arXiv subjects

Matthias Scheffler

Publications and source records attributed to Matthias Scheffler.

At least 55 records · Page 3Linked to original sources

arXiv2022

Hierarchical symbolic regression for identifying key physical parameters correlated with bulk properties of perovskites

Symbolic regression identifies key physical parameters describing materials properties by uncovering correlations as nonlinear analytical expressions. However, the pool of expressions grows rapidly with complexity, compromising its efficiency. We tackle this challenge by a hierarchical approach: identified expressions are used as input parameters for obtaining more complex expressions. Crucially, this framework can transfer knowledge among properties, highlighting physical relationships. We demonstrate this strategy by using the Sure-Independence-Screening-and-Sparsifying-Operator (SISSO) approach to identify expressions correlated with the lattice constant and cohesive energy, which are then used to model the bulk modulus of ABO3 perovskites.

cond-mat.mtrl-sci↗

arXiv2022

Ab initio approach for thermodynamic surface phases with full consideration of anharmonic effects -- the example of hydrogen at Si(100)

A reliable description of surfaces structures in a reactive environment is crucial to understand materials functions. We present a first-principles theory of replica-exchange grand-canonical-ensemble molecular dynamics (REGC-MD) and apply it to evaluate phase equilibria of surfaces in reactive gas-phase environment. We identify the different surface phases and locate phase boundaries including triple and critical points. The approach is demonstrated by addressing open questions for the Si(100) surface in contact with a hydrogen atmosphere. In the range from 300 to 1 000 K, we find 25 distinct thermodynamically stable surface phases, for which we also provide microscopic descriptions. Most of the identified phases, including few order-disorder phase transitions, have not yet been observed experimentally. The REGC-MD-derived phase diagram shows significant, qualitative differences to the description by the state-of-the-art "ab initio atomistic thermodynamics" approach.

cond-mat.mtrl-sci↗

arXiv2022

Numerical Quality Control for DFT-based Materials Databases

Electronic-structure theory is a strong pillar of materials science. Many different computer codes that employ different approaches are used by the community to solve various scientific problems. Still, the precision of different packages has only recently been scrutinized thoroughly, focusing on a specific task, namely selecting a popular density functional, and using unusually high, extremely precise numerical settings for investigating 71 monoatomic crystals. Little is known, however, about method- and code-specific uncertainties that arise under numerical settings that are commonly used in practice. We shed light on this issue by investigating the deviations in total and relative energies as a function of computational parameters. Using typical settings for basis sets and k-grids, we compare results for 71 elemental and 63 binary solids obtained by three different electronic-structure codes that employ fundamentally different strategies. On the basis of the observed trends, we propose a simple, analytical model for the estimation of the errors associated with the basis-set incompleteness. We cross-validate this model using ternary systems obtained from the NOMAD Repository and discuss how our approach enables the comparison of the heterogeneous data present in computational materials databases.

physics.comp-ph↗

arXiv2021

Interpretable Machine Learning for Materials Design

Fueled by the widespread adoption of Machine Learning (ML) and the high-throughput screening of materials, the data-centric approach to materials design has asserted itself as a robust and powerful tool for the in-silico prediction of materials properties. When training models to predict material properties, researchers often face a difficult choice between a model's interpretability or its performance. We study this trade-off by leveraging four different state-of-the-art ML techniques: XGBoost, SISSO, Roost, and TPOT for the prediction of structural and electronic properties of perovskites and 2D materials. We then assess the future outlook of the continued integration of ML into materials discovery and identify key problems that will continue to challenge researchers as the size of the literature's datasets and complexity of models increases. Finally, we offer several possible solutions to these challenges with a focus on retaining interpretability and share our thoughts on magnifying the impact of ML on materials design.

cond-mat.mtrl-sci↗

arXiv2021

OPTIMADE, an API for exchanging materials data

The Open Databases Integration for Materials Design (OPTIMADE) consortium has designed a universal application programming interface (API) to make materials databases accessible and interoperable. We outline the first stable release of the specification, v1.0, which is already supported by many leading databases and several software packages. We illustrate the advantages of the OPTIMADE API through worked examples on each of the public materials databases that support the full API specification.

cond-mat.mtrl-sci↗

arXiv2021

Learning Rules for Materials Properties and Functions

In materials science and engineering, one is typically searching for materials that exhibit exceptional performance for a certain function, and the number of these materials is extremely small. Thus, statistically speaking, we are interested in the identification of *rare phenomena*, and the scientific discovery typically resembles the proverbial hunt for the needle in a haystack.

cond-mat.mtrl-sci↗

arXiv2021

Materials genes of heterogeneous catalysis from clean experiments and artificial intelligence

Heterogeneous catalysis is an example of a complex materials function, governed by an intricate interplay of several processes, e.g., the different surface chemical reactions, and the dynamic re-structuring of the catalyst material at reaction conditions. Modelling the full catalytic progression via first-principles statistical mechanics is impractical, if not impossible. Instead, we show here how a tailored artificial-intelligence approach can be applied, even to a small number of materials, to model catalysis and determine the key descriptive parameters ("materials genes") reflecting the processes that trigger, facilitate, or hinder catalyst performance. We start from a consistent experimental set of "clean data", containing nine vanadium-based oxidation catalysts. These materials were synthesized, fully characterized, and tested according to standardized protocols. By applying the symbolic-regression SISSO approach, we identify correlations between the few most relevant materials properties and their reactivity. This approach highlights the underlying physicochemical processes, and accelerates catalyst design.

cond-mat.mtrl-sci↗

arXiv2021

All-electron periodic $G_0W_0$ implementation with numerical atomic orbital basis functions: algorithm and benchmarks

We present an all-electron, periodic {\GnWn} implementation within the numerical atomic orbital (NAO) basis framework. A localized variant of the resolution-of-the-identity (RI) approximation is employed to significantly reduce the computational cost of evaluating and storing the two-electron Coulomb repulsion integrals. We demonstrate that the error arising from localized RI approximation can be reduced to an insignificant level by enhancing the set of auxiliary basis functions, used to expand the products of two single-particle NAOs. An efficient algorithm is introduced to deal with the Coulomb singularity in the Brillouin zone sampling that is suitable for the NAO framework. We perform systematic convergence tests and identify a set of computational parameters, which can serve as the default choice for most practical purposes. Benchmark calculations are carried out for a set of prototypical semiconductors and insulators, and compared to independent reference values obtained from an independent $G_0W_0$ implementation based on linearized augmented plane waves (LAPW) plus high-energy localized orbitals (HLOs) basis set, as well as experimental results. With a moderate (FHI-aims \textit{tier} 2) NAO basis set, our $G_0W_0$ calculations produce band gaps that typically lie in between the standard LAPW and the LAPW+HLO results. Complementing \textit{tier} 2 with highly localized Slater-type orbitals (STOs), we find that the obtained band gaps show an overall convergence towards the LAPW+HLO results. The algorithms and techniques developed in this work pave the way for efficient implementations of correlated methods within the NAO framework.

cond-mat.mtrl-sci↗

arXiv2020

Electron-phonon coupling in d-electron solids: A temperature dependent study of rutile TiO2 by first-principles theory and two-photon photoemission

Rutile TiO2 is a paradigmatic transition metal oxide with applications in optics, electronics, photocatalysis, etc., that are subject to pervasive electron-phonon interaction. To understand how energies of its electronic bands, and in general semiconductors or metals where the frontier orbitals have a strong d-band character, depend on temperature, we perform a comprehensive theoretical and experimental study of the effects of electron-phonon (e-p) interactions. In a two-photon photoemission (2PP) spectroscopy study we observe an unusual temperature dependence of electronic band energies within the conduction band of reduced rutile TiO2, which is contrary to the well understood sp-band semiconductors and points to a so far unexplained dichotomy in how the e-p interactions affect differently the materials where the frontier orbitals are derived from the sp- and d-orbitals. To develop a broadly applicable model, we employ state-of-the-art first-principles calculations that explain how phonons promote interactions between the Ti-3d orbitals of the conduction band within the octahedral crystal field. The characteristics differences in e-p interactions experienced by the Ti 3d-orbitals of rutile TiO2 crystal lattice are contrasted with the more familiar behavior of the Si 2s-orbitals of stishovite SiO2 polymorph, in which the frontier 2s-orbital experience a similar crystal field with the opposite effect...

cond-mat.mtrl-sci↗

arXiv2020

Anharmonicity Measure for Materials

Theoretical frameworks used to qualitatively and quantitatively describe nuclear dynamics in solids are often based on the harmonic approximation. However, this approximation is known to become inaccurate or to break down completely in many modern functional materials. Interestingly, there is no reliable measure to quantify anharmonicity so far. Thus, a systematic classification of materials in terms of anharmonicity and a benchmark of methodologies that may be appropriate for different strengths of anharmonicity is currently impossible. In this work, we derive and discuss a statistical measure that reliably classifies compounds across temperature regimes and material classes by their "degree of anharmonicity". This enables us to distinguish "harmonic" materials, for which anharmonic effects constitute a small perturbation on top of the harmonic approximation, from strongly "anharmonic" materials, for which anharmonic effects become significant or even dominant and the treatment of anharmonicity in terms of perturbation theory is more than questionable. We show that the analysis of this measure in real and reciprocal space is able to shed light on the underlying microscopic mechanisms, even at conditions close to, e.g., phase transitions or defect formation. Eventually, we demonstrate that the developed approach is computationally efficient and enables rapid high-throughput searches by scanning over a set of several hundred binary solids. The results show that strong anharmonic effects beyond the perturbative limit are not only active in complex materials or close to phase transitions, but already at moderate temperatures in simple binary compounds.

cond-mat.mtrl-sci↗

arXiv2020

Fully Anharmonic, Non-Perturbative Theory of Vibronically Renormalized Electronic Band Structures

We develop a first-principles approach for the treatment of vibronic interactions in solids that overcomes the main limitations of state-of-the-art electron-phonon coupling formalisms. In particular, anharmonic effects in the nuclear dynamics are accounted to all orders via ab initio molecular dynamics simulations. This non-perturbative, self-consistent approach evaluates the response of the wave functions along the computed anharmonic trajectory; thus it fully considers the coupling between nuclear and electronic degrees of freedom. We validate and demonstrate the merits of the concept by calculating temperature-dependent, momentum-resolved spectral functions for silicon and the cubic perovskite SrTiO3, a strongly anharmonic material featuring soft modes. In the latter case, our approach reveals that anharmonicity and higher-order vibronic couplings contribute substantially to the electronic-structure at finite-temperatures, noticeably affecting band gaps and effective masses, and hence macroscopic properties such as transport coefficients.

cond-mat.mtrl-sci↗

arXiv2020

Pentacene and Tetracene Molecules and Films on H/Si(111): Level Alignment from Hybrid Density Functional Theory

The electronic properties of hybrid organic-inorganic semiconductor interfaces depend strongly on the alignment of the electronic carrier levels in the organic/inorganic components. In the present work, we address this energy level alignment from first principles theory for two paradigmatic organic-inorganic semiconductor interfaces, the singlet fission materials tetracene and pentacene on H/Si(111), using all-electron hybrid density functional theory. For isolated tetracene on H/Si(111), a type I-like heterojunction (lowest-energy electron and hole states on Si) is found. For isolated pentacene, the molecular and semiconductor valence band edges are degenerate. For monolayer films, we show how to construct supercell geometries with up to 1,192 atoms, which minimize the strain between the inorganic surface and an organic monolayer film. Based on these models, we predict the formation of type II heterojunctions (electron states on Si, hole-like states on the organic species) for both acenes, indicating that charge separation at the interface between the organic and inorganic components is favored. The paper discusses the steps needed to find appropriate low-energy interface geometries for weakly bonded organic molecules and films on inorganic substrates from first principles, a necessary prerequisite for any computational level alignment prediction.

cond-mat.mtrl-sci↗

arXiv2020

Artificial Intelligence for High-Throughput Discovery of Topological Insulators: the Example of Alloyed Tetradymites

Significant advances have been made in predicting new topological materials using high-throughput empirical descriptors or symmetry-based indicators. To date, these approaches have been applied to materials in existing databases, and are severely limited to systems with well-defined symmetries, leaving a much larger materials space unexplored. Using tetradymites as a prototypical class of examples, we uncover a novel two-dimensional descriptor by applying an artificial intelligence (AI) based approach for fast and reliable identification of the topological characters of a drastically expanded range of materials, without prior determination of their specific symmetries and detailed band structures. By leveraging this descriptor that contains only the atomic number and electronegativity of the constituent species, we have readily scanned a huge number of alloys in the tetradymite family. Strikingly, nearly half of which are identified to be topological insulators, revealing a much larger territory of the topological materials world. The present work also attests the increasingly important role of such AI-based approaches in modern materials discovery.

cond-mat.mtrl-sci↗

arXiv2019

Parametrically Constrained Geometry Relaxations for High-Throughput Materials Science

Reducing parameter spaces via exploiting symmetries has greatly accelerated and increased the quality of electronic-structure calculations. Unfortunately, many of the traditional methods fail when the global crystal symmetry is broken, even when the distortion is only a slight perturbation (e.g. Jahn-Teller like distortions). Here we introduce a flexible and generalizable parametric relaxation scheme, and implement it in the all-electron code FHI-aims. This approach utilizes parametric constraints to maintain symmetry at any level. After demonstrating the method's ability to relax metastable structures, we highlight its adaptability and performance over a test set of 359 materials, across thirteen lattice prototypes. Finally we show how these constraints can reduce the number of steps needed to relax local lattice distortions by an order of magnitude. The flexibility of these constraints enables a significant acceleration of the high-throughput searches for novel materials for numerous applications.

cond-mat.mtrl-sci↗

arXiv2019

The (3$\times$3)-SiC-($\bar{1}\bar{1}\bar{1}$) Reconstruction: Atomic Structure of the Graphene Precursor Surface from a Large-Scale First-Principles Structure Search

Silicon carbide (SiC) is an excellent substrate for growth and manipulation of large scale, high quality epitaxial graphene. On the carbon face (the ($\bar{1}\bar{1}\bar{1}$) or $(000\bar{1}$) face, depending on the polytype), the onset of graphene growth is intertwined with the formation of several competing surface phases, among them a (3$\times$3) precursor phase suspected to hinder the onset of controlled, near-equilibrium growth of graphene. Despite more than two decades of research, the precise atomic structure of this phase is still unclear. We present a new model of the (3$\times$3)-SiC-($\bar{1}\bar{1}\bar{1}$) reconstruction, derived from an {\it ab initio} random structure search based on density functional theory including van der Waals effects. The structure consists of a simple pattern of five Si adatoms in bridging and on-top positions on an underlying, C-terminated substrate layer, leaving one C atom per (3$\times$3) unit cell formally unsaturated. Simulated scanning tunneling microscopy (STM) images are in excellent agreement with previously reported experimental STM images.

cond-mat.mtrl-sci↗

arXiv2019

Determining Surface Phase Diagrams Including Anharmonic Effects

We introduce a massively parallel replica-exchange grand-canonical sampling algorithm to simulate materials at realistic conditions, in particular surfaces and clusters in reactive atmospheres. Its purpose is to determine in an automated fashion equilibrium phase diagrams for a given potential-energy surface (PES) and for any observable sampled in the grand-canonical ensemble. The approach enables an unbiased sampling of the phase space and is embarrassingly parallel. It is demonstrated for a model of Lennard-Jones system describing a surface in contact with a gas phase. Furthermore, the algorithm is applied to Si$_M$ clusters ($M=2, 4$) in contact with an H$_{2}$ atmosphere, with all interactions described at the \textit{ab initio} level, i.e., via density-functional theory, with the PBE gradient-corrected exchange-correlation functional. We identify the most thermodynamically stable phases at finite $T, p$(H$_{2}$) conditions.

cond-mat.mtrl-sci↗

arXiv2019

Big-Data-Driven Materials Science and its FAIR Data Infrastructure

This chapter addresses the forth paradigm of materials research -- big-data driven materials science. Its concepts and state-of-the-art are described, and its challenges and chances are discussed. For furthering the field, Open Data and an all-embracing sharing, an efficient data infrastructure, and the rich ecosystem of computer codes used in the community are of critical importance. For shaping this forth paradigm and contributing to the development or discovery of improved and novel materials, data must be what is now called FAIR -- Findable, Accessible, Interoperable and Re-purposable/Re-usable. This sets the stage for advances of methods from artificial intelligence that operate on large data sets to find trends and patterns that cannot be obtained from individual calculations and not even directly from high-throughput studies. Recent progress is reviewed and demonstrated, and the chapter is concluded by a forward-looking perspective, addressing important not yet solved challenges.

cond-mat.mtrl-sci↗

arXiv2019

Beyond scaling relations for the description of catalytic materials

Computational screening for new and improved catalyst materials relies on accurate and low-cost predictions of key parameters such as adsorption energies. Here, we use recently developed compressed sensing methods to identify descriptors whose predictive power extends over a wide range of adsorbates, multi-metallic transition metal surfaces and facets. The descriptors are expressed as non-linear functions of intrinsic properties of the clean catalyst surface, e.g. coordination numbers, d-band moments and density of states at the Fermi level. From a single density-functional theory calculation of these properties, we predict adsorption energies at all potential surface sites, and thereby also the most stable geometry. Compared to previous approaches such as scaling relations, we find our approach to be both more general and more accurate for the prediction of adsorption energies on alloys with mixed-metal surfaces, already when based on training data including only pure metals. This accuracy can be systematically improved by adding also alloy adsorption energies to the training data.

cond-mat.mtrl-sci↗