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Atomic, electronic, and magnetic structure of LaSrCo$_{1/2}$Fe$_{1/2}$O$_4$ mixed-metal Ruddlesden-Popper oxide is investigated theoretically using self-consistent ACBN0 DFT + $U$ approach. We show that the electronic and magnetic properties strongly depend on the distribution of transition-metal and La/Sr ions in the lattice. Fe-Fe exchange is found to be antiferromagnetic, whereas Co-Co and Fe-Co exchange is ferromagnetic. We find that Co spin states depend on the distribution in both La/Sr and transition-metal ions. The most energetically favorable configuration is ferromagnetic, whereas the majority of metastable configurations are antiferromagnetic. LaSrCo$_{1/2}$Fe$_{1/2}$O$_4$ was synthesized using spray-pyrolysis method. Magnetization measurements revealed antiferromgnetic behavior, thus indicating presence of metastable configurations in the synthesized material. In addition, we show that in complex systems, such as mixed-metal Ruddlesden-Popper phases, Hubbard $U$ values have to be determined for each crystallographically non-equivalent site.

Symbolic-inference methods have recently found a broad application in materials science. In particular, the Sure-Independence Screening and Sparsifying Operator (SISSO) performs symbolic regression and classification by adopting compressed sensing for the selection of an optimized subset of features and mathematical operators out of a given set of candidates. However, SISSO becomes computationally unpractical when the set of candidate features and operators exceeds the size of few tens. In the present work, we combine SISSO with a genetic algorithm (GA) for the global search of the optimal subset of features and operators. We demonstrate that GA-SISSO efficiently finds more accurate predictive models than the original SISSO, due to the possibility to access a larger input feature and operator space. GA-SISSO was applied for the search of the model for the prediction of carbon-dioxide adsorption energies on semiconductor oxides. The obtained with GA-SISSO model has much higher accuracy compared to models previously discussed in the literature (based solely on the O 2p-band center). The analysis of features importance shows that, besides the O 2p-band center, the contribution of the electrostatic potential above adsorption sites and the surface formation energies are also important.

Hardness is a materials' property with implications in several industrial fields, including oil and gas, manufacturing, and others. However, the relationship between this macroscale property and atomic (i.e., microscale) properties is unknown and in the last decade several models have unsuccessfully tried to correlate them in a wide range of chemical space. The understanding of such relationship is of fundamental importance for discovery of harder materials with specific characteristics to be employed in a wide range of fields. In this work, we have found a physical descriptor for Vickers hardness using a symbolic-regression artificial-intelligence approach based on compressed sensing. SISSO (Sure Independence Screening plus Sparsifying Operator) is an artificial-intelligence algorithm used for discovering simple and interpretable predictive models. It performs feature selection from up to billions of candidates obtained from several primary features by applying a set of mathematical operators. The resulting sparse SISSO model accurately describes the target property (i.e., Vickers hardness) with minimal complexity. We have considered the experimental values of hardness for binary, ternary, and quaternary transition-metal borides, carbides, nitrides, carbonitrides, carboborides, and boronitrides of 61 materials, on which the fitting was performed. The found descriptor is a non-linear function of the microscopic properties, with the most significant contribution being from a combination of Voigt-averaged bulk modulus, Poisson's ratio, and Reuss-averaged shear modulus. Results of high-throughput screening of 635 candidate materials using the found descriptor suggest the enhancement of material's hardness through mixing with harder yet metastable structures (e.g., metastable VN, TaN, ReN$_2$, Cr$_3$N$_4$, and ZrB$_6$ all exhibit high hardness).

The band gap is an important parameter of semiconductor materials that influences several functional properties, in particular optical properties. However, a fast and reliable first-principles prediction of band gaps remains a challenging problem. Standard DFT approximations tend to strongly underestimate band gaps, while the more accurate $GW$ and hybrid functionals are much more computationally demanding and unsuitable for high-throughput screening. In this work, we have performed an extensive benchmark of several approximations with different computational complexity ($G_{0}W_{0}$@PBEsol, HSE06, PBEsol, mBJ, PBEsol$-1/2$, and ACBN0) to evaluate and compare their performance in predicting the band gap of semiconductors. The benchmark is based on 114 binary semiconductors of different compositions and crystal structures, where about half of them have experimental band gaps. We find that, as expected, $G_{0}W_{0}$@PBEsol performs well relative to the experiment, with a noticeable underestimation of the band gaps by about 14% on average. Surprisingly, $G_{0}W_{0}$@PBEsol is followed closely by the much computationally cheaper pseudo-hybrid ACBN0 functional, showing an excellent performance with respect to experimental data. The meta-GGA mBJ functional also performs well relative to the experiment, even slightly better than $G_{0}W_{0}$@PBEsol in terms of mean absolute (percentage) error. The HSE06 and PBEsol$-1/2$ schemes perform overall worse than ACBN0 and mBJ schemes but much better than PBEsol. Comparing the calculated band gaps on the whole data set (including the samples with no experimental band gap), we find that HSE06 and mBJ have excellent agreement with respect to the reference $G_{0}W_{0}$@PBEsol band gaps. Thus, we propose the mBJ band gaps as economic descriptors when developing artificial intelligence models for high-throughput screening of semiconductor band gaps.

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.

Thermoelectric (TE) materials are among very few sustainable yet feasible energy solutions of present time. This huge promise of energy harvesting is contingent on identifying/designing materials having higher efficiency than presently available ones. However, due to the vastness of the chemical space of materials, only its small fraction was scanned experimentally and/or computationally so far. Employing a compressed-sensing based symbolic regression in an active-learning framework, we have not only identified a trend in materials' compositions for superior TE performance, but have also predicted and experimentally synthesized several extremely high performing novel TE materials. Among these, we found Ag$_{0.55}$Cu$_{0.45}$GaTe$_2$ to possess an experimental figure of merit as high as ~2.8 at 827 K, which is a breakthrough in the field. The presented methodology demonstrates the importance and tremendous potential of physically informed descriptors in material science, in particular for relatively small data sets typically available from experiments at well-controlled conditions.

Single-atom metal alloy catalysts (SAACs) have recently become a very active new frontier in catalysis research. The simultaneous optimization of both facile dissociation of reactants and a balanced strength of intermediates' binding make them highly efficient and selective for many industrially important reactions. However, discovery of new SAACs is hindered by the lack of fast yet reliable prediction of the catalytic properties of the sheer number of candidate materials. In this work, we address this problem by applying a compressed-sensing data-analytics approach parameterized with density-functional inputs. Our approach is faster and more accurate than the current state-of-the-art linear relationships. Besides consistently predicting high efficiency of the experimentally studied Pd/Cu, Pt/Cu, Pd/Ag, Pt/Au, Pd/Au, Pt/Ni, Au/Ru, and Ni/Zn SAACs (the first metal is the dispersed component), we identify more than two hundred yet unreported candidates. Some of these new candidates are predicted to exhibit even higher stability and efficiency than the reported ones. Our study demonstrates the importance of breaking linear relationships to avoid bias in catalysis design, as well as provides a recipe for selecting best candidate materials from hundreds of thousands of transition-metal SAACs for various applications.

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., Comment: 36 pages, 15 figures, submitted v2: Corrected Affiliation No. 4

Catalytic-materials design requires predictive modeling of the interaction between catalyst and reactants. This is challenging due to the complexity and diversity of structure-property relationships across the chemical space. Here, we report a strategy for a rational design of catalytic materials using the artifcial intelligence approach (AI) subgroup discovery. We identify catalyst \textit{genes} (features) that correlate with mechanisms that trigger, facilitate, or hinder the activation of carbon dioxide (CO$_2$) towards a chemical conversion. The AI model is trained on frst-principles data for a broad family of oxides. We demonstrate that surfaces of experimentally identifed good catalysts consistently exhibit combinations of \textit{genes} resulting in a strong elongation of a C-O bond. The same combinations of \textit{genes} also minimize the OCO-angle, the previously proposed indicator of activation, albeit under the constraint that the Sabatier principle is satisfed. Based on these fndings, we propose a set of new promising catalyst materials for CO$_2$ conversion.

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., Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in ACS Catalysis, copyright American Chemical Society after peer review. To access the final edited and published work see https://pubs.acs.org/doi/10.1021/acscatal.8b04478

We present a code-independent compact representation of one-electron wavefunctions and other volumetric data (electron density, electrostatic potential, etc.) produced by electronic-structure calculations. The compactness of the representation insures minimization of digital storage requirements for the computational data, while the code-independence makes the data ready for "big data" analytics. Our approach allows to minimize differences between original and the new representation, and is in principle information-lossless. The procedure for obtaining the wavefunction representation is closely related to construction of natural atomic orbitals, and benefits from the localization of Wannier functions. Thus, our approach fits perfectly any infrastructure providing a code-independent tool set for electronic-structure data analysis.

Advances in hybrid organic/inorganic architectures for optoelectronics can be achieved by understanding how the atomic and electronic degrees of freedom cooperate or compete to yield the desired functional properties. Here we show how work-function changes are modulated by the structure of the organic components in model hybrid systems. We consider two cyano-quinodimethane derivatives (F4-TCNQ and F6-TCNNQ), which are strong electron-acceptor molecules, adsorbed on H-Si(111). From systematic structure searches employing range-separated hybrid HSE06 functional including many body van der Waals contributions, we predict that despite their similar composition, these molecules adsorb with significantly different densely-packed geometries in the first layer, due to strong intermolecular interaction. F6-TCNNQ shows a much stronger intralayer interaction (primarily due to van der Waals contributions) than F4-TCNQ in multilayered structures. The densely-packed geometries induce a large interface-charge rearrangement that result in a work-function increase of 1.11 and 1.76 eV for F4-TCNQ and F6-TCNNQ, respectively. Nuclear fluctuations at room temperature produce a wide distribution of work-function values, well modeled by a normal distribution with {\sigma}=0.17 eV. We corroborate our findings with experimental evidence of pronounced island formation for F6-TCNNQ on H-Si(111) and with the agreement of trends between predicted and measured work-function changes.

Understanding the applicability and limitations of electronic-structure methods needs careful and efficient comparison with accurate reference data. Knowledge of the quality and errors of electronic-structure calculations is crucial to advanced method development, high-throughput computations, and data analyses. In this paper, we present a test set for computational materials science and engineering (MSE), that aims to provide accurate and easily accessible crystal properties for a hierarchy of exchange-correlation approximations, ranging from the well-established mean-field approximations to the state-of-the-art methods of many-body perturbation theory. We consider cohesive energy, lattice constant and bulk modulus as representatives for the first- and second-row elements and their binaries with cubic crystal structures and various bonding characters. A strong effort is made to push the borders of numerical accuracy for cohesive properties as calculated using the local-density approximation (LDA), several generalized gradient approximations (GGAs), meta-GGAs and hybrids in \textit{all-electron} resolution, and the second-order M\o{}ller-Plesset perturbation theory (MP2) and the random-phase approximation (RPA) with frozen-core approximation based on \textit{all-electron} Hartree-Fock, PBE and/or PBE0 references. This results in over 10,000 calculations, which record a comprehensive convergence test with respect to numerical parameters for a wide range of electronic structure methods within the numerical atom-centered orbital framework. As an indispensable part of the MSE test set, a web site is established \href{http://mse.fhi-berlin.mpg.de}{\texttt{http://mse.fhi-berlin.mpg.de}}. This not only allows for easy access to all reference data but also provides user-friendly graphical tools for post-processing error analysis., Comment: 18 pages, 7 figures

Composition, atomic structure, and electronic properties of TM$_x$Mg$_y$O$_z$ clusters (TM = Cr, Ni, Fe, Co, $x+y \leq 3$) at realistic temperature $T$ and partial oxygen pressure $p_{\textrm{O}_2}$ conditions are explored using the {\em ab initio} atomistic thermodynamics approach. The low-energy isomers of the different clusters are identified using a massively parallel cascade genetic algorithm at the hybrid density-functional level of theory. On analyzing a large set of data, we find that the fundamental gap E$_\textrm{g}$ of the thermodynamically stable clusters are strongly affected by the presence of Mg-coordinated O$_2$ moieties. In contrast, the nature of the transition metal does not play a significant role in determining E$_\textrm{g}$. Using E$_\textrm{g}$ of a cluster as a descriptor of its redox properties, our finding is against the conventional belief that the transition metal plays the key role in determining the electronic and therefore chemical properties of the clusters. High reactivity may be correlated more strongly with oxygen content in the cluster than with any specific TM type., Comment: 7 pages, 5 figures

We present a density functional theory (DFT) based supercell approach for modeling small polarons with proper account for the long-range elastic response of the material. Our analysis of the supercell dependence of the polaron properties (e.g., atomic structure, binding energy, and the polaron level) reveals long-range electrostatic effects and the electron-phonon interaction as the two main contributors. We develop a correction scheme for DFT polaron calculations that significantly reduces the dependence of polaron properties on the DFT exchange-correlation functional and the size of the supercell in the limit of strong electron-phonon coupling. Using our correction approach, we present accurate all-electron full-potential DFT results for small polarons in rocksalt MgO and rutile TiO$_2$.

Realistic oxide materials are often semiconductors, in particular at elevated temperatures, and their surfaces contain undercoordiated atoms at structural defects such as steps and corners. Using hybrid density-functional theory and ab initio atomistic thermodynamics, we investigate the interplay of bond-making, bond-breaking, and charge-carrier trapping at the corner defects at the (100) surface of a p-doped MgO in thermodynamic equilibrium with an O2 atmosphere. We show that by manipulating the coordination of surface atoms one can drastically change and even reverse the order of stability of reduced versus oxidized surface sites., Comment: 5 papges, 4 figures

The availability of big data in materials science offers new routes for analyzing materials properties and functions and achieving scientific understanding. Finding structure in these data that is not directly visible by standard tools and exploitation of the scientific information requires new and dedicated methodology based on approaches from statistical learning, compressed sensing, and other recent methods from applied mathematics, computer science, statistics, signal processing, and information science. In this paper, we explain and demonstrate a compressed-sensing based methodology for feature selection, specifically for discovering physical descriptors, i.e., physical parameters that describe the material and its properties of interest, and associated equations that explicitly and quantitatively describe those relevant properties. As showcase application and proof of concept, we describe how to build a physical model for the quantitative prediction of the crystal structure of binary compound semiconductors.

We report an unexpectedly strong and complex chemical bonding of rare-gas atoms to neutral gold clusters. The bonding features are consistently reproduced at different levels of approximation within density-functional theory and beyond: from GGA, through hybrid and double-hybrid functionals, up to renormalized second-order perturbation theory. The main finding is that the adsorption of Ar, Kr, and Xe reduces electron-electron repulsion within gold dimer, causing strengthening of the Au-Au bond. Differently from the dimer, the rare-gas adsorption effects on the gold trimer's geometry and vibrational frequencies are mainly due to electron occupation of the trimer's lowest unoccupied molecular orbital. For the trimer, the theoretical results are also consistent with far-infrared multiple photon dissociation experiments., Comment: To be published in Inorganic Chemistry Communications

Statistical learning of materials properties or functions so far starts with a largely silent, non-challenged step: the choice of the set of descriptive parameters (termed descriptor). However, when the scientific connection between the descriptor and the actuating mechanisms is unclear, causality of the learned descriptor-property relation is uncertain. Thus, trustful prediction of new promising materials, identification of anomalies, and scientific advancement are doubtful. We analyse this issue and define requirements for a suited descriptor. For a classical example, the energy difference of zincblende/wurtzite and rocksalt semiconductors, we demonstrate how a meaningful descriptor can be found systematically., Comment: Accepted to Phys. Rev. Lett

A first-principles based methodology for efficiently and accurately finding thermodynamically stable and metastable atomic structures is introduced and benchmarked. The approach is demonstrated for gas-phase metal-oxide clusters in thermodynamic equilibrium with a reactive (oxygen) atmosphere at finite pressure and temperature. It consists of two steps. At first, the potential-energy surface is scanned by means of a global-optimization technique, i.e., a massive-parallel first-principles cascade genetic algorithm for which the choice of all parameters is validated against higher-level methods. In particular, we validate a) the criteria for selection and combination of structures used for the assemblage of new candidate structures, and b) the choice of the exchange-correlation functional. The selection criteria are validated against a fully unbiased method: replica-exchange molecular dynamics. Our choice of the exchange-correlation functional, the van-der-Waals-corrected PBE0 hybrid functional, is justified by comparisons up to highest level currently achievable within density-functional theory, i.e., the renormalized second-order perturbation theory, rPT2. In the second step, the low-energy structures are analyzed by means of ab initio atomistic thermodynamics in order to determine compositions and structures that minimize the Gibbs free energy at given temperature and pressure of the reactive atmosphere., Comment: 46 pages, 12 figures

We investigate effects of doping on formation energy and concentration of oxygen vacancies at a metal oxide surface, using MgO (100) as an example. Our approach employs density-functional theory, where the performance of the exchange-correlation functional is carefully analyzed, and the functional is chosen according to a fundamental condition on DFT ionization energies. The approach is further validated by CCSD(T) calculations for embedded clusters. We demonstrate that the concentration of oxygen vacancies at a doped oxide surface is largely determined by formation of a macroscopically extended space charge region.

By applying a genetic algorithm in a cascade approach of increasing accuracy, we calculate the composition and structure of MgMOx clusters at realistic temperatures and oxygen pressures. The stable and metastable systems are identified by ab initio atomistic thermodynamics. We find that small clusters (M <= 5) are in thermodynamic equilibrium when x > M. The non-stoichiometric clusters exhibit peculiar magnetic behavior, suggesting the possibility of tuning magnetic properties by changing environmental pressure and temperature conditions. Furthermore, we show that density-functional theory (DFT) with a hybrid exchange-correlation (xc) functional is needed for predicting accurate phase diagrams of metal-oxide clusters. Neither a (sophisticated) force field nor DFT with (semi)local xc functionals are sufficient for even a qualitative prediction., Comment: 5 pages, 3 Figures, Supporting Information

We present justification and rigorous procedure for electron partitioning among atoms in extended systems. The method is based on wavefunction topology and the modern theory of polarization, rather than charge density partitioning or wavefunction projection, and, as such, re-formulates the concept of oxidation state without assuming real-space charge transfer between atoms. This formulation provides rigorous electrostatics of finite extent solids, including films and nanowires., Comment: 4 pages, 3 figures