arXiv subjects

Jörg Behler

Publications and source records attributed to Jörg Behler.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2024

From electrons to phase diagrams with classical and machine learning potentials: automated workflows for materials science with pyiron

We present a comprehensive and user-friendly framework built upon the pyiron integrated development environment (IDE), enabling researchers to perform the entire Machine Learning Potential (MLP) development cycle consisting of (i) creating systematic DFT databases, (ii) fitting the Density Functional Theory (DFT) data to empirical potentials or MLPs, and (iii) validating the potentials in a largely automatic approach. The power and performance of this framework are demonstrated for three conceptually very different classes of interatomic potentials: an empirical potential (embedded atom method - EAM), neural networks (high-dimensional neural network potentials - HDNNP) and expansions in basis sets (atomic cluster expansion - ACE). As an advanced example for validation and application, we show the computation of a binary composition-temperature phase diagram for Al-Li, a technologically important lightweight alloy system with applications in the aerospace industry.

cond-mat.mtrl-sci↗

arXiv2024

Perspective: Atomistic Simulations of Water and Aqueous Systems with Machine Learning Potentials

As the most important solvent, water has been at the center of interest since the advent of computer simulations. While early molecular dynamics and Monte Carlo simulations had to make use of simple model potentials to describe the atomic interactions, accurate ab initio molecular dynamics simulations relying on the first-principles calculation of the energies and forces have opened the way to predictive simulations of aqueous systems. Still, these simulations are very demanding, which prevents the study of complex systems and their properties. Modern machine learning potentials (MLPs) have now reached a mature state, allowing to overcome these limitations by combining the high accuracy of electronic structure calculations with the efficiency of empirical force fields. In this Perspective we give a concise overview about the progress made in the simulation of water and aqueous systems employing MLPs, starting from early work on free molecules and clusters via bulk liquid water to electrolyte solutions and solid-liquid interfaces.

cond-mat.soft↗

arXiv2023

Hydrogen Atom Scattering at the Al$_2$O$_3$(0001) Surface: A Combined Experimental and Theoretical Study

Investigating atom-surface interactions is the key to an in-depth understanding of chemical processes at interfaces, which are of central importance in many fields -- from heterogeneous catalysis to corrosion. In this work, we present a joint experimental and theoretical effort to gain insights into the atomistic details of hydrogen atom scattering at the $α$-Al$_2$O$_3$(0001) surface. Surprisingly, this system has been hardly studied to date, although hydrogen atoms as well as $α$-Al$_2$O$_3$ are omnipresent in catalysis as reactive species and support oxide, respectively. We address this system by performing hydrogen atom beam scattering experiments and molecular dynamics (MD) simulations based on a high-dimensional machine learning potential trained to density functional theory data. Using this combination of methods we are able to probe the properties of the multidimensional potential energy surface governing the scattering process. Specifically, we compare the angular distribution and the kinetic energy loss of the scattered atoms obtained in experiment with a large number of MD trajectories, which, moreover, allow to identify the underlying impact sites at the surface.

physics.chem-ph↗

arXiv2023

Tutorial: How to Train a Neural Network Potential

The introduction of modern Machine Learning Potentials (MLP) has led to a paradigm change in the development of potential energy surfaces for atomistic simulations. By providing efficient access to energies and forces, they allow to perform large-scale simulations of extended systems, which are not directly accessible by demanding first-principles methods. In these simulations, MLPs can reach the accuracy of electronic structure calculations provided that they have been properly trained and validated using a suitable set of reference data. Due to their highly flexible functional form the construction of MLPs has to be done with great care. In this tutorial, we describe the necessary key steps for training reliable MLPs, from data generation via training to final validation. The procedure, which is illustrated for the example of a high-dimensional neural network potential, is general and applicable to many types of MLPs.

physics.chem-ph↗

arXiv2023

Accurate Fourth-Generation Machine Learning Potentials by Electrostatic Embedding

In recent years, significant progress has been made in the development of machine learning potentials (MLPs) for atomistic simulations with applications in many fields from chemistry to materials science. While most current MLPs are based on environment-dependent atomic energies, the limitations of this locality approximation can be overcome, e.g., in fourth-generation MLPs, which incorporate long-range electrostatic interactions based on an equilibrated global charge distribution. Apart from the considered interactions, the quality of MLPs crucially depends on the information available about the system, i.e., the descriptors. In this work we show that including -- in addition to structural information -- the electrostatic potential arising from the charge distribution in the atomic environments significantly improves the quality and transferability of the potentials. Moreover, the extended descriptor allows to overcome current limitations of two- and three-body based feature vectors regarding artificially degenerate atomic environments. The capabilities of such an electrostatically embedded fourth-generation high-dimensional neural network potential (ee4G-HDNNP), which is further augmented by pairwise interactions, are demonstrated for NaCl as a benchmark system. Employing a data set containing only neutral and negatively charged NaCl clusters, even small energy differences between different cluster geometries can be resolved, and the potential shows an impressive transferability to positively charged clusters as well as the melt.

physics.chem-ph↗

arXiv2022

High-dimensional neural network potentials for accurate vibrational frequencies: The formic acid dimer benchmark

In recent years, machine learning potentials (MLP) for atomistic simulations have attracted a lot of attention in chemistry and materials science. Many new approaches have been developed with the primary aim to transfer the accuracy of electronic structure calculations to large condensed systems containing thousands of atoms. In spite of these advances, the reliability of modern MLPs in reproducing the subtle details of the multi-dimensional potential-energy surface is still difficult to assess for such systems. On the other hand, moderately sized systems enabling the application of tools for thorough and systematic quality-control are nowadays rarely investigated. In this work we use benchmark-quality harmonic and anharmonic vibrational frequencies as a sensitive probe for the validation of high-dimensional neural network potentials. For the case of the formic acid dimer, a frequently studied model system for which stringent spectroscopic data became recently available, we show that high-quality frequencies can be obtained from state-of-the-art calculations in excellent agreement with coupled cluster theory and experimental data.

physics.chem-ph↗

arXiv2022

Insights into lithium manganese oxide-water interfaces using machine learning potentials

Unraveling the atomistic and the electronic structure of solid-liquid interfaces is the key to the design of new materials for many important applications, from heterogeneous catalysis to battery technology. Density functional theory (DFT) calculations can in principle provide a reliable description of such interfaces, but the high computational costs severely restrict the accessible time and length scales. Here, we report machine learning-driven simulations of various interfaces between water and lithium manganese oxide (Li$_x$Mn$_2$O$_4$), an important electrode material in lithium ion batteries and a catalyst for the oxygen evolution reaction. We employ a high-dimensional neural network potential (HDNNP) to compute the energies and forces several orders of magnitude faster than DFT without loss in accuracy. In addition, a high-dimensional neural network for spin prediction (HDNNS) is utilized to analyze the electronic structure of the manganese ions. Combining these methods, a series of interfaces is investigated by large-scale molecular dynamics. The simulations allow us to gain insights into a variety of properties like the dissociation of water molecules, proton transfer processes, and hydrogen bonds, as well as the geometric and electronic structure of the solid surfaces including the manganese oxidation state distribution, Jahn-Teller distortions, and electron hopping.

cond-mat.mtrl-sci↗

arXiv2021

A Hessian-Based Assessment of Atomic Forces for Training Machine Learning Interatomic Potentials

In recent years, many types of machine learning potentials (MLPs) have been introduced, which are able to represent high-dimensional potential-energy surfaces (PES) with close to first-principles accuracy. Most current MLPs rely on atomic energy contributions given as a function of the local chemical environments. Frequently, in addition to total energies also atomic forces are used to construct the potentials, as they provide detailed local information about the PES. Since many systems are too large for electronic structure calculations, obtaining reliable reference forces from smaller subsystems like molecular fragments or clusters can substantially simplify the construction of the training sets. Here, we propose a method to determine structurally converged molecular fragments providing reliable atomic forces based on an analysis of the Hessian. The method, which serves as a locality test and allows to estimate the importance of long-range interactions, is illustrated for a series of molecular model systems and the metal-organic framework MOF-5 as an example for a complex organic-inorganic hybrid material.

cond-mat.mtrl-sci↗

arXiv2021

Neural Network Potentials: A Concise Overview of Methods

In the past two decades, machine learning potentials (MLP) have reached a level of maturity that now enables applications to large-scale atomistic simulations of a wide range of systems in chemistry, physics and materials science. Different machine learning algorithms have been used with great success in the construction of these MLPs. In this review, we discuss an important group of MLPs relying on artificial neural networks to establish a mapping from the atomic structure to the potential energy. In spite of this common feature, there are important conceptual differences, which concern the dimensionality of the systems, the inclusion of long-range electrostatic interactions, global phenomena like non-local charge transfer, and the type of descriptor used to represent the atomic structure, which can either be predefined or learnable. A concise overview is given along with a discussion of the open challenges in the field.

physics.chem-ph↗

arXiv2021

Properties of α-Brass Nanoparticles II: Structure and Composition

Nanoparticles have become increasingly interesting for a wide range of applications, because in principle it is possible to tailor their properties by controlling size, shape and composition. One of these applications is heterogeneous catalysis, and a fundamental understanding of the structural details of the nanoparticles is essential for any knowledge-based improvement of reactivity and selectivity. In this work we investigate the atomic structure of brass nanoparticles containing up to 5000 atoms as a typical example for a binary alloy consisting of Cu and Zn. As systems of this size are too large for electronic structure calculations, in our simulations we use a recently parametrized machine learning potential providing close to density functional theory accuracy. This potential is employed for a structural characterization as a function of chemical composition by various types of simulations like Monte Carlo in the Semi-Grand Canonical Ensemble and simulated annealing molecular dynamics. Our analysis reveals that the distribution of both elements in the nanoparticles is inhomogeneous, and zinc accumulates in the outermost layer, while the first subsurface layer shows an enrichment of copper. Only for high zinc concentrations alloying can be found in the interior of the nanoparticles, and regular patterns corresponding to crystalline bulk phases of $α$-brass can then be observed. The surfaces of the investigated clusters exhibit well-ordered single-crystal facets, which can give rise to grain boundaries inside the clusters. The melting temperature of the nanoparticles is found to decrease with increasing zinc-atom fraction, a trend which is well-known also for the bulk phase diagram of brass.

cond-mat.mtrl-sci↗

arXiv2021

High-Dimensional Neural Network Potentials for Magnetic Systems Using Spin-Dependent Atom-Centered Symmetry Functions

Machine learning potentials have emerged as a powerful tool to extend the time and length scales of first principles-quality simulations. Still, most machine learning potentials cannot distinguish different electronic spin orientations and thus are not applicable to materials in different magnetic states. Here, we propose spin-dependent atom-centered symmetry functions as a new type of descriptor taking the atomic spin degrees of freedom into account. When used as input for a high-dimensional neural network potential (HDNNP), accurate potential energy surfaces of multicomponent systems describing multiple magnetic states can be constructed. We demonstrate the performance of these magnetic HDNNPs for the case of manganese oxide, MnO. We show that the method predicts the magnetically distorted rhombohedral structure in excellent agreement with density functional theory and experiment. Its efficiency allows to determine the Néel temperature considering structural fluctuations, entropic effects, and defects. The method is general and is expected to be useful also for other types of systems like oligonuclear transition metal complexes.

physics.comp-ph↗

arXiv2021

Comparing the Accuracy of High-Dimensional Neural Network Potentials and the Systematic Molecular Fragmentation Method: A Benchmark Study for all-trans Alkanes

Many approaches, which have been developed to express the potential energy of large systems, exploit the locality of the atomic interactions. A prominent example are fragmentation methods, in which quantum chemical calculations are carried out for overlapping small fragments of a given molecule that are then combined in a second step to yield the system's total energy. Here we compare the accuracy of the systematic molecular fragmentation approach with the performance of high-dimensional neural network (HDNN) potentials introduced by Behler and Parrinello. HDNN potentials are similar in spirit to the fragmentation approach in that the total energy is constructed as a sum of environment-dependent atomic energies, which are derived indirectly from electronic structure calculations. As a benchmark set we use all-trans alkanes containing up to eleven carbon atoms at the coupled cluster level of theory. These molecules have been chosen because they allow to extrapolate reliable reference energies for very long chains, enabling an assessment of the energies obtained by both methods for alkanes including up to 10 000 carbon atoms. We find that both methods predict high-quality energies with the HDNN potentials yielding smaller errors with respect to the coupled cluster reference.

physics.chem-ph↗

arXiv2021

High-dimensional neural network potentials for solvation: The case of protonated water clusters in helium

The design of accurate helium-solute interaction potentials for the simulation of chemically complex molecules solvated in superfluid helium has long been a cumbersome task due to the rather weak but strongly anisotropic nature of the interactions. We show that this challenge can be met by using a combination of an effective pair potential for the He-He interactions and a flexible high-dimensional neural network potential (NNP) for describing the complex interaction between helium and the solute in a pairwise additive manner. This approach yields an excellent agreement with a mean absolute deviation as small as 0.04 kJ/mol for the interaction energy between helium and both, hydronium and Zundel cations compared to CCSD(T) reference calculations with an energetically converged basis set. The construction and improvement of the potential can be performed in a highly automated way, which opens the door for applications to a variety of reactive molecules to study the effect of solvation on the solute as well as the solute-induced structuring of the solvent. Furthermore, we show that this NNP approach yields very convincing agreement with the CCSD(T) reference for properties like many-body spatial and radial distribution functions. This holds for the microsolvation of the protonated water monomer and dimer by a few helium atoms up to their solvation in bulk helium as obtained from path integral simulations at about 1 K.

physics.chem-ph↗

arXiv2020

Predicting Oxidation and Spin States by High-Dimensional Neural Networks: Applications to Lithium Manganese Oxide Spinels

Lithium ion batteries often contain transition metal oxides like Li$_{x}$Mn$_2$O$_4$ ($0\leq x\leq2$). Depending on the Li content different ratios of Mn$^\text{III}$ to Mn$^\text{IV}$ ions are present. In combination with electron hopping the Jahn-Teller distortions of the Mn$^\text{III}$O$_6$ octahedra can give rise to complex phenomena like structural transitions and conductance. While for small model systems oxidation and spin states can be determined using density functional theory (DFT), the investigation of dynamical phenomena by DFT is too demanding. Previously, we have shown that a high-dimensional neural network potential can extend molecular dynamics (MD) simulations of Li$_{x}$Mn$_2$O$_4$ to nanosecond time scales, but these simulations did not provide information about the electronic structure. Here we extend the use of neural networks to the prediction of atomic oxidation and spin states. The resulting high-dimensional neural network is able to predict the spins of the Mn ions with an error of only 0.03 $\hbar$. We find that the Mn e$_\text{g}$ electrons are correctly conserved and that the number of Jahn-Teller distorted Mn$^\text{III}$O$_6$ octahedra is predicted precisely for different Li loadings. A charge ordering transition is observed between 280 and 300 K, which matches resistivity measurements. Moreover, the activation energy of the electron hopping conduction above the phase transition is predicted to be 0.18 eV deviating only 0.02 eV from experiment. This work demonstrates that machine learning is able to provide an accurate representation of both, the geometric and the electronic structure dynamics of Li$_x$Mn$_2$O$_4$, on time and length scales that are not accessible by ab initio MD.

cond-mat.mtrl-sci↗

arXiv2020

Closing the gap between theory and experiment for lithium manganese oxide spinels using a high-dimensional neural network potential

Many positive electrode materials in lithium ion batteries include transition metals which are difficult to describe by electronic structure methods like density functional theory (DFT) due to the presence of multiple oxidation states. A prominent example is the lithium manganese oxide spinel Li$_x$Mn$_2$O$_4$ with $0\leq x\leq2$. While DFT, employing the local hybrid functional PBE0r, provides a reliable description, the need for extended computer simulations of large structural models remains a significant challenge. Here, we close this gap by constructing a DFT-based high-dimensional neural network potential (HDNNP) providing accurate energies and forces at a fraction of the computational costs. As different oxidation states and the resulting Jahn-Teller distortions represent a new level of complexity for HDNNPs, the potential is carefully validated by performing X-ray diffraction experiments. We demonstrate that the HDNNP provides atomic level details and is able to predict a series of properties like the lattice parameters and expansion with increasing Li content or temperature, the orthorhombic to cubic transition, the lithium diffusion barrier, and the phonon frequencies. We show that for understanding these properties access to large time and length scales as enabled by the HDNNP is essential to close the gap between theory and experiment.

cond-mat.mtrl-sci↗

arXiv2020

A Fourth-Generation High-Dimensional Neural Network Potential with Accurate Electrostatics Including Non-local Charge Transfer

Machine learning potentials have become an important tool for atomistic simulations in many fields, from chemistry via molecular biology to materials science. Most of the established methods, however, rely on local properties and are thus unable to take global changes in the electronic structure into account, which result from long-range charge transfer or different charge states. In this work we overcome this limitation by introducing a fourth-generation high-dimensional neural network potential that combines a charge equilibration scheme employing environment-dependent atomic electronegativities with accurate atomic energies. The method, which is able to correctly describe global charge distributions in arbitrary systems, yields much improved energies and substantially extends the applicability of modern machine learning potentials. This is demonstrated for a series of systems representing typical scenarios in chemistry and materials science that are incorrectly described by current methods, while the fourth-generation neural network potential is in excellent agreement with electronic structure calculations.

cond-mat.mtrl-sci↗

arXiv2020

A Bin and Hash Method for Analyzing Reference Data and Descriptors in Machine Learning Potentials

In recent years the development of machine learning (ML) potentials (MLP) has become a very active field of research. Numerous approaches have been proposed, which allow to perform extended simulations of large systems at a small fraction of the computational costs of electronic structure calculations. The key to the success of modern ML potentials is the close-to first principles quality description of the atomic interactions. This accuracy is reached by using very flexible functional forms in combination with high-level reference data from electronic structure calculations. These data sets can include up to hundreds of thousands of structures covering millions of atomic environments to ensure that all relevant features of the potential energy surface are well represented. The handling of such large data sets is nowadays becoming one of the main challenges in the construction of ML potentials. In this paper we present a method, the bin-and-hash (BAH) algorithm, to overcome this problem by enabling the efficient identification and comparison of large numbers of multidimensional vectors. Such vectors emerge in multiple contexts in the construction of ML potentials. Examples are the comparison of local atomic environments to identify and avoid unnecessary redundant information in the reference data sets that is costly in terms of both the electronic structure calculations as well as the training process, the assessment of the quality of the descriptors used as structural fingerprints in many types of ML potentials, and the detection of possibly unreliable data points. The BAH algorithm is illustrated for the example of high-dimensional neural network potentials using atom-centered symmetry functions for the geometrical description of the atomic environments, but the method is general and can be combined with any current type of ML potential.

physics.comp-ph↗