arXiv subjects

Jörg Behler

Publications and source records attributed to Jörg Behler.

At least 19 recordsLinked to original sources

arXiv2026

A high-dimensional neural network potential for finite-temperature phenomena in NiTi martensite

We present a high-dimensional neural network potential (HDNNP) for the martensitic phase of the NiTi shape-memory alloy trained to density functional theory (DFT) data. A central aspect of this work is the systematic validation of the potential with respect to the underlying DFT reference method for key properties governing structural evolution, including equilibrium crystal structures, elastic constants, generalized-stacking fault energies, and vibrational spectra. The HDNNP accurately describes the relative stability of the B19$^\prime$ and B33 phases, including subtle energy differences on the order of meV/atom. The predicted stacking-fault energy landscape is strongly anisotropic and reveals a preferential shear pathway, providing atomistic insight into deformation and twinning mechanisms. Finite-temperature molecular dynamics simulations further enable the investigation of unconstrained structural evolution as a function of temperature. Overall, the developed HDNNP provides a robust basis for atomistic simulations of the complex structural and functional behavior of martensitic NiTi systems containing hundreds of thousands of atoms on nanosecond time scales.

cond-mat.mtrl-sci↗

arXiv2026

RuNNer 2.0: A Software Suite for High-Dimensional Neural Network Potentials

We present RuNNer 2.0, the "Ruhr University Neural Network energy representation", a highly optimized software suite for training and evaluating high-dimensional neural network potentials (HDNNPs) of the second, third, and fourth generation. Long-range electrostatics and charge equilibration (QEq) for the description of non-local charge transfer in fourth-generation (4G) HDNNPs are accelerated by quasi-linear-scaling plane-wave methods, reducing QEq computational complexity from $\mathcal{O}(N^3)$ to $\mathcal{O}(N\log^2 N)$ such that linear or quasi-linear scaling is achieved across all HDNNP generations. An optimized memory management strategy eliminates the training overhead traditionally associated with long-range interactions, allowing 4G-HDNNPs to be trained with the same efficiency as their local counterparts. Developed in modern Fortran (2003/2008 standards), combined with a hybrid MPI/OpenMP parallelization scheme, RuNNer 2.0 has been designed to run efficiently in any CPU environment, from cost-effective local workstations to massive HPC clusters. Its modular library architecture facilitates straightforward binding to external simulation software; native interfaces to LAMMPS and the Atomic Simulation Environment (ASE) provide full access to all its features, including built-in committee-based uncertainty quantification. The high efficiency and scalability of the RuNNer 2.0 ecosystem are demonstrated through detailed benchmarks.

physics.chem-ph↗

arXiv2026

Roadmap on Advancements of the FHI-aims Software Package

Electronic-structure theory is the foundation of the description of materials including multiscale modeling of their properties and functions. Obviously, without sufficient accuracy at the base, reliable predictions are unlikely at any level that follows. The software package FHI-aims has proven to be a game changer for accurate free-energy calculations because of its scalability, numerical precision, and its efficient handling of density functional theory (DFT) with hybrid functionals and van der Waals interactions. It treats molecules, clusters, and extended systems (solids and liquids) on an equal footing. Besides DFT, FHI-aims also includes quantum-chemistry methods, descriptions for excited states and vibrations, and calculations of various types of transport. Recent advancements address the integration of FHI-aims into an increasing number of workflows and various artificial intelligence (AI) methods. This Roadmap describes the state-of-the-art of FHI-aims and advancements that are currently ongoing or planned.

cond-mat.mtrl-sci↗

arXiv2025

Molecular Dynamics Simulations of $γ$-Belite(010)-Water Interfaces with High-Dimensional Neural Network Potentials

Belite -- dicalcium silicate Ca$_2$SiO$_4$ -- is a main constituent of low-carbon cement. In this work, we study several terminations of the (010) surface of $γ$-belite, its most stable polymorph, by molecular dynamics simulations. The energies and forces are provided by a high-dimensional neural network potential trained to density functional theory data. Water can interact in molecular form as well as dissociatively with the investigated interfaces, and the degree of dissociation is determined primarily by the protonation of SiO$_4$ groups accessible at the surface. A major part of the simultaneously formed hydroxide ions is adsorbed at surface calcium atoms, whose octahedral coordination spheres are completed by additional water molecules. The T3 termination, which is most stable in vacuum, shows only little reactivity in water. For the only slightly less stable T2 termination, however, two distinct types of surface defects are observed. The type I defect is even stable in vacuum and leads to a reconstruction of the entire surface, while the type II defect is only found in the presence of water. Overall, our results suggest that a variety of structures may be formed at the Ca$_2$SiO$_4$(010) surface, which are stabilized in the presence of water.

cond-mat.mtrl-sci↗

arXiv2025

A Combined Theoretical and Experimental Study of Oxygen Vacancies in Co$_3$O$_4$ for Liquid-Phase Oxidation Catalysis

In the present work, we investigate oxygen vacancies (V$_\mathrm{O}$) in Co$_3$O$_4$, both in the bulk phase and under liquid-phase ethylene glycol oxidation, by combining theoretical and experimental techniques. Density functional theory calculations for bulk Co$_3$O$_4$ show that introducing an oxygen vacancy reduces two adjacent Co$^{3+}$ ions to Co$^{2+}$ and narrows the band gap. The newly formed Co$^{2+}$ ions adopt high-spin configurations in distorted octahedral sites and remain stable in this state in ab initio molecular dynamics simulations at $300$ K. Computed O and Co K-edge X-ray absorption spectra for ideal and vacancy-containing Co$_3$O$_4$ show excellent agreement with the experimental data and serve as references to analyze the liquid-phase ethylene glycol oxidation. The comparison with experimental O K-edge spectra of fresh and post-reaction catalysts shows that fresh samples resemble the vacancy-containing reference, whereas post-reaction spectra shift toward the ideal reference. These results suggest that under liquid-phase ethylene glycol oxidation conditions, Co$_3$O$_4$ becomes more oxidized rather than reduced, by refilling preexisting oxygen vacancies. This is further supported by the observation that higher O$_2$ pressures increase the conversion and that the catalyst remains stable and active over several cycles.

cond-mat.mtrl-sci↗

arXiv2025

Atomistic Simulations of Oxide-Water Interfaces using Machine Learning Potentials

Oxide-water interfaces govern a wide range of physical and chemical processes fundamental to many fields like catalysis, geochemistry, corrosion, electrochemistry, and sensor technology. Near solid oxide surfaces, water behaves differently than in the bulk, exhibiting pronounced structuring and increased reactivity, typically requiring ab initio-level accuracy for reliable modeling. However, explicit ab initio calculations are often computationally prohibitive, especially if large system sizes and long simulation time scales are required. By learning the potential energy surface (PES) from data obtained from electronic structure calculations, machine learning potentials (MLPs) have emerged as transformative tools, enabling simulations with ab initio accuracy at dramatically reduced computational expense. Here, we provide an overview of recent progress in the application of MLPs to atomistic simulations of oxide-water interfaces. Specifically, we review insights that have been gained into the reactivity of interfacial systems involving the dissociation and recombination of water molecules, proton transfer processes between the solvent and the surface and the dynamic nature of aqueous oxide surfaces. Moreover, we discuss open challenges and future possible research directions in this rapidly evolving but challenging field.

physics.chem-ph↗

arXiv2025

Computation of the heat capacity of water from first principles

Water is a unique solvent with many remarkable properties. An example is its exceptionally high heat capacity, which plays an important role in storing and transporting thermal energy, with implications for many processes from regulating the body temperature of living organisms to moderating our climate at the global scale. To elucidate the microscopic origin of the heat capacity of water from first principles, highly accurate computer simulations are required. Apart from a reliable description of the atomic interactions, the presence of light hydrogen atoms necessitates the explicit consideration of nuclear quantum effects through path integral molecular dynamics (PIMD) simulations. The high computational costs of PIMD simulations, which are even further increased by the need for an extensive statistical sampling of energy fluctuations to determine the heat capacity, can be strongly reduced by replacing first principles calculations with machine learning potentials to represent the atomic interactions. In this study, we use high-dimensional neural network potentials (HDNNPs) constructed from density functional theory calculations employing the RPBE-D3 and revPBE0-D3 functionals. To further enhance the computational performance, we introduce a highly efficient PIMD algorithm computing in parallel not only the energies and forces but also the coordinate and thermostat time evolutions. Using this approach, we are able to determine converged data for the heat capacity from a 4 ns simulation employing 128 beads. In particular, for the revPBE0-D3 functional we find excellent agreement with experiment, providing evidence that our approach represents a promising framework for the quantitative understanding of the thermodynamic properties of water and aqueous solutions.

physics.chem-ph↗

arXiv2025

Insights into the Structure and Dynamics of Water at Co$_3$O$_4$(001) Using a High-Dimensional Neural Network Potential

Co$_3$O$_4$ is an important catalyst for the oxidation of organic molecules in the liquid phase. Still, understanding the atomistic details of Co$_3$O$_4$-water interfaces under operando conditions remains extremely challenging. While ab initio molecular dynamics have become an essential tool for investigating these dynamic interfaces in silico, they are limited to only a few picoseconds and a few hundred atoms. In this work, we overcome these limitations by training a high-dimensional neural network potential (HDNNP) on density functional theory data, which allows us to significantly extend the accessible time and length scales. Employing this HDNNP, we perform simulations to unravel the structure, dynamics, and reactivity of Co$_3$O$_4$(001)-water interfaces in detail. Our simulations reveal distinct characteristics of the two possible A and B terminations. The B-terminated surface stabilizes a compact, quasi-epitaxial hydration layer with strong templating effects, enhanced hydroxylation, and a well-organized hydrogen-bond network. In contrast, the A-termination forms a more diffuse contact layer with weaker templating, lower hydroxylation, and less ordered interfacial water. Extended simulations further uncover proton transfer pathways, including intermittent protonation of surface hydroxyls, migration of water molecules into the epitaxial layer, and rare hydronium-like configurations.

physics.chem-ph↗

arXiv2025

Impact of the damping function in dispersion-corrected density functional theory on the properties of liquid water

Accounting for dispersion interactions is essential in approximate density functional theory (DFT). Often, a correction potential based on the London formula is added, which is damped at short distances to avoid divergence and double counting of interactions treated locally by the exchange-correlation functional. Most commonly, two forms of damping, known as zero- and Becke-Johnson (BJ)-damping, are employed and it is generally assumed that the choice has only a minor impact on performance even though the resulting correction potentials differ quite dramatically. Recent studies have cast doubt on this assumption pointing to a significant effect of damping for liquid water, but the underlying reasons have not yet been investigated. Here, we analyze this effect in detail for the widely used Tkatchenko-Scheffler and DFT-D3 dispersion models. We demonstrate that, regardless of the dispersion model, both types of damping perform equally well for interaction energies of water clusters, but find that for the two investigated functionals zero-damping outperforms BJ-damping in dynamic simulations of liquid water. Compared to BJ-damping, zero-damping provides, e.g., an improved structural description, self-diffusion, and density of liquid water. This can be explained by the repulsive gradient at small distances resulting from damping to zero that artificially destabilizes water's tetrahedral hydrogen-bonding network. Therefore, zero-damping can compensate for deficiencies often observed for generalized gradient functionals, which is not possible for strictly attractive BJ-damping. Consequently, the improvement that can be achieved by applying a dispersion correction strongly depends on the employed damping function suggesting that the role of damping in dispersion-corrected DFT needs to be generally reevaluated.

physics.chem-ph↗

arXiv2025

Iterative charge equilibration for fourth-generation high-dimensional neural network potentials

Machine learning potentials (MLP) allow to perform large-scale molecular dynamics simulations with about the same accuracy as electronic structure calculations provided that the selected model is able to capture the relevant physics of the system. For systems exhibiting long-range charge transfer, fourth-generation MLPs need to be used, which take global information about the system and electrostatic interactions into account. This can be achieved in a charge equilibration (QEq) step, but the direct solution (dQEq) of the set of linear equations results in an unfavorable cubic scaling with system size making this step computationally demanding for large systems. In this work, we propose an alternative approach that is based on the iterative solution of the charge equilibration problem (iQEq) to determine the atomic partial charges. We have implemented the iQEq method, which scales quadratically with system size, in the parallel molecular dynamics software LAMMPS for the example of a fourth-generation high-dimensional neural network potential (4G-HDNNP) intended to be used in combination with the n2p2 library. The method itself is general and applicable to many different types of fourth-generation MLPs. An assessment of the accuracy and the efficiency is presented for a benchmark system of FeCl$_3$ in water.

cond-mat.mtrl-sci↗

arXiv2025

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

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

physics.chem-ph↗

arXiv2025

Accuracy of Charge Densities in Electronic Structure Calculations

Accurate charge densities are essential for reliable electronic structure calculations because they significantly impact predictions of various chemical properties and in particular, according to the Hellmann-Feynman theorem, atomic forces. This study examines the accuracy of charge densities obtained from different DFT exchange-correlation functionals in comparison with coupled cluster calculations with single and double excitations. We find that modern DFT functionals can provide highly accurate charge densities, particularly in case of meta-GGA and hybrid functionals. In connection with Gaussian basis sets, it is necessary to use the largest basis sets available to obtain densitites that are nearly basis set error free. These findings highlight the importance of selecting appropriate computational methods for generating high-precision charge densities, which are for instance needed to generate reference data for training modern machine learned potentials.

physics.chem-ph↗

arXiv2024

Machine Learning Potentials for Heterogeneous Catalysis

The sustainable production of many bulk chemicals relies on heterogeneous catalysis. The rational design or improvement of the required catalysts critically depends on insights into the underlying mechanisms at the atomic scale. In recent years, substantial progress has been made in applying advanced experimental techniques to complex catalytic reactions in operando, but in order to achieve a comprehensive understanding, additional information from computer simulations is indispensable in many cases. In particular, ab initio molecular dynamics (AIMD) has become an important tool to explicitly address the atomistic level structure, dynamics, and reactivity of interfacial systems, but the high computational costs limit applications to systems consisting of at most a few hundred atoms for simulation times of up to tens of picoseconds. Rapid advances in the development of modern machine learning potentials (MLP) now offer a new approach to bridge this gap, enabling simulations of complex catalytic reactions with ab initio accuracy at a small fraction of the computational costs. In this perspective, we provide an overview of the current state of the art of applying MLPs to systems relevant for heterogeneous catalysis along with a discussion of the prospects for the use of MLPs in catalysis science in the years to come.

physics.chem-ph↗

arXiv2024

Nuclear Quantum Effects in Liquid Water Are Negligible for Structure but Significant for Dynamics

Isotopic substitution, which can be realized both in experiment and computer simulations, is a direct approach to assess the role of nuclear quantum effects on the structure and dynamics of matter. Yet, the impact of nuclear quantum effects on the structure of liquid water as probed in experiment by comparing normal to heavy water has remained controversial. To settle this issue, we employ a highly accurate machine-learned high-dimensional neural network potential to perform converged coupled cluster-quality path integral simulations of liquid H$_2$O versus D$_2$O at ambient conditions. We find substantial H/D quantum effects on the rotational and translational dynamics of water, in close agreement with the experimental benchmarks. However, in stark contrast to the role for dynamics, H/D quantum effects turn out to be unexpectedly small, on the order of 1/1000 Å, on both intramolecular and H-bonding structure of water. The most probable structure of water remains nearly unaffected by nuclear quantum effects, but effects on fluctuations away from average are appreciable, rendering H$_2$O substantially more "liquid" than D$_2$O.

physics.chem-ph↗

arXiv2024

Random sampling versus active learning algorithms for machine learning potentials of quantum liquid water

Training accurate machine learning potentials requires electronic structure data comprehensively covering the configurational space of the system of interest. As the construction of this data is computationally demanding, many schemes for identifying the most important structures have been proposed. Here, we compare the performance of high-dimensional neural network potentials (HDNNPs) for quantum liquid water at ambient conditions trained to data sets constructed using random sampling as well as various flavors of active learning based on query by committee. Contrary to the common understanding of active learning, we find that for a given data set size, random sampling leads to smaller test errors for structures not included in the training process. In our analysis we show that this can be related to small energy offsets caused by a bias in structures added in active learning, which can be overcome by using instead energy correlations as an error measure that is invariant to such shifts. Still, all HDNNPs yield very similar and accurate structural properties of quantum liquid water, which demonstrates the robustness of the training procedure with respect to the training set construction algorithm even when trained to as few as 200 structures. However, we find that for active learning based on preliminary potentials, a reasonable initial data set is important to avoid an unnecessary extension of the covered configuration space to less relevant regions.

physics.chem-ph↗

arXiv2024

Machine learning potentials for redox chemistry in solution

Machine learning potentials (MLPs) represent atomic interactions with quantum mechanical accuracy offering an efficient tool for atomistic simulations in many fields of science. However, most MLPs rely on local atomic energies without information about the global composition of the system. To date, this has prevented the application of MLPs to redox reactions in solution, which involve chemical species in different oxidation states and electron transfer between them. Here, we show that fourth-generation MLPs overcome this limitation and can provide a physically correct description of redox chemical reactions. For the example of ferrous (Fe$^{2+}$) and ferric (Fe$^{3+}$) ions in water we show that the correct oxidation states are obtained matching the number of chloride counter ions irrespective of their positions in the system. Moreover, we demonstrate that our method can describe electron-transfer processes between ferrous and ferric ions, paving the way to simulations of general redox chemistry in solution.

physics.chem-ph↗

arXiv2024

A High-Dimensional Neural Network Potential for Co$_3$O$_4$

The Co$_3$O$_4$ spinel is an important material in oxidation catalysis. Its properties under catalytic conditions, i.e., at finite temperatures, can be studied by molecular dynamics simulations, which critically depend on an accurate description of the atomic interactions. Due to the high complexity of Co$_3$O$_4$, which is related to the presence of multiple oxidation states of the cobalt ions, to date \textit{ab initio} methods have been essentially the only way to reliably capture the underlying potential energy surface, while more efficient atomistic potentials are very challenging to construct. Consequently, the accessible length and time scales of computer simulations of systems containing Co$_3$O$_4$ are still severely limited. Rapid advances in the development of modern machine learning potentials (MLPs) trained on electronic structure data now make it possible to bridge this gap. In this work, we employ a high-dimensional neural network potential (HDNNP) to construct a MLP for bulk Co$_3$O$_4$ spinel based on density functional theory calculations. After a careful validation of the potential, we compute various structural, vibrational, and dynamical properties of the Co$_3$O$_4$ spinel with a particular focus on its temperature-dependent behavior, including the thermal expansion coefficient.

cond-mat.mtrl-sci↗

arXiv2024

Accelerating fourth-generation machine learning potentials by quasi-linear scaling particle mesh charge equilibration

Machine learning potentials (MLP) have revolutionized the field of atomistic simulations by describing the atomic interactions with the accuracy of electronic structure methods at a small fraction of the costs. Most current MLPs construct the energy of a system as a sum of atomic energies, which depend on information about the atomic environments provided in form of predefined or learnable feature vectors. If, in addition, non-local phenomena like long-range charge transfer are important, fourth-generation MLPs need to be used, which include a charge equilibration (Qeq) step to take the global structure of the system into account. This Qeq can significantly increase the computational cost and thus can become the computational bottleneck for large systems. In this paper we present a highly efficient formulation of Qeq that does not require the explicit computation of the Coulomb matrix elements resulting in a quasi-linearly scaling method. Moreover, our approach also allows for the efficient calculation of energy derivatives, which explicitly consider the global structure-dependence of the atomic charges as obtained from Qeq. Due to its generality, the method is not restricted to MLPs but can also be applied within a variety of other force fields.

physics.comp-ph↗