We present two models with explicit long-range electrostatics in the form of Coulomb interactions. Both models include point charges depending on their local atomic environments, and the second model also conserves a total charge of an atomic system. We combine the proposed long-range models with local Moment Tensor Potential and demonstrate that they reduce the training errors of the MTP models fitted on the same training sets including the CH_3COO^-+4-methylphenol and CH_3COO^-+4-methylimidazole organic dimers (non-periodic systems) and the NaCl crystal (periodic system). For the organic dimers, the proposed models also give qualitatively correct predictions of the binding curves. Furthermore, in this study we introduce a method for calculating phonon spectra of isotropic materials only via these long-range models fitted to energies, forces, and stresses. The developed long-range model with point charges dependent on atomic environments and conserving total charge is capable of predicting the correct value of the LO-TO splitting in the Γ-point in the isotropic NaCl. For this system, we also predict dielectric constant from dipole moment fluctuations calculated with molecular dynamics simulations conducted with the developed long-range model. The calculated dielectric constant is in good agreement with experiment. Finally, we demonstrate the broader applicability of the introduced approach by computing the phonon spectrum of uniaxial tetragonal PbTiO_3. Although the method is formally derived for isotropic materials, we show that it is also perspective for uniaxial materials (e.g., PbTiO_3) as the spectrum obtained with our long-range interatomic potential corresponds to the one calculated with density functional theory.

Conflicting experiments disagree on whether the titanium-vanadium (Ti-V) binary alloy exhibits a body-centered cubic (BCC) miscibility gap or remains completely soluble. A leading hypothesis attributes the miscibility gap to oxygen contamination during alloy preparation. To resolve this disagreement, we use an ab initio + machine-learning workflow that couples an actively-trained Moment Tensor Potential with Bayesian inference of free energy surface. This workflow enables construction of the Ti-V phase diagram across the full composition range with systematically reduced statistical and finite-size errors. The resulting diagram reproduces all experimental features, demonstrating the robustness of our approach, and clearly favors the variant with a BCC miscibility gap terminating at Tcr it = 980 K and ccr it = 0.67. Because our simulations model a perfectly oxygen-free Ti-V system, the observed gap cannot originate from impurity effects, in contrast to recent CALPHAD reassessments.

We have investigated the effect of interlayer twist angle on lattice thermal conductivity (LTC) and band gap renormalization in boron nitride and carbon Moir & eacute; diamanes. Moment tensor potentials were used for calculating energies and forces of interatomic interactions. The methods based on the solution of Boltzmann transport equation (BTE) for phonons and the Green-Kubo (GK) formula were utilized to calculate LTC. The 20%-40% difference in LTC values obtained with GK and BTE-based methods showed the importance of high-order anharmonic contributions to LTC. Significant reduction (by 4.5-9 times) of the in-plane LTC with the twist angle increase caused by the growth of structural disorder was observed in the Moir & eacute; diamanes. This growth of disorder also leads to higher band gap renormalization (induced by classical nuclei motion) in the structures with higher twist angles. Significant band gap renormalization values obtained considering the quantum nuclear effects are caused by the high phonon frequencies related to the bonds with hydrogen atoms on the Moir & eacute; diamanes surfaces. Understanding of the twist angle effect on LTC and electron-phonon coupling in the Moir & eacute; diamanes provides a fundamental basis for manipulating their thermal and electronic properties, making these materials promising for thermoelectrics, microelectronics and optoelectronics.

In this work, we incorporate long-range electrostatic interactions in the form of the Coulomb model with fixed charges into the functional form of short-range machine-learning interatomic potentials (MLIPs), particularly in the moment tensor potential and equivariant tensor network potential. We show that the explicit incorporation of the Coulomb interactions with fixed charges leads to a significant reduction of energy fitting errors, namely, more than four times, of short-range MLIPs trained on organic dimers of charged molecules. Furthermore, with our long-range models, we demonstrate a significant improvement in the prediction of the binding curves of the organic dimers of charged molecules. Finally, we show that the results calculated with MLIPs are in good correspondence with those obtained with density functional theory for organic dimers of charged molecules.

Machine learning interatomic potentials (MLIPs) offer near-ab initio accuracy with the efficiency of classical force fields, making them attractive for modeling electrolytes. Collecting a diverse training set is essential for their accuracy and reliability, and explicit treatment of strong electrostatic interactions may be necessary. In this work, we demonstrated that active learning can automatically generate diverse training sets for moment tensor potentials (MTPs), enabling reliable molecular dynamics simulations of pure ethylene carbonate (EC), ethyl methyl carbonate (EMC), their mixtures, and LiPF6 solutions. The resulting MTPs exhibit excellent transferability across various EC/EMC compositions, producing ionic conductivities within 11% mean deviations from experiments. In addition, we assessed the impact of explicitly incorporating electrostatics by extending MTP with a charge redistribution scheme. Our results show that this extended MTP achieves accuracy comparable to MTP for EC/EMC mixtures with fewer parameters and reproduces ionic conductivity with only a 6% mean deviation from experiment.

Exploring the chemistry of materials at high pressures has lead to the discovery of previously unknown exotic compounds. Here, we systematically search for all thermodynamically stable Sr-C compounds under pressure (up to 100 GPa) using the ab initio evolutionary crystal structure prediction method. Our search lead to the discovery of hitherto unknown phases of SrC3, Sr2C5, Sr2C3, Sr2C, Sr3C2, and SrC. The newly discovered crystal structures feature a variety of different carbon environments ranging from isolated C anions and C-dimers to exotic polyatomic carbon anions including chains, stripes, and infinite ribbons consisting of pentagonal C5 and hexagonal C6 rings. Dynamical stability of all predicted compounds is confirmed by phonons calculations. Bader analysis unravels very diverse chemistry in these compounds and bonding patterns in some of them can be described using Zintl-Klemm rule.

Ubiquitous van der Waals (vdW) interactions play a subtle yet crucial role in determining the precise atomic arrangements in solids, particularly in molecular crystals where these weak forces are the primary link between constituent building blocks. Within density functional (DF) theory, the most natural approach for addressing vdW forces is the use of vdW-inclusive density functionals. Through a detailed analysis of the underlying formalism, we have developed a computational scheme that combines vdW functionals of type DF1 and DF2 and serves as a well optimizable tool to improve the theoretical description and prediction of molecular crystals and other sparse materials. The proof of principle is demonstrated by our consideration of the molecular crystals from the X23 dataset.

Tungsten is used as a material capable of withstanding extreme conditions, particularly in Generation IV fusion and fission reactors. To relate structure and properties and to solve other problems in materials science, atomistic modeling is an indispensable approach. The predictive power of molecular dynamics modeling depends largely on the quality of the interatomic potentials used in the simulations. Recently, machine learning interatomic potentials (MLIPs) have become popular because they provide better accuracy compared to potentials based on the embedded atom method (EAM). MLIPs are often trained to reproduce the density functional theory (DFT) results obtained for the randomly generated atomic configurations. Here, we develop a MLIP for tungsten that is trained to reproduce the frequency response of the exact oscillatory solutions to the dynamic equations of atomic motion, called delocalized nonlinear vibrational modes (DNVMs). The quality of the potential is then improved by training on thermal fluctuations and uniform deformation configurations. The accuracy and high simulation speed of the developed potential are demonstrated, and the potential is prepared for public use by embedding it into the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code. The presented approach can be easily applied to other non-magnetic bcc crystals.

We present an algorithm for accelerating the search of a molecule's adsorption sites based on global optimization of surface adsorbate geometries. Our approach uses a machine-learning interatomic potential (moment tensor potential) to approximate the potential energy surface and an active learning algorithm for the automatic construction of an optimal training dataset. To validate our methodology, we compare the results across various well-known catalytic systems with surfaces of different crystallographic orientations and adsorbate geometries, including CO/Pd(111), NO/Pd(100), NH3/Cu(100), C6H6/Ag(111), and CH2CO/Rh(211). In all the cases, we observed an agreement of our results with the literature.

Inspired by the recent success of machine-learned interatomic potentials for crystal structure prediction of inorganic crystals, we present a methodology that exploits moment tensor potentials (MTP) and active learning (based on maxvol algorithm) to accelerate structure prediction of molecular crystals. Benzene and glycine are used as test systems. The obtained potentials are able to rank different benzene and glycine polymorphs in good agreement with density-functional theory. Hence, we argue that MTP can be used to accelerate the computationally guided polymorph search.

Abstract An interatomic potential, traditionally regarded as a mathematical function, serves to depict atomic interactions within molecules or solids by expressing potential energy concerning atom positions. These potentials are pivotal in materials science and engineering, facilitating atomic-scale simulations, predictive material behavior, accelerated discovery, and property optimization. Notably, the landscape is evolving with machine learning transcending conventional mathematical models. Various machine learning-based interatomic potentials, such as artificial neural networks, kernel-based methods, deep learning, and physics-informed models, have emerged, each wielding unique strengths and limitations. These methods decode the intricate connection between atomic configurations and potential energies, offering advantages like precision, adaptability, insights, and seamless integration. The transformative potential of machine learning-based interatomic potentials looms large in materials science and engineering. They promise tailor-made materials discovery and optimized properties for specific applications. Yet, formidable challenges persist, encompassing data quality, computational demands, transferability, interpretability, and robustness. Tackling these hurdles is imperative for nurturing accurate, efficient, and dependable machine learning-based interatomic potentials primed for widespread adoption in materials science and engineering. This roadmap offers an appraisal of the current machine learning-based interatomic potential landscape, delineates the associated challenges, and envisages how progress in this domain can empower atomic-scale modeling of the composition-processing-microstructure-property relationship, underscoring its significance in materials science and engineering.

We present a protocol for automated fitting of magnetic Moment Tensor Potential explicitly including magnetic moments in its functional form. For the fitting of this potential we use energies, forces, stresses, and magnetic forces (negative derivatives of energies with respect to magnetic moments) of configurations selected with an active learning algorithm. These selected configurations are computed using constrained density functional theory, which enables calculating energies and their derivatives for both equilibrium and non-equilibrium (excited) magnetic states. We test our protocol on the system of B1-CrN and demonstrate that the automatically trained magnetic Moment Tensor Potential reproduces mechanical, dynamical, and thermal properties, of B1-CrN in the paramagnetic state with respect to density functional theory and experiments.

In this study, we investigate the effect of incorporating explicit dispersion interactions in the functional form of machine learning interatomic potentials (MLIPs), particularly in the moment tensor potential and equivariant tensor network potential, for accurate modeling of liquid carbon tetrachloride, methane, and toluene. We demonstrate that the explicit incorporation of dispersion interactions via D2 and D3 corrections significantly improves the accuracy of MLIPs when the cutoff radius is set to the commonly used value of 5-6 Å. We also show that for carbon tetrachloride and methane, a substantial improvement in accuracy can be achieved by extending the cutoff radius to 7.5 Å. However, for accurate modeling of toluene, the explicit incorporation of dispersion remains important. Furthermore, we find that MLIPs incorporating dispersion interactions via D2 reach a level of accuracy comparable to those incorporating D3, implying that D2 is suitable for accurate modeling of the systems in the study, while being less computationally expensive. We benchmarked the accuracy of the MLIPs on dimer binding curves compared to ab initio data and on predicting density and radial distribution functions compared to experiments.

Fluoride salts demonstrate significant potential for applications in next-generation nuclear reactors, necessitating a comprehensive understanding of their thermophysical properties for technological advancements. Experimental measurement of these properties poses challenges, due to factors such as high temperatures, impurity control, and corrosion. Consequently, precise computational modeling methods become essential for predicting the thermophysical properties of molten salts. In this work, we performed molecular dynamics (MD) simulations of several thermophysical properties of the eutectic salt mixture LiF-NaF-KF (FLiNaK) melt, including density, self-diffusion coefficients, viscosity, and thermal conductivity. We demonstrated the successful application of moment tensor potentials (MTP) as an accurate model for interatomic interactions in FLiNaK. Our results on thermophysical properties calculations exhibit strong agreement with experimental data. An important aspect of our methodology is the incorporation of an active learning scheme, which enables the generation of a robust and accurate potential, while maintaining a moderate-sized training dataset.

Machine-learning interatomic potentials (MLIPs) have made a significant contribution to the recent progress in the fields of computational materials and chemistry due to the MLIPs’ ability of accurately approximating energy landscapes of quantum-mechanical models while being orders of magnitude more computationally efficient. However, the computational cost and number of parameters of many state-of-the-art MLIPs increases exponentially with the number of atomic features. Tensor (non-neural) networks, based on low-rank representations of high-dimensional tensors, have been a way to reduce the number of parameters in approximating multidimensional functions, however, it is often not easy to encode the model symmetries into them. In this work we develop a formalism for rank-efficient equivariant tensor networks (ETNs), i.e. tensor networks that remain invariant under actions of SO(3) upon contraction. All the key algorithms of tensor networks like orthogonalization of cores and DMRG-based algorithms carry over to our equivariant case. Moreover, we show that many elements of modern neural network architectures like message passing, pulling, or attention mechanisms, can in some form be implemented into the ETNs. Based on ETNs, we develop a new class of polynomial-based MLIPs that demonstrate superior performance over existing MLIPs for multicomponent systems.

Calculations of elastic and mechanical characteristics of non-crystalline solids are challenging due to high computation cost of ab initio methods and low accuracy of empirical potentials. We propose a computational technique towards efficient calculations of mechanical properties of polycrystals, composites, and multi-phase systems from atomistic simulation with high accuracy and reasonable computational cost. It is based on using actively learned machine learning interatomic potentials (MLIPs) trained on a local fragments of the polycrystalline system for which forces, stresses and energies are computed by using ab initio calculations. Developed approach is used for calculation the dependence of elastic moduli of polycrystalline diamond on the grain size. This technique allows one to perform large-scale calculations of mechanical properties of complex solids of various compositions and structures with high accuracy making the transition from ideal (single crystal) systems to more realistic ones.

Molecular dynamics (MD) is a powerful tool for modeling the phase and structural transformations and the evolution of defects and their influence on the metallic material properties. The accuracy of MD modeling directly depends on the quality of interatomic potentials. Modern machine-learning potentials are typically trained on random atomic configurations. This approach has significantly improved the quality of new potentials over traditional EAM potentials. In this work, exact solutions to the equations of atomic motion are offered to train the machine learning potentials.

We combined Moment Tensor Potential (MTP) and Ring Polymer Molecular Dynamics (RPMD) for calculating the thermal rate constants of the OH + HBr system. We used the active learning (AL) algorithm for constructing a training set during RPMD. We compared the obtained RPMD-AL-MTP rate constants with the ones previously calculated using the quasi-classical trajectories (QCT) and the POTLIB potential energy surface, and with the experimental ones. We demonstrated that the RPMD rate constants were systematically closer to the experimental rate constants than the QCT ones at 200 K, 300 K, and 500 K.

We present an algorithm for the high-throughput computational discovery of intermetallic compounds in systems with a large number of components. It is particularly important for high entropy alloys (HEAs), where multiple principal elements can form numerous potential intermetallic compounds during the condensation process, making it challenging to predict the dominant phase. Our algorithm is based on a brute-force evaluation of candidate structures with a fixed underlying lattice (FCC or BCC) accelerated by machine-learning interatomic potentials. The algorithm takes a set of chemical elements and a crystal lattice type as inputs and produces structures on and near the convex hull of thermodynamically stable structures. The candidate structures are evaluated using the low-rank potential (LRP), trained to reproduce energies of structures equilibrated with density functional theory (DFT). Thanks to extreme computational effectiveness of the LRP, it is feasible to evaluate hundreds of thousands of structures per second, per CPU core. Thus, our algorithm screens a complete set of candidate structures for a given system without missing any configurations. We validated our method on systems with BCC (Nb-W, Nb-Mo-W, V-Nb-Mo-Ta-W) and FCC (Cu-Pt, Cu-Pd-Pt, Cu-Pd-Ag-Pt-Au) lattices and discovered 268 new alloys not reported in the AFLOW database1, which we used as a benchmark.

We present the electronic moment tensor potentials (eMTPs), a class of machine-learning interatomic models and a generalization of the classical MTPs, reproducing both the electronic and vibrational degrees of freedom, up to the accuracy of ab initio calculations. Following the original polynomial interpolation idea of the MTPs, the eMTPs are defined as polynomials of vibrational and electronic degrees of freedom, corrected to have a finite interatomic cutoff. Practically, an eMTP is constructed from the classical MTPs fitted to a training set, whose energies and forces are calculated with electronic temperatures corresponding to the Chebyshev nodes on a given temperature interval. The eMTP energy is hence a Chebyshev interpolation of the classical MTPs. Using the eMTP, one can obtain the temperature-dependent vibrational free energy including anharmonicity coming from phonon interactions, the electronic free energy coming from electron interactions, and the coupling of atomic vibrations and electronic excitations. Each of the contributions can be accessed individually using the proposed formalism. The performance of eMTPs is demonstrated for two refractory systems which have a significant electronic, vibrational and coupling contribution up to the melting point—unary Nb, and a disordered TaVCrW high-entropy alloy. Highly accurate thermodynamic and kinetic quantities can now be obtained just by using eMTPs, without any further ab initio calculations. The proposed construction to include the electronic degree of freedom can also be applied to other machine-learning models.