Algorithm For Crystal Structure Prediction Research Articles

Crystal structure prediction using neural network potential and age-fitness Pareto genetic algorithm

While crystal structure prediction (CSP) remains a longstanding challenge, we introduce ParetoCSP, a novel algorithm for CSP, which combines a multi-objective genetic algorithm (GA) with a neural network inter-atomic potential model to find energetically optimal crystal structures given chemical compositions. We enhance the updated multi-objective GA (NSGA-III) by incorporating the genotypic age as an independent optimization criterion and employ the M3GNet universal inter-atomic potential to guide the GA search. Compared to GN-OA, a state-of-the-art neural potential-based CSP algorithm, ParetoCSP demonstrated significantly better predictive capabilities, outperforming by a factor of $$ 2.562 $$ across $$ 55 $$ diverse benchmark structures, as evaluated by seven performance metrics. Trajectory analysis of the traversed structures of all algorithms shows that ParetoCSP generated more valid structures than other algorithms, which helped guide the GA to search more effectively for the optimal structures. Our implementation code is available at https://github.com/sadmanomee/ParetoCSP .

Accelerating search for the polar phase stability of ferroelectric oxide by machine learning

Machine learning emerges to accelerate first-principles calculations in materials discovery and property prediction, but developing high-accuracy prediction models requires training on large datasets of relaxed structures, which can be computationally expensive. Besides, the crystal structure prediction algorithms show promising aspects but often deviate from the ground state, leading to poor predictions. Using a crystal graph convolutional neural network, we propose an alternative and efficient method of finding the ground state by utilizing the total energy of random unrelaxed structures. The prediction model is trained on a small dataset of unrelaxed energy obtained from first-principles calculations and effectively predicts the total energy of random structures with an accuracy almost equivalent to first-principles calculations. The resulting energy landscape is then reconstructed in terms of polarity. This leads to establishing an energy landscape of a perovskite oxide in a cost-effective way, enabling a polar phase stability map of strained BaTiO3, a representative ferroelectric oxide. The proposed methodology efficiently allows to obtain the ground state by eliminating the computationally intensive procedure of structure optimization, thus accelerating the ground state search to map out the phase stability of strained perovskite materials in a practical manner.

Deep Learning-Based Prediction of Contact Maps and Crystal Structures of Inorganic Materials.

Crystal structure prediction is one of the major unsolved problems in materials science. Traditionally, this problem is formulated as a global optimization problem for which global search algorithms are combined with first-principles free energy calculations to predict the ground-state crystal structure of a given material composition. These ab initio algorithms are currently too slow for predicting complex material structures. Inspired by the AlphaFold algorithm for protein structure prediction, herein, we propose AlphaCrystal, a crystal structure prediction algorithm that combines a deep residual neural network model for predicting the atomic contact map of a target material followed by three-dimensional (3D) structure reconstruction using genetic algorithms. Extensive experiments on 20 benchmark structures showed that our AlphaCrystal algorithm can predict structures close to the ground truth structures, which can significantly speed up the crystal structure prediction and handle relatively large systems.

Novel Topological Motifs and Superconductivity in Li-Cs System.

In this work, we determined the phase diagram and electronic properties of the Li-Cs system by using an evolutionary crystal structure prediction algorithm coupled with first-principles calculations. We found that Li-rich compounds are more easily formed in a wide range of pressures, while the only predicted Cs-rich compound LiCs3 is thermodynamically stable at pressures above 359 GPa. A topological analysis of crystal structures concludes that both Li6Cs and Li14Cs have a unique topology that has not been reported in existing intermetallics. Of particular interest is the fact that four Li-rich compounds (Li14Cs, Li8Cs, Li7Cs, and Li6Cs) are found to be superconductors with a high critical temperature (∼54 K for Li8Cs at 380 GPa), due to their peculiar structural topologies and notable charge transfer from Li to Cs atoms. Our results not only extend an in-depth understanding of the high-pressure behavior of intermetallic compounds but also provide a new route to design new superconductors.

Crystal structure prediction of quasi-two-dimensional lead halide perovskites

Two-dimensional lead halide perovskites are promising materials for optoelectronics due to the tunability of their properties with the number of lead halide layers and the choice of an organic spacer. Physical understanding for the rational design of materials primarily requires knowledge of crystal structure. Two-dimensional lead halide perovskites are usually prepared in the form of films, complicating the experimental determination of structure. To enable theoretical studies of experimentally unresolvable structures as well as high-throughput virtual screening, we present an algorithm for crystal structure prediction of lead halide perovskites. Using an automatically prepared classical potential we show that our algorithm enables fast access to a structure that can be used for further first-principles studies.

Computational discovery of two-dimensional rare-earth iodides: promising ferrovalley materials for valleytronics

Two-dimensional Ferrovalley materials with intrinsic valley polarization are rare but highly promising for valley-based nonvolatile random access memory and valley filter devices. These ferromagnetic materials exhibit valleys at or near the Fermi level with intrinsic magnetism. The strong coupling between magnetism and spin–orbit coupling induces intrinsic valley polarization. Using Kinetically Limited Minimization, an unconstrained crystal structure prediction algorithm, and prototype sampling based on first-principles calculations, we have discovered new Ferrovalley materials, rare-earth iodides RI2, where R is a rare-earth element belonging to Sc, Y, or La-Lu, and I is Iodine. The rare-earth iodides are layered and demonstrate either 2H, 1T, or 1T d phase as the ground state in bulk, analogous to transition metal dichalcogenides (TMDCs). The calculated exfoliation energy of monolayers (MLs) is comparable to that of graphene and TMDCs, suggesting possible experimental synthesis. The MLs in the 2H phase exhibit ferromagnetism due to unpaired electrons in d and f orbitals. Throughout the rare-earth series, d bands have valley polarization at K and points in the Brillouin zone in the vicinity of the Fermi level. Large intrinsic valley polarization in the range of 15–143 meV without external stimuli is observed in these Ferrovalley materials, which can be enhanced further by applying an in-plane bi-axial strain. These valleys can selectively be probed and manipulated for information storage and processing, potentially offering superior performance beyond conventional electronics and spintronics. We further show that the 2H ferromagnetic phase of RI2 MLs possesses non-zero Berry curvature and exhibits anomalous valley Hall effect with considerable anomalous Hall conductivity. Our work will incite exploratory synthesis of the predicted Ferrovalley materials and their application in valleytronics and beyond.

High-pressure stability and superconductivity of vanadium hydrides*

Using variable-composition crystal structure prediction algorithm USPEX combined with first-principles calculations, we systematically explore stable vanadium hydrides (VxHy) in the pressure range from 0 to 300 GPa. Besides reproducing all previously reported VxHy compounds, we discover three new V-rich (C222–V2H, I4/mmm-V3H2 and C222–V6H5) and three new H-rich (R-3m-V3H7, I-42m-V4H11 and Cmmm-VH11) stable phases. All stable VxHy compounds are metallic, as indicated by their electronic structures. Electron-phonon coupling calculations reveal the potential superconductive nature of VH3 (Fm-3m), VH5 (P6/mmm) and VH11 (Cmmm), with estimated critical temperature of 2.4–2.5 K for VH3, 14.5–15.5 K for VH5 and 90.9–122.6 K for VH11 at 200 GPa, respectively. Superconductivity of VH3 comes largely from coupling of the electrons with V vibrations, while in VH5 and VH11 coupling with H vibrations becomes more important as hydrogen content increases.

Stable compounds in the CaO-Al2O3 system at high pressures

Using evolutionary crystal structure prediction algorithm USPEX, we showed that at pressures of the Earth's lower mantle CaAl2O4 is the only stable calcium aluminate. At pressures above 7.0 GPa it has the CaFe2O4-type structure and space group Pnma. This phase is one of prime candidate aluminous phases in the lower mantle of the Earth. We show that at low pressures 5CaO * 3Al2O3 (C5A3) with space group Cmc21, CaAl4O7 (C2/c) and CaAl2O4 (P21/m) structures are stable at pressures of up to 2.1, 1.8 and 7.0 GPa respectively. The previously unknown structure of the orthorhombic 'CA-III' phase is also found from our calculations. This phase is metastable and has a layered structure with space group P21212.

Exploring high pressure structural transformations, electronic properties and superconducting properties of MH2 (M = Nb, Ta)

The high-pressure structures and properties of MH2 (M = Nb, Ta) are explored through an ab initio evolutionary algorithm for crystal structure prediction and first-principles calculations. It is found that NbH2 undergoes a phase transition from a cubic Fm3¯m structure with regular NbH8 cubes to an orthorhombic Pnma structure with fascinating distorted NbH9 tetrakaidecahedrons at 48.8 GPa, while the phase transition pressure of TaH2 from a hexagonal P63mc phase with slightly distorted TaH7 decahedron to an orthorhombic Pnma phase with attractive distorted TaH9 tetrakaidecahedrons is about 90.0 GPa. Besides, the calculated electronic band structure and density of states demonstrate that all of these structures are metallic. The Poisson’s ratio, electron localization function, and Bader charge analysis suggest that these phases possess dominant ionic bonding character with the effective charges transferring from the metal atom to H. From our electron–phonon calculations, the calculated superconducting critical temperature Tc of the Pnma-NbH2 is 6.903 K at 50 GPa. Finally, via the quasi-harmonic approximation method, the phase diagrams at pressure up to 300 GPa and temperature up to 1000 K of MH2 (M = Nb, Ta) are established, where the transition pressure of Fm3¯m-NbH2 → Pnma-NbH2 and P63mc-TaH2 → Pnma-TaH2 were found to decrease with increasing temperature.

Data-augmentation for graph neural network learning of the relaxed energies of unrelaxed structures

Computational materials discovery has grown in utility over the past decade due to advances in computing power and crystal structure prediction algorithms (CSPA). However, the computational cost of the ab initio calculations required by CSPA limits its utility to small unit cells, reducing the compositional and structural space the algorithms can explore. Past studies have bypassed unneeded ab initio calculations by utilizing machine learning to predict the stability of a material. Specifically, graph neural networks trained on large datasets of relaxed structures display high fidelity in predicting formation energy. Unfortunately, the geometries of structures produced by CSPA deviate from the relaxed state, which leads to poor predictions, hindering the model’s ability to filter unstable material. To remedy this behavior, we propose a simple, physically motivated, computationally efficient perturbation technique that augments training data, improving predictions on unrelaxed structures by 66%. Finally, we show how this error reduction can accelerate CSPA.

Crystal Structure Prediction via Efficient Sampling of the Potential Energy Surface.

The crystal structure prediction (CSP) has emerged in recent years as a major theme in research across many scientific disciplines in physics, chemistry, materials science, and geoscience, among others. The central task here is to find the global energy minimum on the potential energy surface (PES) associated with the vast structural configuration space of pertinent crystals of interest, which presents a formidable challenge to efficient and reliable computational implementation. Considerable progress in recent CSP algorithm developments has led to many methodological advances along with successful applications, ushering in a new paradigm where computational research plays a leading predictive role in finding novel material forms and properties which, in turn, offer key insights to guide experimental synthesis and characterization. In this Account, we first present a concise summary of major advances in various CSP methods, with an emphasis on the overarching fundamentals for the exploration of the PES and its impact on CSP. We then take our developed CALYPSO method as an exemplary case study to give a focused overview of the current status of the most prominent issues in CSP methodology. We also provide an overview of the basic theory and main features of CALYPSO and emphasize several effective strategies in the CALYPSO methodology to achieve a good balance between exploration and exploitation. We showcase two exemplary cases of the theory-driven discovery of high-temperature superconducting superhydrides and a select group of atypical compounds, where CSP plays a significant role in guiding experimental synthesis toward the discovery of new materials. We finally conclude by offering perspectives on major outstanding issues and promising opportunities for further CSP research.

Machine learning accelerated random structure searching: Application to yttrium superhydrides.

The search for new superhydrides, promising materials for both hydrogen storage and high temperature superconductivity, made great progress, thanks to atomistic simulations and Crystal Structure Prediction (CSP) algorithms. When they are combined with Density Functional Theory (DFT), these methods are highly reliable and often match a great part of the experimental results. However, systems of increasing complexity (number of atoms and chemical species) become rapidly challenging as the number of minima to explore grows exponentially with the number of degrees of freedom in the simulation cell. An efficient sampling strategy preserving a sustainable computational cost then remains to be found. We propose such a strategy based on an active-learning process where machine learning potentials and DFT simulations are jointly used, opening the way to the discovery of complex structures. As a proof of concept, this method is applied to the exploration of tin crystal structures under various pressures. We showed that the α phase, not included in the learning process, is correctly retrieved, despite its singular nature of bonding. Moreover, all the expected phases are correctly predicted under pressure (20 and 100GPa), suggesting the high transferability of our approach. The method has then been applied to the search of yttrium superhydrides (YHx) crystal structures under pressure. The YH6 structure of space group Im-3m is successfully retrieved. However, the exploration of more complex systems leads to the appearance of a large number of structures. The selection of the relevant ones to be included in the active learning process is performed through the analysis of atomic environments and the clustering algorithm. Finally, a metric involving a distance based on x-ray spectra is introduced, which guides the structural search toward experimentally relevant structures. The global process (active-learning and new selection methods) is finally considered to explore more complex and unknown YHx phases, unreachable by former CSP algorithms. New complex phases are found, demonstrating the ability of our approach to push back the exponential wall of complexity related to CSP.

New stable structures of OsN4 predicted using first-principles calculations

ABSTRACT The crystal structure prediction algorithm has been performed using the swarm-intelligence-based CALYPSO method combined with density functional theory. The P4/mmm phase and R-3c phase are found for potential superhard OsN4, energetically much superior to the previously proposed Pbca-type structure. It is confirmed that the stable ground-state structure of OsN4 is the P4/mmm phase. More importantly, the phase transformation is firstly found from the P4/mmm phase to the R-3c phase at nearly 65.3 GPa. And the two phases of the OsN4 not only have the high bulk and shear modulus but also the low Poisson’s ratio. This suggests that the OsN4 compound has the potential to be a low-compression material. According to a detailed analysis of the density of states and electronic local functions, it is revealed that the covalent bonding of Os–N and N–N are responsible for their structural stability and high hardness.

TCSP: a Template-Based Crystal Structure Prediction Algorithm for Materials Discovery.

Fast and accurate crystal structure prediction (CSP) algorithms and web servers are highly desirable for the exploration and discovery of new materials out of the infinite chemical design space. However, currently, the computationally expensive first-principles calculation-based CSP algorithms are applicable to relatively small systems and are out of reach of most materials researchers. Several teams have used an element substitution approach for generating or predicting new structures, but usually in an ad hoc way. Here we develop a template-based crystal structure prediction (TCSP) algorithm and its companion web server, which makes this tool accessible to all materials researchers. Our algorithm uses elemental/chemical similarity and oxidation states to guide the selection of template structures and then rank them based on the substitution compatibility and can return multiple predictions with ranking scores in a few minutes. A benchmark study on the 98290 formulas of the Materials Project database using leave-one-out evaluation shows that our algorithm can achieve high accuracy (for 13145 target structures, TCSP predicted their structures with root-mean-square deviation < 0.1) for a large portion of the formulas. We have also used TCSP to discover new materials of the Ga-B-N system, showing its potential for high-throughput materials discovery. Our user-friendly web app TCSP can be accessed freely at www.materialsatlas.org/crystalstructure on our MaterialsAtlas.org web app platform.

Crystal Structure Prediction Using an Age-Fitness Multiobjective Genetic Algorithm and Coordination Number Constraints.

Crystal structure prediction (CSP) has emerged as one of the most important approaches for discovering new materials. CSP algorithms based on evolutionary algorithms and particle swarm optimization have discovered a great number of new materials. However, these algorithms based on ab initio calculation of free energy are inefficient. Moreover, they have severe limitations in terms of scalability. We recently proposed a promising crystal structure prediction method based on atomic contact maps, using global optimization algorithms to search for the Wyckoff positions by maximizing the match between the contact map of the predicted structure and the contact map of the true crystal structure. However, our previous contact-map-based CSP algorithms have two major limitations: (1) the loss of search capability due to getting trapped in local optima; (2) it only uses the connection of atoms in the unit cell to predict the crystal structure, ignoring the chemical environment outside the unit cell, which may lead to unreasonable coordination environments. Herein, we propose a novel multiobjective genetic algorithm for contact-map-based crystal structure prediction by optimizing three objectives, including contact map match accuracy, individual age, and coordination number match. Furthermore, we assign the age values to all the individuals of the GA and try to minimize the age, aiming to avoid the premature convergence problem. Our experimental results show that compared to our previous CMCrystal algorithm, our multiobjective crystal structure prediction algorithm (CMCrystalMOO) can reconstruct the crystal structure with higher quality and alleviate the problem of premature convergence. The source code is open sourced and can be accessed at https://github.com/usccolumbia/MOOCSP.

Intrinsic Valley Polarization in Computationally Discovered Two‐Dimensional Ferrovalley Materials: LaI2 and PrI2 Monolayers

AbstractFerrovalley materials with intrinsic valley polarization present a novel space for materials exploration suitable for valleytronic applications. Here, two Ferrovalley materials, LaI2 and PrI2 monolayers, exhibiting intrinsic valley polarizations of 28 and 35 meV, respectively, mediated by strong magnetic exchange interaction and spin‐orbit coupling are computationally discovered. The unconstrained crystal structure prediction algorithm is used to predict the structures of bulk LaI2 and PrI2, which are layered and analogous to the 2H phase of transition metal dichalcogenides. The monolayers have small exfoliation energy (smaller than MoS2) and exhibit dynamical, mechanical, and thermodynamical stability, advocating their experimental realization. Valley polarization under the effect of bi‐axial strain is preserved and can be used to enhance valley splitting. Finally, the anomalous hall properties of both the monolayers under the effect of in‐plane electric field are discussed. Both the materials exhibit significant anomalous Hall conductivity with proper tuning of the Fermi level.

High-pressure transformations of CaC2O5 - a full structural trend from double [CO3] triangles through the isolated group of [CO4] tetrahedra to framework and layered structures.

Over the past few years, the concept of carbonates, as the salts of MCO3 or composition with [CO3] triangles in the crystal structures, was sufficiently extended. In addition to carbonates, crystal structures with stoichiometry M3CO5, M2CO4 and MC2O5 were predicted and successfully synthesized. In the present study, based on density functional theory and crystal structure prediction algorithms, we found a novel structure of CaC2O5, namely Ca-pyrocarbonate with monoclinic symmetry Cc, which is one of the possible agents of the global carbon cycle. This structure is characterized by the isolated [C2O5] groups consisting of two [CO3] triangles connected through a common oxygen atom. The thermodynamic stability field of Ca-pyrocarbonate with respect to the decomposition reaction into calcium carbonate and carbon dioxide begins at a pressure of 10 GPa. As the pressure increases to 21 GPa, the structure of Ca-pyrocarbonate transforms into the recently synthesized tetragonal modification I4̄2d, in the structure of which carbon is in the sp3-hybridized state and [CO4] tetrahedra form isolated pyramidal [C4O10] anionic groups. At 59 GPa in the temperature range of 0-2500 K, CaC2O5-I4̄2d undergoes a phase transition to CaC2O5-Fdd2, with the framework structure of [CO4] tetrahedra. On further compression to about 80 GPa, the framework structure transforms into layered ones, C2 and Pc. In addition, we estimated the thermodynamic stability of CaC2O5 with respect to the minerals of the Earth's mantle. We found that CaC2O5 can coexist with bridgmanite up to pressures of 54 GPa at 300 K, where it reacts with the formation of a Ca-perovskite, magnesite, and solid CO2-V.

COPEX: co-evolutionary crystal structure prediction algorithm for complex systems

Crystal structure prediction has been widely used to accelerate the discovery of new materials in recent years. Up to this day, it remains a challenge to predict the stable stoichiometries and structures of ternary or more complex systems due to the explosive increase of the size of the chemical and configurational space. Numerous novel materials with a series of unique characteristics are expected to be found in this virgin territory while new algorithms to predict crystal structures in complex systems are urgently called for. Inspired by co-evolution in biology, here we propose a co-evolutionary algorithm, which we name COPEX, and which is based on the well-known evolutionary algorithm USPEX. Within this proposed algorithm, a few USPEX calculations for ternary systems and multiple for energetically-favored pseudobinary or fixed-composition systems are carried out in parallel, and co-evolution is achieved by sharing structural information on the fittest individuals among different USPEX sub-processes during the joint evolution. We have applied the algorithm to W–Cr–B, Mg–Si–O, and Hf–Ta–C, three very different systems, and many ternary compounds have been identified. Our results clearly demonstrate that the COPEX algorithm combines efficiency and reliability even for complex systems.

Nutraceuticals in Bulk and Dosage Forms: Analysis by 35Cl and 14N Solid-State NMR and DFT Calculations.

This study uses 35Cl and 14N solid-state NMR (SSNMR) spectroscopy and dispersion-corrected plane-wave density functional theory (DFT) calculations for the structural characterization of chloride salts of nutraceuticals in their bulk and dosage forms. For eight nutraceuticals, we measure the 35Cl EFG tensor parameters of the chloride ions and use plane-wave DFT calculations to elucidate relationships between NMR parameters and molecular-level structure, which provide rapid NMR crystallographic assessments of structural features. We employ both 35Cl direct excitation and 1H→35Cl cross-polarization methods to characterize a dosage form containing α-d-glucosamine HCl, observe possible impurity and/or adulterant phases, and quantify the weight percent of the active ingredient. To complement this, we also investigate 14N SSNMR spectroscopy and DFT calculations to characterize nitrogen atoms in the nutraceuticals. This includes a discussion of targeted acquisition experimental protocols (i.e., acquiring a select region of the overall pattern that features key discontinuities) that allow ultrawideline spectra to be acquired rapidly, even for unreceptive samples (i.e., those with long values of T1(14N), short values of T2eff(14N), or very broad patterns). It is hoped that these experimental and computational protocols will be useful for the characterization of various solid forms of nutraceuticals (i.e., salts, polymorphs, hydrates, solvates, cocrystals, amorphous solid dispersions, etc.), help detect impurity and counterfeit solid phases in dosage forms, and serve as a foundation for future NMR crystallographic studies of nutraceutical solid forms, including studies using ab initio crystal structure prediction algorithms.

Alkali Metal (Li, Na, and K) Orthocarbonates: Stabilization of sp3-Bonded Carbon at Pressures above 20 GPa

In the present work, based on the density functional theory and crystal structure prediction algorithms, we found novel structures of alkali metal orthocarbonates Li4CO4-C2/c, Na4CO4-C2/c, and K4CO4-P21/c. The pressure of thermodynamic stabilization of the obtained orthocarbonates with respect to decomposition into the corresponding carbonate and oxide ranges from 21 GPa (for K4CO4) to 25 GPa (for Li4CO4). All obtained structures contain isolated groups of [CO4]tetrahedra. The structures of lithium and sodium orthocarbonates were found to be isotypic. As well as alkaline earth orthocarbonates, orthocarbonates of alkali metals are structurally similar to orthosilicates of the same metal. Na4CO4-C2/c was found to be dynamically stable at ambient pressure, while all other structures are destabilized on decompression. In addition, the P–T phase diagrams of lithium, sodium, and potassium oxides have been calculated for the first time. All oxides have a high-pressure phase transition from the Fm3̅m (anti-fluorite) structure to the Pnma (anti-cotunnite) structure at 34 GPa for Li2O, at 10 GPa for Na2O, and at 5 GPa for K2O at low temperatures. In the Na2O and K2O systems, high-temperature phase transition to the P6̅2m (barringerite) structure was revealed at temperatures above 1300 and 650 K, respectively.