VASP Software (Austria)

This study uses meta‐analytic procedures to examine the relationship between growing up in a violent home and subsequently becoming part of a violent marital relationship. Our meta‐analysis examines published and unpublished research studies that investigate the relationship between witnessing or experiencing family violence in childhood and receiving or perpetrating violence in an adult heterosexual cohabiting or marital relationship. The findings of this meta‐analysis suggest there is a weak‐to‐moderate relationship between growing up in an abusive family and becoming involved in a violent marital relationship. Differential effects of gender and sample type are also discussed.

An on-the-fly force field generation method is developed and applied to liquid-solid phase transitions. The method allows the machine to automatically self-learn interatomic potentials during molecular dynamics simulations and to generate force fields with the distinctive chemical precision of first-principles methods. Applications show that more than 99% of the expensive first-principles calculations are bypassed, and molecular dynamics simulations are accelerated by more than two orders of magnitude already during learning, with many more orders during production runs.

Realistic finite temperature simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of computing time. Here we present an on-the-fly machine learning scheme that generates force fields automatically during molecular dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chemical precision of first principles methods and minimizing the need for human intervention. The method is widely applicable to multielement complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which have never been accurately described in simulations. Using machine learned potentials, isothermal-isobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temperatures of different perovskites to the radii of the involved species, and we determine the order of the transitions in Landau theory.

BACKGROUND: To quantify the association between effects of interventions on carotid intima-media thickness (cIMT) progression and their effects on cardiovascular disease (CVD) risk. METHODS: We systematically collated data from randomized, controlled trials. cIMT was assessed as the mean value at the common-carotid-artery; if unavailable, the maximum value at the common-carotid-artery or other cIMT measures were used. The primary outcome was a combined CVD end point defined as myocardial infarction, stroke, revascularization procedures, or fatal CVD. We estimated intervention effects on cIMT progression and incident CVD for each trial, before relating the 2 using a Bayesian meta-regression approach. RESULTS: We analyzed data of 119 randomized, controlled trials involving 100 667 patients (mean age 62 years, 42% female). Over an average follow-up of 3.7 years, 12 038 patients developed the combined CVD end point. Across all interventions, each 10 μm/y reduction of cIMT progression resulted in a relative risk for CVD of 0.91 (95% Credible Interval, 0.87-0.94), with an additional relative risk for CVD of 0.92 (0.87-0.97) being achieved independent of cIMT progression. Taken together, we estimated that interventions reducing cIMT progression by 10, 20, 30, or 40 μm/y would yield relative risks of 0.84 (0.75-0.93), 0.76 (0.67-0.85), 0.69 (0.59-0.79), or 0.63 (0.52-0.74), respectively. Results were similar when grouping trials by type of intervention, time of conduct, time to ultrasound follow-up, availability of individual-participant data, primary versus secondary prevention trials, type of cIMT measurement, and proportion of female patients. CONCLUSIONS: The extent of intervention effects on cIMT progression predicted the degree of CVD risk reduction. This provides a missing link supporting the usefulness of cIMT progression as a surrogate marker for CVD risk in clinical trials.

When determining machine-learning models for inter-atomic potentials, the potential energy surface is often described as a non-linear function of descriptors representing two- and three-body atomic distribution functions. It is not obvious how the choice of the descriptors affects the efficiency of the training and the accuracy of the final machine-learned model. In this work, we formulate an efficient method to calculate descriptors that can separately represent two- and three-body atomic distribution functions, and we examine the effects of including only two- or three-body descriptors, as well as including both, in the regression model. Our study indicates that non-linear mixing of two- and three-body descriptors is essential for an efficient training and a high accuracy of the final machine-learned model. The efficiency can be further improved by weighting the two-body descriptors more strongly. We furthermore examine a sparsification of the three-body descriptors. The three-body descriptors usually provide redundant representations of the atomistic structure, and the number of descriptors can be significantly reduced without loss of accuracy by applying an automatic sparsification using a principal component analysis. Visualization of the reduced descriptors using three-body distribution functions in real-space indicates that the sparsification automatically removes the components that are less significant for describing the distribution function.

The on-the-fly generation of machine-learning force fields by active-learning schemes attracts a great deal of attention in the community of atomistic simulations. The algorithms allow the machine to self-learn an interatomic potential and construct machine-learned models on the fly during simulations. State-of-the-art query strategies allow the machine to judge whether new structures are out of the training data set or not. Only when the machine judges the necessity of updating the data set with the new structures are first-principles calculations carried out. Otherwise, the yet available machine-learned model is used to update the atomic positions. In this manner, most of the first-principles calculations are bypassed during training, and overall, simulations are accelerated by several orders of magnitude while retaining almost first-principles accuracy. In this Perspective, after describing essential components of the active-learning algorithms, we demonstrate the power of the schemes by presenting recent applications.

Abstract Machine-learned interatomic potentials enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. It is not yet clear, however, how accurately they describe anharmonic properties, which are crucial for predicting the lattice thermal conductivity and phase transitions in solids and, thus, shape their technological applications. Here we employ a recently developed on-the-fly learning technique based on molecular dynamics and Bayesian inference in order to generate an interatomic potential capable to describe the thermodynamic properties of zirconia, an important transition metal oxide. This machine-learned potential accurately captures the temperature-induced phase transitions below the melting point. We further showcase the predictive power of the potential by calculating the heat transport on the basis of Green–Kubo theory, which allows to account for anharmonic effects to all orders. This study indicates that machine-learned potentials trained on the fly offer a routine solution for accurate and efficient simulations of the thermodynamic properties of a vast class of anharmonic materials.

Density-functional theory methods and codes adopting periodic boundary conditions are extensively used in condensed matter physics and materials science research. In 2016, their precision (how well properties computed with different codes agree among each other) was systematically assessed on elemental crystals: a first crucial step to evaluate the reliability of such computations. In this Expert Recommendation, we discuss recommendations for verification studies aiming at further testing precision and transferability of density-functional-theory computational approaches and codes. We illustrate such recommendations using a greatly expanded protocol covering the whole periodic table from Z = 1 to 96 and characterizing 10 prototypical cubic compounds for each element: four unaries and six oxides, spanning a wide range of coordination numbers and oxidation states. The primary outcome is a reference dataset of 960 equations of state cross-checked between two all-electron codes, then used to verify and improve nine pseudopotential-based approaches. Finally, we discuss the extent to which the current results for total energies can be reused for different goals. Verification efforts of density-functional theory (DFT) calculations are of crucial importance to evaluate the reliability of simulation results. In this Expert Recommendation, we suggest metrics for DFT verification, illustrating them with an all-electron reference dataset of 960 equations of state covering the whole periodic table (hydrogen to curium) and discuss the importance of improving pseudopotential codes.

The chemical potentials of atoms and molecules in condensed matter are fundamental properties that allow one to predict a wide variety of thermodynamic properties. However, predictions using first principles are challenging. Here, an efficient and accurate method using machine-learned force fields is presented. A key point is that it requires training only at the end points of the thermodynamic pathway, rendering the training simple and efficient. Applications to liquid Si, and Li and F ions hydrated by water show that the method can predict accurate chemical potentials at low computational cost.

Machine-learned force fields (MLFFs) are becoming an increasingly important tool in materials science and physics. However, most MLFFs are constructed based on density functional theory (DFT) calculations, which come with significant limitations. Here, the authors combine an efficient on-the-fly active learning procedure and a ∆-machine learning approach, enabling the generation of MLFFs with an accuracy that exceeds DFT accuracy at a modest computational cost. Using this method, they generated an MLFF for the random phase approximation that allows highly accurate predictions of the phase transition temperatures of zirconia.

Adsorption of carbon monoxide (CO) on transition-metal surfaces is a prototypical process in surface sciences and catalysis. Despite its simplicity, it has posed great challenges to theoretical modeling. Pretty much all existing density functionals fail to accurately describe surface energies and CO adsorption site preference as well as adsorption energies simultaneously. Although the random phase approximation (RPA) cures these density functional theory failures, its large computational cost makes it prohibitive to study the CO adsorption for any but the simplest ordered cases. Here, we address these challenges by developing a machine-learned force field (MLFF) with near RPA accuracy for the prediction of coverage-dependent adsorption of CO on the Rh(111) surface through an efficient on-the-fly active learning procedure and a Δ-machine learning approach. We show that the RPA-derived MLFF is capable to accurately predict the Rh(111) surface energy and CO adsorption site preference as well as adsorption energies at different coverages that are all in good agreement with experiments. Moreover, the coverage-dependent ground-state adsorption patterns and adsorption saturation coverage are identified.

We demonstrate an approach for calculating temperature-dependent quantum and anharmonic effects with beyond density-functional theory accuracy. By combining machine-learned potentials and the stochastic self-consistent harmonic approximation, we investigate the cubic to tetragonal transition in strontium titanate and show that the paraelectric phase is stabilized by anharmonic quantum fluctuations. We find that a quantitative understanding of the quantum paraelectric behavior requires a higher-level treatment of electronic correlation effects via the random phase approximation. This approach enables detailed studies of emergent properties in strongly anharmonic materials beyond density-functional theory.

In this paper, we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE + D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1500 structures, as well as a smaller dataset, about half the size, obtained using only on-the-fly learning. This study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, this study emphasizes the relevance of the database over the fitting method. Finally, this study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests.

Abstract In this paper we study the stability and approximability of the 𝒫 1 –𝒫 0 element (continuous piecewise linear for the velocity and piecewise constant for the pressure on triangles) for Stokes equations. Although this element is unstable for all meshes, it provides optimal approximations for the velocity and the pressure in many cases. We establish a relation between the stabilities of the 𝒬 1 –𝒫 0 element (bilinear/constant on quadrilaterals) and the 𝒫 1 –𝒫 0 element. We apply many stability results on the 𝒬 1 –𝒫 0 element to the analysis of the 𝒫 1 –𝒫 0 element. We prove that the element has the optimal order of approximations for the velocity and the pressure on a variety of mesh families. As a byproduct, we also obtain a basis of divergence‐free piecewise linear functions on a mesh family on squares. Numerical tests are provided to support the theory and to show the efficiency of the newly discovered, truly divergence‐free, 𝒫 1 finite element spaces in computation. Copyright © 2006 John Wiley & Sons, Ltd.

The accurate prediction of solid-solid structural phase transitions at finite temperature is a challenging task, since the dynamics is so slow that direct simulations of the phase transitions by first-principles (FP) methods are typically not possible. Here, we study the $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\beta}$ phase transition of Zr at ambient pressure by means of on-the-fly machine-learned force fields. These are automatically generated during FP molecular dynamics (MD) simulations without the need of human intervention, while retaining almost FP accuracy. Our MD simulations successfully reproduce the first-order displacive nature of the phase transition, which is manifested by an abrupt jump of the volume and a cooperative displacement of atoms at the phase transition temperature. The phase transition is further identified by the simulated x-ray powder diffraction, and the predicted phase transition temperature is in reasonable agreement with experiment. Furthermore, we show that using a singular value decomposition and pseudo inversion of the design matrix generally improves the machine-learned force field compared to the usual inversion of the squared matrix in the regularized Bayesian regression.

Electron-phonon physics has become an integral part of today's materials science world. In this work, the authors present $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ results for the zero-point renormalization of the band gap of various semiconductors and insulators. They use a new implementation of the VASP code that utilizes the sophisticated projector augmented wave method to calculate the electron-phonon perturbation. Two complementary ways of treating the all-electron information are discussed in this context.

We present a compressive sensing approach for the long-standing problem of Matsubara summation in many-body perturbation theory. By constructing low-dimensional, almost isometric subspaces of the Hilbert space we obtain optimum imaginary time and frequency grids that allow for extreme data compression of fermionic and bosonic functions in a broad temperature regime. The method is applied to the random phase and self-consistent $GW$ approximation of the grand potential. Integration and transformation errors are investigated for Si and ${\mathrm{SrVO}}_{3}$.

Abstract We present a method combining first-principles calculations and machine learning to predict the redox potentials of half-cell reactions on the absolute scale. By applying machine learning force fields for thermodynamic integration from the oxidized to the reduced state, we achieve efficient statistical sampling over a broad phase space. Furthermore, through thermodynamic integration from machine learning force fields to potentials of semi-local functionals, and from semi-local functionals to hybrid functionals using Δ-machine learning, we refine the free energy with high precision step-by-step. Utilizing a hybrid functional that includes 25% exact exchange (PBE0), this method predicts the redox potentials of the three redox couples, Fe 3+ /Fe 2+ , Cu 2+ /Cu + , and Ag 2+ /Ag + , to be 0.92, 0.26, and 1.99 V, respectively. These predictions are in good agreement with the best experimental estimates (0.77, 0.15, 1.98 V). This work demonstrates that machine-learned surrogate models provide a flexible framework for refining the accuracy of free energy from coarse approximation methods to precise electronic structure calculations, while also facilitating sufficient statistical sampling.

A new infrastructure for computed molecular properties, including a web app and API, is incorporated into the Materials Project, enabling the creation of a database currently containing over 170 000 molecules.

Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can often be quite challenging. Although density functional theory has been reasonably successful to carry out such calculations, efficient, accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk bandgaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performance of several advanced meta-GGA functionals in the computational prediction of band offsets at semiconductor heterojunctions. In particular, we investigate the performance of r2SCAN (two times revised strongly constrained and appropriately normed functional), rMGGAC (revised semilocal functional based on cuspless hydrogen model and Pauli kinetic energy density functional), mTASK (modified Aschebrock and Kümmel meta-GGA functional), and local modified Becke–Johnson exchange-correlation functionals. Our results strongly suggest that these meta-GGA functionals for supercell calculations perform quite well, especially, when compared to computationally more demanding GW calculations. We also present band offsets calculated using ionization potentials and electron affinities, as well as band alignment via the branch point energies. Overall, our study shows that the aforementioned meta-GGA functionals can be used within the density functional theory framework to estimate the band offsets in semiconductor heterostructures with predictive accuracy.