High-throughput density-functional calculations of solids are highly time consuming. As an alternative, we propose a machine learning approach for the fast prediction of solid-state properties. To achieve this, LSDA calculations are used as training set. We focus on predicting the value of the density of electronic states at the Fermi energy. We find that conventional representations of the input data, such as the Coulomb matrix, are not suitable for the training of learning machines in the case of periodic solids. We propose a novel crystal structure representation for which learning and competitive prediction accuracies become possible within an unrestricted class of spd systems of arbitrary unit-cell size.In recent years ab-initio high-throughput computational methods (HTM) have proven to be a powerful and successful tool to predict new materials and to optimize desired materials properties. Phase diagrams of multicomponent crystals [1][2][3] and alloys [4] have been successfully predicted. High-impact technological applications have been achieved by improving the performance of Lithium based batteries [5][6][7], by tailoring the nonlinear optical response in organic molecules [8] for optical signal processing, by designing desired current-voltage characteristics [9] for photovoltaic materials, by optimizing the electrode transparency and conductivity [10] for solar cell technology, and by screening metals for the highest amalgamation enthalpy [11] to efficiently remove Hg pollutants in coal gasification.However, the computational cost of electronic structure calculations poses a serious bottleneck for HTM. Thinking of quaternary, quinternary, etc., compounds, the space of possible materials becomes so large, and the complexity of the unit cells so high that, even within efficient Kohn-Sham density functional theory (KS-DFT), a systematic high-throughput exploration grows beyond reach for present-day computing facilities. As a way out, one would like to have a more direct way to access the physical property of interest without actually solving the KS-DFT equations. Machine learning (ML) techniques offer an attractive possibility of this type. ML-based calculations are very fast, typically requiring only fractions of a second to predict a specific property of a given material, after having trained the ML model on a representative training set of materials.ML methods rely on two main ingredients, the learning algorithm itself and the representation of the input data. There are many different ways of representing a given material or compound. While, from the physicist's point of view, the information is simply given by the charges and the positions of the nuclei, for ML algorithms the specific mathematical form in which this information is given to the machine, is crucial. Roughly speaking, ML algorithms assume a nonlinear map between input data (representing the materials or compounds in our case) and the material-specific property to be predicted. Whether or not a machine can approximate the unknown nonlinear ...

Starting from the experimental data contained in the inorganic crystal structure database, we use a statistical analysis to determine the likelihood that a chemical element A can be replaced by another B in a given structure. This information can be used to construct a matrix where each entry ( ) A B, is a measure of this likelihood. By ordering the rows and columns of this matrix in order to reduce its bandwidth, we construct a one-dimension ordering of the chemical elements, analogous to the famous Pettifor scale. The new scale shows large similarities with the one of Pettifor, but also striking differences, especially in what comes to the ordering of the non-metals.

Superconductivity in intercalated graphite CaC 6 and H under extreme pressure is discussed in the framework of superconducting density functional theory. A detailed analysis of how the electron-phonon and electron-electron interactions combine together to determine the superconducting gap and critical temperature (T c ) of these systems is presented. In particular, we discuss the effect on the calculated T c of the anisotropy of the electron-phonon interaction and of the different approximations for screening the Coulomb repulsion. These results contribute to the understanding of multigap and anisotropic superconductivity, which has received a lot of attention since the discovery of MgB 2 , and show how it is possible to describe the superconducting properties of real materials on a fully ab initio basis.

We apply density functional theory for superconductors (SCDFT) to doped tungsten oxide in three forms: electrostatically doped WO 3 , perovskite WO 3−x F x , and hexagonal Cs x WO 3 . We achieve a consistent picture in which the experimental superconducting transition temperature T c is reproduced, and superconductivity is understood as a weak-coupling state sustained by soft vibrational modes of the WO 6 octahedra. SCDFT simulations of Cs x WO 3 allow us to explain the anomalous T c behavior observed in most tungsten bronzes, where T c decreases with increasing carrier density. Here, the opening of structural channels to host Cs atoms induces a softening of strongly coupled W-O modes. By increasing the Cs content, these modes are screened and T c is strongly reduced.

Superconductivity in Pb, H under extreme pressure and CaBeSi, in the framework of the density functional theory for superconductors, is discussed. A detailed analysis on how the electron-phonon and electron-electron interactions combine together to determine the superconducting gap and critical temperature of these systems is presented. Pb, H under pressure and CaBeSi are multigap superconductors. We will address the question under which conditions does a system exhibits this phenomenon. The presented results contribute to the understanding of multiband and anisotropic superconductivity, which has received a lot of attention since the discovery of MgB2, and show how it is possible to describe the superconducting properties of real materials on a fully ab-initio basis.