Crystal Structure Prediction Methods Research Articles

Phase Transition and Physical Properties of InS**Supported by the National Natural Science Foundation of China under Grant Nos. 11404099, 11304140, 11147167 and Funds of Outstanding Youth of Henan Polytechnic University, China under Grant No. J2014–05

Using the crystal structure prediction method based on particle swarm optimization algorithm, three phases (Pnnm, C2/m and Pm-3m) for InS are predicted. The new phase Pm-3m of InS under high pressure is firstly reported in the work. The structural features and electronic structure under high pressure of InS are fully investigated. We predicted the stable ground-state structure of InS was the Pnnm phase and phase transformation of InS from Pnnm phase to Pm-3m phase is firstly found at the pressure of about 29.5 GPa. According to the calculated enthalpies of InS with four structures in the pressure range from 20 GPa to 45 GPa, we find the C2/m phase is a metastable phase. The calculated band gap value of about 2.08 eV for InS with Pnnm structure at 0 GPa agrees well with the experimental value. Moreover, the electronic structure suggests that the C2/m and Pm-3m phase are metallic phases.

Crystal structure prediction accelerated by Bayesian optimization

We propose a crystal structure prediction method based on Bayesian optimization. Our method is classified as a selection-type algorithm which is different from evolution-type algorithms such as an evolutionary algorithm and particle swarm optimization. Crystal structure prediction with Bayesian optimization can efficiently select the most stable structure from a large number of candidate structures with a lower number of searching trials using a machine learning technique. Crystal structure prediction using Bayesian optimization combined with random search is applied to known systems such as NaCl and ${\mathrm{Y}}_{2}{\mathrm{Co}}_{17}$ to discuss the efficiency of Bayesian optimization. These results demonstrate that Bayesian optimization can significantly reduce the number of searching trials required to find the global minimum structure by 30--40% in comparison with pure random search, which leads to much less computational cost.

Computational modelling of solvent effects in a prolific solvatomorphic porous organic cage.

Crystal structure prediction methods can enable the in silico design of functional molecular crystals, but solvent effects can have a major influence on relative lattice energies, sometimes thwarting predictions. This is particularly true for porous solids, where solvent included in the pores can have an important energetic contribution. We present a Monte Carlo solvent insertion procedure for predicting the solvent filling of porous structures from crystal structure prediction landscapes, tested using a highly solvatomorphic porous organic cage molecule, CC1. Using this method, we can understand why the predicted global energy minimum structure for CC1 is never observed from solvent crystallisation. We also explain the formation of three different solvatomorphs of CC1 from three structurally-similar chlorinated solvents. Calculated solvent stabilisation energies are found to correlate with experimental results from thermogravimetric analysis, suggesting a future computational framework for a priori materials design that factors in solvation effects.

Crystal structure prediction of flexible pharmaceutical-like molecules: density functional tight-binding as an intermediate optimisation method and for free energy estimation.

Successful methodologies for theoretical crystal structure prediction (CSP) on flexible pharmaceutical-like organic molecules explore the lattice energy surface to find a set of plausible crystal structures. The initial search stages of CSP studies use relatively simple lattice energy approximations as hundreds of thousands of minima have to be considered. These generated crystal structures often have poor molecular geometries, as well as inaccurate lattice energy rankings, and performing reasonably accurate but computationally affordable optimisations of the crystal structures generated in a search would be highly desirable. Here, we seek to explore whether semi-empirical quantum-mechanical methods can perform this task. We employed the dispersion-corrected tight-binding Hamiltonian (DFTB3-D3) to relax all the inter- and intra-molecular degrees of freedom of several thousands of generated crystal structures of five pharmaceutical-like molecules, saving a large amount of computational effort compared to earlier studies. The computational cost scales better with molecular size and flexibility than other CSP methods, suggesting that it could be extended to even larger and more flexible molecules. On average, this optimisation improved the average reproduction of the eight experimental crystal structures (RMSD15) and experimental conformers (RMSD1) by 4% and 23%, respectively. The intermolecular interactions were then further optimised using distributed multipoles, derived from the molecular wave-functions, to accurately describe the electrostatic components of the intermolecular energies. In all cases, the experimental crystal structures are close to the top of the lattice energy ranking. Phonon calculations on some of the lowest energy structures were also performed with DFTB3-D3 methods to calculate the vibrational component of the Helmholtz free energy, providing further insights into the solid-state behaviour of the target molecules. We conclude that DFTB3-D3 is a cost-effective method for optimising flexible molecules, bridging the gap between the approximate methods used in CSP searches for generating crystal structures and more accurate methods required in the final energy ranking.

Exchange-Hole Dipole Dispersion Model for Accurate Energy Ranking in Molecular Crystal Structure Prediction II: Nonplanar Molecules.

The crystal structure prediction (CSP) of a given compound from its molecular diagram is a fundamental challenge in computational chemistry with implications in relevant technological fields. A key component of CSP is the method to calculate the lattice energy of a crystal, which allows the ranking of candidate structures. This work is the second part of our investigation to assess the potential of the exchange-hole dipole moment (XDM) dispersion model for crystal structure prediction. In this article, we study the relatively large, nonplanar, mostly flexible molecules in the first five blind tests held by the Cambridge Crystallographic Data Centre. Four of the seven experimental structures are predicted as the energy minimum, and thermal effects are demonstrated to have a large impact on the ranking of at least another compound. As in the first part of this series, delocalization error affects the results for a single crystal (compound X), in this case by detrimentally overstabilizing the π-conjugated conformation of the monomer. Overall, B86bPBE-XDM correctly predicts 16 of the 21 compounds in the five blind tests, a result similar to the one obtained using the best CSP method available to date (dispersion-corrected PW91 by Neumann et al.). Perhaps more importantly, the systems for which B86bPBE-XDM fails to predict the experimental structure as the energy minimum are mostly the same as with Neumann's method, which suggests that similar difficulties (absence of vibrational free energy corrections, delocalization error,...) are not limited to B86bPBE-XDM but affect GGA-based DFT-methods in general. Our work confirms B86bPBE-XDM as an excellent option for crystal energy ranking in CSP and offers a guide to identify crystals (organic salts, conjugated flexible systems) where difficulties may appear.

Oxysulfide Lialso: A Lithium Superionic Conductor from First Principles

Searching for lithium superionic conductors attracts a lot of attention over the past few decades, especially for the development of all-solid-state lithium batterie. So far, the only kinds of solid material with ionic conductivity over 10-2 S/cm at room temperature are among sulfide materials (Li10GeP2S12 and its derivative, Li7P3S11 glass-ceramic, and Li9.54Si1.74P1.44S11.7Cl0.3). However, sulfides generally suffer from high sensitive to moisture and poor stability of solid electrolyte/oxide cathode interfaces. Compared with sulfides, the oxide SEs have significantly better chemical and electrochemical stability, whereas the highest ionic conductivity achieved in them is still one order of magnitude lower than those of liquid electrolytes. To combine the advantages of sulfides and oxides, anion mixing is expected to be a promising strategy to design the lithium superionic conductors with improved stabilities and high ionic conductivity. To the best of our knowledge, there is still no discovery of crystalline oxysulfide for SEs used in lithium batteries. In this work for the first time we identify a new layered oxysulfide LiAlSO in orthorhombic structure as a novel lithium superionic conductor through first-principles calculations and crystal structure prediction techniques. Two kinds of stacking sequences of AlS2O2 layer are found in different temperature ranges. Phonon and molecular dynamics simulations verify their dynamic stabilities, and wide band gaps up to 5.6 eV are found by electronic structure calculations. The lithium migration energy barrier simulations reveal the collective interstitial-host ion “kick-off” hopping mode with barriers lower than 50 meV as the dominating conduction mechanism for LiAlSO, making it a promising solid state electrolyte in lithium secondary batteries with fast ionic conductivity and wide electrochemical window. This is a first attempt that the lithium superionic conductors are designed by crystal structure prediction method and may help explore other mixed-anion battery materials. Acknowledgment We acknowledge the National Natural Science Foundation of China (Grant No. 11234013), ‘‘863’’ Project (Grant No. 2015AA034201), and the Beijing S&T Project (Grant No. D161100002416003) for financial support and the Shanghai Supercomputer Center for providing computing resources. We would like to express our thanks to Prof. Jiawang Hong (Beijing Institute of Technology) for his fruitful discussion.

Tetrahedron-tiling method for crystal structure prediction

Reliable and robust methods of predicting the crystal structure of a compound, based only on its chemical composition, is crucial to the study of materials and their applications. Despite considerable ongoing research efforts, crystal structure prediction remains a challenging problem that demands large computational resources. Here we propose an efficient approach for first-principles crystal structure prediction. The new method explores and finds crystal structures by tiling together elementary tetrahedra that are energetically favorable and geometrically matching each other. This approach has three distinguishing features: a favorable building unit, an efficient calculation of local energy, and a stochastic Monte Carlo simulation of crystal growth. By applying the method to the crystal structure prediction of various materials, we demonstrate its validity and potential as a promising alternative to current methods.

High-pressure phase diagram, structural transitions, and persistent nonmetallicity of BaBiO3 : Theory and experiment

${\mathrm{BaBiO}}_{3}$ is a mixed-valence perovskite, which escapes the metallic state through a Bi valence (and Bi-O bond) disproportionation or CDW distortion, resulting in a semiconductor with a gap of 0.8 eV at zero pressure. The evolution of structural and electronic properties at high pressure is, however, largely unknown. Pressure, one might have hoped, could reduce the disproportionation, making the two Bi ions equivalent and bringing the system closer to metallicity or even to superconductivity, such as is attained at ambient pressure upon metal doping. We address the high-pressure phase diagram of pristine ${\mathrm{BaBiO}}_{3}$ by ab initio DFT calculations based on GGA and hybrid functionals in combination with crystal structure prediction methods based on evolutionary algorithms, molecular dynamics, and metadynamics. The calculated phase diagram from 0 to 50 GPa indicates that pristine ${\mathrm{BaBiO}}_{3}$ resists metallization under pressure, undergoing instead at room temperature structural phase transitions from monoclinic I2/m to nearly tetragonal P-1 at 7 GPa, possibly to monoclinic C2/m at 27 GPa, and to triclinic P1 at 43 GPa. Remarkably, all these phases sustain and in fact increase the inequivalence of two Bi neighboring sites and of their Bi-O bonds and, in all cases except semimetallic C2/m, the associated insulating character. We then present high-pressure resistivity data, which generally corroborate these results, and show that the insulating character persists at least up to 80 GPa, suggesting that the C2/m phase is probably an artifact of the small computational cell.

Oxysulfide LiAlSO: A Lithium Superionic Conductor from First Principles.

Through first-principles calculations and crystal structure prediction techniques, we identify a new layered oxysulfide LiAlSO in orthorhombic structure as a novel lithium superionic conductor. Two kinds of stacking sequences of layers of AlS_{2}O_{2} are found in different temperature ranges. Phonon and molecular dynamics simulations verify their dynamic stabilities, and wide band gaps up to 5.6eV are found by electronic structure calculations. The lithium migration energy barrier simulations reveal the collective interstitial-host ion "kick-off" hopping mode with barriers lower than 50meV as the dominating conduction mechanism for LiAlSO, indicating it to be a promising solid-state electrolyte in lithium secondary batteries with fast ionic conductivity and a wide electrochemical window. This is a first attempt in which the lithium superionic conductors are designed by the crystal structure prediction method and may help explore other mixed-anion battery materials.

Ground state structure of high-energy-density polymeric carbon monoxide

Crystal structure prediction methods and first-principles calculations have been used to explore low-energy structures of carbon monoxide (CO). Contrary to the standard wisdom, the most stable structure of CO at ambient pressure was found to be a polymeric structure of $Pna{2}_{1}$ symmetry rather than a molecular solid. This phase is formed from six-membered (four carbon + two oxygen) rings connected by C=C double bonds with two double-bonded oxygen atoms attached to each ring. Interestingly, the polymeric $Pna{2}_{1}$ phase of CO has a much higher energy density than trinitrotoluene (TNT). On compression to about 7 GPa, $Pna{2}_{1}$ is found to transform into another chainlike phase of $Cc$ symmetry which has similar ring units to $Pna{2}_{1}$. On compression to 12 GPa, it is energetically favorable for CO to polymerize into a purely single bonded $Cmca$ phase, which is stable over a wide pressure range and transforms into the previously known $Cmcm$ phase at around 100 GPa. Thermodynamic stability of these structures was verified using calculations with different density functionals, including hybrid and van der Waals corrected functionals.

Clathrate Structure Determination by Combining Crystal Structure Prediction with Computational and Experimental 129 Xe NMR Spectroscopy.

An approach is presented for the structure determination of clathrates using NMR spectroscopy of enclathrated xenon to select from a set of predicted crystal structures. Crystal structure prediction methods have been used to generate an ensemble of putative structures of o‐ and m‐fluorophenol, whose previously unknown clathrate structures have been studied by 129Xe NMR spectroscopy. The high sensitivity of the 129Xe chemical shift tensor to the chemical environment and shape of the crystalline cavity makes it ideal as a probe for porous materials. The experimental powder NMR spectra can be used to directly confirm or reject hypothetical crystal structures generated by computational prediction, whose chemical shift tensors have been simulated using density functional theory. For each fluorophenol isomer one predicted crystal structure was found, whose measured and computed chemical shift tensors agree within experimental and computational error margins and these are thus proposed as the true fluorophenol xenon clathrate structures.

The Structure of Glycine Dihydrate: Implications for the Crystallization of Glycine from Solution and Its Structure in Outer Space.

Glycine, the simplest amino acid, is also the most polymorphous. Herein, we report the structure determination of a long unknown phase of glycine, which was first reported by Pyne and Suryanarayanan in 2001. To date, this phase has only been prepared at 208 K as nanocrystals within ice. Through computational crystal-structure prediction and powder X-ray diffraction methods, we identified this elusive phase as glycine dihydrate (GDH), representing the first report on the structure of a hydrated glycine structure. The structure of GDH has important implications for the state of glycine in aqueous solution and the mechanisms of glycine crystallization. GDH may also be the form of glycine that comes to Earth from extraterrestrial sources.

Powder diffraction and crystal structure prediction identify four new coumarin polymorphs.

Coumarin, a simple, commodity chemical isolated from beans in 1820, has, to date, only yielded one solid state structure. Here, we report a rich polymorphism of coumarin grown from the melt. Four new metastable forms were identified and their crystal structures were solved using a combination of computational crystal structure prediction algorithms and X-ray powder diffraction. With five crystal structures, coumarin has become one of the few rigid molecules showing extensive polymorphism at ambient conditions. We demonstrate the crucial role of advanced electronic structure calculations including many-body dispersion effects for accurate ranking of the stability of coumarin polymorphs and the need to account for anharmonic vibrational contributions to their free energy. As such, coumarin is a model system for studying weak intermolecular interactions, crystallization mechanisms, and kinetic effects.

Exploration of crystal structures and phase transitions in Hf3N4

Using the adaptive genetic algorithm (AGA) crystal structure prediction method, we explored the stable/meta-stable phases of Hf3N4. A new ground-stage phase (C2/m) of Hf3N4 at ambient pressure was predicted. Calculated phonon dispersion and elastic constants of this phase showed it to be dynamically and mechanically stable. We also produced a pressure–temperature phase diagram of Hf3N4 that included the C2/m, orthorhombic Zr3N4-type (Pnam) and I3d phases. Our results revealed that increasing the pressure and temperature would transform the C2/m phase of Hf3N4 to the I3d and Pnam phases, respectively. Although the orthorhombic Zr3N4-type phase was indicated to be metastable over all pressures, the contributions from its larger vibrational entropies than for C2/m indicated it to be stable only between temperatures of ∼414 and ∼686 K at low pressure. The I3d structure was calculated to be stable at a wide range of temperatures at high pressure and at a wide range of pressures at high temperature, with this result being in good agreement with the experimental results.

Pharmaceutical polymorph control in a drug-mimetic supramolecular gel.

We report the synthesis of a bis(urea) gelator designed to specifically mimic the chemical structure of the highly polymorphic drug substance ROY. Crystallization of ROY from toluene gels of this gelator results in the formation of the metastable red form instead of the thermodynamic yellow polymorph. In contrast, all other gels and solution control experiments give the yellow form. Conformational and crystal structure prediction methods have been used to propose the structure of the gel and show that the templation of the red form by the targeted gel results from conformational matching of the gelator to the ROY substrate coupled with overgrowth of ROY onto the local periodic structure of the gel fibres.

Electronic structure and photocatalytic band offset of few-layer GeP2

Based on a sophisticated crystal structure prediction method, we propose two-dimensional (2D) GeP2in the tetragonal (T) phase never observed for other group IV–V compounds.

Accurate and efficient representation of intramolecular energy in ab initio generation of crystal structures. I. Adaptive local approximate models.

The global search stage of crystal structure prediction (CSP) methods requires a fine balance between accuracy and computational cost, particularly for the study of large flexible molecules. A major improvement in the accuracy and cost of the intramolecular energy function used in the CrystalPredictor II [Habgood et al. (2015). J. Chem. Theory Comput. 11, 1957-1969] program is presented, where the most efficient use of computational effort is ensured via the use of adaptive local approximate model (LAM) placement. The entire search space of the relevant molecule's conformations is initially evaluated using a coarse, low accuracy grid. Additional LAM points are then placed at appropriate points determined via an automated process, aiming to minimize the computational effort expended in high-energy regions whilst maximizing the accuracy in low-energy regions. As the size, complexity and flexibility of molecules increase, the reduction in computational cost becomes marked. This improvement is illustrated with energy calculations for benzoic acid and the ROY molecule, and a CSP study of molecule (XXVI) from the sixth blind test [Reilly et al. (2016). Acta Cryst. B72, 439-459], which is challenging due to its size and flexibility. Its known experimental form is successfully predicted as the global minimum. The computational cost of the study is tractable without the need to make unphysical simplifying assumptions.

Report on the sixth blind test of organic crystal structure prediction methods.

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

Exploring polymorphism of benzene and naphthalene with free energy based enhanced molecular dynamics

Prediction and exploration of possible polymorphism in organic crystal compounds are of great importance for industries ranging from organic electronics to pharmaceuticals to high-energy materials. Here we apply our crystal structure prediction procedure and the enhanced molecular dynamics based sampling approach called the Crystal-Adiabatic Free Energy Dynamics (Crystal-AFED) method to benzene and naphthalene. Crystal-AFED allows the free energy landscape of structures to be explored efficiently at any desired temperature and pressure. For each system, we successfully predict the most stable crystal structures at atmospheric pressure and explore the relative Gibbs free energies of predicted polymorphs at high pressures. Using Crystal-AFED sampling, we find that mixed structures, which typically cannot be discovered by standard crystal structure prediction methods, are prevalent in the solid forms of these compounds at high pressure.

Revision of the Crystal Structure of the First Molecular Polymorph in History

Despite being the earliest reported case of polymorphism in a molecular crystal, the unstable form II of benzamide has thus far evaded thorough structural characterization because collection of experimental data at atomic resolution has proven extremely challenging. Using a highly validated computational crystal structure prediction (CSP) method based on dispersion-corrected density functional theory, we correctly predict the stable form I with the lowest energy among all sampled structures and its polytypic form III with slightly higher energy. From Rietveld refinement of selected CSP models against synchrotron X-ray powder diffraction data of the historical polymorph, we are able to identify a subtle weakness in the available experimental data and arrive at a revised structure of form II. The revised crystal structure is the first benzamide structure to form catemers rather than dimers and possesses the rare space-group symmetry Fdd2 with two molecules in the asymmetric unit, which is necessary to suppo...