arXiv subjects

Stefan Goedecker

Publications and source records attributed to Stefan Goedecker.

At least 19 recordsLinked to original sources

arXiv2026

Planar Structures of Medium-Sized Gold Clusters Become Ground States upon Ionization

This study investigates the structural stability of ionized gold clusters of sizes ranging from 22 to 100 atoms, contrasting compact, cage and planar structures. While it is well known that neutral clusters in the upper part of this size range predominantly favor compact structures, our results reveal that positively ionized gold clusters exhibit structural transitions in which planar structures become energetically preferred once the charge is sufficiently large. In addition, we study the finite-temperature stability of the structures and find that thermodynamic effects further stabilize planar configurations relative to their compact counterparts. To explore the potential energy surface, we use the Minima Hopping algorithm combined with a machine-learned potential. Since the machine-learned potential does not apply to ionized clusters, we introduce a charge-correction term to incorporate Coulomb interactions and charge screening.

cond-mat.mtrl-sci↗

arXiv2026

The transformation mechanisms among cuboctahedra, Ino's decahedra and icosahedra structures of magic-size gold nanoclusters

Gold nanoclusters possess multiple competing structural motifs with small energy differences, enabling structural coexistence and interconversion. Using a high-accuracy machine learned potential trained on some 20'000 density functional theory reference data points, we investigate transformation pathways connecting both high-symmetry and amorphous cuboctahedra, Ino's decahedra and icosahedra for Au55, Au147, Au309 and Au561 nanoclusters. Our saddle point searches reveal that high-symmetry transformations from cuboctahedra and Ino's decahedra to icosahedra proceed through a single barrier and represent soft-mode-driven jitterbug-type and slip-dislocation motions. In addition, we identify lower-barrier asymmetric transformation pathways that drive the system into disordered, Jahn-Teller-stabilized amorphous icosahedra. Minima Hopping sampling further uncovers, in this context, many such low-symmetry minima. Some of the newly identified global minima for Au309 and Au561 have energies that are up to 2.8 eV lower than the previously reported global minima. Hence, both the shapes and the transformation pathways studied in previous investigations are not the physically relevant ones. In contrast to the previously studied pathways, our transformation pathways give reasonable transformation times that are in rough agreement with experiments.

cond-mat.mtrl-sci↗

arXiv2025

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

Implications of the multi-minima character of molecular crystal phases onto the free energy

In recent years, significant advancements in computational methods have dramatically enhanced the precision in determining the energetic ranking of different phases of molecular crystals. The developments mainly focused on providing accurate dispersion corrected exchange correlation functionals and methods for describing the vibrational entropy contributions to the free energy at finite temperatures. Several molecular crystals phases were recently found to have of multi-minima character. For our investigations we highlight the multi-minima character in the example of the molecular crystal consisting of N-(4-Methylbenzylidene)-4-methylalanine. We explore its potential energy landscape on the full DFT level or with a machine learned potential that was fitted to DFT data. We calculate not only many local minima but also exact barriers along transformation pathways to demonstrate the multi-minima character of our system. Furthermore, we present a framework, based on the quantum superposition method, that includes both configurational and vibrational entropy. As an example, we show for our system that the transition temperature between two of its phases is afflicted by an error of about 200 K if the multi-minima character is not taken into account. This indicates that it is absolutely essential to consider configurational entropy to obtain reliable finite temperature free energy rankings for complex molecular crystals.

cond-mat.mtrl-sci↗

arXiv2024

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

Noise Tolerant Force Calculations in Density Functional Theory: A Surface Integral Approach for Wavelet-Based Methods

We introduce a method for computing quantum mechanical forces through surface integrals over the stress tensor within the framework of density functional theory. This approach avoids the inaccuracies of traditional force calculations using the Hellmann-Feynman theorem when applied to multiresolution wavelet representations of orbitals. By integrating the quantum mechanical stress tensor over surfaces that enclose individual nuclei, we achieve highly accurate forces that exhibit superior consistency with the potential energy surface. Extensive benchmarks show that surface integrals over the stress tensor offer a robust and reliable alternative to the direct use of the Hellmann-Feynman theorem for force computations in DFT with discontinuous basis sets, particularly in cases where wavelet-based methods are employed. In addition, we integrate this approach with machine learning techniques, demonstrating that the forces obtained through surface integrals are sufficiently accurate to be used as training data for machine-learned potentials. This stands in contrast to forces calculated using the Hellmann-Feynman theorem, which do not offer this level of accuracy.

physics.chem-ph↗

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↗

arXiv2023

Performing highly efficient Minima Hopping structure predictions using the Atomic Simulation Environment (ASE)

In the dynamic field of materials science, the quest to find optimal structures with low potential energy is of great significance. Over the past two decades, the minima hopping algorithm has emerged as a successful tool in this pursuit. We present a robust, user friendly and efficient implementation of the minima hopping algorithm as a Python library, enhancing in this way the global structure optimization simulations significantly. Our implementation significantly accelerates the exploration the potential energy surfaces, leveraging an MPI parallelization scheme that allows for multi level parallelization. In this scheme, multiple minima hopping processes are running simultaneously communicating their findings to a single database and, therefore, sharing information with each other about which parts of the potential energy surface have already been explored. Also multiple features from several existing implementations such as variable cell shape molecular dynamics and combined atomic position and cell geometry optimization for bulk systems, enhanced temperature feedback and fragmentation fixing for clusters are included in this implementation. Finally, this implementation takes advantage of the Atomic Simulation Environment (ASE) Python library allowing for high flexibility regarding the underlying energy and force evaluation.

physics.comp-ph↗

arXiv2023

Ternary Phase Diagram of Nitrogen Doped Lutetium Hydrides

This paper presents the results of an extensive structural search of ternary solids containing lutetium, nitrogen and hydrogen. Based on thousands of thermodynamically stable structures, available online, the convex hull of the formation enthalpies is constructed. To obtain the correct energetic ordering, the highly accurate RSCAN DFT functional is used in high quality all-electron calculations. In this way possible pseudopotential errors are eliminated. A novel lutetium hydride structure (HLu$_2$) that is on the convex hull is found in our search. An electron phonon analysis however shows that it is not a candidate structure for near ambient superconductivity. Besides this structure, which appears to have been missed in previous searches, possibly due to different DFT methodologies, our results agree closely with the results of previously published structure search efforts. This shows, that the field of crystal structure prediction has matured to a state where independent methodologies produce consistent and reproducible results, underlining the trustworthiness of modern crystal structure predictions. Hence it is quite unlikely that a structure, that would give rise within standard BCS theory to the superconducting properties, claimed to have been observed by Dasenbrock-Gammon et al. 10.1038/s41586-023-05742-0 , exists. This solidifies the evidence that no structure with conventional superconducting properties exists that could explain the experimental observation made by Dasenbrock-Gammon et al. 10.1038/s41586-023-05742-0

cond-mat.supr-con↗

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

Targeting high symmetry in structure predictions by biasing the potential energy surface

Ground state structures found in nature are in many cases of high symmetry. But structure prediction methods typically render only a small fraction of high symmetry structures. Especially for large crystalline unit cells there are many low energy defect structures. For this reason methods have been developed where either preferentially high symmetry structures are used as input or where the whole structural search is done within a certain symmetry group. In both cases it is necessary to specify the correct symmetry group beforehand. However it can in general not be predicted which symmetry group is the correct one leading to the ground state. For this reason we introduce a potential energy biasing scheme that favors symmetry and where it is not necessary to specify any symmetry group beforehand. On this biased potential energy surface, high symmetry structures will be found much faster than on an unbiased surface and independently of the symmetry group to which they belong. For our two test cases, a $C_{60}$ fullerene and bulk silicon carbide, we get a speedups of 25 and 63. In our data we also find a clear correlation between the similarity of the atomic environments and the energy. In low energy structures all the atoms of a species tend to have similar environments.

physics.comp-ph↗

arXiv2022

Efficient variable cell shape geometry optimization

A fast and reliable geometry optimization algorithm is presented that optimizes atomic positions and lattice vectors simultaneously. Using a series of benchmarks, it is shown that the method presented in this paper outperforms in most cases the standard optimization methods implemented in popular codes such as QUANTUM ESPRESSO and VASP. To motivate the variable cell shape optimization method presented in here, the eigenvalues of the lattice Hessian matrix are investigated thoroughly. It is shown that they change depending on the shape of the cell and the number of particles inside the cell. For certain cell shapes the resulting condition number of the lattice matrix can grow quadratically with respect to the number of particles. By a coordinate transformation which can be applied to all variable cell shape optimization methods, the undesirable conditioning of the lattice Hessian matrix is eliminated.

physics.comp-ph↗

arXiv2021

Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions

Atomic fingerprints are commonly used for the characterization of local environments of atoms in machine learning and other contexts. In this work, we study the behavior of two widely used fingerprints, namely the smooth overlap of atomic positions (SOAP) and the atom-centered symmetry functions (ACSF), under finite changes of atomic positions and demonstrate the existence of manifolds of quasi-constant fingerprints. These manifolds are found numerically by following eigenvectors of the sensitivity matrix with quasi-zero eigenvalues. The existence of such manifolds in ACSF and SOAP causes a failure to machine learn four-body interactions such as torsional energies that are part of standard force fields. No such manifolds can be found for the Overlap Matrix (OM) fingerprint due to its intrinsic many-body character.

cond-mat.other↗

arXiv2021

Missing theoretical evidence for conventional room temperature superconductivity in low enthalpy structures of carbonaceous sulfur hydrides

To elucidate the geometric structure of the putative room temperature superconductor, carbonaceous sulfur hydride, at high pressure, we present the results of an extensive computational structure search of bulk C-S-H at 250 gigapascals. Using the minima hopping structure prediction method coupled to the GPU accelerated Sirius library, more than 17,000 local minima with different stochiometries in large simulation cells were investigated. Only 24 stochiometries are favourable against elemental decomposition, all of them are carbon doped H$_3$S crystals. The absence of van Hove singularities or similar peaks in the electronic density of states of more than 3.000 candidate phases rules out conventional superconductivity in C-S-H at room-temperature.

cond-mat.supr-con↗

arXiv2021

Large Scale Structure Prediction of Near-Stoichiometric Magnesium Oxide Based on a Machine-Learned Interatomic Potential: Novel Crystalline Phases and Oxygen-Vacancy Ordering

Using a fast and accurate neural network potential we are able to systematically explore the energy landscape of large unit cells of bulk magnesium oxide with the minima hopping method. The potential is trained with a focus on the near-stoichiometric compositions, in particular on suboxides, i.e., Mg$_x$O$_{1-x}$ with $0.50<x<0.60$. Our extensive exploration demonstrates that for bulk stoichiometric compounds, there are several new low-energy rocksalt-like structures in which Mg atoms are octahedrally six--coordinated and form trigonal prismatic motifs with different stacking sequences. Furthermore, we find a dense spectrum of novel non-stoichiometric crystal phases of Mg$_x$O$_{1-x}$ for each composition of $x$. These structures are mostly similar to the rock salt structure with octahedral coordination and five--coordinated Mg atoms. Due to the removal of one oxygen atom, the energy landscape becomes more glass-like with oxygen-vacancy type structures that all lie very close to each other energetically. For the same number of magnesium and oxygen atoms our oxygen-deficient structures are lower in energy if the vacancies are aligned along lines or planes than rock salt structures with randomly distributed oxygen vacancies. We also found the putative global minima configurations for each composition of the non-stoichiometric suboxide structures. These structures are predominantly composed of (111) slabs of the rock salt structure which are terminated with Mg atoms at the top and bottom, and are stacked in different sequences along the $z$-direction. Like other Magnéli-type phases, these structures have properties that differ considerably from their stoichiometric counterparts such as low lattice thermal conductivity and high electrical conductivity.

cond-mat.mtrl-sci↗

arXiv2021

Potential energy surface study of X@Si$_{32}$X$^-_{44}$(X=Cl, Br) clusters to decipher the stabilization process of Si$_{20}$ fullerene

Efforts toward stabilization of the Si$_{20}$ fullerene through different schemes have failed despite several theoretical predictions. However, recently Tillmann {\it et. al.} succeeded to stabilize the Si$_{20}$ fullerene through exohedral decoration with eight Cl substituents and twelve SiCl$_3$ groups on the surface and enclosing Cl$^-$ ion. A deeper understanding on what factors lead to stabilization will open the path for stabilizing other systems of interest. Here, we employ the minima hopping method within density functional theory to understand the potential energy surface. The study shows that the exo-endo halide decoration of the cage alters the glassy nature of the potential energy surface of pure cage to structure seeker. Further analysis of different properties of the global minima, reveal that the extra electron instead of residing on the central encapsulated atom in the cage, it is distributed on the cage and increases the encapsulation energy; thereby stabilizing the system. We also provide estimates of the stability for different kind of exo-endo halide decorations and their feasible realization in experiments.

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

Maximum volume simplex method for automatic selection and classification of atomic environments and environment descriptor compression

Fingerprint distances, which measure the similarity of atomic environments, are commonly calculated from atomic environment fingerprint vectors. In this work we present the simplex method which can perform the inverse operation, i.e. calculating fingerprint vectors from fingerprint distances. The fingerprint vectors found in this way point to the corners of a simplex. For a large data set of fingerprints, we can find a particular largest volume simplex, whose dimension gives the effective dimension of the fingerprint vector space. We show that the corners of this simplex correspond to landmark environments that can by used in a fully automatic way to analyse structures. In this way we can for instance detect atoms in grain boundaries or on edges of carbon flakes without any human input about the expected environment. By projecting fingerprints on the largest volume simplex we can also obtain fingerprint vectors that are considerably shorter than the original ones but whose information content is not significantly reduced.

physics.comp-ph↗