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We perform femtosecond electron diffuse scattering measurements on black phosphorus. We reproduce the non-equilibrium structural dynamics using ultrafast dynamics simulations based on the time-dependent Boltzmann formalism and calculations of the all-phonon structure factor.

We combine femtosecond electron diffuse scattering experiments and first-principles calculations of the coupled electron-phonon dynamics to provide a detailed momentum-resolved picture of the ultrafast lattice thermalization in a thin film of black phosphorus. The measurements reveal the emergence of highly anisotropic non-thermal phonon populations which persist for several picoseconds following excitation of the electrons with a light pulse. Combining ultrafast dynamics simulations based on the time-dependent Boltzmann formalism and calculations of the structure factor, we reproduce the experimental data and identify the vibrational modes primarily responsible for the carrier relaxation via electron-phonon coupling and the subsequent lattice thermalization via phonon-phonon scattering. In particular, we attribute the non-equilibrium lattice dynamics of black phosphorus to highly-anisotropic phonon-assisted scattering processes, which are primarily mediated by high-energy optical phonons. Our approach paves the way towards unravelling and controlling microscopic energy-flow pathways in two-dimensional materials and van der Waals heterostructures, and may also be extended to other non-equilibrium phenomena involving coupled electron-phonon dynamics such as superconductivity, phase transitions or polaron physics.

The electronic band structure and crystal structure are the two complementary identifiers of solid-state materials. Although convenient instruments and reconstruction algorithms have made large, empirical, crystal structure databases possible, extracting the quasiparticle dispersion (closely related to band structure) from photoemission band mapping data is currently limited by the available computational methods. To cope with the growing size and scale of photoemission data, here we develop a pipeline including probabilistic machine learning and the associated data processing, optimization and evaluation methods for band-structure reconstruction, leveraging theoretical calculations. The pipeline reconstructs all 14 valence bands of a semiconductor and shows excellent performance on benchmarks and other materials datasets. The reconstruction uncovers previously inaccessible momentum-space structural information on both global and local scales, while realizing a path towards integration with materials science databases. Our approach illustrates the potential of combining machine learning and domain knowledge for scalable feature extraction in multidimensional data.

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 for to all orders via ab initio molecular dynamics simulations. This nonperturbative, 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 ${\mathrm{SrTiO}}_{3}$, 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.

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.

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., Comment: 17 figures, 2 tables, and 12 pages

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., Comment: 10 pages, 7 figures

The authors present experimental and theoretical results on the electron-phonon interaction in TiO2 and SiO2 and show that the different behavior can be attributed to the split of the degeneracy of atomic orbitals induced by the crystal field of the ligand species.

The solution of (generalized) eigenvalue problems for symmetric or Hermitian matrices is a common subtask of many numerical calculations in electronic structure theory or materials science. Depending on the scientific problem, solving the eigenvalue problem can easily amount to a sizeable fraction of the whole numerical calculation, and quite often is even the dominant part by far. For researchers in the field of computational materials science, an efficient and scalable solution of the eigenvalue problem is thus of major importance. The ELPA-library (Eigenvalue SoLvers for Petaflop-Applications) is a well-established dense direct eigenvalue solver library, which has proven to be very efficient and scalable up to very large core counts. It is in a wide-spread production use on a large variety of HPC systems worldwide, and is applied by many codes in the field of materials science. In this paper, we describe the latest optimizations of the ELPA-library for new HPC architectures of the Intel Skylake processor family with an AVX-512 SIMD instruction set, or for HPC systems accelerated with recent GPUs. Apart from those direct hardware-related optimizations, we also describe a complete redesign of the API in a modern modular way, which, apart from a much simpler and more flexible usability, leads to a new path to access system-specific performance optimizations. In order to ensure optimal performance for a particular scientific setting or a specific HPC system, the new API allows the user to influence in a straightforward way the internal details of the algorithms and of performance-critical parameters used in the ELPA-library. On top of that, we introduce an autotuning functionality, which allows for finding the best settings in a self-contained automated way, without the need of much user effort. In situations where many eigenvalue problems with similar settings have to be solved consecutively, the autotuning process of the ELPA-library can be done “on-the-fly”, without the need of preceding the simulation with an “artificial” autotuning step. Practical applications from materials science which rely on reaching a numerical convergence limit by so-called self-consistency iterations can profit from the on-the-fly autotuning. On some examples of scientific interest, simulated with the FHI-aims application, the advantages of the latest optimizations of the ELPA-library are demonstrated.

Significant advances have been made in predicting new topological materials using high-throughput empirical descriptors or symmetry-based indicators. This line of research has produced extensive lists of candidate topological materials that still await experimental validation. To date, these approaches have been limited to materials already known in databases, leaving a much larger portion of the materials space unexplored. Here we uncover a novel two-dimensional descriptor for fast and reliable identification of the topological characters of complex alloyed systems. Using tetradymites with widely varying stoichiometric compositions as examples, we obtain this descriptor by applying a recently developed data-analytics approach named SISSO (Sure Independence Screening and Sparsifying Operator) to training data from high-level electronic structure calculations. By leveraging this descriptor that contains only two elemental properties (the atomic number and electronegativity) of the constituent species, we can readily scan over four million alloys in the tetradymite family. Strikingly, nearly two million new topological insulators are discovered, thus drastically expanding the territory of the topological materials world. The strong predictive power of the descriptor beyond the initial scope of the training data also testifies the increasing importance of such data-driven approaches in materials discovery.

Boron carbide, the simple chemical combination of boron and carbon, is one of the best?known binary ceramic materials. Despite that, a coherent description of its crystal structure and physical properties resembles one of the most challenging problems in materials science. By combining ab?initio computational studies, precise crystal structure determination from diffraction experiments, and state?of?the?art high?resolution transmission electron microscopy imaging, this concerted investigation reveals hitherto unknown local structure modifications together with the known structural alterations. The mixture of different local atomic arrangements within the real crystal structure reduces the electron deficiency of the pristine structure CBC+B12, answering the question about electron precise character of boron carbide and introducing new electronic states within the band gap, which allow a better understanding of physical properties.

We first briefly report on the status and recent hievements of the ELPA-AEO (Eigen-value Solvers for Petaflop Applications -- Algorithmic Extensions and Optimizations) and ESSEX II (Equipping Sparse Solvers for Exascale) projects. In both collaboratory efforts, scientists from the application areas, mathematicians, and computer scientists work together to develop and make available efficient highly parallel methods for the solution of eigenvalue problems. Then we focus on a topic addressed in both projects, the use of mixed precision computations to enhance efficiency. We give a more detailed description of our approaches for benefiting from either lower or higher precision in three selected contexts and of the results thus obtained.

The formation of framework vacancies in Si- and Ge-based type-I clathrates is studied as function of filling the cages with K and Ba atoms using density-functional theory. Our analysis reveals the relevance of structural disorder, geometric relaxation, electronic saturation, as well as vibrational and configurational entropy. In the Si clathrates we find that vacancies are unstable, but very differently, in Ge clathrates up to three vacancies per unit cell can be stabilized. This contrasting behavior is largely driven by the different energy gain on populating the electronic vacancy states, which originates from the different degree of localization of the valence orbitals of Si and Ge. This also actuates a qualitatively different atomic relaxation of the framework., 5 pages, 6 figures, submitted to a journal

The identification of descriptors of materials properties and functions thatcapture the underlying physical mechanisms is a critical goal in data-drivenmaterials science. Only such descriptors will enable a trustful and efficientscanning of materials spaces and possibly the discovery of new materials.Recently, the sure-independence screening and sparsifying operator (SISSO) hasbeen introduced and was successfully applied to a number of materials-scienceproblems. SISSO is a compressed-sensing based methodology yielding predictivemodels that are expressed in form of analytical formulas, built from simplephysical properties. These formulas are systematically selected from an immensenumber (billions or more) of candidates. In this work, we describe a powerfulextension of the methodology to a 'multi-task learning' approach, whichidentifies a single descriptor capturing multiple target materials propertiesat the same time. This approach is specifically suited for a heterogeneousmaterials database with scarce or partial data, e.g., in which not allproperties are reported for all materials in the training set. As showcaseexamples, we address the construction of materials-properties maps for therelative stability of octet-binary compounds, considering several crystalphases simultaneously, and the metal/insulator classification of binarymaterials distributed over many crystal-prototypes.

The electrical, optical, and magnetic properties of semiconductors are controlled by the defects and impurities they contain. Device manufacturing requires placing specific impurities at specific sites in the crystal while avoiding their diffusion and preventing unwanted contamination. But device processing includes annealing steps, and defects can diffuse within the annealing time. Many defects have a donor and/or acceptor level in the forbidden energy gap, and their diffusivity depends on their charge state, in other words, on the Fermi level or the exposure to photons at or above the bandgap energy. A defect-related gap level may also shift from the gap into a band (or vice versa) during a diffusion step, which can lead to a change in the charge state of the defect. Herein we focus on the simple issue of defect diffusion by thermally stimulated “over-the-barrier” hopping. We compare the activation energies (Ea) obtained with the same supercell, pseudopotentials, basis set, and k-point sampling, but different exchange-correlation functionals (Exc). The charge and spin are fixed in each calculation. In harmonic transition-state theory, the diffusivity of a defect is given by D(T)=D0exp{ Ea/kBT} [cms ], where the prefactor D0 contains the attempt frequency, [5] Ea is the total energy difference between the saddle point and the minimum of the potential-energy surface, and kB is the Boltzmann constant. Experimentally determined Arrhenius plots (logD vs. 1/ T) are often very close to a straight line. A fit produces Ea (negative of the slope) and D0 (y-intercept for T !0). For defects in semiconductors, the almost perfectly constant slope of Arrhenius plots over wide ranges of temperatures justifies the assumption that the temperature dependence of the vibrational frequencies, which enter in the prefactor D0, can be safely ignored. Ab initio molecular dynamics (MD) simulations of D(T) require very long simulation times. Direct calculations of activation energies are much faster, but they require the knowledge of the diffusion path and saddle point. In any case, the errors associated with local and semilocal exchangecorrelation functionals in density functional theory (DFT) are different at minima and saddle-point configurations as the Kohn–Sham orbitals are differently extended, sometimes leading to underestimations of Ea. In order to quantify these arguments, we performed nudged elastic band (NEB) calculations with various Exc functionals. In the Kohn–Sham formulation of DFT, the (electronic) many-body problem is mapped exactly onto a single-particle Hamiltonian. All many-body effects are subsumed into an exchange-correlation potential. Were this functional known exactly, the solution of the single-particle equations would yield the exact ground-state electron density n of the many-body system. But the exact Exc[n] (and Vxc[n]= dExc/dn) is not known. Useful approximations to it have been proposed over the years. The local density approximation (LDA) is derived from the Exc of a homogeneous electron gas. It reproduces satisfactorily the basic geometric properties of bulk structures with a few percent error margins. However, it is not uncommon to find errors of the order of 20% for the cohesive energies of solids while the adsorption energies of molecules at surfaces can only be determined with limited accuracy. Functionals based on the generalized gradient approximation (GGA) partially correct for these flaws since they account for changes in the electronic density in a semilocal fashion. The most prominent one, the Perdew– Burke–Ernzerhof (PBE) functional, is derived from first principles. All the parameters are basically fundamental constants, but some flexibility remains in the formulation of the exchange part. The “simplest conceivable dimensionally consistent expression” was selected for the exchange enhancement factor, previously derived by Becke. The parameter k was chosen such that the exchange interaction complies with the local Lieb–Oxford inequality, which ensures that the integrated Lieb–Oxford condition is fulfilled. Zhang andYang pointed out that the local Lieb–Oxford inequality is a sufficient but not a necessary condition for the fulfillment of the integrated Lieb–Oxford condition. They proposed a revised PBE functional (revPBE), which is not based on the local Lieb–Oxford inequality. The parameter k is such that the total energies computed by optimized exchange potential simulations for isolated atoms are reproduced. [*] Prof. Dr. S. K. Estreicher Physics Department, Texas Tech University Lubbock, TX 79409-1051 (USA) E-mail: stefan.estreicher@ttu.edu

openaire: EC/H2020/676580/EU//NoMaD A real-space formalism for density-functional perturbation theory (DFPT) is derived and applied for the computation of harmonic vibrational properties in molecules and solids. The practical implementation using numeric atom-centered orbitals as basis functions is demonstrated exemplarily for the all-electron Fritz Haber Institute ab initio molecular simulations (FHI-aims) package. The convergence of the calculations with respect to numerical parameters is carefully investigated and a systematic comparison with finite-difference approaches is performed both for finite (molecules) and extended (periodic) systems. Finally, the scaling tests and scalability tests on massively parallel computer systems demonstrate the computational efficiency.

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, asymptotically 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 ZrO$_2$., Comment: 5 pages, 4 figures

Based on potential–energy curves that were derived from ab initio calculations within the framework of many-body perturbation theory, mixed quantum–classical simulations have been performed to understand the dynamics of the photodesorption process of iodine from KI(100). Dissipation and recoil processes were included by adding a surface oscillator to the ab initio potentials. Using this approach, we reproduce and explain qualitatively the desorption spectrum and the kinetic energy distribution of the desorbing iodine.

Nature Communications 6: Article number: 6901 (2015); Published 22 April 2015; Updated 30 June 2015 In the Methods section of this Article, there are three references that do not refer to the correct articles. The sentence ‘The sample surface was cleaned using standard procedures’ incorrectly directs to reference 2, whereas the correct reference is ref.

The reliable high-dimensional theoretical description of reactions at surfaces with electronic transitions still represents a considerable challenge since the electrons have to be treated quantum mechanically. A full quantum treatment of both electrons and nuclei is computationally not feasible at the moment. Therefore we propose a mixed quantum-classical approach for the simulation of reactions at surfaces with electronic transitions. In this method, the nuclear motion is described classically while the electrons are treated quantum mechanically. Still the feedback between nuclei and electrons is taken into account self-consistently. The computational efficiency of this method allows a more realistic multidimensional treatment of electronically nonadiabatic processes at surfaces. We will discuss two recent applications of this approach. First we will address the charge transfer in the scattering of I, from a diamond surface. As a second example we present dynamical simulations of the laser-induced desorption of NO from NiO(100).

Despite their pronounced importance for oxide-based photochemistry, optoelectronics and photovoltaics, only fairly little is known about the polaron lifetimes and binding energies. Polarons represent a crucial intermediate step populated immediately after dissociation of the excitons formed in the primary photoabsorption process. Here we present a novel approach to studying photoexcited polarons in an important photoactive oxide, ZnO, using infrared (IR) reflection–absorption spectroscopy (IRRAS) with a time resolution of 100 ms. For well-defined (10-10) oriented ZnO single-crystal substrates, we observe intense IR absorption bands at around 200 meV exhibiting a pronounced temperature dependence. On the basis of first-principles-based electronic structure calculations, we assign these features to hole polarons of intermediate coupling strength.

The properties of materials at high temperatures are often determined by complex thermodynamic mechanisms. One of the most prominent examples is the stabilization of tetragonal and cubic zirconia, which we investigate using density functional theory. The results show that the minimum energy path for the tetragonal-to-cubic phase transformation differs significantly from the paths discussed in the literature so far. This provides insight into the properties of compositions codoped with yttria and titania, an approach that has recently been proposed for the design of thermal barrier coatings.

We review recent progress in the theoretical description of the O2 adsorption dynamics at metal surfaces. Intriguing conceptual challenges to a quantitative modeling arise from the spin triplet ground state of the free oxygen molecule, the typically highly corrugated potential energy surfaces (PESs), and the high exothermicity of dissociative adsorption processes. This dictates extensive dynamical simulations (either through direct ab initio molecular dynamics or PES interpolating divide and conquer approaches), an account of electronic non-adiabaticity, as well as heat dissipation channels. We critically discuss the present status of corresponding methodology and the physical insight gained through it, using the oxygen adsorption at Al(111), Pt(111), Pt(211) and Pd(100) as showcases.

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.

The adsorption behavior of CO on bimetallic Ni/Cu(110) surfaces has been studied experimentally by thermal-desorption spectroscopy and theoretically by density-functional theory (DFT) calculations. The bimetallic surfaces were produced either by evaporation of nickel or by decomposition of $\text{Ni}{(\text{CO})}_{4}$ on Cu(110). Adsorption of CO at 180 K on such a bimetallic surface yields three new adsorption states with adsorption energies between that of CO on clean Cu(110) and clean Ni(110). The new desorption peaks from the bimetallic surface, designated as ${\ensuremath{\beta}}_{1}\text{\ensuremath{-}}{\ensuremath{\beta}}_{3}$, can be observed at 250, 300, and 360 K, respectively. These new states are most pronounced when $\frac{1}{2}$ monolayer of nickel is present on the copper surface. DFT calculations, using the Vienna ab initio simulation package code, were performed to identify the most probable Ni/Cu atomic arrangements at the bimetallic surface to reconcile with the experimental results. It turned out that CO adsorption on nickel dimers consisting of in-surface and adjacent subsurface atoms can best explain the observed experimental data. The result shows that CO adsorption is determined by local (geometric) effects rather than by long-range (electronic) effects. These findings should contribute to a better understanding of tailoring catalytic processes with the help of bimetallic catalysts.

Recently, spin selection rules have been invoked to explain the discrepancy between measured and calculated adsorption probabilities of molecular oxygen reacting with Al(111). In this work, we inspect the impact of nonadiabatic spin transitions on the dynamics of this system from first principles. For this purpose the motion on two distinct potential-energy surfaces associated to different spin configurations and possible transitions between them are inspected by means of the Fewest Switches algorithm. Within this framework we especially focus on the influence of such spin transitions on observables accessible to molecular beam experiments. On this basis we suggest experimental setups that can validate the occurrence of such transitions and discuss their feasibility., Comment: 13 pages, 7 figures

We performed mixed quantum-classical molecular dynamics simulations based on first-principles potential-energy surfaces to demonstrate that the scattering of a beam of singlet O2 molecules at Al(111) will enable an unambiguous assessment of the role of spin-selection rules for the adsorption dynamics. At thermal energies we predict a sticking probability that is substantially less than unity, with the repelled molecules exhibiting characteristic kinetic, vibrational and rotational signatures arising from the non-adiabatic spin transition., 4 pages including 3 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.html

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.