Low-energy Crystal Structures Research Articles

LoGAN: local generative adversarial network for novel structure prediction

Abstract The efficient generation and filtering of candidate structures for new materials is becoming increasingly important as starting points for computational studies. In this work, we introduce an approach to Wasserstein generative adversarial networks for predicting unique crystal and molecular structures. Leveraging translation- and rotation-invariant atom-centered local descriptors addresses some of the major challenges faced by similar methods. Our models require only small sets of known structures as training data. Furthermore, the approach is able to generate both non-periodic and periodic structures based on local coordination. We showcase the data efficiency and versatility of the approach by recovering all stable C5H12O isomers using only 39 C4H10O and C6H14O training examples, as well as a few randomly selected known low-energy SiO2 crystal structures utilizing only 167 training examples of other SiO2 crystal structures. We also introduce a filtration technique to reduce the computational cost of subsequent characterization steps by selecting samples from unique basins on the potential energy surface, which allows to minimize the number of geometry relaxations needed after structure generation. The present method thus represents a new, versatile approach to generative modeling of crystal and molecular structures in the low-data regime, and is available as open-source.

Exploration of novel crystal structures of CsPbBr3 and RbPbBr3 via density functional theory

We report the screening of low-energy crystal structures of CsPbBr3 and RbPbBr3 from approximately 740 structural prototypes using high-flux density functional theory (DFT). These structures are well compared in terms of thermodynamics, band structures and optical properties. Calculated phonon spectra and Gibbs free energy indicate that the Pbnm structure possesses the best kinetic and thermodynamic stability. Band-structure calculations reveal that many CsPbBr3 and RbPbBr3 structures have direct band gap. Optical calculations show a positive correlation between the band gap and photon energy. The structures with low band gap have faster light response, while structures having wider band gap exhibit better optical properties because of their higher photon energies.

Fast and accurate prediction of material properties with three-body tight-binding model for the periodic table.

Parametrized tight-binding models fit to first-principles calculations can provide an efficient and accurate quantum mechanical method for predicting properties of molecules and solids. However, well-tested parameter sets are generally only available for a limited number of atom combinations, making routine use of this method difficult. Furthermore, many previous models consider only simple two-body interactions, which limits accuracy. To tackle these challenges, we develop a density functional theory database of nearly 1 000 000 materials, which we use to fit a universal set of tight-binding parameters for 65 elements and their binary combinations. We include both two-body and three-body effective interaction terms in our model, plus self-consistent charge transfer, enabling our model to work for metallic, covalent, and ionic bonds with the same parameter set. To ensure predictive power, we adopt a learning framework where we repeatedly test the model on new low-energy crystal structures and then add them to the fitting data set, iterating until predictions improve. We distribute the materials database and tools developed in this paper publicly.

Finding stable multi-component materials by combining cluster expansion and crystal structure predictions

A desired prerequisite when performing a quantum mechanical calculation is to have an initial idea of the atomic positions within an approximate crystal structure. The atomic positions combined should result in a system located in, or close to, an energy minimum. However, designing low-energy structures may be a challenging task when prior knowledge is scarce, specifically for large multi-component systems where the degrees of freedom are close to infinite. In this paper, we propose a method for identification of low-energy crystal structures within multi-component systems by combining cluster expansion and crystal structure predictions with density-functional theory calculations. Crystal structure prediction searches are applied to the Mo2AlB2 and Sc2AlB2 ternary systems to identify candidate structures, which are subsequently used to explore the quaternary (pseudo-binary) (MoxSc1–x)2AlB2 system through the cluster expansion formalism utilizing the ground-state search approach. Furthermore, we show that utilizing low-energy structures found within the cluster expansion ground-state search as seed structures within crystal structure predictions of (MoxSc1–x)2AlB2 can significantly reduce the computational demands. With this combined approach, we not only correctly identified the recently discovered Mo4/3Sc2/3AlB2i-MAB phase, comprised of in-plane chemical ordering of Mo and Sc and with Al in a Kagomé lattice, but also predict additional low-energy structures at various concentrations. This result demonstrates that combining crystal structure prediction with cluster expansion provides a path for identifying low-energy crystal structures in multi-component systems by employing the strengths from both frameworks.

Crystal structure prediction in a continuous representative space

Here we report a method of finding multiple crystal structures similar to the known crystal structures of materials on database through machine learning. The radial distribution function is used to represent the general characteristics of the known crystal structures, and then the variational autoencoder is employed to generate a set of representative crystal replicas defined in a two-dimensional optimal continuous space. For given chemical compositions and crystal volume, we generate random crystal structures using constraints for crystal symmetry and atomic positions and directly compare their radial distribution functions with those of the known and/or replicated crystals. For selected crystal structures, energy minimization is subsequently performed through first-principles electronic structure calculations. This approach enables us to predict a set of new low-energy crystal structures using only the information on the radial distribution functions of the known structures.

Random Structure Searching with Orbital-Free Density Functional Theory.

The properties of a material depend on how its atoms are arranged, and predicting these arrangements from first principles is a longstanding challenge. Orbital-free density functional theory provides a quantum-mechanical model based solely on the electron density, not individual wave functions. The resulting speedups make it attractive for random structure searching, whereby random configurations of atoms are relaxed to local minima in the energy landscape. We use this strategy to map the low-energy crystal structures of Li, Na, Mg, and Al at zero pressure. For Li and Na, our searching finds numerous close-packed polytypes of almost-equal energy, consistent with previous efforts to understand their low-temperature forms. For Mg and Al, the searching identifies the expected ground state structures unambiguously, in addition to revealing other low-energy structures. This new role for orbital-free density functional theory—particularly as continued advances make it accurate for more of the periodic table—will expedite crystal structure prediction over wide ranges of compositions and pressures.

Training machine-learning potentials for crystal structure prediction using disordered structures

Prediction of the stable crystal structure for multinary (ternary or higher) compounds with unexplored compositions demands fast and accurate evaluation of free energies in exploring the vast configurational space. The machine-learning potential such as the neural network potential (NNP) is poised to meet this requirement but a dearth of information on the crystal structure poses a challenge in choosing training sets. Herein we propose constructing the training set from densityfunctional-theory (DFT) based dynamical trajectories of liquid and quenched amorphous phases, which does not require any preceding information on material structures except for the chemical composition. To demonstrate suitability of the trained NNP in the crystal structure prediction, we compare NNP and DFT energies for Ba2AgSi3, Mg2SiO4, LiAlCl4, and InTe2O5F over experimental phases as well as low-energy crystal structures that are generated theoretically. For every material, we find strong correlations between DFT and NNP energies, ensuring that the NNPs can properly rank energies among low-energy crystalline structures. We also find that the evolutionary search using the NNPs can identify low-energy metastable phases more efficiently than the DFTbased approach. By proposing a way to developing reliable machine-learning potentials for the crystal structure prediction, this work will pave the way to identifying unexplored multinary phases efficiently.

Pauling’s rules guided Monte Carlo search (PAMCARS): A shortcut of predicting inorganic crystal structures

The rapid development of the high-throughput calculations and materials genome approaches in recent years has improved researchers’ ability to design advanced materials. Crystal structure prediction techniques play an important role in high-throughput calculations and materials genome approaches. However, the huge computational cost of the widely used crystal structure prediction techniques based on the global optimization algorithms hinders the researchers from predicting the large or medium-sized crystal structures. In recent years, some metastable materials with excellent electrical, magnetic, optical and catalytic properties have attracted a lot of attention. However, there is currently a lack of a structure prediction technique with high energy resolution near the ground-state structures to meet the growing demands for the prediction of low-energy metastable materials. In this article, a set of easy-operation guidelines for constructing crystal structures is extracted from Pauling’s rules. Based on this set of guidelines, we have designed an algorithm called Pauling’s rules guided Monte Carlo search (PAMCARS), which predict the ground-state and meta-stable inorganic crystal structures of a given composition by combining a classical Monte Carlo search in the configuration space constrained by Pauling’s rules with ab initio structural relaxations. In the actual tests, the crystal structures of carbon allotropes, CaSO4, Ba2TiSi2O8 and BaAlBO3F2 are successfully predicted by this crystal structure prediction algorithm. In addition, a number of unreported high-symmetric metastable crystal structures of carbon, CaSO4 and Ba2TiSi2O8 are also predicted. The successful prediction of graphite layers indicates that PAMCARS is able to predict some layered materials assembled by the Van der Waals forces. Two of the predicted low-energy metastable crystal structures of Ba2TiSi2O8 may explain the property anomaly of Ba2TiSi2O8 around 160 °C. Pauling’s rules guided Monte Carlo search exhibits high efficiency and energy resolution in predicting the ground-state and metastable crystal structures in the tests.

Heterogeneous Interactions Promote Crystallization and Spontaneous Resolution of Chiral Molecules.

Predicting the crystallization of chiral molecules from solution is a major challenge in the chemical sciences. In this paper, we use molecular dynamics computer simulations to study the crystallization of a family of coarse-grained models of chiral molecules with a broad range of molecular shapes and interactions. Our simulations reproduce the experimental crystallization behavior of real chiral molecules, including racemic and enantiopure crystals, as well as amorphous solids. Using efficient algorithms for the packing of shapes, we enumerate millions of low-energy crystal structures for each model and analyze the thermodynamic landscape of polymorphs. In agreement with recent conjectures, our analysis shows that the ease of crystallization is largely determined by the number of competing polymorphs with low free energy. We find that this number and, hence, crystallization outcomes depend on molecular interactions in a simple way: Strongly heterogeneous interactions across molecules promote crystallization and favor the spontaneous resolution of racemic mixtures. Our results help rationalize a number of experimental observations and can provide guidance for the design of molecules and experimental conditions for desired crystallization outcomes.

The ground state of two-dimensional silicon

We perform ab initio structure-prediction calculations of the low-energy crystal structures of two-dimensional silicon. Besides the well-known silicene and a few other allotropes proposed earlier in the literature, we discover a wealth of new phases with interesting properties. In particular, we find that the ground state of two-dimensional silicon is an unreported structure formed by a honeycomb lattice with dumbbell atoms arranged in a zigzag pattern. This material, that we call zigzag dumbbell silicene, is 218 meV/atom more stable than silicene and displays a quasi-direct band gap of around 1.11 eV, with a very dispersive electron band. These properties should make it easier to synthesize than silicene and interesting for a wealth of opto-electronic applications.

New structures of Fe3S for rare-earth-free permanent magnets

We applied an adaptive genetic algorithm (AGA) to search for low-energy crystal structures of Fe3S. A number of structures with energies lower than that of the experimentally reported Pnma and I-4 structures have been obtained from our AGA searches. These low-energy structures can be classified as layer-motif and column-motif structures. In the column-motif structures, Fe atoms self-assemble into rods with a bcc type of underlying lattice, which are separated by the holes terminated by S atoms. In the layer-motif structures, the bulk Fe is broken into slabs of several layers passivated by S atoms. Magnetic property calculations showed that the column-motif structures exhibit reasonably high uniaxial magnetic anisotropy. In addition, we examined the effect of Co doping to Fe3S and found that magnetic anisotropy can be enhanced through Co doping.

Use of Crystal Structure Informatics for Defining the Conformational Space Needed for Predicting Crystal Structures of Pharmaceutical Molecules.

Determining the range of conformations that a flexible pharmaceutical-like molecule could plausibly adopt in a crystal structure is a key to successful crystal structure prediction (CSP) studies. We aim to use conformational information from the crystal structures in the Cambridge Structural Database (CSD) to facilitate this task. The conformations produced by the CSD Conformer Generator are reduced in number by considering the underlying rotamer distributions, an analysis of changes in molecular shape, and a minimal number of molecular ab initio calculations. This method is tested for five pharmaceutical-like molecules where an extensive CSP study has already been performed. The CSD informatics-derived set of crystal structure searches generates almost all the low-energy crystal structures previously found, including all experimental structures. The workflow effectively combines information on individual torsion angles and then eliminates the combinations that are too high in energy to be found in the solid state, reducing the resources needed to cover the solid-state conformational space of a molecule. This provides insights into how the low-energy solid-state and isolated-molecule conformations are related to the properties of the individual flexible torsion angles.

Ionic and superionic phases in ammonia dihydrate NH3·2H2O under high pressure

Water and ammonia have long been seen as the main species of extraterrestrial space, especially on solar giants, moons, comets, and numerous extrasolar planets. The phases formed by their admixtures under temperature and pressure conditions of the giant planets are important for understanding many observable properties (gravitational moments, atmospheric composition, and magnetic field). Here we employ a Monte Carlo packing algorithm combined with first-principles calculations to search the low-energy crystal structures of ammonia dihydrate (ADH). At high pressure above 11.81 GPa, we predict an unusual ionic phase (tetragonal, $I{4}_{1}cd)$ consisting of three alternating layers of ${\mathrm{H}}_{2}\mathrm{O},{\mathrm{NH}}_{4}{}^{+}$, and $\mathrm{O}{\mathrm{H}}^{\ensuremath{-}}$. The occurrence of ionic phase is attributed to the ${\mathrm{NH}}_{4}{}^{+}$ and $\mathrm{O}{\mathrm{H}}^{\ensuremath{-}}$ electrostatic interaction induced volume reduction, which lowers the energy barrier of molecular to ionic phase transition. Analysis of proton transfer under pressure further supports the transformation mechanism between molecular and ionic phase. According to the mobility of hydrogen atoms from ab initio molecular dynamics, this ionic crystal will transform into a superionic phase under high temperature and high pressure. The existence of ionic or superionic ADH may have important implications for understanding the interiors of Neptune, Uranus, and many extrasolar planets.

Structural Properties, Order–Disorder Phenomena, and Phase Stability of Orotic Acid Crystal Forms

Orotic acid (OTA) is reported to exist in the anhydrous (AH), monohydrate (Hy1), and dimethyl sulfoxide monosolvate (SDMSO) forms. In this study we investigate the (de)hydration/desolvation behavior, aiming at an understanding of the elusive structural features of anhydrous OTA by a combination of experimental and computational techniques, namely, thermal analytical methods, gravimetric moisture (de)sorption studies, water activity measurements, X-ray powder diffraction, spectroscopy (vibrational, solid-state NMR), crystal energy landscape, and chemical shift calculations. The Hy1 is a highly stable hydrate, which dissociates above 135 °C and loses only a small part of the water when stored over desiccants (25 °C) for more than one year. In Hy1, orotic acid and water molecules are linked by strong hydrogen bonds in nearly perfectly planar arranged stacked layers. The layers are spaced by 3.1 Å and not linked via hydrogen bonds. Upon dehydration the X-ray powder diffraction and solid-state NMR peaks become broader, indicating some disorder in the anhydrous form. The Hy1 stacking reflection (122) is maintained, suggesting that the OTA molecules are still arranged in stacked layers in the dehydration product. Desolvation of SDMSO, a nonlayer structure, results in the same AH phase as observed upon dehydrating Hy1. Depending on the desolvation conditions, different levels of order–disorder of layers present in anhydrous OTA are observed, which is also suggested by the computed low energy crystal structures. These structures provide models for stacking faults as intergrowth of different layers is possible. The variability in anhydrate crystals is of practical concern as it affects the moisture dependent stability of AH with respect to hydration.

Fe-Si networks in Na2FeSiO4 cathode materials.

Using a combination of adaptive genetic algorithm search, motif-network search scheme and first-principles calculations, we have systematically studied the low-energy crystal structures of Na2FeSiO4. We show that the low-energy crystal structures with different space group symmetries can be classified into several families based on the topologies of their Fe-Si networks. In addition to the diamond-like network which is shared by most of the low-energy structures, another three robust Fe-Si networks are also found to be stable during the charge/discharge process. The electrochemical properties of representative structures from these four different Fe-Si networks in Na2FeSiO4 and Li2FeSiO4 are investigated and found to be strongly correlated with the Fe-Si network topologies. Our studies provide a new route to characterize the crystal structures of Na2FeSiO4 and Li2FeSiO4 and offer useful guidance for the design of promising cathodes for Na/Li ion batteries.

Crystal-Chemistry Guidelines for Noncentrosymmetric A2BO4Ruddlesden−Popper Oxides

Noncentrosymmetric (NCS) phases are seldom seen in layered A2BO4 Ruddlesden-Popper (214 RP) oxides. In this work, we uncover the underlying crystallographic symmetry restrictions that enforce the spatial parity operation of inversion and then subsequently show how to lift them to achieve NCS structures. Simple octahedral distortions alone, while impacting the electronic and magnetic properties, are insufficient. We show using group theory that the condensation of two distortion modes, which describe suitable symmetry unique octahedral distortions or a combination of a single octahedral distortion with a "compositional" A or B cation ordering mode, is able to transform the centrosymmetric aristotype into a NCS structure. With these symmetry guidelines, we formulate a data-driven model founded on Bayesian inference that allows us to rationally search for combinations of A- and B-site elements satisfying the inversion symmetry lifting criterion. We describe the general methodology and apply it to 214 iridates with A(2+) cations, identifying RP-structured Ca2IrO4 as a potential NCS oxide, which we evaluate with density functional theory. We find a strong energetic competition between two closely related polar and nonpolar low-energy crystal structures in Ca2IrO4 and suggest pathways to stabilize the NCS structure.

Is the Fenamate Group a Polymorphophore? Contrasting the Crystal Energy Landscapes of Fenamic and Tolfenamic Acids

The concept of a polymorphophore was investigated by contrasting the crystal energy landscapes of monomorphic fenamic acid (2-(phenylamino)-benzoic acid, FA) and one of its highly polymorphic derivatives, tolfenamic acid (2-[(3-chloro-2-methylphenyl)amino]-benzoic acid, TA). The crystal energy landscapes of both molecules show that the benzoic acid R22(8) dimer motif is found in all low energy crystal structures, but conformational flexibility of the phenyl rings leads to a wide range of crystal structures with different packings of this dimer. Many of the observed fenamate crystal structures can overlay a significant proportion of the coordination environment with other observed or calculated structures, but the substituents of the phenyl group affect the ordering of the related low energy crystal structures. The crystal energy landscape of tolfenamic acid has several crystal structures, including the observed polymorphs, tightly clustered around the global minimum, whereas the corresponding cluster contains only the observed and a closely related structure for fenamic acid. Hence, the fenamate fragment is potentially permissive of a large number of structures because of the conformational flexibility, but the substituents determine whether a specific fenamate will be polymorphic. Thus, a polymorphophore promotes but does not guarantee polymorphism.

Atomic structure and magnetic properties of Fe1–xCox alloys

Using genetic algorithm with first-principle calculations, we searched for low-energy crystal structures of Fe1−xCox alloys. We found that Fe1−xCox alloys are highly configurationally degenerate with many additional off-stoichiometric stable structures to the well-known B2 structure. The average magnetic moment of Fe atom increases with concentration of Co in the alloy, while that of Co atom is almost constant, which are consistent with experiments and earlier studies. The magnetic moment of Fe atom is strongly dependent on the number of Co nearest neighbor and it increases with this number.

First-principles prediction of phase stability and crystal structures in Li-Zn and Na-Zn mixed-metal borohydrides

We use a combination of first-principles density functional theory (DFT) calculations and the recently developed prototype electrostatic ground state (PEGS) method to predict low-energy crystal structures and study phase stability of Li-Zn and Na-Zn mixed-metal borohydride compounds [i.e., NaZn(BH${}_{4}$)${}_{3}$, NaZn${}_{2}$(BH${}_{4}$)${}_{5}$, LiZn(BH${}_{4}$)${}_{3}$, and LiZn${}_{2}$(BH${}_{4}$)${}_{5}$]. We find the following: (i) DFT $+$ PEGS successfully predicts low-energy structures in these mixed-metal borohydride systems. (ii) DFT calculations show negative mixing energies in both the Li-Zn and Na-Zn borohydride systems, consistent with the observation of mixed-metal ordering in these systems. (iii) Our DFT calculations of the recently reported experimental crystal structures of NaZn${}_{2}$(BH${}_{4}$)${}_{5}$ and NaZn(BH${}_{4}$)${}_{3}$ show that the former has a negative mixing energy, while the latter has a positive mixing energy. (iv) Using the PEGS approach, we predict a new crystal structure of NaZn(BH${}_{4}$)${}_{3}$ with negative mixing energy and find that the experimental structure of NaZn${}_{2}$(BH${}_{4}$)${}_{5}$ and the PEGS obtained structure of NaZn(BH${}_{4}$)${}_{3}$ lie on the ground state convex hull. (v) In the Li-Zn borohydride system, we have used the PEGS $+$ DFT approach to predict a stable crystal structure of new, previously unobserved stoichiometry, LiZn(BH${}_{4}$)${}_{3}$. As a consequence of this predicted low-energy compound, DFT calculations of the experimentally reported structure of LiZn${}_{2}$(BH${}_{4}$)${}_{5}$ show that it is unstable with respect to decomposition into LiZn(BH${}_{4}$)${}_{3}$ $+$ Zn(BH${}_{4}$)${}_{2}$. (vi) In addition, we also elucidate the ground state crystal structure of NaBH${}_{4}$, and confirm that reorientation of (BH${}_{4}$)${}^{\ensuremath{-}}$ units is the driving force behind the order-disorder phase transition in NaBH${}_{4}$. (vii) Finally, we predict a new low-energy crystal structure of Zn(BH${}_{4}$)${}_{2}$, and illustrate its similarities with the crystal structure of Mg(BH${}_{4}$)${}_{2}$.

Structural richness of ionic binary materials: An exploration of the energy landscape of magnesium oxide

We search for polymorphs of magnesium oxide (MgO) close in energy to the rocksalt global minimum by using variants of the basin hopping approach. Our exploration clearly demonstrates that the energy landscape of this nominally octahedrally coordinated, densely packed solid is much more complicated than suggested by previous work. Specifically, we find that MgO has a dense spectrum of as yet undiscovered low-energy polymorphs, many of which have a much lower density than the rocksalt structure (as also recently shown for tetrahedrally coordinated binary solids (e.g., ZnO) [Phys. Rev. Lett. 104, 175503 (2010)]). Unlike in the case of tetrahedrally coordinated materials, we further find low-energy crystal structures with four-, five-, or six-coordinated atoms. Strikingly, some of these structures also have pores that are arguably large enough for small molecular species to enter, while others are found to be quasi-amorphous. We also discuss the problem of searching for systems that are currently too large to study by basin hopping (or similar approaches) in a tractable fashion, and the implications of our findings for other solids.