To solve the Kohn-Sham equation within the framework of density functional theory, we develop a scheme to construct numerical atomic orbital (NAO) basis sets by contracting truncated spherical waves (TSWs). The contraction minimizes the trace of the kinetic operator in the residual space, generalizing the spillage minimizing scheme [M. Chen et al., J. Phys. Condens. Matter 22, 445501 (2010); P. Lin et al., Phys. Rev. B 103, 235131 (2021)]. In addition to the systematic improvability inherited from previous schemes, the use of TSW instead of plane waves as the expansion basis bridges reference states and NAOs more effectively, and eliminates spurious interactions between periodic images, thereby enabling better transferability through the inclusion of extensive reference states. Benchmarks demonstrate that the constructed NAO achieves satisfactory precision for various properties of both molecules and bulk systems, including total energy, bond length, atomization energy, lattice constant, cohesive energy, band gap, and energy-level alignment. By incorporating unoccupied states, the improved transferability in describing the conduction band is demonstrated to be effective and substantial.

Abstract Quantum mechanics plays a key role in warm dense matter plasmas and high-energy fusion particles under extreme conditions. Real-time time-dependent orbital-free density functional theory (OFDFT) avoids the orthogonal operations on wavefunctions and the use of k -point sampling in the Brillouin zone, showing advantages over the Kohn-Sham DFT. With an appropriate dynamic kinetic energy potential, OFDFT is suitable for simulating dynamic properties of materials under extreme conditions, such as electronic stopping power in warm dense matter. We propose a revised form of the dynamic kinetic energy potential by introducing a scaling factor to refine the approximation of the dynamic Lindhard function’s derivative. Compared with the Kohn-Sham DFT results, the proposed method effectively mitigates the overestimation of the Bragg peak in the electronic stopping power observed in previous OFDFT results. By testing bulk materials including Al, Si, D, Li, and Mg up to 512 atoms, our results show that this method is efficient and applicable for studying stopping power in large-scale material systems.

Reduced density matrix functional theory (RDMFT) offers a route beyond Kohn-Sham density functional theory for strongly correlated systems, yet practical calculations for periodic solids are still out of reach. We formulate RDMFT for extended systems in a basis-independent way and present a planewave implementation using iterative minimization for periodic solids, evaluating nonlocal exchange-correlation functionals through the existing adaptive compressed exchange machinery. Natural occupations are optimized under N-representability constraints with a spectral projected gradient (SPG) method or an first-order explicit-by-implicit (EBI) map, while natural orbitals are updated by Riemannian optimization on the complex Stiefel manifolds. Benchmarks on typical systems of H2, silicon, and sodium with the Hartree-Fock functional show that SPG reproduces converged hybrid references, whereas EBI can stall when occupations approach 0 or 1. With the power and Müller functionals, SPG yields lower energies and more stable convergence than EBI. Applications to fractionally charged LiH, dissociating H2 and N2 molecules, and equation of state of silicon show that the algorithm presented in this implementation is reliable and robust.

Tin (Sn) plays a crucial role in studying the dynamic mechanical responses of ductile metals under shock loading. Atomistic simulations serves to unveil the nano-scale mechanisms for critical behaviors of dynamic responses. However, existing empirical potentials for Sn often lack sufficient accuracy when applied in such simulation. Particularly, the solid-solid phase transition behavior of Sn poses significant challenges to the accuracy of interatomic potentials. To address these challenges, this study introduces a machine-learning potential model for Sn, specifically optimized for shock-response simulations. The model is trained using a dataset constructed through a concurrent learning framework and is designed for molecular simulations across thermodynamic conditions ranging from 0 to 100 GPa and 0 to 5000 K, encompassing both solid and liquid phases as well as structures with free surfaces. It accurately reproduces density functional theory (DFT)-derived basic properties, experimental melting curves, solid-solid phase boundaries, and shock Hugoniot results. This demonstrates the model's potential to bridge ab initio precision with large-scale dynamic simulations of Sn.

Spallation, a critical mode of dynamic fracture, remains a central focus in the study of material response under extreme conditions. While widely studied in common metals, the spallation of tin (Sn), a group IV element exhibiting multiple solid phase along the shock-Hugoniot, presents significant challenges due to its complex pressure-temperature phase diagram. This complexity poses significant challenges for experimental characterization and reliability of interatomic potentials used in atomistic simulations. Consequently, the phase transition pathways and their influence on spallation in Sn remain poorly understood. In this work, we employ non-equilibrium molecular dynamics simulations using a first-principles accuracy machine learning potential to simulate the dynamic response of Sn at strain rates down to ∼6×109/s, which is comparable to experiments. Our simulations successfully capture critical behaviors such as shock-induced phase transitions and melting, and reproduce their experimental shock pressures. Meanwhile, the results clearly elucidate the β-to-bct transition pathway, revealing a two-stage mechanism mediated by an intermediate simple-hexagonal phase. Furthermore, we identify two distinct dynamic behaviors along the loading-unloading thermodynamic pathway: phase transition-mediated release amorphization and shock-induced kinetic metastable cold melting below the equilibrium melting point. These behaviors are shown to originate from the large differences in the slopes of the melting lines between adjacent solid phases. These findings provide atomistic-scale evidence directly linking phase transformations to spallation failure, offering new insights into the fundamental physics of dynamic fracture in Sn.

ABSTRACT The design of a low‐Ir‐loading anode catalyst with high activity and stability is crucial for the proton exchange membrane water electrolysis (PEMWE), yet it remains a formidable challenge. Herein, an ordered Ba 2 EuIrO 6 double perovskite is demonstrated as a promising anode material for catalyzing oxygen evolution reaction (OER) in acid electrolyte. The Ba 2 EuIrO 6 achieves a low overpotential of 250 mV at 10 mA cm −2 and high mass activity with 1.39 A mg −1 toward OER, outperforming BaIrO 3 and commercial IrO 2 catalysts. It is discovered that the oxygen bridged Ir─O bri ─Eu unit in Ba 2 EuIrO 6 plays a critical role as the catalytically active center. In situ spectroscopic studies, isotope labeling measurements and theoretical calculations reveal that the Ir─O bri ─Eu units possess strong proton affinity for proton capture from OOH* and OH*, triggering the bridging oxygen‐mediated deprotonation mechanism to break traditional scaling relationships during the OER. Furthermore, the incorporation of Eu modulates the Ir d z2 orbital to increase the spin density of adsorbed oxygen, accelerating ─OH attack and reducing the energy barrier for OOH* formation. The Ba 2 EuIrO 6 ‐loading PEMWE delivers over 1.0 A cm −2 at only 1.67 V and operates stably for 350 h at 1.0 A cm −2 , demonstrating its good potential for practical applications.

Abstract Machine learning interatomic potentials (MLIPs) have greatly extended the temporal and spatial scales of atomistic simulations, enabling the theoretical study of complex processes at affordable computational cost compared with conventional density functional theory (DFT). Recently, large atomistic models (LAMs) have drawn intense interest, as their unified encoders embed extensive chemical knowledge and support fine-tuning methodologies for efficiently adapting models to domain-specific downstream tasks. While many active learning frameworks exist for building MLIP datasets from scratch, dedicated data generation pipelines for fine-tuning pre-trained LAMs remain scarce. Here, we introduce the Deep Potential EVolution Accelerator (DP-EVA), a data-efficient fine-tuning framework that maximizes the utilization of LAMs’ pre-trained knowledge during data generation, accelerating the evolution of domain-specific fine-tuned models with minimal datasets. DP-EVA collects highly representative data through a dual-dimensional shallow-ensemble-based uncertainty quantification (2D-UQ) method based on parallel fine-tuning on the LAM decoder, and a DImensionality-Reduced Encoded Clusters with sTratified (DIRECT) sampling strategy based on the LAM encoder. Tests show that DP-EVA delivers optimal chemical space coverage in the task of drastically reducing the size of an existing MLIP dataset for iron-based Fischer–Tropsch synthesis. DP-EVA fills the gap of active learning frameworks suitable for fine-tuning LAMs toward domain-specific MLIPs, and it is also open-source, Slurm native, and agent-ready for the coming era of agentic scientific research.

Understanding the dynamic behavior of microstructures formed under fusion conditions is critical for designing high-performance materials for fusion reactors. Under fusion conditions, cavities of core-shell structures are formed in structural materials result from interactions between irradiation-induced vacancies and accumulated H and He atoms. In this study, thermodynamic analysis and molecular dynamics simulations are combined to investigate the atomic-scale mechanisms and dynamic response of core-shell cavities formed in BCC-Fe under applied stress/strain fields. The thermodynamic analysis provides both the foundational reference for cavity structures under fusion neutron irradiation and the initial configurations for atomistic simulations. Building on this framework, atomic-scale simulations demonstrate that H and He play a decisive role in the stress-strain response and the evolution of elastic-plastic deformation within the cavities. In core-shell configurations, H atoms serve a function analogous to that in He-filled cavities, synergistically interacting with He to induce cavity deformation under mechanical loading.

The Wang-Teter-like nonlocal kinetic energy density functional (KEDF) in the framework of orbital-free density functional theory, while successful in some bulk systems, exhibits a critical Blanc-Cances instability [J. Chem. Phys. 122, 214106 (2005)] when applied to isolated systems, where the total energy becomes unbounded from below. We trace this instability to the use of an ill-defined average charge density, which causes the functional to simultaneously violate the scaling law and the positivity of the Pauli energy. By rigorously constructing a density-functional-dependent kernel, we resolve these pathologies while preserving the formal exactness of the original framework. By systematically benchmarking single-atom systems of 56 elements, we find the resulting KEDF retains computational efficiency while achieving an order-of-magnitude accuracy enhancement over the WT KEDF. In addition, the new KEDF preserves WT's superior accuracy in bulk metals, outperforming the semilocal functionals in both regimes.

We propose a non-collinear spin-constrained method that generates training data for deep-learning-based magnetic model, which provides a powerful tool for studying complex magnetic phenomena that requires large-scale simulations at the atomic level. First, we propose a basis-independent projection method for calculating atomic magnetic moments by applying a radial truncation to numerical atomic orbitals. A double-loop Lagrange multiplier method is utilized to ensure the satisfaction of constraint conditions while achieving accurate magnetic torque. The method is implemented in ABACUS with both plane wave basis and numerical atomic orbital basis. We benchmark the iron (Fe) systems and analyze differences from calculations with the plane wave basis and numerical atomic orbitals basis in describing magnetic energy barriers. Based on an automated workflow composed of first-principles calculations, magnetic model, active learning, and dynamics simulation, more than 30,000 first-principles data with the information of magnetic torque are generated to train a deep-learning-based magnetic model DeePSPIN for the Fe system. By utilizing the model in large-scale molecular dynamics simulations, we successfully predict Curie temperatures of α-Fe close to experimental values.

After melting, at ambient pressure, the density of water continues to increase with temperature until it reaches a maximum around 4°C. For nearly a century, this phenomenon has been qualitatively attributed to a mixture of ordered and disordered structures. Here, we use a deep neural network to train a machine-learned (ML) interatomic potential for water using electronic structure data from advanced density functional theory. Notably, molecular dynamics simulations with the ML potential reproduce both the experimental water density anomaly and the thermal expansion coefficient. Detailed structural analysis of the computed hydrogen-bond network reveals that the density anomaly arises from an emergent liquid structure that retains nearly ideal tetrahedral coordination at short range but collapses at intermediate range. Our findings point to a more delicate mechanism causing the density maximum than the conventional picture, emphasizing the collective roles of structural orderings at different length scales.

We present a unified heterogeneous computing framework for real-time time-dependent density functional theory (RT-TDDFT) based on numerical atomic orbitals (NAOs), implemented in the ABACUS package. We introduce three co-designed abstraction layers, including unified data containers, unified linear algebra operators, and unified grid integration interfaces. These layers collectively accelerate the two most demanding parts of NAO-based RT-TDDFT: explicit real-time wavefunction propagation and real-space grid operations such as Hamiltonian construction and force evaluation under external fields. We validate the method by computing optical properties for systems ranging from finite molecules to periodic solids, showing excellent agreement with standard benchmarks. Performance evaluations on bulk silicon demonstrate that a single GPU can achieve substantial wall-clock speedup over a fully utilized dual-socket CPU node. Furthermore, distributed multi-GPU strong-scaling tests confirm high parallel efficiency over tens of GPUs. This work establishes a high-performance, portable platform for large-scale first-principles simulations of ultrafast electron dynamics.

Accurate prediction of the thermal and electrical conductivities of materials under extremely high temperatures is essential in high-ener-gy-density physics.These properties govern processes such as stellar core dynamics,planetary magnetic field generation,and laser-driven plasma evolution.However,first-principles methods like Kohn-Sham(KS)density functional theory(DFT)face challenges in predicting these properties due to prohibitively high computational costs.We propose a scheme that integrates the Kubo formalism with a mixed stochastic-deterministic DFT(mDFT)method,which substantially enhances efficiency in computing thermal and electrical conductivities of dense plasmas under extremely high temperatures.As a showcase,this approach enables ab initio calculations of the thermal and electrical conductivities of aluminum(AI)up to 1000 eV.Compared to traditional transport models,our first-principles results reveal significant deviations in the thermal and electrical conductivities of AI within the warm dense matter regime,underscoring the importance of accounting for quantum effects when investigating these transport properties of warm dense matter.

ABACUS (Atomic-orbital Based Ab initio Computation at USTC) is an open-source software for first-principles electronic structure calculations and molecular dynamics simulations. It mainly features density functional theory (DFT) and molecular dynamics functions and is compatible with both plane wave basis sets and numerical atomic orbital basis sets. ABACUS serves as a platform that facilitates the integration of various electronic structure methods, such as Kohn-Sham DFT, stochastic DFT, orbital-free DFT, real-time time-dependent DFT, etc. In addition, with the aid of high-performance computing, ABACUS is designed to perform efficiently and provide massive amounts of first-principles data for generating general-purpose machine learning potentials, such as deep potential with attention models. Furthermore, ABACUS serves as an electronic structure platform that interfaces with several artificial intelligence-assisted algorithms and packages, such as DeePKS-kit, DeePMD, DP-GEN, DeepH, DeePTB, HamGNN, etc.

Machine-learning-enriched interatomic potential frameworks are notable catalysts that transform the realm of computational materials science. By skillfully combining quantum mechanical accuracy with the computational efficiency of classical empirical potentials, these methods significantly enhance the capabilities of molecular dynamics simulations and related investigative fields. The integration of these frameworks provides researchers with the ability to analyze the complex dynamics of material systems with an unprecedented combination of accuracy and speed. The increasing application of machine learning potential function methods and the accumulating data lay a solid foundation for the construction of a large atomic model (LAM) that comprehensively covers the elements of the periodic table, turning the vision into a feasible reality. Within this paradigm, the open large atomic model (OpenLAM) project aims to build a high-precision, high-efficiency pre-trained model suitable for complex material systems. The efficient and accurate interatomic potential models can archive through further downstream fine-tuning and distillation. A key factor in this endeavor is the comprehensive collection of advanced training data, which relies on the accuracy provided by first-principles software. ABACUS, a leading open-source tool in the density functional theory landscape, plays a pivotal role in advancing the OpenLAM project. With support for plane waves and numerical atomic orbital basis sets, ABACUS enables researchers to select the most suitable basis set for their specific research needs. Additionally, ABACUS provides an accessible pseudopotential and numerical atomic orbital library, and enables users to conveniently select pseudopotentials and orbits. ABACUS also fosters a collaborative framework for first-principles computation, creating a community-oriented research environment. And at present, ABACUS has supported lots of algorithms that combine DFT and AI, such as DeepKS, DeepH, etc. ABACUS's hardware versatility, demonstrated by its successful adaptation across various platforms, significantly enhances its utility by leveraging the computational power of diverse architectures. The successful adaptation on domestic deep computing unit (DCU) hardware makes ABACUS be a cost-effective choice. This flexibility has been instrumental in enabling ABA-CUS to contribute a substantial amount of density functional theory data to the OpenLAM project, covering a wide range of material systems including alloys, semiconductors, and perovskites. The use of ABACUS for generating large amounts of data in these fields has validated the stability and reliability of ABACUS, with the potential to unlock novel functionalities and applications in modern technology. The evolution of ABACUS is closely aligned with the rapidly advancing field of AI for Science. As artificial intelligence continues to integrate into scientific research, ABACUS is well-positioned to incorporate emerging AI-driven methodologies and algorithms. Moving forward, ABACUS will remain a cornerstone of the OpenLAM project and a catalyst for new discoveries, driving materials science into a new era of AI-enhanced research and development.

Aluminum oxide (alumina, Al2O3) exists in various structures and has broad industrial applications. While the crystal structure of alpha-Al2O3 is well-established, those of transitional aluminas remain highly debated. In this study, we propose a universal machine learning interatomic potential (MLIP) for aluminas, trained using the neuroevolution potential (NEP) approach. The dataset is constructed through iterative training and farthest point sampling, ensuring the generation of the most representative configurations for an exhaustive sampling of the potential energy surface. The accuracy and generality of the potential are validated through simulations under a wide range of conditions, including high temperatures and pressures. A phase diagram is presented that includes both transitional aluminas and alpha-Al2O3 based on the NEP. We also successfully extrapolate the phase diagram of aluminas under extreme conditions ([0, 4000] K and [0, 200] GPa ranges of temperature and pressure, respectively), while maintaining high accuracy in describing their properties under more moderate conditions. Furthermore, combined with our developed structure search workflow, the NEP provides an evaluation of existing gamma-Al2O3 structure models. The NEP developed in this work enables highly accurate dynamic simulations of various aluminas on larger scales and longer timescales, while also offering new insights into the study of transitional aluminas structures.

Density-functional theory (DFT)-based atomistic simulation methods have been essential in studying the structure-property relationships in heterogeneous catalysis. However, for complex catalytic processes, such as iron-based Fischer-Tropsch synthesis (FTS), the temporal or spatial scales involved are generally too large to perform DFT calculations. Recently, the development of machine learning potentials (MLPs) has demonstrated the capability for atomistic simulation on a large scale and long duration, and the rise of large atomic models (LAMs) is gaining much attention with unified descriptors incorporating a wide range of chemical knowledge and fine-tuning methodology for efficiently deploying the model to downstream tasks. In this work, we construct a MLP named fine-tuned Fischer-Tropsch deep potential (FT$$ ^2 $$ DP) model, which is fine-tuned from upstream DPA-2 LAM on a downstream dataset focused on the iron-based FTS process. We further applied this model to investigate iron-based FTS in both surface reactions and reconstructions of edge sites combined with the double-to-single transition state optimization method and the local genetic algorithm. Our work demonstrated the capability and efficiency of our model for iron-based FTS simulations, while revealing the reaction mechanism on common active sites containing [Fe$$ _4 $$ C] squares, and the abundant formation of [Fe$$ _4 $$ C] squares on several reconstructed surfaces. These insights highlight the potential of utilizing LAM for atomistic simulation for iron-based FTS processes and other complex catalytic reactions.

This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the warm dense matter physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations & experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments and contemporary challenges that are faced by theoretical methods, and experimental techniques needed to create and diagnose warm dense matter. A large part of this roadmap is dedicated to specific warm dense matter systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

Tungsten-copper (W-Cu) compounds are widely utilized in various industrial fields due to their exceptional mechanical properties. In this study, we have developed a neural-network-based deep potential (DP) model that covers a wide range of temperatures, ranging from 0 to 3,000 K, and pressures, varying from 0 to 10 GPa. This study presents a model trained using density functional theory data for full concentration CuxW100-x compounds. Through this model, we systematically investigate the structural and mechanical properties of W-Cu alloys and have the following findings. First, the bulk modulus (B) and Young's modulus (E) of W-Cu alloys exhibit a linear decline as the Cu content increases, indicating a softening trend in the CuxW100-x compounds as the Cu concentration rises. Second, a higher Cu content results in higher critical strain and lower critical stress for these compounds. A brittle-to-ductile transition in the deformation mode predicted is predicted at around 37.5 at. Cu content. Third, tensile loading tests in the W-Cu gradient structure reveal that Cu-poor region serves as a barrier, hindering shear band propagation while promoting new shear band formation in the Cu-rich region. The above results from the DP model are anticipated to aid in exploring the physical mechanisms underlying the complex phenomena of W-Cu systems and contribute to the advancement of methodologies for materials simulation.