Electron-Induced Nonmonotonic Pressure Dependence of the Lattice Thermal Conductivity of θ-TaN.

Recent theoretical and experimental research suggests that θ-TaN is a semimetal with high thermal conductivity (κ), primarily due to the contribution of phonons (κ_{ph}). By using first-principles calculations, we show a nonmonotonic pressure dependence of the κ of θ-TaN. κ_{ph} first increases until it reaches a maximum at around 60 GPa, and then decreases. This anomalous behavior is a consequence of the competing pressure responses of phonon-phonon and phonon-electron interactions, in contrast to the known materials BAs and BP, where the nonmonotonic pressure dependence is caused by the interplay between different phonon-phonon scattering channels. Although TaN has phonon dispersion features similar to BAs at ambient pressure, its response to pressure is different and an overall stiffening of the phonon branches takes place. Consequently, the relevant phonon-phonon scattering weakens as pressure increases. However, the increased electronic density of states near the Fermi level, and specifically the emergence of additional pockets of the Fermi surface at the high-symmetry L point in the Brillouin zone, leads to a substantial increase in phonon-electron scattering at high pressures, driving a decrease in κ_{ph}. At intermediate pressures (∼20-70 GPa), the κ of TaN surpasses that of BAs. Our Letter provides deeper insight into phonon transport in semimetals and metals where phonon-electron scattering is relevant.

Origin of the success of mGGAs for bandgaps.

One of the well-known limitations of Kohn-Sham density functional theory is the tendency to strongly underestimate bandgaps. Meta-generalized gradient approximations (mGGAs), which include the kinetic energy density in the functional form, have been shown to significantly alleviate this deficiency. In this study, we explore the mechanisms responsible for this improvement from the angle of the underlying local densities. We find that the highest occupied and lowest unoccupied states are distinct in the space of the underlying descriptors. The gap opening is compared to a simple scaling of the local density approximation, and two mechanisms responsible for opening the mGGA gaps are identified. First of all, the relatively large negative derivative of the functional form with respect to reduced kinetic energy tends to elevate the lowest unoccupied state. Second, the curvature of functional, which ensures that it is bounded, tends to lower the highest occupied state. Remarkably, these two mechanisms are found to be transferable over a large and diverse database of compounds.

Deep ensembles vs committees for uncertainty estimation in neural-network force fields: Comparison and application to active learning.

A reliable uncertainty estimator is a key ingredient in the successful use of machine-learning force fields for predictive calculations. Important considerations are correlation with error, overhead during training and inference, and efficient workflows to systematically improve the force field. However, in the case of neural-network force fields, simple committees are often the only option considered due to their easy implementation. Here, we present a generalization of the deep-ensemble design based on multiheaded neural networks and a heteroscedastic loss. It can efficiently deal with uncertainties in both energy and forces and take sources of aleatoric uncertainty affecting the training data into account. We compare uncertainty metrics based on deep ensembles, committees, and bootstrap-aggregation ensembles using data for an ionic liquid and a perovskite surface. We demonstrate an adversarial approach to active learning to efficiently and progressively refine the force fields. That active learning workflow is realistically possible thanks to exceptionally fast training enabled by residual learning and a nonlinear learned optimizer.

A Differentiable Neural-Network Force Field for Ionic Liquids.

We present NeuralIL, a model for the potential energy of an ionic liquid that accurately reproduces first-principles results with orders-of-magnitude savings in computational cost. Built on the basis of a multilayer perceptron and spherical Bessel descriptors of the atomic environments, NeuralIL is implemented in such a way as to be fully automatically differentiable. It can thus be trained on ab initio forces instead of just energies, to make the most out of the available data, and can efficiently predict arbitrary derivatives of the potential energy. Using ethylammonium nitrate as the test system, we obtain out-of-sample accuracies better than 2 meV atom-1 (<0.05 kcal mol-1) in the energies and 70 meV Å-1 in the forces. We show that encoding the element-specific density in the spherical Bessel descriptors is key to achieving this. Harnessing the information provided by the forces drastically reduces the amount of atomic configurations required to train a neural network force field based on atom-centered descriptors. We choose the Swish-1 activation function and discuss the role of this choice in keeping the neural network differentiable. Furthermore, the possibility of training on small data sets allows for an ensemble-learning approach to the detection of extrapolation. Finally, we find that a separate treatment of long-range interactions is not required to achieve a high-quality representation of the potential energy surface of these dense ionic systems.

What is the optimal mGGA exchange functional for solids?

The space of generalized gradient approximation (GGA) and meta-GGA (mGGA) exchange approximations is systematically explored by training 25 new functionals to produce accurate lattice parameter, cohesive energy, and bandgap predictions. The trained functionals are used to reproduce exact constraints in a data-driven way and to understand the accuracy trade-off between the mentioned properties. The functionals are compared to notable mGGA functionals to analyze how changes in the enhancement factor maps influence the accuracy of predictions. Some of the trained functionals are found to perform on par with specialized functionals for bandgaps, while outperforming them on the other two properties. The error surface of our trained functionals can serve as a soft-limit of what mGGA functionals can achieve.

Ultrahigh Thermal Conductivity of θ-Phase Tantalum Nitride.

Extracting long-lasting performance from electronic devices and improving their reliability through effective heat management requires good thermal conductors. Taking both three- and four-phonon scattering as well as electron-phonon and isotope scattering into account, we predict that semimetallic θ-phase tantalum nitride (θ-TaN) has an ultrahigh thermal conductivity (κ), of 995 and 820 W m^{-1} K^{-1} at room temperature along the a and c axes, respectively. Phonons are found to be the main heat carriers, and the high κ hinges on a particular combination of factors: weak electron-phonon scattering, low isotopic mass disorder, and a large frequency gap between acoustic and optical phonon modes that, together with acoustic bunching, impedes three-phonon processes. On the other hand, four-phonon scattering is found to be significant. This study provides new insight into heat conduction in semimetallic solids and extends the search for high-κ materials into the realms of semimetals and noncubic crystal structures.

A comparative first-principles investigation on the defect chemistry of TiO2 anatase.

Understanding native point defects is fundamental in order to comprehend the properties of TiO2 anatase in technological applications. The previous first-principles reports of defect-relevant quantities, such as formation energies and charge transition levels, are, however, scattered over a wide range. We perform a comparative study employing different approaches based on semilocal with Hubbard correction (DFT+U) and screened hybrid functionals in order to investigate the dependence defect properties on the employed computational method. While the defects in TiO2 anatase, as in most transition-metal oxides, generally induce the localization of electrons or holes on atomic sites, we notice that, provided an alignment of the valence bands has been performed, the calculated defect formation energies and transition levels using semilocal functionals are in a fair agreement with those obtained using hybrid functionals. A similar conclusion can be reached for the thermochemistry of the Ti-O system and the limit values of the elemental chemical potentials. We interpret this as a cancellation of error between the self-interaction error and the overbinding of the O2 molecule in semilocal functionals. Inclusion of a U term in the electron Hamiltonian offers a convenient way for obtaining more precise geometric and electronic configurations of the defective systems.

WIEN2k: An APW+lo program for calculating the properties of solids.

The WIEN2k program is based on the augmented plane wave plus local orbitals (APW+lo) method to solve the Kohn-Sham equations of density functional theory. The APW+lo method, which considers all electrons (core and valence) self-consistently in a full-potential treatment, is implemented very efficiently in WIEN2k, since various types of parallelization are available and many optimized numerical libraries can be used. Many properties can be calculated, ranging from the basic ones, such as the electronic band structure or the optimized atomic structure, to more specialized ones such as the nuclear magnetic resonance shielding tensor or the electric polarization. After a brief presentation of the APW+lo method, we review the usage, capabilities, and features of WIEN2k (version 19) in detail. The various options, properties, and available approximations for the exchange-correlation functional, as well as the external libraries or programs that can be used with WIEN2k, are mentioned. References to relevant applications and some examples are also given.

Using nanotubes to study the phonon spectrum of two-dimensional materials.

We propose a convenient method to characterize the acoustic phonon branches of 2D monolayer materials using measurements of the infrared- and Raman-active vibrational modes of nanotubes. The relations we employ are derived from a symmetry analysis based directly on the line groups of nanotubes. We perform extensive ab initio calculations for the MoS2 monolayer and nanotubes to evaluate the method and illustrate all our results. Specifically, we show how the low-energy phonon transmission, a determining factor in thermal transport, can be easily and successfully reconstructed by this procedure.

Comparative study of the PBE and SCAN functionals: The particular case of alkali metals.

The SCAN meta-generalized gradient approximation (GGA) functional is known to describe multiple properties of various materials with different types of bonds with greater accuracy, compared to the widely used PBE GGA functional. Yet, for alkali metals, SCAN shows worse agreement with experimental results than PBE despite using more information about the system. In the current study, this behavior for alkali metals is explained by identifying an inner semicore region which, within SCAN, contributes to an underbinding. The inner semicore push toward larger lattice constants is a general feature but is particularly important for very soft materials, such as the alkali metals, while for harder materials the valence region dominates.

Vibrational Properties of Metastable Polymorph Structures by Machine Learning.

Despite vibrational properties being critical for the ab initio prediction of finite-temperature stability as well as thermal conductivity and other transport properties of solids, their inclusion in ab initio materials repositories has been hindered by expensive computational requirements. Here we tackle the challenge, by showing that a good estimation of force constants and vibrational properties can be quickly achieved from the knowledge of atomic equilibrium positions using machine learning. A random-forest algorithm trained on 121 different mechanically stable structures of KZnF3 reaches a mean absolute error of 0.17 eV/Å2 for the interatomic force constants, and it is less expensive than training the complete force field for such compounds. The predicted force constants are then used to estimate phonon spectral features, heat capacities, vibrational entropies, and vibrational free energies, which compare well with the ab initio ones. The approach can be used for the rapid estimation of stability at finite temperatures.

Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: Tests on solids.

A recent study of Mejia-Rodriguez and Trickey [Phys. Rev. A 96, 052512 (2017)] showed that the deorbitalization procedure (replacing the exact Kohn-Sham kinetic-energy density by an approximate orbital-free expression) applied to exchange-correlation functionals of the meta-generalized gradient approximation (MGGA) can lead to important changes in the results for molecular properties. For the present work, the deorbitalization of MGGA functionals is further investigated by considering various properties of solids. It is shown that depending on the MGGA, common orbital-free approximations to the kinetic-energy density can be sufficiently accurate for the lattice constant, bulk modulus, and cohesive energy. For the bandgap, calculated with the modified Becke-Johnson MGGA potential, the deorbitalization has a larger impact on the results.

Exceptionally Strong Phonon Scattering by B Substitution in Cubic SiC.

We use ab initio calculations to predict the thermal conductivity of cubic SiC with different types of defects. An excellent quantitative agreement with previous experimental measurements is found. The results unveil that B_{C} substitution has a much stronger effect than any of the other defect types in 3C-SiC, including vacancies. This finding contradicts the prediction of the classical mass-difference model of impurity scattering, according to which the effects of B_{C} and N_{C} would be similar and much smaller than that of the C vacancy. The strikingly different behavior of the B_{C} defect arises from a unique pattern of resonant phonon scattering caused by the broken structural symmetry around the B impurity.

Two-Step Phase Transition in SnSe and the Origins of its High Power Factor from First Principles.

The interest in improving the thermoelectric response of bulk materials has received a boost after it has been recognized that layered materials, in particular SnSe, show a very large thermoelectric figure of merit. This result has received great attention while it is now possible to conceive other similar materials or experimental methods to improve this value. Before we can now think of engineering this material it is important we understand the basic mechanism that explains this unusual behavior, where very low thermal conductivity and a high thermopower result from a delicate balance between the crystal and electronic structure. In this Letter, we present a complete temperature evolution of the Seebeck coefficient as the material undergoes a soft crystal transformation and its consequences on other properties within SnSe by means of first-principles calculations. Our results are able to explain the full range of considered experimental temperatures.

Extrinsic doping of the half-Heusler compounds.

Controlling the p- and n-type doping is a key tool to improve the power-factor of thermoelectric materials. In the present work we provide a detailed understanding of the defect thermochemistry in half-Heusler compounds. We calculate the formation energies of intrinsic and extrinsic defects in state of the art n-type TiNiSn and p-type TiCoSb thermoelectric materials. It is shown how the incorporation of online repositories can reduce the workload in these calculations. In TiNiSn we find that Ni- and Ti-interstitial defects play a crucial role in the carrier concentration of TiNiSn. Furthermore, we find that extrinsic doping with Sb can substantially enhance the carrier concentration, in agreement with experiment. In case of TiCoSb, we find ScTi, FeCo and SnSb being possible p-type dopants. While experimental work has mainly focussed on Sn-doping of the Sb site, the present result underlines the possibility to p-dope TiCoSb on all lattice sites.

Achieving optimum carrier concentrations in p-doped SnS thermoelectrics.

Tin(II)sulfide, SnS, is a commercially viable and environmentally friendly thermoelectric material. Recently it was shown how the carrier concentration and the thermoelectric power factor can be optimized by Ag-doping in a sulphur rich environment. Theoretical calculations lead to a fairly accurate estimation of the carrier concentration, whereas the potential of doping with Li(+) is strongly overestimated. Two principally ubiquitous effects that can result in decreasing the hole concentration, namely the formation of coupled defect complexes and oxidation of the dopant, are discussed as possible origins of this disagreement. It is shown that oxidation limits the chemical potential of Li beyond that already set by the formation of Li2S. This work serves as a comprehensive guide to achieve an efficient p-doped SnS thermoelectric material.

Integrated computational materials discovery of silver doped tin sulfide as a thermoelectric material.

Accelerating the discovery of new materials is crucial for realizing the vision of need-driven materials development. In the present study we employ an integrated computational and experimental approach to search for new thermoelectric materials. High-throughput first principles calculations of thermoelectric transport coefficients are used to screen sulfide compounds conforming to the boundary conditions of abundant and innocuous components. A further computational screening step of substitutional defects is introduced, whereby SnS doped with monovalent cations is identified as having favorable transport properties. By silver doping of SnS under S-rich conditions an electric conductivity more than an order of magnitude higher than reported previously is realized. The obtained thermoelectric power-factor at room temperature is comparable to the state of the art for thermoelectric materials based on earth abundant, non-toxic elements. The high-throughput screening of extrinsic defects solves a long standing bottleneck in search of new thermoelectric materials. We show how the intrinsic carrier concentration in the low-temperature phase of SnSe is two orders of magnitude higher than in SnS. We furthermore find that the carrier concentration in SnSe can still be further optimized by silver doping.

Phonon Transport in Defect-Laden Bilayer Janus PtSTe Studied Using Neural-Network Force Fields.

We explore the phonon transport properties of defect-laden bilayer PtSTe using equilibrium molecular dynamics simulations based on a neural-network force field. Defects prove very efficient at depressing the thermal conductivity of the structure, and flower defects have a particularly powerful effect, comparable to that of double vacancies. Furthermore, the conductivity of the structure with flower defects exhibits an unusual temperature dependence due to structural instability at high temperatures. We look into the distortion to normal modes around the defect by means of the projected phonon density of states and find diverse phenomena including localized modes and blue shifts.

Quantitative Predictions of the Thermal Conductivity in Transition Metal Dichalcogenides: Impact of Point Defects in MoS2 and WS2 Monolayers.

Transition metal dichalcogenides are investigated for various applications at the nanoscale because of their unique combination of properties and dimensionality. For many of the anticipated applications, heat conduction plays an important role. At the same time, these materials often contain relatively large amounts of point defects. Here, we provide a systematic analysis of the impact of intrinsic and selected extrinsic defects on the lattice thermal conductivity of MoS2 and WS2 monolayers. We combine Boltzmann transport theory and Green's function-based T-matrix approach for the calculation of scattering rates. The force constants for the defect configurations are obtained from density functional theory calculations via a regression approach, which allows us to sample a rather large number of defects at a moderate computational cost and to systematically enforce both the translational and rotational acoustic sum rules. The calculated lattice thermal conductivity is in quantitative agreement with the experimental data for heat transport and defect concentrations for both MoS2 and WS2. Crucially, this demonstrates that the strong deviation from a 1/T temperature dependence of the lattice thermal conductivity observed experimentally can be fully explained by the presence of point defects. We furthermore predict the scattering strengths of the intrinsic defects to decrease in the sequence VMo ≈ V2S= > V2S⊥ > VS > Sad in both materials, while the scattering rates for the extrinsic (adatom) defects decrease with increasing mass such that Liad > Naad > Kad. Compared with earlier work, we find that both intrinsic and extrinsic adatoms are relatively weak scatterers. We attribute this difference to the treatment of the translational and rotational acoustic sum rules, which, if not enforced, can lead to spurious contributions in the zero-frequency limit.

EnzymeMap: curation, validation and data-driven prediction of enzymatic reactions.

Enzymatic reactions are an ecofriendly, selective, and versatile addition, sometimes even alternative to organic reactions for the synthesis of chemical compounds such as pharmaceuticals or fine chemicals. To identify suitable reactions, computational models to predict the activity of enzymes on non-native substrates, to perform retrosynthetic pathway searches, or to predict the outcomes of reactions including regio- and stereoselectivity are becoming increasingly important. However, current approaches are substantially hindered by the limited amount of available data, especially if balanced and atom mapped reactions are needed and if the models feature machine learning components. We therefore constructed a high-quality dataset (EnzymeMap) by developing a large set of correction and validation algorithms for recorded reactions in the literature and showcase its significant positive impact on machine learning models of retrosynthesis, forward prediction, and regioselectivity prediction, outperforming previous approaches by a large margin. Our dataset allows for deep learning models of enzymatic reactions with unprecedented accuracy, and is freely available online.