran's 'normal limits' (distance shorter than what is allowed by the standard vdW bond) between chemically nonbonded atoms.

Large-amplitude molecular motions which occur during isomerization can cause significant changes in electronic structure. These variations in electronic properties can be used to identify vibrationally-excited eigenstates which are localized along the potential energy surface. This work demonstrates that nuclear quadrupole hyperfine interactions can be used as a diagnostic marker of progress along the isomerization path in both the HC14N/H14NC and DC15N/D15NC chemical systems. Ab initio calculations at the CCSD(T)/cc-pCVQZ level indicate that the hyperfine interaction is extremely sensitive to the chemical bonding of the quadrupolar 14N nucleus and can therefore be used to determine in which potential well the vibrational wavefunction is localized. A natural bonding orbital analysis along the isomerization path further demonstrates that hyperfine interactions arise from the asphericity of the electron density at the quadrupolar nucleus. Using the CCSD(T) potential surface, the quadrupole coupling constants of highly-excited vibrational states are computed from a one-dimensional internal coordinate path Hamiltonian. The excellent agreement between ab initio calculations and recent measurements demonstrates that nuclear quadrupole hyperfine structure can be used as a diagnostic tool for characterizing localized HCN and HNC vibrational states.

The stacking-dependent polarization and excitonic response of MoS_2/MoSe_2 heterostructures were investigated using GW+BSE many-body perturbation theory. While homobilayer MoS_2 exhibited a switchable interlayer dipole driven by registry-induced symmetry breaking, the MoS_2/MoSe_2 hetero-interface remained pinned by the intrinsic chemical potential mismatch between sulfur and selenium. In 2L-MoS_2/MoSe_2 trilayers, the stacking sequence enabled a deterministic control of photogenerated electrons between the central and bottom MoS_2 layers, governed by internal electric fields and quasiparticle band-edge shifts of 60--70~meV. Our calculations predicted a 36~meV interlayer excitonic shift, in remarkable agreement with recent experiments. These results elucidate the microscopic link between atomic registry and many-body interactions, establishing transition metal dichalcogenide trilayers as a potential platform for sliding ferroelectricity and programmable optoelectronic functionalities.

The mobility edge (ME) is a critical energy delineates the boundary between extended and localized states within the energy spectrum, and it plays a crucial role in understanding the metal-insulator transition in disordered or quasiperiodic systems. While there have been extensive studies on MEs in one-dimensional non-Hermitian (NH) quasiperiodic lattices recently, the investigation of exact NH MEs in two-dimensional (2D) cases remains rare. In the present study, we introduce a 2D dissipative Lieb lattice (DLL) model with imaginary quasiperiodic potentials applied solely to the vertices of the Lieb lattice. By mapping this DLL model to the 2D NH Aubry-Andr{é}-Harper (AAH) model, we analytically derive the exact ME and find it associated with the absolute eigenenergies. We find that the eigenvalues of extended states are purely imaginary when the quasiperiodic potential is strong enough. Additionally, we demonstrate that the introduction of imaginary quasiperiodic potentials does not disrupt the flat bands inherent in the system. Finally, we propose a theoretical framework for realizing our model using the Lindblad master equation. Our results pave the way for further investigation of exact NH MEs and flat bands in 2D dissipative quasiperiodic systems.

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.

Graphene stands as a promising material with vast potential across energy storage, electronics, etc. Here, we present a novel mechanical approach utilizing ultrasonic high-energy intercalation exfoliation to extract monolayer graphene from graphite, offering a simple yet efficient alternative to conventional methods. Through a comprehensive series of characterizations involving atomic force microscopy, scanning electron microscopy, Raman spectroscopy, X-ray diffraction, and X-ray photoelectron spectroscopy, the resulting graphene nanosheets demonstrate superior crystallinity compared to those obtained via the conventional method. The high-crystalline freestanding graphene nanosheets derived from this method not only facilitate easier separation but also significantly enhance the physical performance of the original materials. This method showcases the potential for scalable production of layered materials with increased yield and crystallinity, paving the way for their utilization in various applications.

I investigate the spontaneous-fission (SF) half-lives of ^{254,256}Rf within the multidimensionally constrained relativistic Hartree-Bogoliubov (MDC-RHB) model combined with the local quasiparticle random-phase approximation (LQRPA) method. The collective inertia is evaluated using the finite-amplitude method (FAM), which enables a fully self-consistent treatment of dynamical residual effects beyond the conventional cranking approximation. The effective collective potential is constructed by subtracting both the vibrational zero-point energy and rotational energy correction from the deformation energy surface. The SF half-lives are evaluated within the Wentzel-Kramers-Brillouin (WKB) approximation. Compared with the nonperturbative and perturbative cranking approximation, the FAM-LQRPA collective inertia is significantly enhanced, especially around the ground-state minimum, due to the dynamical residual interaction included in the QRPA. As a consequence, the predicted SF half-lives increase by several orders of magnitude and become consistent with experimental data. The calculated SF half-lives are 5.65 μs for ^{254}Rf and 0.95 ms for ^{256}Rf, both within approximately two orders of magnitude of the corresponding experimental values. These results indicate that a self-consistent treatment of dynamical residual effects and beyond mean-field correlations is crucial for quantitative microscopic descriptions of SF within covariant density functional theory.

We present a scheme to obtain an inexpensive and reliable estimate of the uncertainty associated with the predictions of a machine-learning model of atomic and molecular properties. The scheme is based on resampling, with multiple models being generated based on sub-sampling of the same training data. The accuracy of the uncertainty prediction can be benchmarked by maximum likelihood estimation, which can also be used to correct for correlations between resampled models, and to improve the performance of the uncertainty estimation by a cross-validation procedure. In the case of sparse Gaussian Process Regression models, this resampled estimator can be evaluated at negligible cost. We demonstrate the reliability of these estimates for the prediction of molecular energetics, and for the estimation of nuclear chemical shieldings in molecular crystals. Extension to estimate the uncertainty in energy differences, forces, or other correlated predictions is straightforward. This method can be easily applied to other machine learning schemes, and will be beneficial to make data-driven predictions more reliable, and to facilitate training-set optimization and active-learning strategies.

In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form, F(f(x)), and obtain a generalized Mielnik construction of one-parameter isospectral potentials when we use the general Riccati solution. Some examples for special cases of F and f are given to illustrate the method. An interesting result is obtained in the case of a parametric double well potential generated by this method, for which it is shown that the parameter of the potential controls the heights of the localization probability in the two wells, and for certain values of the parameter the height of the localization probability can be higher in the smaller well

We investigate the effects of spatially localized conserved quantities on transport and thermalization in quantum and classical many-body systems. We consider several related models: the integrable quantum Volterra model, its nonintegrable classical limit, and two cellular automata derived from the latter. Although localized constraints are often associated with lattice gauge theories, our models do not admit such an interpretation. In systems with discrete degrees of freedom, these constraints induce uniform fragmentation of the Hilbert or configuration space. In the quantum Volterra model, we derive an exact mapping of the dynamics within each Hilbert-space fragment onto a quantum chiral Potts chain. We find that energy transport is ballistic, with identical transport coefficients across all fragments. In the nonintegrable classical limit, energy transport is diffusive, and we similarly find the diffusion constant to be independent of whether or not the constraints are fixed (resolved). Finally, in the cellular automata, we show that, despite leaving transport unaffected, localized constraints lead to a strong breakdown of local ergodicity.

Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate change. These calculations are traditionally performed using Density Functional Theory, which is computationally very expensive. Machine learning has the potential to dramatically improve the efficiency of these calculations from days or hours to seconds. We propose the Spherical Channel Network (SCN) to model atomic energies and forces. The SCN is a graph neural network where nodes represent atoms and edges their neighboring atoms. The atom embeddings are a set of spherical functions, called spherical channels, represented using spherical harmonics. We demonstrate, that by rotating the embeddings based on the 3D edge orientation, more information may be utilized while maintaining the rotational equivariance of the messages. While equivariance is a desirable property, we find that by relaxing this constraint in both message passing and aggregation, improved accuracy may be achieved. We demonstrate state-of-the-art results on the large-scale Open Catalyst dataset in both energy and force prediction for numerous tasks and metrics.

The many-body nature of nuclear physics problems poses significant computational challenges. These challenges become even more pronounced when studying the resonance states of nuclear systems, which are governed by the non-Hermitian Hamiltonian. Quantum computing, particularly for quantum many-body systems, offers a promising alternative, especially within the constraints of current noisy intermediate-scale quantum (NISQ) devices. This work aims to simulate nuclear resonances using quantum algorithms by developing a variational framework compatible with non-Hermitian Hamiltonians and implementing it fully on a quantum simulator. We employ the complex scaling technique to extract resonance positions classically and adapt it for quantum simulations using a two-step algorithm. First, we transform the non-Hermitian Hamiltonian into a Hermitian form by using the energy variance as a cost function within a variational framework. Second, we perform theta-trajectory calculations to determine optimal resonance positions in the complex energy plane. To address resource constraints on NISQ devices, we utilize Gray Code (GC) encoding to reduce qubit requirements. We first validate our approach using a schematic potential model that mimics a nuclear potential, successfully reproducing known resonance energies with high fidelity. We then extend the method to a more realistic alpha-alpha nuclear potential and compute the resonance energies with a basis size of 16, using only four qubits. This study demonstrates, for the first time, that the complete theta-trajectory method can be implemented on a quantum computer without relying on any classical input beyond the Hamiltonian. The results establish a scalable and efficient quantum framework for simulating resonance phenomena in nuclear systems. This work represents a significant step toward quantum simulations of open quantum systems.

The presence of point defects such as vacancies plays an important role in material design. Here, we demonstrate that a graph neural network (GNN) model trained only on perfect materials can also be used to predict vacancy formation energies (E_{vac}) of defect structures without the need for additional training data. Such GNN-based predictions are considerably faster than density functional theory (DFT) calculations with reasonable accuracy and show the potential that GNNs are able to capture a functional form for energy predictions. To test this strategy, we developed a DFT dataset of 508 E_{vac} consisting of 3D elemental solids, alloys, oxides, nitrides, and 2D monolayer materials. We analyzed and discussed the applicability of such direct and fast predictions. We applied the model to predict 192494 E_{vac} for 55723 materials in the JARVIS-DFT database.

A dynamical model based on a phenomenological charm quark-nucleon(c-N) potential v_{cN} and the Pomeron-exchange mechanism is constructed to investigate the J/Psi photo-production on the nucleon from threshold to invariant mass W=300 GeV. The J/Psi-N potential,V_{J/Psi N}(r),is constructed by folding v_{cN} into the wavefunction Phi_{J/Psi}(cc) of J/Psi within a Constituent Quark Model(CQM) of Ref.[43]. A photo-production amplitude is also generated by v_{cN} by a cc-loop integration over the gammarightarrow cc vertex function and Phi_{J/Psi}(cc). No commonly used Vector Meson Dominance assumption is used to define this photo-production amplitude which is needed to describe the data near the threshold. The potential v_{cN}(r) is parameterized in a form such that the predicted V_{J/Psi N}(r) at large distances has the same Yukawa potential form extracted from a Lattice QCD(LQCD) calculation of Ref.[18]. The parameters of v_{cN} are determined by fitting the total cross section data of JLab by performing calculations that include J/Psi-N final state interactions(FSI). The resulting differential cross sections are found in good agreements with the data. It is shown that the FSI effects dominate the cross section in the very near threshold region, allowing for sensitive testing of the predicted J/Psi-N scattering amplitudes. By imposing the constraints of J/Psi-N potential extracted from the LQCD calculation, we have obtained three J/Psi-N potentials which fit the JLab data equally well. The resulting J/Psi-N scattering lengths are in the range of a=(-0.05 fm sim -0.25 fm). With the determined v_{cN}(r) and the wavefunctions generated from the same CQM, the constructed model is used to predict the cross sections of photo-production of eta_c(1S) and Psi(2S) mesons for future experimental tests.

Unified atomistic modeling has the potential to accelerate discovery in chemistry, materials science, and biology by bridging data-rich chemical domains and data-scarce biological contexts. However, existing generative approaches to atomistic modeling remain highly specialized to scientific disciplines (chemistry vs. biology) or do not leverage both high-volume organic (molecule) and inorganic (material) data for general-purpose pretraining. To this end, we introduce Zatom-2, an atomistic generative model pretrained on approximately five million structures from the OMol25 and OMat24 electronic structure datasets. Zatom-2 features a multiscale Transformer architecture coupled with conditional flow matching that supports force conditioning and foundational pretraining tasks such as generation, structure prediction, and prediction of molecular and material energies and forces. Empirically, Zatom-2 achieves better molecular distribution fidelity than Zatom-1 and achieves strong performance on existing molecule and material generation benchmarks. Zatom-2 demonstrates the ability to control sample generation across low- and high-force regimes, and enhances protein generation in a low-data setting through joint generative-predictive pretraining and transfer learning, increasing protein backbone designability in a length extrapolation setting from 67.8% without pretraining to 74.8% after finetuning on 2,000 protein domains.

In this paper, we introduce a mesh-free two-level hybrid Tucker tensor format for approximation of multivariate functions, which combines the product Chebyshev interpolation with the ALS-based Tucker decomposition of the tensor of Chebyshev coefficients. It allows to avoid the expenses of the rank-structured approximation of function-related tensors defined on large spacial grids, while benefiting from the Tucker decomposition of the rather small core tensor of Chebyshev coefficients. This leads to nearly optimal Tucker rank parameters which are close to the results for well established Tucker-ALS algorithm applied to the large grid-based tensors. These rank parameters inherited from the Tucker-ALS decomposition of the coefficient tensor can be much less than the polynomial degrees of the initial Chebyshev interpolant via function independent basis set. Furthermore, the tensor product Chebyshev polynomials discretized on a tensor grid leads to a low-rank two-level orthogonal algebraic Tucker tensor that approximates the initial function with controllable accuracy. It is shown that our techniques could be gainfully applied to the long-range part of the electrostatic potential of multi-particle systems approximated in the range-separated tensor format. Error and complexity estimates of the proposed methods are presented. We demonstrate the efficiency of the suggested method numerically on examples of the long-range components of multi-particle interaction potentials generated by 3D Newton kernel for large bio-molecule systems and lattice-type compounds.

The rapid advancements in artificial intelligence (AI) are catalyzing transformative changes in atomic modeling, simulation, and design. AI-driven potential energy models have demonstrated the capability to conduct large-scale, long-duration simulations with the accuracy of ab initio electronic structure methods. However, the model generation process remains a bottleneck for large-scale applications. We propose a shift towards a model-centric ecosystem, wherein a large atomic model (LAM), pre-trained across multiple disciplines, can be efficiently fine-tuned and distilled for various downstream tasks, thereby establishing a new framework for molecular modeling. In this study, we introduce the DPA-2 architecture as a prototype for LAMs. Pre-trained on a diverse array of chemical and materials systems using a multi-task approach, DPA-2 demonstrates superior generalization capabilities across multiple downstream tasks compared to the traditional single-task pre-training and fine-tuning methodologies. Our approach sets the stage for the development and broad application of LAMs in molecular and materials simulation research.

In this paper, we examine the thermodynamic behavior of a quantum harmonic oscillator with a position-dependent mass (PDM), where spatial inhomogeneity is modeled through a deformation parameter α. Based on the exact energy spectrum, we explore the resulting thermodynamic quantities and superstatistics. Our findings reveal that increasing α leads to a decrease in entropy and specific heat, reflecting a confinement-induced reduction in the number of accessible states. The partition function and free energy exhibit smooth behavior across all parameter regimes, indicating the absence of critical phase transitions. This study underscores the influence of mass deformation on quantum thermal responses and demonstrates that, while the overall thermodynamic trends are consistent with those reported in the literature, certain distinctive features emerge due to the specific form of the deformation.

We present anyakrakusuma, an open-source Python library that solves the discrete static Schrödinger bridge problem, the entropically regularized counterpart of optimal transport, through a log-domain Sinkhorn--Knopp iteration and reconstructs the entropic interpolation between two empirical point clouds. The solver is paired with a diagnostic pipeline that characterizes the optimal coupling and the intermediate distributions through information-theoretic and geometric measures. We exercise the library on four idealized planar cases spanning a circle-to-circle dilation, a spiral-to-mixture fragmentation, a rigid reorientation of two moons, and a Lissajous-to-trefoil deformation. The log-domain formulation is necessary rather than merely convenient at the parameters studied, where the cost-to-regularization ratio reaches four hundred and the Gibbs kernel underflows double precision across most of its range; the iteration nonetheless attains a marginal residual of 10^{-9} and unit marginal fidelity in every case. Residual histories decay geometrically over approximately eight decades at per-iteration contraction factors between 0.966 and 0.976, which are local rates near the fixed point that lie many orders of magnitude below the worst-case Hilbert-metric bound. The covariance analysis recovers an imposed ninety-degree reorientation to within 0.07^circ, roughly forty times smaller than its uncertainty, across a masked interval of near-isotropy on which the principal axis is unobservable. The diagnostics are reported with explicit attention to the regimes in which each is well defined, including the differential entropy, which is meaningful only on the open interpolation interval. The presented cases are constructed rather than measured; quantitative application to empirical point clouds requires further study.

Chemical intercalation provides a powerful route for tuning the electronic and magnetic properties of transition metal dichalcogenides (TMDs), enabling the emergence of magnetic phases and phenomena that are otherwise inaccessible in their pristine forms. Here, we investigate the structural, electronic, and magnetic properties of magnetically intercalated Cr_{1+x}Te_2 through a combination of scanning tunneling microscopy, angle-resolved photoemission spectroscopy, magnetization, electrical transport, and Lorentz transmission electron microscopy measurements. We uncover a rich magnetic phase diagram comprising paramagnetic, in-plane spin-fluctuation, out-of-plane ferromagnetic, and field-induced Néel-type skyrmion phases. In particular, Lorentz transmission electron microscopy directly reveals the formation of Néel-type skyrmion textures slightly below the Curie temperature, with their configurations evolving strongly with temperature and magnetic field. The skyrmions exhibit pronounced thermal hysteresis and coexist with stripe domains, indicative of a complex magnetic energy landscape arising from the competition among disorder-induced local Dzyaloshinskii-Moriya interactions, perpendicular magnetic anisotropy, and dipolar interactions. Our results demonstrate that chemical intercalation can profoundly reshape the magnetic interactions and phase behavior of TMDs, establishing Cr_{1+x}Te_2 as a versatile platform for exploring tunable magnetism, skyrmion physics, and unconventional thermodynamic phenomena in low-dimensional quantum materials.

The independent atom ansatz of density functional theory yields an accurate analytical expression for dynamic correlation energy in the H_{2} molecule: E_{c} = 0.5(1 - 2)(ab|ba) for the atom-additive self-consistent density rho = |a|^{2} + |b|^{2}. Combined with exact atomic self-exchange, it recovers more than 99.5 % of nearly exact SCAN exchange-correlation energy at R > 0.5 A, differing by less than 0.12 eV. The total energy functional correctly dissociates the H-H bond and yields absolute errors of 0.002 A, 0.19 eV, and 13 cm^{-1} relative to experiment at the tight binding computational cost. The chemical bond formation is attributed to the asymptotic Heitler-London resonance of quasi-orthogonal atomic states (- (ab|ba)) with no contributions from kinetic energy or charge accumulation in the bond.

Experiments in recent years on high T_c superconductors find a puzzling nodal scale-covariant self-energy with an exponent varying continuously with doping. We propose a mechanism: nonlocality induced by poorly screened effective repulsions V_α(r) sim 1/r^α, where a continuously doping-dependent exponent 1 le αle 3 naturally interpolates between the Mott insulating and Fermi liquid limits. We develop a phenomenology of hydrodynamic screening, finding a scale-covariant quasiparticle decay rate Γ(ω,T) propto T^γ Φ(ω/T) in energy ω and temperature T, with γ= 2-1α for nonlocal 1 < α< 2. Our results naturally capture the optimally doped to overdoped regimes, whereas the underdoped regime is qualitatively distinct. In our theory, spectroscopy-fitted exponents directly probe the charged fluid's effective spatial nonlocality. Nonlocality shows that quantum criticality is not necessary to explain scale-covariant phenomena.

Initial states of dense matter with nonzero electron chiral imbalance could potentially give rise to strong magnetic fields through chiral plasma instability. Previous work indicated that unless chiral chemical potential is as large as the electron vector chemical potential, the growth of magnetic fields due to the instability is washed out by chirality flipping rate enabled by electron mass. We re-examine this claim in a broader range of parameters and find that at higher temperatures the hierarchy is reversed supporting a growing magnetic field for an initial electron chiral chemical potential much smaller than the electron vector chemical potential. Further, we identify a qualitatively new effect relevant for magnetized hot and dense medium where chiral magnetic effect (CME) sourced by density fluctuation acts as a powerful source of Joule heating. Remarkably, even modest chiral chemical potentials (keV) in such environment can deposit energy densities set by the QCD scale in a relatively short time of the order of a few milliseconds or seconds. We speculate how this mechanism makes CME-driven Joule heating a potentially critical ingredient in the dynamics of turbulent density fluctuation of supernovae and neutron star mergers.

It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}Ψprobability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this probability axiom to the complex plane, we first attempt to find a probability density by solving an appropriate conservation equation. The characteristic curves of this conservation equation are found to be the same as the complex paths of particles in the new representation. The boundary condition in this case is that the extended probability density should agree with the quantum probability rule along the real line. For the simple, time-independent, one-dimensional problems worked out here, we find that a conserved probability density can be derived from the velocity field of particles, except in regions where the trajectories were previously suspected to be nonviable. An alternative method to find this probability density in terms of a trajectory integral, which is easier to implement on a computer and useful for single particle solutions, is also presented. Most importantly, we show, by using the complex extension of Schrodinger equation, that the desired conservation equation can be derived from this definition of probability density.

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in d+1 dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a Z_2 spin liquid has been hypothesized recently.