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.

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.

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.

Integration of generative machine learning with the heuristic crystal structure prediction code FUSE.

The prediction of new compounds via crystal structure prediction may transform how the materials chemistry community discovers new compounds. In the prediction of inorganic crystal structures there are three distinct classes of prediction: performing crystal structure prediction via heuristic algorithms, using a range of established crystal structure prediction codes, an emerging community using generative machine learning models to predict crystal structures directly and the use of mathematical optimisation to solve crystal structures exactly. In this work, we demonstrate the combination of heuristic and generative machine learning, the use of a generative machine learning model to produce the starting population of crystal structures for a heuristic algorithm and discuss the benefits, demonstrating the method on eight known compounds with reported crystal structures and three hypothetical compounds. We show that the integration of machine learning structure generation with heuristic structure prediction results in both faster compute times per structure and lower energies. This work provides to the community a set of eleven compounds with varying chemistry and complexity that can be used as a benchmark for new crystal structure prediction methods as they emerge.

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.

Recognition and order of multiple sidechains by metal-organic framework enhances the separation of hexane isomers.

Porous materials perform molecular sorting, separation and transformation by interaction between their framework structures and the substrates. Proteins also interact with molecules to effect chemical transformations, but rely on the precise sequence of the amino acid building units along a common polypeptide backbone to maximise their performance. Design strategies that positionally order sidechains over a defined porous framework to diversify the internal surface chemistry would enhance control of substrate processing. Here we show that different sidechains can be ordered over a metal-organic framework through recognition of their distinct chemistries during synthesis. The sidechains are recognised because each one forces the common building unit that defines the backbone of the framework into a different conformation in order to form the extended structure. The resulting sidechain ordering affords hexane isomer separation performance superior to that of the same framework decorated only with sidechains of a single kind. The separated molecules adopt distinct arrangements within the resulting modified pore geometry, reflecting their strongly differentiated environments precisely created by the ordered sidechains. The development of frameworks that recognise  and  order multiple sidechain functionality by conformational control offers tailoring of the internal surfaces within families of porous materials to direct interactions at the molecular level.

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.

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.

Hydration of a 2D Supramolecular Assembly: Bitartrate on Cu(110).

Hydration layers play a key role in many technical and biological systems, but our understanding of these structures remains very limited. Here, we investigate the molecular processes driving hydration of a chiral metal-organic surface, bitartrate on Cu(110), which consists of hydrogen-bonded bitartrate rows separated by exposed Cu. Initially water decorates the metal channels, hydrogen bonding to the exposed O ligands that bind bitartrate to Cu, but does not wet the bitartrate rows. At higher temperature, water inserts into the structure, breaks the existing intermolecular hydrogen bonds, and changes the adsorption site and footprint. Calculations show this process is driven by the creation of stable adsorption sites between the carboxylate ligands, to allow hydration of O-Cu ligands within the interior of the structure. This work suggests that hydration of polar metal-adsorbate ligands will be a dominant factor in many systems during surface hydration or self-assembly from solution.

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.

Chemically directed structure evolution for crystal structure prediction.

We present a new method of evolving crystal structures for crystal structure prediction. The method of chemically directed structure evolution uses chemical models to quantify the environment of atoms and vacancy sites in a crystal structure, with that information used to inform how to modify the structure to make a move on the potential energy surface. We have developed a method of chemically directed swapping, where we swap atoms in the least favourable chemical environments. This method has been implemented in the crystal structure prediction code ChemDASH (Chemically Directed Atom Swap Hopping), which explores the potential energy surface using a basin-hopping approach, and evaluates chemical environments using either the bond valence sum or electrostatic site potential. ChemDASH has a variety of methods of initialising structures, optimising structures, and swapping atoms. This gives ChemDASH the flexibility to be applied to a wide range of systems. We used ChemDASH to examine the effectiveness of the directed swapping method. Directed swapping finds the ground states of TiO2 and SrTiO3 faster than random (non-directed) swapping, but is less effective than random swapping for Y2Ti2O7.

Ice Nucleation on a Corrugated Surface.

Heterogeneous ice nucleation is a key process in many environmental and technical fields and is of particular importance in modeling atmospheric behavior and the Earth's climate. Despite an improved understanding of how water binds at solid surfaces, no clear picture has emerged to describe how 3D ice grows from the first water layer, nor what makes a particular surface efficient at nucleating bulk ice. This study reports how water at a corrugated, hydrophilic/hydrophobic surface restructures from a complex 2D network, optimized to match the solid surface, to grow into a continuous ice film. Unlike the water networks formed on plane surfaces, the corrugated Cu(511) surface stabilizes a buckled hexagonal wetting layer containing both hydrogen acceptor and donor sites. First layer water is able to relax into an "icelike" arrangement as further water is deposited, creating an array of donor and acceptor sites with the correct spacing and corrugation to stabilize second layer ice and allow continued commensurate multilayer ice growth. Comparison to previous studies of flat surfaces indicates nanoscale corrugation strongly favors ice nucleation, implying surface corrugation will be an important aspect of the surface morphology on other natural or engineered surfaces.

Computational Prediction and Experimental Realization of p-Type Carriers in the Wide-Band-Gap Oxide SrZn1- xLi xO2.

It is challenging to achieve p-type doping of zinc oxides (ZnO), which are of interest as transparent conductors in optoelectronics. A ZnO-related ternary compound, SrZnO2, was investigated as a potential host for p-type conductivity. First-principles investigations were used to select from a range of candidate dopants the substitution of Li+ for Zn2+ as a stable, potentially p-type, doping mechanism in SrZnO2. Subsequently, single-phase bulk samples of a new p-type-doped oxide, SrZn1- xLi xO2 (0 < x < 0.06), were prepared. The structural, compositional, and physical properties of both the parent SrZnO2 and SrZn1- xLi xO2 were experimentally verified. The band gap of SrZnO2 was calculated using HSE06 at 3.80 eV and experimentally measured at 4.27 eV, which confirmed the optical transparency of the material. Powder X-ray diffraction and inductively coupled plasma analysis were combined to show that single-phase ceramic samples can be accessed in the compositional range x < 0.06. A positive Seebeck coefficient of 353(4) µV K-1 for SrZn1- xLi xO2, where x = 0.021, confirmed that the compound is a p-type conductor, which is consistent with the pO2 dependence of the electrical conductivity observed in all SrZn1- xLi xO2 samples. The conductivity of SrZn1- xLi xO2 is up to 15 times greater than that of undoped SrZnO2 (for x = 0.028 σ = 2.53 µS cm-1 at 600 °C and 1 atm of O2).

Polymorphism control of superconductivity and magnetism in Cs(3)C(60) close to the Mott transition.

The crystal structure of a solid controls the interactions between the electronically active units and thus its electronic properties. In the high-temperature superconducting copper oxides, only one spatial arrangement of the electronically active Cu(2+) units-a two-dimensional square lattice-is available to study the competition between the cooperative electronic states of magnetic order and superconductivity. Crystals of the spherical molecular C(60)(3-) anion support both superconductivity and magnetism but can consist of fundamentally distinct three-dimensional arrangements of the anions. Superconductivity in the A(3)C(60) (A = alkali metal) fullerides has been exclusively associated with face-centred cubic (f.c.c.) packing of C(60)(3-) (refs 2, 3), but recently the most expanded (and thus having the highest superconducting transition temperature, T(c); ref. 4) composition Cs(3)C(60) has been isolated as a body-centred cubic (b.c.c.) packing, which supports both superconductivity and magnetic order. Here we isolate the f.c.c. polymorph of Cs(3)C(60) to show how the spatial arrangement of the electronically active units controls the competing superconducting and magnetic electronic ground states. Unlike all the other f.c.c. A(3)C(60) fullerides, f.c.c. Cs(3)C(60) is not a superconductor but a magnetic insulator at ambient pressure, and becomes superconducting under pressure. The magnetic ordering occurs at an order of magnitude lower temperature in the geometrically frustrated f.c.c. polymorph (Néel temperature T(N) = 2.2 K) than in the b.c.c.-based packing (T(N) = 46 K). The different lattice packings of C(60)(3-) change T(c) from 38 K in b.c.c. Cs(3)C(60) to 35 K in f.c.c. Cs(3)C(60) (the highest found in the f.c.c. A(3)C(60) family). The existence of two superconducting packings of the same electronically active unit reveals that T(c) scales universally in a structure-independent dome-like relationship with proximity to the Mott metal-insulator transition, which is governed by the role of electron correlations characteristic of high-temperature superconducting materials other than fullerides.

Reported and predicted structures of Ba(Co,Nb)(1-δ)O3 hexagonal perovskite phases.

The Extended Module Materials Assembly computational method for structure solution and prediction has been implemented for close-packed lattices. Exploring the family of B-site deficient materials in hexagonal perovskite barium cobalt niobates, it is found that the EMMA procedure returns the experimental structures as the most stable for the known compositions of Ba3CoNb2O9, Ba5Nb4O15 and Ba8CoNb6O24. The unknown compositions Ba11Co2Nb8O33 and Ba13CoNb10O39, having longer stacking sequences, are predicted to form as intergrowths of Ba3CoNb2O9 and Ba5Nb4O15, and are found to have similar stability to pure Ba3CoNb2O9 and Ba5Nb4O15, indicating that it is likely they can be synthesised.

Guest-adaptable and water-stable peptide-based porous materials by imidazolate side chain control.

The peptide-based porous 3D framework, ZnCar, has been synthesized from Zn(2+) and the natural dipeptide carnosine (ß-alanyl-L-histidine). Unlike previous extended peptide networks, the imidazole side chain of the histidine residue is deprotonated to afford Zn-imidazolate chains, with bonding similar to the zeolitic imidazolate framework (ZIF) family of porous materials. ZnCar exhibits permanent microporosity with a surface area of 448 m(2) g(-1) , and its pores are 1D channels with 5 Šopenings and a characteristic chiral shape. This compound is chemically stable in organic solvents and water. Single-crystal X-ray diffraction (XRD) showed that the ZnCar framework adapts to MeOH and H2 O guests because of the torsional flexibility of the main His-ß-Ala chain, while retaining the rigidity conferred by the Zn-imidazolate chains. The conformation adopted by carnosine is driven by the H bonds formed both to other dipeptides and to the guests, permitting the observed structural transformations.

Hydroxyl on Stepped Copper and its Interaction with Water.

We describe the hydroxyl and mixed hydroxyl-water structures formed on a stepped copper surface following the reaction of adsorbed O with water at a low temperature and compare them to the structures found previously on plane copper surfaces. Thermal desorption profiles, STM, and low-energy electron diffraction show that water reacts with O at temperatures below 130 K on Cu(511). Two well-defined phases appear as the OH/H2O layer is heated to desorb excess water, a 1OH:1H2O phase and a pure OH phase. The 1OH:1H2O structure consists of 1D chains binding across two adjacent copper steps, with a double period along the step. Electronic structure calculations show that the structure has a zigzag chain of water along the terrace, stabilized by hydrogen bonds to OH groups adsorbed in the step bridge sites. This structure binds OH in its favored site and is similar to the structure observed on other open faces of Cu and Ni, suggesting that this structural arrangement may be common on other surfaces that have steps or rows of close packed metal atoms. The hydroxyl/water chains decompose at 210 K to leave OH adsorbed in the Cu step bridge site, with some forming H-bonded trimers that bridge between two Cu steps. Heating the surface causes hydroxyl to disproportionate near 300 K, desorbing water to leave chemisorbed O.

Artificial construction of the layered Ruddlesden-Popper manganite La2Sr2Mn3O10 by reflection high energy electron diffraction monitored pulsed laser deposition.

Pulsed laser deposition has been used to artificially construct the n = 3 Ruddlesden-Popper structure La(2)Sr(2)Mn(3)O(10) in epitaxial thin film form by sequentially layering La(1-x)Sr(x)MnO(3) and SrO unit cells aided by in situ reflection high energy electron diffraction monitoring. The interval deposition technique was used to promote two-dimensional SrO growth. X-ray diffraction and cross-sectional transmission electron microscopy indicated that the trilayer structure had been formed. A site ordering was found to differ from that expected thermodynamically, with the smaller Sr(2+) predominantly on the R site due to kinetic trapping of the deposited cation sequence. A dependence of the out-of-plane lattice parameter on growth pressure was interpreted as changing the oxygen content of the films. Magnetic and transport measurements on fully oxygenated films indicated a frustrated magnetic ground state characterized as a spin glass-like magnetic phase with the glass temperature T(g) ≈ 34 K. The magnetic frustration has a clear in-plane (ab) magnetic anisotropy, which is maintained up to temperatures of 150 K. Density functional theory calculations suggest competing antiferromagnetic and ferromagnetic long-range orders, which are proposed as the origin of the low-temperature glassy state.

Chemical bonding and atomic structure in Y2O3:ZrO2-SrTiO3 layered heterostructures.

Repeating boundaries: the buried interfaces in artificial heterostructures produced by sequential deposition of nanosized units are critical to their properties. With density functional theory it was shown that in Y(2)O(3):ZrO(2) (YSZ) and SrTiO(3) (STO) heterostructures reconstruction of the interfaces between the component units is required to access the most favorable structure.

Tailoring the structure of water at a metal surface: a structural analysis of the water bilayer formed on an alloy template.

Recent studies show that structures based on the traditional "icelike" water bilayer are not stable on flat transition metal surfaces and, instead, more complex wetting layers are formed. Here we show that an ordered bilayer can be formed on a SnPt(111) alloy template and determine the structure of the water layer by low energy electron diffraction. Close agreement is found between experiment and the structure calculated by density functional theory. Corrugation of the alloy surface allows only alternate water molecules to chemisorb, stabilizing the H-down water bilayer by reducing the metal-hydrogen repulsion compared to a flat surface.