Crystal Structure Prediction Methods Research Articles

The seventh blind test of crystal structure prediction: structure generation methods

A seventh blind test of crystal structure prediction was organized by the Cambridge Crystallographic Data Centre featuring seven target systems of varying complexity: a silicon and iodine-containing molecule, a copper coordination complex, a near-rigid molecule, a cocrystal, a polymorphic small agrochemical, a highly flexible polymorphic drug candidate, and a polymorphic morpholine salt. In this first of two parts focusing on structure generation methods, many crystal structure prediction (CSP) methods performed well for the small but flexible agrochemical compound, successfully reproducing the experimentally observed crystal structures, while few groups were successful for the systems of higher complexity. A powder X-ray diffraction (PXRD) assisted exercise demonstrated the use of CSP in successfully determining a crystal structure from a low-quality PXRD pattern. The use of CSP in the prediction of likely cocrystal stoichiometry was also explored, demonstrating multiple possible approaches. Crystallographic disorder emerged as an important theme throughout the test as both a challenge for analysis and a major achievement where two groups blindly predicted the existence of disorder for the first time. Additionally, large-scale comparisons of the sets of predicted crystal structures also showed that some methods yield sets that largely contain the same crystal structures.

Two-dimensional Sc2O3 monolayer with tunable ultrawide bandgap for solar-blind ultraviolet photodetector

A novel 2D scandia (Sc2O3) monolayer was identified using an evolutionary algorithm-based crystal structure prediction method. The Sc2O3 monolayer exhibits a P3‾m1 symmetry and excellent energetic, thermal, dynamical, and mechanical stability, as well as good mechanical flexibility. The monolayer possesses an ultrawide indirect band gap of 6.246 eV. The monolayer is transparent in the visible light zone, while the large exciton effect leads to significant absorption in the solar-blind and vacuum ultraviolet regions. The band gap of this monolayer can be reduced monotonically by external biaxial tensile strain, resulting in the absorption spectrum covering the entire solar blind spectral region when the load reaches 5.0 %. Additionally, the monolayer has an ultra-high in-plane dielectric constant of approximately 50. The superior stability, flexibility, and strain-tunable electronic and optical properties, as well as the ultra-high dielectric constant, suggest its potential application in a solar-blind photodetector in harsh environments.

Emergence of superconductivity and superionicity in the electride [formula omitted]La under extreme conditions

Superconducting electrides, a unique type of conventional superconductors, have recently attracted considerable attention. Inspired by the discovery of high critical temperature (Tc) in lanthanum hydrides and the feasibility of forming electrides in lithium-based compounds, we have conducted a systematic investigation the phase diagram and superconductivity of Li-La alloys under high pressure. Using the crystal structure prediction method and first-principles calculations, we uncovered three pressure-stabilized compounds with stoichiometries LiLa3, LiLa2 and Li6La. All three compounds exhibit metallic behavior with electrons transferred from Li to La atoms. Notably, Li6La emerges as a prototypical superconducting electride with Tc of 11.6 K at 350 GPa, which increases to 16.3 K as pressure decreases to 200 GPa. Electron–phonon analysis reveal that the enhancement of superconductivity mainly originates from the coupling between the increased interstitial quasiatoms (ISQs) and low-frequencies phonons. Additionally, akin to lanthanum hydrides, Li6La is predicted to enter a superionic phase characterized by high lithium diffusion coefficients under high pressure and temperature. Our findings indicate the coexistence of superconductivity and superionicity in the electride Li6La, which may prompt further experimental investigations.

Assessment of the exchange-hole dipole moment dispersion correction for the energy ranking stage of the seventh crystal structure prediction blind test.

The seventh blind test of crystal structure prediction (CSP) methods substantially increased the level of complexity of the target compounds relative to the previous tests organized by the Cambridge Crystallographic Data Centre. In this work, the performance of density-functional methods is assessed using numerical atomic orbitals and the exchange-hole dipole moment dispersion correction (XDM) for the energy-ranking phase of the seventh blind test. Overall, excellent performance was seen for the two rigid molecules (XXVII, XXVIII) and for the organic salt (XXXIII). However, for the agrochemical (XXXI) and pharmaceutical (XXXII) targets, the experimental polymorphs were ranked fairly high in energy amongst the provided candidate structures and inclusion of thermal free-energy corrections from the lattice vibrations was found to be essential for compound XXXI. Based on these results, it is proposed that the importance of vibrational free-energy corrections increases with the number of rotatable bonds.

Quantitatively Deciphering the Local Structure and Luminescence Spectroscopy of Pr3+-Doped Yttrium Lithium Fluoride.

Praseodymium (Pr3+)-doped LiYF4 nanophosphors have garnered significant interest for their potential applications in lasers, phosphors, and quantum memories. However, there remains a lack of comprehensive research on the local coordination environment and luminescence spectroscopy of Pr3+:LiYF4 nanocrystals. This study presents the first investigation of the ground-state structure of Pr3+:LiYF4 crystals by employing the crystal structure prediction method, and a [PrF8]5- ligand complex with S4 local symmetry is determined. The complete energy levels of the Pr3+ ions in LiYF4 nanocrystals are unveiled by using our newly developed well-established parametrization matrix diagonalization method. A novel set of free-ion and crystal-field parameters is derived through a good simulation with 45 experimental energy levels. Many of the emissions of Pr3+-doped LiYF4 are successfully reproduced based on Judd-Ofelt theory, and these transitions are comparable to the experimental ones. Moreover, two new prominent emission bands with their peaks at 675 and 849 nm originating from 1I6 → 3F4 and 1I6 → 1G4 transitions, respectively, are predicted by us for the first time. This study could provide a feasible method to search for practical laser transition channels of solid-state lasers based on Pr3+: LiYF4 nanophosphors.

A Machine-Learning-Assisted Crystalline Structure Prediction Framework To Accelerate Materials Discovery.

Modern crystal structure prediction methods based on structure generation algorithms and first-principles calculations play important roles in the design of new materials. However, the cost of these methods is very expensive because their success mostly relies on the efficient sampling of structures and the accurate evaluation of energies for those sampled structures. Herein, we develop a Machine-learning-Assisted CRYStalline Materials sAmpling sysTem (MAXMAT) aiming to accelerate the prediction of new crystal structures. For a given chemical composition, MAXMAT can generate efficient crystal structures with the help of a Python package for crystal structure generation (PyXtal) and can quickly evaluate the energies of these generated structures using a well-developed machine learning interaction potential model (M3GNET). We have used MAXMAT to perform crystal structure searches for three different chemical systems (TiO2, MgAl2O4, and BaBOF3) to test its accuracy and efficiency. Furthermore, we apply MAXMAT to predict new nonlinear optical materials, suggesting several thermodynamically synthesizable structures with high performance in LiZnGaS3 and CaBOF3 systems.

Observation of Iron with Eight Coordination in Iron Trifluoride under High Pressure.

The chemistry of hypercoordination has been a subject of fundamental interest, especially for understanding structures that challenge conventional wisdom. The small ionic radii of Fe ions typically result in coordination numbers of 4 or 6 in stable Fe-bearing ionic compounds. While 8-coordinated Fe has been observed in highly compressed oxides, the pursuit of hypercoordinated Fe still faces significant challenges due to the complexity of synthesizing the anticipated compound with another suitable anion. Through first-principles simulation and advanced crystal structure prediction methods, we predict that an orthorhombic phase of FeF3 with exclusively 8-coordinated Fe is energetically stable above 18 GPa-a pressure more feasibly achieved compared to oxides. Inspired by this theoretical result, we conducted extensive experiments using a laser-heated diamond anvil cell technique to investigate the crystal structures of FeF3 at high-pressure conditions. We successfully synthesized the predicted orthorhombic phase of FeF3 at 46 GPa, as confirmed by in situ experimental X-ray diffraction data. This work establishes a new ionic compound featuring rare 8-coordinated Fe in a simple binary Fe-bearing system and paves the way for discovering Fe hypercoordination in similar systems.

Observation of Iron with Eight Coordination in Iron Trifluoride under High Pressure

AbstractThe chemistry of hypercoordination has been a subject of fundamental interest, especially for understanding structures that challenge conventional wisdom. The small ionic radii of Fe ions typically result in coordination numbers of 4 or 6 in stable Fe‐bearing ionic compounds. While 8‐coordinated Fe has been observed in highly compressed oxides, the pursuit of hypercoordinated Fe still faces significant challenges due to the complexity of synthesizing the anticipated compound with another suitable anion. Through first‐principles simulation and advanced crystal structure prediction methods, we predict that an orthorhombic phase of FeF3 with exclusively 8‐coordinated Fe is energetically stable above 18 GPa—a pressure more feasibly achieved compared to oxides. Inspired by this theoretical result, we conducted extensive experiments using a laser‐heated diamond anvil cell technique to investigate the crystal structures of FeF3 at high‐pressure conditions. We successfully synthesized the predicted orthorhombic phase of FeF3 at 46 GPa, as confirmed by in situ experimental X‐ray diffraction data. This work establishes a new ionic compound featuring rare 8‐coordinated Fe in a simple binary Fe‐bearing system and paves the way for discovering Fe hypercoordination in similar systems.

Quasi-2D spin-Peierls transition through interstitial anionic electrons in K(NH3)2

Electron–phonon interactions and electron–electron correlations represent two crucial facets of condensed matter physics. For instance, in a half-filled spin-1/2 anti-ferromagnetic chain, the lattice dimerization induced by electron-nucleus interaction can be intensified by onsite Coulomb repulsion, resulting in a spin-Peierls state. Through first-principles calculations and crystal structure prediction methods, we have identified that under mild pressures, potassium and ammonia can form stable compounds: R3¯m K(NH3)2, Pm3¯m K(NH3)2, and Cm K2(NH3)3. Our predictions suggest that the R3¯m K(NH3)2 exhibits electride characteristics, marked by the formation of interstitial anionic electrons (IAEs) in the interlayer space. These IAEs are arranged in quasi-two-dimensional triangular arrays. With increasing pressure, the electronic van-Hove singularity shifts toward the Fermi level, resulting in an augmented density of states and the onset of both Peierls and magnetic instabilities. Analyzing these instabilities, we determine that the ground state of the R3¯m K(NH3)2 is the dimerized P21/m phase with zigzag-type anti-ferromagnetic IAEs. This state can be described by the triangular-lattice antiferromagnetic Heisenberg model with modulated magnetic interactions. Furthermore, we unveil the coexistence and positive interplay between magnetic and Peierls instability, constituting a scenario of spin-Peierls instability unprecedented in realistic 2D materials, particularly involving IAEs. This work provides valuable insights into the coupling of IAEs with the adjacent lattice and their spin correlations in quantum materials.

Cocrystals of polynitrogen compounds as a basis for promising energetic materials: crystal structure prediction methods, their experimental verification, and evaluation of cocrystal properties

Cocrystals of polynitrogen compounds as a basis for promising energetic materials: crystal structure prediction methods, their experimental verification, and evaluation of cocrystal properties

Machine learning assisted crystal structure prediction made simple

Crystal structure prediction (CSP) plays a crucial role in condensed matter physics and materials science, with its importance evident not only in theoretical research but also in the discovery of new materials and the advancement of novel technologies. However, due to the diversity and complexity of crystal structures, trial-and-error experimental synthesis is time-consuming, labor-intensive, and insufficient to meet the increasing demand for new materials. In recent years, machine learning (ML) methods have significantly boosted CSP. In this review, we present a comprehensive review of the ML models applied in CSP. We first introduce the general steps for CSP and highlight the bottlenecks in conventional CSP methods. We further discuss the representation of crystal structures and illustrate how ML-assisted CSP works. In particular, we review the applications of graph neural networks (GNNs) and ML force fields in CSP, which have been demonstrated to significantly speed up structure search and optimization. In addition, we provide an overview of advanced generative models in CSP, including variational autoencoders (VAEs), generative adversarial networks (GANs), and diffusion models. Finally, we discuss the remaining challenges in ML-assisted CSP.

Accessing forbidden phases

Abstract Thanks to the development of quantum mechanics-based crystal structure prediction methods in the past decade, numerous new compounds with low temperature thermodynamic stability, mainly binary intermetallic compounds, have been predicted. Differing from conventional alloy materials, the synthesis of these low temperature stable compounds may be impossible relying on traditional thermal activation methods since thermally activated atomic diffusion at low temperatures is so slow that phase formation may require cosmic-scale time. Strikingly, it has been shown that some special experimental methods can successfully synthesize low temperature stable compounds by introducing a large number of vacancies and defects into the material to enable atomic rearrangement and simultaneously increasing the phase transformation driving force to accelerate the reaction kinetics. This review summarizes the predictions of compounds that have not been experimentally reported to be stable at low temperatures and provides some experimental approaches that can be used for future synthesis. We describe the basic thermodynamics and kinetics of phase formation, show how compound formation is constrained at low temperatures, and illustrate that the formation of some compounds is nearly impossible without enhanced kinetics.

Combined First-Principles and Experimental Investigation into the Reactivity of Codeposited Chromium-Carbon under Pressure.

High-pressure synthesis in the diamond anvil cell suffers from the lack of a general approach for the control of precursor stoichiometry and homogeneity. Here, we present results from a new method we have developed that uses magnetron cosputtering to prepare stoichiometrically precise and atomically mixed amorphous films of Cr:C. Laser-heated diamond anvil cell experiments carried out on a flake of this sample at pressures between 13.5 and 24.3 GPa lead to the observation of Cr3C (Pnma) over the entire pressure range-in good agreement with our in-house theoretical predictions-but also reveal two other metastable phases that were not expected: a novel monoclinic chromium carbide phase and the NaCl-type CrC (Fm3̅m) phase. The unexpected stability of CrC is investigated by using first-principles methods, revealing a large stabilizing effect tied to substoichiometry at the carbon site. These results offer an important case study into the current limitations of crystal structure prediction methods with regard to phase complexity and bolster the growing need for advanced theoretical approaches that can more completely survey experimentally unexplored phase space.

Structurally Constrained Evolutionary Algorithm for the Discovery and Design of Metastable Phases.

Metastable materials are abundant in nature and technology, showcasing remarkable properties that inspire innovative materials design. However, traditional crystal structure prediction methods, which rely solely on energetic factors to determine a structure's fitness, are not suitable for predicting the vast number of potentially synthesizable phases that represent a local minimum corresponding to a state in thermodynamic equilibrium. Here, we present a new approach for the prediction of metastable phases with specific structural features and interface this method with the XtalOpt evolutionary algorithm. Our method relies on structural features that include the local crystalline order (e.g, the coordination number or chemical environment), and symmetry (e.g, Bravais lattice and space group) to filter the breeding pool of an evolutionary crystal structure search. The effectiveness of this approach is benchmarked on three known metastable systems: XeN8, with a two-dimensional polymeric nitrogen sublattice, brookite TiO2, and a high pressure BaH4 phase, which was recently characterized. Additionally, a newly predicted metastable melaminate salt, P1̅ WC3N6, was found to possess an energy that is lower than that of two phases proposed in a recent computational study. The method presented here could help in identifying the structures of compounds that have already been synthesized, and in developing new synthesis targets with desired properties.

Stability and Equilibrium Structures of Unknown Ternary Metal Oxides Explored by Machine-Learned Potentials.

Ternary metal oxides are crucial components in a wide range of applications and have been extensively cataloged in experimental materials databases. However, there still exist cation combinations with unknown stability and structures of their compounds in oxide forms. In this study, we employ extensive crystal structure prediction methods, accelerated by machine-learned potentials, to investigate these untapped chemical spaces. We examine 181 ternary metal oxide systems, encompassing most cations except for partially filled 3d or f shells, and determine their lowest-energy crystal structures with representative stoichiometry derived from prevalent oxidation states or recommender systems. Consequently, we discover 45 ternary oxide systems containing stable compounds against decomposition into binary or elemental phases, the majority of which incorporate noble metals. Comparisons with other theoretical databases highlight the strengths and limitations of informatics-based material searches. With a relatively modest computational resource requirement, we contend that heuristic-based structure searches, as demonstrated in this study, offer a promising approach for future materials discovery endeavors.

Evolutionary Algorithm-Based Crystal Structure Prediction of CuxZnyOz Ternary Oxides.

Binary zinc(II) oxide (ZnO) and copper(II) oxide (CuO) are used in a number of applications, including optoelectronic and semiconductor applications. However, no crystal structures have been reported for ternary Cu-Zn-O oxides. In that context, we investigated the structural characteristics and thermodynamics of CuxZnyOz ternary oxides to map their experimental feasibility. We combined evolutionary crystal structure prediction and quantum chemical methods to investigate potential CuxZnyOz ternary oxides. The USPEX algorithm and density functional theory were used to screen over 4000 crystal structures with different stoichiometries. When comparing compositions with non-magnetic CuI ions, magnetic CuII ions, and mixed CuI-CuII compositions, the magnetic Cu2Zn2O4 system is thermodynamically the most favorable. At ambient pressures, the thermodynamically most favorable ternary crystal structure is still 2.8 kJ/mol per atom higher in Gibbs free energy compared to experimentally known binary phases. The results suggest that thermodynamics of the hypothetical CuxZnyOz ternary oxides should also be evaluated at high pressures. The predicted ternary materials are indirect band gap semiconductors.

Polymeric nitrogen in alkaline earth metal N-rich nitrides (MN2, M = Be, Mg, Ca, Sr, and Ba): A first-principles study

The distinctive chemical and physical characteristics of all-nitrogen salts have attracted significant interest. Some stable polymeric nitrogen with novel chemical bonding patterns are predicted using first-principles calculations and crystal structure prediction methods. However, the element effects of the chemical bonding pattern and structural stability are still unclear. Here, we select the cmcm-MgN2 structure, which is predicted to be free energy favorable between 5 and 40 GPa, and substitute the Mg atoms with other alkaline earth elements (beryllium, calcium, strontium, and barium) to systematically study the influence of the elements on the properties of the compound. We found that the N = N bonds are all covalent, but have metallic properties in BeN2 and BaN2, semiconductor properties in MgN2, CaN2, and SrN2 and the width of the indirect band gap increases with increasing pressure. The charge transfer between metal and N atoms is closely related to the electronegativity of metal elements. Furthermore, thermal stability is investigated based on the phonon spectrum and the imaginary phonons of unstable systems correspond to special vibrational modes of the N = N bond. The anisotropy of lattice constant compressibility is found to be a signal of structural thermal instability. Our results shed some light on the influence of elements on the physical properties of all-nitrogen salts under high pressure, thus accelerating the prediction of crystal structure.

Mapping superconductivity in high-pressure hydrides: The Superhydra project

The discovery of high-${T}_{c}$ conventional superconductivity in high-pressure hydrides has helped establish computational methods as a formidable tool to guide material discoveries in a field traditionally dominated by serendipitous experimental search. This paves the way to an ever-increasing use of data-driven approaches to the study and design of superconductors. In this work, we propose a new adaptive method to generate meaningful datasets of superconductors, based on element substitution into a small set of representative structural templates, generated by crystal structure prediction methods---adapted high-throughput approach. Our approach realizes an optimal compromise between structural variety and computational efficiency and can be easily generalized to other elements and compositions. As a first application, we apply it to binary hydrides at high pressure, realizing a database of 880 hypothetical structures, characterized with a set of electronic, vibrational, and chemical descriptors. In our Superhydra Database, 139 structures are superconducting according to the McMillan-Allen-Dynes approximation. Studying the distribution of ${T}_{c}$ and other properties across the database with advanced statistical and visualization techniques, we are able to obtain comprehensive material maps of the phase space of binary hydrides. The Superhydra database can be thought as a first step of a generalized effort to map conventional superconductivity.

MAGUS: machine learning and graph theory assisted universal structure searcher.

Crystal structure predictions based on first-principles calculations have gained great success in materials science and solid state physics. However, the remaining challenges still limit their applications in systems with a large number of atoms, especially the complexity of conformational space and the cost of local optimizations for big systems. Here, we introduce a crystal structure prediction method, MAGUS, based on the evolutionary algorithm, which addresses the above challenges with machine learning and graph theory. Techniques used in the program are summarized in detail and benchmark tests are provided. With intensive tests, we demonstrate that on-the-fly machine-learning potentials can be used to significantly reduce the number of expensive first-principles calculations, and the crystal decomposition based on graph theory can efficiently decrease the required configurations in order to find the target structures. We also summarized the representative applications of this method on several research topics, including unexpected compounds in the interior of planets and their exotic states at high pressure and high temperature (superionic, plastic, partially diffusive state, etc.); new functional materials (superhard, high-energy-density, superconducting, photoelectric materials), etc. These successful applications demonstrated that MAGUS code can help to accelerate the discovery of interesting materials and phenomena, as well as the significant value of crystal structure predictions in general.

An unexpectedly stable Y2B5 compound with the fractional stoichiometry under ambient pressure

Boron-rich yttrium borides are an exceptional group of compounds not only with excellent mechanical properties, but also with particular superconducting and thermoelectric properties. Although the Y–B compounds with integral components have been extensively investigated experimentally and theoretically, the yttrium borides with the fractional stoichiometries are rarely observed. Herein, utilizing a combination of the CALYPSO method for crystal structure prediction and first-principles calculations, we made an investigation on a broad range of stoichiometries of yttrium borides. An extraordinary stable Y2B5 compound possessing the fractional stoichiometry with the monoclinic P121/c1 phase is firstly uncovered. Structurally, the P121/c1-Y2B5 crystalline consists of the distorted B6 octahedrons and seven-member B rings. Remarkably, the B–B covalent network following the increment of the boron content in six concerned yttrium borides undergoes an increasing dimension, quasi one-dimensional chain → two-dimensional B ring → a combination of two-dimensional B ring and three-dimensional B6 octahedron → three-dimensional B24 cage. According to a microscopic hardness model, P121/c1–Y2B5 is considered as an incompressible and hard material with the hardness of 18.83 GPa. More importantly, Fm-3 m-YB12 can be classified into an ultra-incompressible material with the appreciable Vickers hardness of 33.16 GPa. The present consequences can provide important insights for understanding the complex crystal structures of boron-rich yttrium borides and stimulate further experimental synthesis of novel multifunctional materials with the fractional compositions.