Fully anharmonic nonperturbative 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 spectral functions and band gaps 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 can contribute substantially to the electronic-structure at finite-temperatures, noticeably affecting macroscopic properties, such as absorption coefficients as well as thermal and electrical conductivities

Ab Initio Green-Kubo Approach for the Thermal Conductivity of Solids

We herein present a first-principles formulation of the Green-Kubo method that allows the accurate assessment of the non-radiative thermal conductivity of solid semiconductors and insulators in equilibrium ab initio molecular dynamics calculations. Using the virial for the nuclei, we propose a unique ab initio definition of the heat flux. Accurate size- and time convergence are achieved within moderate computational effort by a robust, symptotically exact extrapolation scheme. We demonstrate the capabilities of the technique by investigating the thermal conductivity of extreme high and low heat conducting materials, namely diamond Si and tetragonal ZrO2

SISSO++: A C++ Implementation of the Sure-Independence Screening and Sparisifying Operator Approach

The sure independence screening and sparsifying operator (SISSO) approach (Ouyang et al., 2018) is an algorithm belonging to the field of artificial intelligence and more specifically a combination of symbolic regression and compressed sensing. As a symbolic regression method, SISSO is used to identify mathematical functions, i.e. the descriptors, that best predict the target property of a data set. Furthermore, the compressed sensing aspect of SISSO, allows it to find sparse linear models using tens to thousands of data points. SISSO is introduced for both regression and classification tasks. In practice, SISSO first constructs a large and exhaustive feature space of trillions of potential descriptors by taking in a set of user-provided primary features as a dataframe, and then iteratively applying a set of unary and binary operators, e.g. addition, multiplication, exponentiation, and squaring, according to a user-defined specification. From this exhaustive pool of candidate descriptors, the ones most correlated to a target property are identified via sure-independence screening, from which the low-dimensional linear models with the lowest error are found via an l0 regularization. Because symbolic regression generates an interpretable equation, it has become an increasingly popular concept across scientific disciplines (Neumann et al., 2020; Udrescu & Tegmark, 2020; Wang et al., 2019). A particular advantage of these approaches are their capability to model complex phenomena using relatively simple descriptors. SISSO has been used successfully in the past to model, explore, and predict important material properties, including the stability of different phases (Bartel et al., 2018; Schleder et al., 2020); the catalytic activity and reactivity (Andersen et al., 2019; Andersen & Reuter, 2021; Han et al., 2021; W. Xu et al., 2021); and glass transition temperatures (Pilania et al., 2019). Beyond regression problems, SISSO has also been used successfully to classify materials into different crystal prototypes (Ouyang et al., 2019), or whether a material crystallizes in its ground state as a perovskite (Bartel et al., 2019), or to determine whether a material is a topological insulator or not (Cao et al., 2020). The SISSO++ package is an open-source (Apache-2.0 licence), modular, and extensible C++ implementation of the SISSO method with Python bindings. Specifically, SISSO++ applies this methodology for regression, log regression, and classification problems. Additionally, the library includes multiple Python functions to facilitate the post-processing, analyzing, and visualizing of the resulting models

Analysis of Topological Transitions in Two-dimensional Materials by Compressed Sensing

Quantum spin-Hall insulators (QSHIs), i.e., two-dimensional topological insulators (TIs) with a symmetry-protected band inversion, have attracted considerable scientific interest in recent years. In this work, we have computed the topological Z2 invariant for 220 functionalized honeycomb lattices that are isoelectronic to functionalized graphene. Besides confirming the TI character of well-known materials such as functionalized stanene, our study identifies 45 yet unreported QSHIs. We applied a compressed-sensing approach to identify a physically meaningful descriptor for the Z2 invariant that only depends on the properties of the material's constituent atoms. This enables us to draw a map of materials, in which metals, trivial insulators, and QSHI form distinct regions. This analysis yields fundamental insights in the mechanisms driving topological transitions. The transferability of the identified model is explicitly demonstrated for an additional set of honeycomb lattices with different functionalizations that are not part of the original set of 220 graphene-type materials used to identify the descriptor. In this class, we predict 74 more novel QSHIs that have not been reported in literature yet

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 13 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 high-throughput searches for novel materials for numerous applications

Thermal conductivity of Si nanostructures containing defects: Methodology, isotope effects, and phonon trapping

A first-principles method to calculate the thermal conductivity in nanostructures that may contain defects or impurities is described in detail. The method mimics the so-called "laser-flash" technique to measure thermal conductivities. It starts with first-principles density-functional theory and involves the preparation of various regions of a supercell at slightly different temperatures. The temperature fluctuations are minimized without using a thermostat and, after averaging over random initial conditions, temperature changes as small as 5 K can be monitored (from 120 to 125 K). The changes to the phonon density of states and the specific heat induced by several atomic percent of impurities are discussed. The thermal conductivity of Si supercells is calculated as a function of the temperature and of the impurity content. For most impurities, the drop in thermal conductivity is unremarkable. However, there exist narrow ranges of impurity parameters (mass, bond strength, etc.) for which substantial drops in the thermal conductivity are predicted. These drops are isotope dependent and appear to be related to the vibrational lifetime of specific impurity-related modes

ELPA: A parallel solver for the generalized eigenvalue problem

For symmetric (hermitian) (dense or banded) matrices the computation of eigenvalues and eigenvectors Ax = λBx is an important task, e.g. in electronic structure calculations. If a larger number of eigenvectors are needed, often direct solvers are applied. On parallel architectures the ELPA implementation has proven to be very efficient, also compared to other parallel solvers like EigenExa or MAGMA. The main improvement that allows better parallel efficiency in ELPA is the two-step transformation of dense to band to tridiagonal form. This was the achievement of the ELPA project. The continuation of this project has been targeting at additional improvements like allowing monitoring and autotuning of the ELPA code, optimizing the code for different architectures, developing curtailed algorithms for banded A and B, and applying the improved code to solve typical examples in electronic structure calculations. In this paper we will present the outcome of this project

Shared Metadata for Data-Centric Materials Science

The expansive production of data in materials science, their widespread sharing and repurposing requires educated support and stewardship. In order to ensure that this need helps rather than hinders scientific work, the implementation of the FAIR-data principles (Findable, Accessible, Interoperable, and Reusable) must not be too narrow. Besides, the wider materials-science community ought to agree on the strategies to tackle the challenges that are specific to its data, both from computations and experiments. In this paper, we present the result of the discussions held at the workshop on "Shared Metadata and Data Formats for Big-Data Driven Materials Science". We start from an operative definition of metadata, and what features a FAIR-compliant metadata schema should have. We will mainly focus on computational materials-science data and propose a constructive approach for the FAIRification of the (meta)data related to ground-state and excited-states calculations, potential-energy sampling, and generalized workflows. Finally, challenges with the FAIRification of experimental (meta)data and materials-science ontologies are presented together with an outlook of how to meet them

Accurate thermal conductivities from optimally short molecular dynamics simulations

The evaluation of transport coefficients in extended systems, such as thermal conductivity or shear viscosity, is known to require impractically long simulations, thus calling for a paradigm shift that would allow to deploy state-of-the-art quantum simulation methods. We introduce a new method to compute these coefficients from optimally short molecular dynamics simulations, based on the Green-Kubo theory of linear response and the cepstral analysis of time series. Information from the full sample power spectrum of the relevant current for a single and relatively short trajectory is leveraged to evaluate and optimally reduce the noise affecting its zero-frequency value, whose expectation is proportional to the corresponding conductivity. Our method is unbiased and consistent, in that both the resulting bias and statistical error can be made arbitrarily small in the long-time limit. A simple data-analysis protocol is proposed and validated with the calculation of thermal conductivities in the paradigmatic cases of elemental and molecular fluids (liquid Ar and H2O) and of crystalline and glassy solids (MgO and a-SiO2). We find that simulation times of one to a few hundred picoseconds are sufficient in these systems to achieve an accuracy of the order of 10% on the estimated thermal conductivities