Optimality guarantees for crystal structure prediction.

Crystalline materials enable essential technologies, and their properties are determined by their structures. Crystal structure prediction can thus play a central part in the design of new functional materials1,2. Researchers have developed efficient heuristics to identify structural minima on the potential energy surface3-5. Although these methods can often access all configurations in principle, there is no guarantee that the lowest energy structure has been found. Here we show that the structure of a crystalline material can be predicted with energy guarantees by an algorithm that finds all the unknown atomic positions within a unit cell by combining combinatorial and continuous optimization. We encode the combinatorial task of finding the lowest energy periodic allocation of all atoms on a lattice as a mathematical optimization problem of integer programming6,7, enabling guaranteed identification of the global optimum using well-developed algorithms. A single subsequent local minimization of the resulting atom allocations then reaches the correct structures of key inorganic materials directly, proving their energetic optimality under clear assumptions. This formulation of crystal structure prediction establishes a connection to the theory of algorithms and provides the absolute energetic status of observed or predicted materials. It provides the ground truth for heuristic or data-driven structure prediction methods and is uniquely suitable for quantum annealers8-10, opening a path to overcome the combinatorial explosion of atomic configurations.

MethMotif.Org 2024: a database integrating context-specific transcription factor-binding motifs with DNA methylation patterns.

MethMotif (https://methmotif.org) is a publicly available database that provides a comprehensive repository of transcription factor (TF)-binding profiles, enriched with DNA methylation patterns. In this release, we have enhanced the platform, expanding our initial collection to over 700 position weight matrices (PWM), all of which include DNA methylation profiles. One of the key advancements in this release is the segregation of TF-binding motifs based on their cofactors and DNA methylation status. We have previously demonstrated that gene ontology (GO) enriched terms associated with TF target genes may differ based on their association with alternative cofactors and DNA methylation status. MethMotif provides precomputed GO annotations for each human TF of interest, as well as for TF-co-TF complexes, enabling a comprehensive analysis of TF functions in the context of their co-factors. Additionally, MethMotif has been updated to encompass data for two new species, Mus musculus and Arabidopsis thaliana, widening its applicability to a broader community. MethMotif stands out as the first and only TF-binding motifs database to incorporate context-specific PWM coupled with epigenetic information, thereby enlightening context-specific TF functions. This enhancement allows the community to explore and gain deeper insights into the regulatory mechanisms governing transcriptional processes.

Chemical control of structure and guest uptake by a conformationally mobile porous material.

Metal-organic frameworks (MOFs) are crystalline synthetic porous materials formed by binding organic linkers to metal nodes: they can be either rigid1,2 or flexible3. Zeolites and rigid MOFs have widespread applications in sorption, separation and catalysis that arise from their ability to control the arrangement and chemistry of guest molecules in their pores via the shape and functionality of their internal surface, defined by their chemistry and structure4,5. Their structures correspond to an energy landscape with a single, albeit highly functional, energy minimum. By contrast, proteins function by navigating between multiple metastable structures using bond rotations of the polypeptide6,7, where each structure lies in one of the minima of a conformational energy landscape and can be selected according to the chemistry of the molecules that interact with the protein. These structural changes are realized through the mechanisms of conformational selection (where a higher-energy minimum characteristic of the protein is stabilized by small-molecule binding) and induced fit (where a small molecule imposes a structure on the protein that is not a minimum in the absence of that molecule)8. Here we show that rotation about covalent bonds in a peptide linker can change a flexible MOF to afford nine distinct crystal structures, revealing a conformational energy landscape that is characterized by multiple structural minima. The uptake of small-molecule guests by the MOF can be chemically triggered by inducing peptide conformational change. This change transforms the material from a minimum on the landscape that is inactive for guest sorption to an active one. Chemical control of the conformation of a flexible organic linker offers a route to modifying the pore geometry and internal surface chemistry and thus the function of open-framework materials.

Unveiling the Morphology of Carbon-Supported Ru Nanoparticles by Multiscale Modeling.

Simulating the behavior of metal nanoparticles on supports is crucial for boosting their catalytic performance and various nanotechnology applications; however, such simulations are limited by the conflicts between accuracy and efficiency. Herein, we introduce a multiscale modeling strategy to unveil the morphology of Ru supported on pristine and N-doped graphene. Our multiscale modeling started with the electronic structures of a supported Ru single atom, revealing the strong metal-support interaction around pyridinic nitrogen sites. To determine the stable configurations of Ru2-13 clusters on three different graphene supports, global energy minimum searches were performed. The sintering of the global minimum Ru13 clusters on supports was further simulated by ab initio molecular dynamics (AIMD). The AIMD data set was then collected for deep potential molecular dynamics to study the melting of Ru nanoparticles. This study presents comprehensive descriptions of carbon-supported Ru and develops modeling approaches that bridge different scales and can be applied to various supported nanoparticle systems.

Statistically Derived Proxy Potentials Accelerate Geometry Optimization of Crystal Structures.

The crystal structures of known materials contain the information about the interatomic interactions that produced these stable compounds. Similar to the use of reported protein structures to extract effective interactions between amino acids, that has been a useful tool in protein structure prediction, we demonstrate how to use this statistical paradigm to learn the effective inter-atomic interactions in crystalline inorganic solids. By analyzing the reported crystallographic data for inorganic materials, we have constructed statistically derived proxy potentials (SPPs) that can be used to assess how realistic or unusual a computer-generated structure is compared to the reported experimental structures. The SPPs can be directly used for structure optimization to improve this similarity metric, that we refer to as the SPP score. We apply such optimization step to markedly improve the quality of the input crystal structures for DFT calculations and demonstrate that the SPPs accelerate geometry optimization for three systems relevant to battery materials. As this approach is chemistry-agnostic and can be used at scale, we produced a database of all possible pair potentials in a tabulated form ready to use.

Inferring energy-composition relationships with Bayesian optimization enhances exploration of inorganic materials.

Computational exploration of the compositional spaces of materials can provide guidance for synthetic research and thus accelerate the discovery of novel materials. Most approaches employ high-throughput sampling and focus on reducing the time for energy evaluation for individual compositions, often at the cost of accuracy. Here, we present an alternative approach focusing on effective sampling of the compositional space. The learning algorithm PhaseBO optimizes the stoichiometry of the potential target material while improving the probability of and accelerating its discovery without compromising the accuracy of energy evaluation.

Enhancement of Low Temperature Superionic Conductivity by Suppression of Li Site Ordering in Li7Si2-xGexS7I.

Ge4+ substitution into the recently discovered superionic conductor Li7Si2S7I is demonstrated by synthesis of Li7Si2-xGexS7I, where x ≤ 1.2. The anion packing and tetrahedral silicon location of Li7Si2S7I are retained upon substitution. Single crystal X-ray diffraction shows that substitution of larger Ge4+ for Si4+ expands the unit cell volume and further increases Li+ site disorder, such that Li7Si0.88Ge1.12S7I has one Li+ site more (sixteen in total) than Li7Si2S7I. The ionic conductivity of Li7Si0.8Ge1.2S7I (x = 1.2) at 303 K is 1.02(3) × 10-2 S cm-1 with low activation energies for Li+ transport demonstrated over a wide temperature range by AC impedance and 7Li NMR spectroscopy. All sixteen Li+ sites remain occupied to temperatures as low as 30 K in Li7Si0.88Ge1.12S7I as a result of the structural expansion. This differs from Li7Si2S7I, where the partial Li+ site ordering observed below room temperature reduces the ionic conductivity. The suppression of Li+ site depopulation by Ge4+ substitution retains the high mobility to temperatures as low as 200 K, yielding low temperature performance comparable with state-of-the-art Li ion conducting materials.

Control of Polarity in Kagome-NiAs Bismuthides.

A 2×2×1 superstructure of the P63/mmc NiAs structure is reported in which kagome nets are stabilized in the octahedral transition metal layers of the compounds Ni0.7Pd0.2Bi, Ni0.6Pt0.4Bi, and Mn0.99Pd0.01Bi. The ordered vacancies that yield the true hexagonal kagome motif lead to filling of trigonal bipyramidal interstitial sites with the transition metal in this family of "kagome-NiAs" type materials. Further ordering of vacancies within these interstitial layers can be compositionally driven to simultaneously yield kagome-connected layers and a net polarization along the c axes in Ni0.9Bi and Ni0.79Pd0.08Bi, which adopt Fmm2 symmetry. The polar and non-polar materials exhibit different electronic transport behaviour, reflecting the tuneability of both structure and properties within the NiAs-type bismuthide materials family.

Accessing Mg-Ion Storage in V2PS10 via Combined Cationic-Anionic Redox with Selective Bond Cleavage.

Magnesium batteries attract interest as alternative energy-storage devices because of elemental abundance and potential for high energy density. Development is limited by the absence of suitable cathodes, associated with poor diffusion kinetics resulting from strong interactions between Mg2+ and the host structure. V2PS10 is reported as a positive electrode material for rechargeable magnesium batteries. Cyclable capacity of 100 mAh g-1 is achieved with fast Mg2+ diffusion of 7.2 × ${\times }$ 10-11-4 × ${\times }$ 10-14 cm2 s-1. The fast insertion mechanism results from combined cationic redox on the V site and anionic redox on the (S2)2- site; enabled by reversible cleavage of S-S bonds, identified by X-ray photoelectron and X-ray absorption spectroscopy. Detailed structural characterisation with maximum entropy method analysis, supported by density functional theory and projected density of states analysis, reveals that the sulphur species involved in anion redox are not connected to the transition metal centres, spatially separating the two redox processes. This facilitates fast and reversible Mg insertion in which the nature of the redox process depends on the cation insertion site, creating a synergy between the occupancy of specific Mg sites and the location of the electrons transferred.

Control of Ionic Conductivity by Lithium Distribution in Cubic Oxide Argyrodites Li6+xP1-xSixO5Cl.

Argyrodite is a key structure type for ion-transporting materials. Oxide argyrodites are largely unexplored despite sulfide argyrodites being a leading family of solid-state lithium-ion conductors, in which the control of lithium distribution over a wide range of available sites strongly influences the conductivity. We present a new cubic Li-rich (>6 Li+ per formula unit) oxide argyrodite Li7SiO5Cl that crystallizes with an ordered cubic (P213) structure at room temperature, undergoing a transition at 473 K to a Li+ site disordered F4̅3m structure, consistent with the symmetry adopted by superionic sulfide argyrodites. Four different Li+ sites are occupied in Li7SiO5Cl (T5, T5a, T3, and T4), the combination of which is previously unreported for Li-containing argyrodites. The disordered F4̅3m structure is stabilized to room temperature via substitution of Si4+ with P5+ in Li6+xP1-xSixO5Cl (0.3 < x < 0.85) solid solution. The resulting delocalization of Li+ sites leads to a maximum ionic conductivity of 1.82(1) × 10-6 S cm-1 at x = 0.75, which is 3 orders of magnitude higher than the conductivities reported previously for oxide argyrodites. The variation of ionic conductivity with composition in Li6+xP1-xSixO5Cl is directly connected to structural changes occurring within the Li+ sublattice. These materials present superior atmospheric stability over analogous sulfide argyrodites and are stable against Li metal. The ability to control the ionic conductivity through structure and composition emphasizes the advances that can be made with further research in the open field of oxide argyrodites.

An Analysis of 5-Level Version of EQ-5D Adjusting for Treatment Switching: The Case of Patients With Epidermal Growth Factor Receptor T790M-Positive Nonsmall Cell Lung Cancer Treated With Osimertinib.

OBJECTIVES: Treatment switching from control to treatment after disease progression is common in oncology trials. Analyses of survival data typically adjust for this bias, but such adjustments are rarely performed in analyses of patient-reported outcomes. This analysis aimed to examine the impact of adjusting for treatment switching on estimated treatment effects on 5-level version of EQ-5D (EQ-5D-5L) utilities and quality-adjusted life-years (QALYs). The AURA3 trial (NCT02151981) was a randomized controlled trial comparing osimertinib with platinum-based doublet chemotherapy (standard care) in patients with locally advanced or metastatic epidermal growth factor receptor mutant- and T790M-positive nonsmall cell lung cancer whose disease has progressed with previous epidermal growth factor receptor tyrosine kinase inhibitor therapy. METHODS: Descriptive analyses were used to compare treatment arms. The primary analysis used a 2-stage least squares instrumental variable regression to estimate treatment effect adjusting for treatment crossover. Time to deterioration, defined from baseline to minimally important deterioration in EQ-5D-5L utility, was assessed using a rank preserving structural failure time model. RESULTS: Intention-to-treat analysis of imputed data showed incremental QALYs for osimertinib of 0.23 at 60 weeks. Accounting for treatment switching increased this to 0.52 in the primary analysis and to 0.63 QALYs in sensitivity analysis at 150 weeks. Time to deterioration analysis showed longer health-related quality of life maintenance with osimertinib, of 12.76 weeks, although this was at the borderline of statistical significance (acceleration factor, ψ = -0.275; 95% confidence interval -0.50 to 0.00). CONCLUSIONS: This analysis demonstrates methods to adjust for treatment switching in the analysis of EQ-5D-5L from clinical trials. Failure to account for crossover substantially underestimated the QALY gain for osimertinib.

Predicting spinel solid solutions using a random atom substitution method.

Exploration of chemical composition and structural configuration space is the central problem in crystal structure prediction. Even in limiting structure space to a single structure type, many different compositions and configurations are possible. In this work, we attempt to address this problem using an extension to the existing ChemDASH code in which variable compositions can be explored. We show that ChemDASH is an efficient method for exploring a fixed-composition space of spinel structures and build upon this to include variable compositions in the Mn-Fe-Zn-O spinel phase field. This work presents the first basin-hopping crystal structure prediction method that can explore variable compositions.

Machine-Learning Prediction of Metal-Organic Framework Guest Accessibility from Linker and Metal Chemistry.

The choice of metal and linker together define the structure and therefore the guest accessibility of a metal-organic framework (MOF), but the large number of possible metal-linker combinations makes the selection of components for synthesis challenging. We predict the guest accessibility of a MOF with 80.5 % certainty based solely on the identity of these two components as chosen by the experimentalist, by decomposing reported experimental three-dimensional MOF structures in the Cambridge Structural Database into metal and linker and then learning the connection between the components' chemistry and the MOF porosity. Pore dimensions of the guest-accessible space are classified into four ranges with three sequential models. Both the dataset and the predictive models are available to download and offer simple guidance in prioritization of the choice of the components for exploratory MOF synthesis for separation and catalysis based on guest accessibility considerations.

Extended Condensed Ultraphosphate Frameworks with Monovalent Ions Combine Lithium Mobility with High Computed Electrochemical Stability.

Extended anionic frameworks based on condensation of polyhedral main group non-metal anions offer a wide range of structure types. Despite the widespread chemistry and earth abundance of phosphates and silicates, there are no reports of extended ultraphosphate anions with lithium. We describe the lithium ultraphosphates Li3P5O14 and Li4P6O17 based on extended layers and chains of phosphate, respectively. Li3P5O14 presents a complex structure containing infinite ultraphosphate layers with 12-membered rings that are stacked alternately with lithium polyhedral layers. Two distinct vacant tetrahedral sites were identified at the end of two distinct finite Li6O1626- chains. Li4P6O17 features a new type of loop-branched chain defined by six PO43- tetrahedra. The ionic conductivities and electrochemical properties of Li3P5O14 were examined by impedance spectroscopy combined with DC polarization, NMR spectroscopy, and galvanostatic plating/stripping measurements. The structure of Li3P5O14 enables three-dimensional lithium migration that affords the highest ionic conductivity (8.5(5) × 10-7 S cm-1 at room temperature for bulk), comparable to that of commercialized LiPON glass thin film electrolytes, and lowest activation energy (0.43(7) eV) among all reported ternary Li-P-O phases. Both new lithium ultraphosphates are predicted to have high thermodynamic stability against oxidation, especially Li3P5O14, which is predicted to be stable to 4.8 V, significantly higher than that of LiPON and other solid electrolytes. The condensed phosphate units defining these ultraphosphate structures offer a new route to optimize the interplay of conductivity and electrochemical stability required, for example, in cathode coatings for lithium ion batteries.

Highly Absorbing Lead-Free Semiconductor Cu2AgBiI6 for Photovoltaic Applications from the Quaternary CuI-AgI-BiI3 Phase Space.

Since the emergence of lead halide perovskites for photovoltaic research, there has been mounting effort in the search for alternative compounds with improved or complementary physical, chemical, or optoelectronic properties. Here, we report the discovery of Cu2AgBiI6: a stable, inorganic, lead-free wide-band-gap semiconductor, well suited for use in lead-free tandem photovoltaics. We measure a very high absorption coefficient of 1.0 × 105 cm-1 near the absorption onset, several times that of CH3NH3PbI3. Solution-processed Cu2AgBiI6 thin films show a direct band gap of 2.06(1) eV, an exciton binding energy of 25 meV, a substantial charge-carrier mobility (1.7 cm2 V-1 s-1), a long photoluminescence lifetime (33 ns), and a relatively small Stokes shift between absorption and emission. Crucially, we solve the structure of the first quaternary compound in the phase space among CuI, AgI and BiI3. The structure includes both tetrahedral and octahedral species which are open to compositional tuning and chemical substitution to further enhance properties. Since the proposed double-perovskite Cs2AgBiI6 thin films have not been synthesized to date, Cu2AgBiI6 is a valuable example of a stable Ag+/Bi3+ octahedral motif in a close-packed iodide sublattice that is accessed via the enhanced chemical diversity of the quaternary phase space.

Ordered Oxygen Vacancies in the Lithium-Rich Oxide Li4CuSbO5.5, a Triclinic Structure Type Derived from the Cubic Rocksalt Structure.

Li-rich rocksalt oxides are promising candidates as high-energy density cathode materials for next-generation Li-ion batteries because they present extremely diverse structures and compositions. Most reported materials in this family contain as many cations as anions, a characteristic of the ideal cubic closed-packed rocksalt composition. In this work, a new rocksalt-derived structure type is stabilized by selecting divalent Cu and pentavalent Sb cations to favor the formation of oxygen vacancies during synthesis. The structure and composition of the oxygen-deficient Li4CuSbO5.5□0.5 phase is characterized by combining X-ray and neutron diffraction, ICP-OES, XAS, and magnetometry measurements. The ordering of cations and oxygen vacancies is discussed in comparison with the related Li2CuO2□1 and Li5SbO5□1 phases. The electrochemical properties of this material are presented, with only 0.55 Li+ extracted upon oxidation, corresponding to a limited utilization of cationic and/or anionic redox, whereas more than 2 Li+ ions can be reversibly inserted upon reduction to 1 V vs Li+/Li, a large capacity attributed to a conversion reaction and the reduction of Cu2+ to Cu0. Control of the formation of oxygen vacancies in Li-rich rocksalt oxides by selecting appropriate cations and synthesis conditions affords a new route for tuning the electrochemical properties of cathode materials for Li-ion batteries. Furthermore, the development of material models of the required level of detail to predict phase diagrams and electrochemical properties, including oxygen release in Li-rich rocksalt oxides, still relies on the accurate prediction of crystal structures. Experimental identification of new accessible structure types stabilized by oxygen vacancies represents a valuable step forward in the development of predictive models.

Polymorph of LiAlP2O7: Combined Computational, Synthetic, Crystallographic, and Ionic Conductivity Study.

We report a new polymorph of lithium aluminum pyrophosphate, LiAlP2O7, discovered through a computationally guided synthetic exploration of the Li-Mg-Al-P-O phase field. The new polymorph formed at 973 K, and the crystal structure, solved by single-crystal X-ray diffraction, adopts the orthorhombic space group Cmcm with a = 5.1140(9) Å, b = 8.2042(13) Å, c = 11.565(3) Å, and V = 485.22(17) Å3. It has a three-dimensional framework structure that is different from that found in other LiMIIIP2O7 materials. It transforms to the known monoclinic form (space group P21) above ∼1023 K. Density functional theory (DFT) calculations show that the new polymorph is the most stable low-temperature structure for this composition among the seven known structure types in the AIMIIIP2O7 (A = alkali metal) families. Although the bulk Li-ion conductivity is low, as determined from alternating-current impedance spectroscopy and variable-temperature static 7Li NMR spectra, a detailed analysis of the topologies of all seven structure types through bond-valence-sum mapping suggests a potential avenue for enhancing the conductivity. The new polymorph exhibits long (>4 Å) Li-Li distances, no Li vacancies, and an absence of Li pathways in the c direction, features that could contribute to the observed low Li-ion conductivity. In contrast, we found favorable Li-site topologies that could support long-range Li migration for two structure types with modest DFT total energies relative to the new polymorph. These promising structure types could possibly be accessed from innovative doping of the new polymorph.

Chemical Control of the Dimensionality of the Octahedral Network of Solar Absorbers from the CuI-AgI-BiI3 Phase Space by Synthesis of 3D CuAgBiI5.

A newly reported compound, CuAgBiI5, is synthesized as powder, crystals, and thin films. The structure consists of a 3D octahedral Ag+/Bi3+ network as in spinel, but occupancy of the tetrahedral interstitials by Cu+ differs from those in spinel. The 3D octahedral network of CuAgBiI5 allows us to identify a relationship between octahedral site occupancy (composition) and octahedral motif (structure) across the whole CuI-AgI-BiI3 phase field, giving the ability to chemically control structural dimensionality. To investigate composition-structure-property relationships, we compare the basic optoelectronic properties of CuAgBiI5 with those of Cu2AgBiI6 (which has a 2D octahedral network) and reveal a surprisingly low sensitivity to the dimensionality of the octahedral network. The absorption onset of CuAgBiI5 (2.02 eV) barely changes compared with that of Cu2AgBiI6 (2.06 eV) indicating no obvious signs of an increase in charge confinement. Such behavior contrasts with that for lead halide perovskites which show clear confinement effects upon lowering dimensionality of the octahedral network from 3D to 2D. Changes in photoluminescence spectra and lifetimes between the two compounds mostly derive from the difference in extrinsic defect densities rather than intrinsic effects. While both materials show good stability, bulk CuAgBiI5 powder samples are found to be more sensitive to degradation under solar irradiation compared to Cu2AgBiI6.

Discovery of a Low Thermal Conductivity Oxide Guided by Probe Structure Prediction and Machine Learning.

We report the aperiodic titanate Ba10 Y6 Ti4 O27 with a room-temperature thermal conductivity that equals the lowest reported for an oxide. The structure is characterised by discontinuous occupancy modulation of each of the sites and can be considered as a quasicrystal. The resulting localisation of lattice vibrations suppresses phonon transport of heat. This new lead material for low-thermal-conductivity oxides is metastable and located within a quaternary phase field that has been previously explored. Its isolation thus requires a precisely defined synthetic protocol. The necessary narrowing of the search space for experimental investigation was achieved by evaluation of titanate crystal chemistry, prediction of unexplored structural motifs that would favour synthetically accessible new compositions, and assessment of their properties with machine-learning models.

Amino Acid Residues Determine the Response of Flexible Metal-Organic Frameworks to Guests.

Flexible metal-organic frameworks (MOFs) undergo structural transformations in response to physical and chemical stimuli. This is hard to control because of feedback between guest uptake and host structure change. We report a family of flexible MOFs based on derivatized amino acid linkers. Their porosity consists of a one-dimensional channel connected to three peripheral pockets. This network structure amplifies small local changes in linker conformation, which are strongly coupled to the guest packing in and the shape of the peripheral pockets, to afford large changes in the global pore geometry that can, for example, segment the pore into four isolated components. The synergy among pore volume, guest packing, and linker conformation that characterizes this family of structures can be determined by the amino acid side chain, because it is repositioned by linker torsion. The resulting control optimizes noncovalent interactions to differentiate the uptake and structure response of host-guest pairs with similar chemistries.