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A recommender system based on experimental databases is useful for the efficient discovery of inorganic compounds. Here, we review studies on the discovery of as-yet-unknown compounds using recommender systems. The first method used compositional descriptors made up of elemental features. Chemical compositions registered in the inorganic crystal structure database (ICSD) were supplied to machine learning for binary classification. The other method did not use any descriptors, but a tensor decomposition technique was adopted. The predictive performance for currently unknown chemically relevant compositions (CRCs) was determined by examining their presence in other databases. According to the recommendation, synthesis experiments of two pseudo-ternary compounds with currently unknown structures were successful. Finally, a synthesis-condition recommender system was constructed by machine learning of a parallel experimental data-set collected in-house using a polymerized complex method. Recommendation scores for unexperimented conditions were then evaluated. Synthesis experiments under the targeted conditions found two yet-unknown pseudo-binary oxides.

The advanced data structure of the zero-suppressed binary decision diagram (ZDD) enables us to efficiently enumerate nonequivalent substitutional structures. Not only can the ZDD store a vast number of structures in a compressed manner, but also a set of structures satisfying given constraints can be extracted from the ZDD efficiently. Here, we present a ZDD-based efficient algorithm for exhaustively searching for special quasirandom structures (SQSs) that mimic the perfectly random substitutional structure. We demonstrate that the current approach can extract only a tiny number of SQSs from a ZDD composed of many substitutional structures (>10¹²). As a result, we find SQSs that are optimized better than those proposed in the literature. A series of SQSs should be helpful for estimating the properties of substitutional solid solutions. Furthermore, the present ZDD-based algorithm should be useful for applying the ZDD to the other structure enumeration problems.

Oxygen vacancy ordering in perovskite-type transition-metal oxides plays an important role in the emergence of exotic electronic properties, as typified by superconducting cuprates. In this study, we predict the stability of oxygen-deficient perovskite structures in ACuO₃₋ₓ (A = Ca, Sr, Ba, Sc, Y, La) by density functional theory calculation. We introduce a combination of the cluster expansion method, Gaussian process, and Bayesian optimization to find stable oxygen-deficient structures among a considerable number of candidates. Our calculations not only reproduce the reported structures but suggest the presence of several unknown oxygen-deficient perovskite structures, some of which are stabilized at high pressures. This work demonstrates the great applicability of the present computational procedure for the elucidation of the structural stability of strongly correlated oxides with a large tolerance for oxygen deficiency.

Machine learning potentials (MLPs) are becoming powerful tools for performing accurate atomistic simulations and crystal structure optimizations. An approach to developing MLPs employs a systematic set of polynomial invariants including high-order ones to represent the neighboring atomic density. In this study, a formulation of the polynomial invariants is extended to the case of multicomponent systems. The extended formulation is more complex than the formulation for elemental systems. This study also shows its application to the Ti-Al binary system. As a result, an MLP with the lowest error and MLPs with high computational cost performance are selected from the many MLPs developed systematically. The predictive powers of the developed MLPs for many properties, such as the formation energy, elastic constants, thermodynamic properties, and mechanical properties, are examined. The MLPs exhibit high predictive power for the properties in a wide variety of ordered structures. The present scheme should be systematically applicable to other multicomponent systems.

Many rotational invariants for crystal structure representations have been used to describe the structure-property relationship by machine learning. The machine learning interatomic potential (MLIP) is one of the applications of rotational invariants, which provides the relationship between the energy and the crystal structure. Therefore, the enumeration of rotational invariants should be useful for constructing MLIPs with the desired accuracy. In this study, we introduce high-order linearly independent rotational invariants up to the sixth order based on spherical harmonics and apply them to linearized MLIPs for elemental aluminum. A set of rotational invariants is derived by the general process of reducing the Kronecker products of irreducible representations for the SO(3) group using a group-theoretical projector method. A high predictive power for a wide range of structures is accomplished by using high-order invariants with low-order invariants equivalent to pair and angular structural features.

A first-principles-based computational tool for simulating phonons of magnetic random solid solutions including thermal magnetic fluctuations is developed. The method takes fluctuations of force constants due to magnetic excitations as well as due to chemical disorder into account. The developed approach correctly predicts the experimentally observed unusual phonon hardening of a transverse acoustic mode in Fe–Pd an Fe–Pt Invar alloys with increasing temperature. This peculiar behavior, which cannot be explained within a conventional harmonic picture, turns out to be a consequence of thermal magnetic fluctuations. The proposed methodology can be straightforwardly applied to a wide range of materials to reveal new insights into physical behaviors and to design materials through computation, which were not accessible so far.

A first-principles-based computational tool for simulating phonons of magnetic random solid solutions including thermal magnetic fluctuations is developed. The method takes fluctuations of force constants due to magnetic excitations as well as due to chemical disorder into account. The developed approach correctly predicts the experimentally observed unusual phonon hardening of a transverse acoustic mode in Fe-Pd an Fe-Pt Invar alloys with increasing temperature. This peculiar behavior, which cannot be explained within a conventional harmonic picture, turns out to be a consequence of thermal magnetic fluctuations. The proposed methodology can be straightforwardly applied to a wide range of materials to reveal new insights into physical behaviors and to design materials through computation, which were not accessible so far., (OLD) MSE-7

Interatomic potentials have been widely used in atomistic simulations such as molecular dynamics. Recently, frameworks to construct accurate interatomic potentials that combine a set of density functional theory (DFT) calculations with machine learning techniques have been proposed. One of these methods is to use compressed sensing to derive a sparse representation for the interatomic potential. This facilitates the control of the accuracy of interatomic potentials. In this study, we demonstrate the applicability of compressed sensing to deriving the interatomic potential of ten elemental metals, namely, Ag, Al, Au, Ca, Cu, Ga, In, K, Li, and Zn. For each elemental metal, the interatomic potential is obtained from DFT calculations using elastic net regression. The interatomic potentials are found to have prediction errors of less than 3.5 meV/atom, 0.03 eV/Å, and 0.15 GPa for the energy, force, and the stress tensor, respectively, which enable the accurate prediction of physical properties such as lattice constants and the phonon dispersion relationship.

Compounds of low lattice thermal conductivity (LTC) are essential for seeking thermoelectric materials with high conversion efficiency. Some strategies have been used to decrease LTC. However, such trials have yielded successes only within a limited exploration space. Here, we report the virtual screening of a library containing 54 779 compounds. Our strategy is to search the library through Bayesian optimization using for the initial data the LTC obtained from first-principles anharmonic lattice-dynamics calculations for a set of 101 compounds. We discovered 221 materials with very low LTC. Two of them even have an electronic band gap <1 eV, which makes them exceptional candidates for thermoelectric applications. In addition to those newly discovered thermoelectric materials, the present strategy is believed to be powerful for many other applications in which the chemistry of materials is required to be optimized.

The use of a special quasirandom structure (SQS) is a rational and efficient way to approximate random alloys. A wide variety of physical properties of metallic and semiconductor random alloys have been successfully estimated by a combination of an SQS and density functional theory calculation. Here, we investigate the application of an SQS to the ionic multicomponent systems with configurations of heterovalent ions, including point-charge lattices, MgAl[2]O[4] and ZnSnP[2]. It is found that the physical properties do not converge with the supercell size of the SQS. This is ascribed to the fact that the correlation functions of long-range clusters larger than the period of the supercell are not optimized in the SQS. However, we demonstrate that the physical properties of the perfectly disordered structure can be estimated by linear extrapolation using the inverse of the supercell size.

We have been examining factors determining the accuracy of cluster expansion (CE), which is used in combination with many density functional theory (DFT) calculations. With the exception of multicomponent metallic or isovalent ionic systems, the contributions of long-range effective cluster interactions (ECIs) to configurational energetics are not negligible, which is ascribed to long-range electrostatic interactions. The truncation of ECIs in such systems leads to systematic errors. A typical problem with such errors can be seen in Monte Carlo simulations, since simulation supercells composed of a larger number of atoms than those of the input DFT structures are used. The prediction errors for long-period structures beyond the cell size of the input DFT structures in addition to those for short-period structures within the cell size of the input DFT structures need to be carefully examined to control the accuracy of CE. In this study, we quantitatively discuss the contribution of the truncation of long-range ECIs to the accuracy of CE. Two types of system, namely a point-charge spinel lattice and a real MgAl2O4 spinel crystal, are examined. The prediction error of the long-period structures can be improved both by increasing the number of pairs and by also considering the effective screened electrostatic energy.

We propose an efficient approach to accurately finding the ground-state structures in alloys based on the cluster expansion method. In this approach, a small number of candidate ground-state structures are obtained without any information regarding the energy. To generate the candidates, we employ the convex hull constructed from the correlation functions of all possible structures by using an efficient algorithm. This approach is applicable to not only simple lattices, but also complex lattices. First, we evaluate the convex hulls for binary alloys with four types of simple lattice. Then we discuss the structures on the vertices. To examine the accuracy of this approach, we perform a set of density functional theory calculations and the cluster expansion for the Ag-Au alloy and compare the formation energies of the vertex structures with those of all possible structures. As applications, the ground-state structures of the intermetallic compounds CuAu, CuAg, CuPd, AuAg, AuPd, AgPd, MoTa, MoW, and TaW are similarly evaluated. Finally, the energy distribution is obtained for different cation arrangements in the MgAl[2]O[4] spinel, for which long-range interactions are essential for the accurate description of its energetics.

A combination of systematic density-functional theory (DFT) calculations and machine learning techniques has a wide range of potential applications. This study presents an application of the combination of systematic DFT calculations and regression techniques to the prediction of the melting temperature for single and binary compounds. Here we adopt the ordinary least-squares regression, partial least-squares regression, support vector regression, and Gaussian process regression. Among the four kinds of regression techniques, SVR provides the best prediction. The inclusion of physical properties computed by the DFT calculation to a set of predictor variables makes the prediction better. In addition, limitation of the predictive power is shown when extrapolation from the training dataset is required. Finally, a simulation to find the highest melting temperature toward the efficient materials design using kriging is demonstrated. The kriging design finds the compound with the highest melting temperature much faster than random designs. This result may stimulate the application of kriging to efficient materials design for a broad range of applications.