Computational materials discovery is a booming field of science, which helps in predicting new unexpected materials with optimal combinations of various physical properties. Going beyond the targeted search for new materials within prespecified systems, the recently developed method, Mendelevian search, allows one to look for materials with the desired properties across the entire Periodic Table, indicating possibly superhard (or other) materials that could be obtained experimentally. From this viewpoint, we discuss the recently developed methods for crystal structure prediction and empirical models of Vickers hardness and fracture toughness that allow fast screening for materials with optimal mechanical properties. We also discuss the results of the computational search for hard and superhard materials obtained in the last few years using these novel approaches and present a “treasure map” of hard and superhard materials, which summarizes known and predicted materials and points to promising future directions of superhard materials discovery.

Nitrides, carbides, and borides of transition metals are an attractive class of hard materials. Our recent preliminary explorations of the binary chemical compounds indicated that chromium-based materials are among the hardest transition metal compounds. Motivated by this, here we explore in detail the binary Cr-B, Cr-C, and Cr-N systems using global optimization techniques. Calculated enthalpy of formation and hardness of predicted materials were used for Pareto optimization to define the hardest materials with the lowest energy. Our calculations recover all numerous known stable compounds (except CrC with its large unit cell) and discover a novel stable phase Pmn2-CrC. We resolve the structure of CrN and find it to be of anti-CaCl type (space group Pnnm). Many of these phases possess remarkable hardness, but only CrB is superhard (Vickers hardness 48 GPa). Among chromium compounds, borides generally possess the highest hardnesses and greatest stability. Under pressure, we predict stabilization of a layered TMDC-like phase of CrN, a WC-type phase of CrN, and a new compound CrN. Nitrogen-rich chromium nitride CrN is a high-energy-density material featuring polymeric nitrogen chains. In the presence of metal atoms (e.g., Cr), polymerization of nitrogen takes place at much lower pressures; CrN becomes stable at ∼15 GPa (cf. 110 GPa for synthesis of pure polymeric nitrogen).

In this study, we perform a systematic search to find the possible lowest energy structure of silicon nanoclusters Si ( = 8-80) by means of an evolutionary algorithm. The fitness function for this search is the total energy of density functional tight binding (DFTB). To be on firm ground, we take several low energy structures of DFTB and perform further geometrical optimization by density functional theory (DFT). Then we choose structures with the lowest DFT total energy and compare them with the reported lowest energy structures in the literature. In our search, we found several lowest energy structures that were previously unreported. We further observe a geometrical transition at = 27 from elongated to globular structures. In addition, the optical gap of the lowest energy structures is investigated by time-dependent DFTB (TD-DFTB) and time-dependent DFT (TD-DFT). The results show the same trend in TD-DFTB and TD-DFT for the optical gap. We also find a sudden drop in the optical gap at = 27, precisely where the geometrical transition occurs.

Organizing a chemical space so that elements with similar properties would take neighboring places in a sequence can help to predict new materials. In this paper, we propose a universal method of generating such a one-dimensional sequence of elements, i.e. at arbitrary pressure, which could be used to create a well-structured chemical space of materials and facilitate the prediction of new materials. This work clarifies the physical meaning of Mendeleev numbers, which was earlier tabulated by Pettifor. We compare our proposed sequence of elements with alternative sequences formed by different Mendeleev numbers using the data for hardness, magnetization, enthalpy of formation, and atomization energy. For an unbiased evaluation of the MNs, we compare clustering rates obtained with each system of MNs.

Over the past decade, evolutionary algorithms, data mining, and other methods showed great success in solving the main problem of theoretical crystallography: finding the stable structure for a given chemical composition. Here, we develop a method that addresses the central problem of computational materials science: the prediction of material(s), among all possible combinations of all elements, that possess the best combination of target properties. This nonempirical method combines our new coevolutionary approach with the carefully restructured “Mendelevian” chemical space, energy filtering, and Pareto optimization to ensure that the predicted materials have optimal properties and a high chance to be synthesizable. The first calculations, presented here, illustrate the power of this approach. In particular, we find that diamond (and its polytypes, including lonsdaleite) are the hardest possible materials and that bcc-Fe has the highest zero-temperature magnetization among all possible compounds.

Efficient thermoelectric materials are highly desirable, and the quest for finding them has intensified as they could be promising alternatives to fossil energy sources. Here we present a general first-principles approach to predict, in multicomponent systems, efficient thermoelectric compounds. The method combines a robust evolutionary algorithm, a Pareto multiobjective optimization, density functional theory and a Boltzmann semi-classical calculation of thermoelectric efficiency. To test the performance and reliability of our overall framework, we use the well-known system Bi2Te3-Sb2Te3.

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