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.

Superionic lithium transport via multiple coordination environments defined by two-anion packing.

Fast cation transport in solids underpins energy storage. Materials design has focused on structures that can define transport pathways with minimal cation coordination change, restricting attention to a small part of chemical space. Motivated by the greater structural diversity of binary intermetallics than that of the metallic elements, we used two anions to build a pathway for three-dimensional superionic lithium ion conductivity that exploits multiple cation coordination environments. Li7Si2S7I is a pure lithium ion conductor created by an ordering of sulphide and iodide that combines elements of hexagonal and cubic close-packing analogously to the structure of NiZr. The resulting diverse network of lithium positions with distinct geometries and anion coordination chemistries affords low barriers to transport, opening a large structural space for high cation conductivity.

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.

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.

High-Throughput Discovery of a Rhombohedral Twelve-Connected Zirconium-Based Metal-Organic Framework with Ordered Terephthalate and Fumarate Linkers.

We report a metal-organic framework where an ordered array of two linkers with differing length and geometry connect [Zr6 (OH)4 O4 ]12+ clusters into a twelve-connected fcu net that is rhombohedrally distorted from cubic symmetry. The ordered binding of equal numbers of terephthalate and fumarate ditopic carboxylate linkers at the trigonal antiprismatic Zr6 core creates close-packed layers of fumarate-connected clusters that are connected along the single remaining threefold axis by terephthalates. This well-defined linker arrangement retains the three-dimensional porosity of the Zr cluster-based UiO family while creating two distinct windows within the channels that define two distinct guest diffusion paths. The ordered material is accessed by a restricted combination of composition and process parameters that were identified by high-throughput synthesis.

Differential guest location by host dynamics enhances propylene/propane separation in a metal-organic framework.

Energy-efficient approaches to propylene/propane separation such as molecular sieving are of considerable importance for the petrochemical industry. The metal organic framework NbOFFIVE-1-Ni adsorbs propylene but not propane at room temperature and atmospheric pressure, whereas the isostructural SIFSIX-3-Ni does not exclude propane under the same conditions. The static dimensions of the pore openings of both materials are too small to admit either guest, signalling the importance of host dynamics for guest entrance to and transport through the channels. We use ab initio calculations together with crystallographic and adsorption data to show that the dynamics of the two framework-forming units, polyatomic anions and pyrazines, govern both diffusion and separation. The guest diffusion occurs by opening of the flexible window formed by four pyrazines. In NbOFFIVE-1-Ni, (NbOF5)2- anion reorientation locates propane away from the window, which enhances propylene/propane separation.

High-throughput screening of metal-organic frameworks for kinetic separation of propane and propene.

We apply molecular simulations to screen a database of reported metal-organic framework structures from the computation-ready, experimental (CoRE) MOF database to identify materials potentially capable of separating propane and propene by diffusion. We report a screening workflow that uses descriptor analysis, conventional molecular dynamics (MD), and Nudged Elastic Band (NEB) energy barrier calculations at both classical force field and Density Functional Theory (DFT) levels. For the first time, the effects of framework flexibility on guest transport properties were fully considered in a screening process and led to the identification of candidate MOFs. The hits identified by this proof-of-concept workflow include ZIF-8 and ZIF-67 previously shown to have large differences in propane and propene diffusivities as well as two other materials that have not been tested experimentally yet. This work emphasises the importance of taking into account framework flexibility when studying guest transport in porous materials, demonstrates the potential of the data-driven identification of high-performance materials and highlights the ways of improving the predictive power of the screening workflow.

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.

The Anisotropic Responses of a Flexible Metal-Organic Framework Constructed from Asymmetric Flexible Linkers and Heptanuclear Zinc Carboxylate Secondary Building Units.

A new porous and flexible metal-organic framework (MOF) has been synthesized from the flexible asymmetric linker N-(4-carboxyphenyl)succinamate (CSA) and heptanuclear zinc oxo-clusters of formula [Zn7O2(carboxylate)10DMF2] involving two coordinated terminal DMF ligands. The structural response of this MOF to the removal or exchange of its guest molecules has been probed using a combination of experimental and computational approaches. The topology of the material, involving double linker connections in the a and b directions and single linker connections along the c axis, is shown to be key in the material's anisotropic response. The a and b directions remain locked during guest removal, whereas the c axis linker undergoes large changes significantly reducing the material's void space. The changes to the c axis linker involve a combination of a hinge motion on the linker's rigid side and conformational rearrangements on its flexible end, which were probed in detail during this process despite the presence of crystallographic disorder along this axis, which prevented accurate characterization by experimental methods alone. Although inactive during guest removal, the flexible ends of the a and b axis linkers are observed to play a prominent role during DMF to DMSO solvent exchange, facilitating the exchange reaction arising in the cluster.

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.

Stable and ordered amide frameworks synthesised under reversible conditions which facilitate error checking.

ABSTARCT: Covalent organic frameworks (COFs) are network polymers with long-range positional order whose properties can be tuned using the isoreticular chemistry approach. Making COFs from strong bonds is challenging because irreversible rapid formation of the network produces amorphous materials with locked-in disorder. Reversibility in bond formation is essential to generate ordered networks, as it allows the error-checking that permits the network to crystallise, and so candidate network-forming chemistries such as amide that are irreversible under conventional low temperature bond-forming conditions have been underexplored. Here we show that we can prepare two- and three-dimensional covalent amide frameworks (CAFs) by devitrification of amorphous polyamide network polymers using high-temperature and high-pressure reaction conditions. In this way we have accessed reversible amide bond formation that allows crystalline order to develop. This strategy permits the direct synthesis of practically irreversible ordered amide networks that are stable thermally and under both strong acidic and basic hydrolytic conditions.

Peptide Metal-Organic Frameworks for Enantioselective Separation of Chiral Drugs.

We report the use of a chiral Cu(II) 3D metal-organic framework (MOF) based on the tripeptide Gly-l-His-Gly (GHG) for the enantioselective separation of metamphetamine and ephedrine. Monte Carlo simulations suggest that chiral recognition is linked to preferential binding of one of the enantiomers as a result of either stronger or additional H-bonds with the framework that lead to energetically more stable diastereomeric adducts. Solid-phase extraction of a racemic mixture by using Cu(GHG) as the extractive phase permits isolating >50% of the (+)-ephedrine enantiomer as target compound in only 4 min. To our knowledge, this represents the first example of a MOF capable of separating chiral polar drugs.

Chemical and structural stability of zirconium-based metal-organic frameworks with large three-dimensional pores by linker engineering.

The synthesis of metal-organic frameworks with large three-dimensional channels that are permanently porous and chemically stable offers new opportunities in areas such as catalysis and separation. Two linkers (L1=4,4',4'',4'''-([1,1'-biphenyl]-3,3',5,5'-tetrayltetrakis(ethyne-2,1-diyl)) tetrabenzoic acid, L2=4,4',4'',4'''-(pyrene-1,3,6,8-tetrayltetrakis(ethyne-2,1-diyl))tetrabenzoic acid) were used that have equivalent connectivity and dimensions but quite distinct torsional flexibility. With these, a solid solution material, [Zr6 O4 (OH)4 (L1)2.6 (L2)0.4 ]⋅(solvent)x , was formed that has three-dimensional crystalline permanent porosity with a surface area of over 4000 m(2) g(-1) that persists after immersion in water. These properties are not accessible for the isostructural phases made from the separate single linkers.

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.

Effect of particle size on energy dissipation in viscoelastic granular collisions.

We analyze the scaling properties of the Hertz-Kuwabara-Kono (HKK) model, which is commonly used in numerical simulations to describe the collision of macroscopic noncohesive viscoelastic spherical particles. Parameters describing the elastic and viscous properties of the material, its density, and the size of the colliding particles affect the restitution coefficient ɛ and collision time τ only via appropriate rescaling but do not change the shape of ɛ(v) and τ(v) curves, where v is the impact velocity. We have measured the restitution coefficient experimentally for relatively large (1 cm) particles of microcrystalline cellulose to deduce material parameters and then to predict collision properties for smaller microcrystalline cellulose (MCC) particles by assuming the scaling properties of the HKK model. In particular, we demonstrate that the HKK model predicts the restitution coefficient of microscopic particles of about 100 µm to be considerably smaller than that of the macroscopic particles. In fact, the energy dissipation is so large that only completely inelastic collisions occur for weakly attractive particles. We propose a straightforward self-consistent extension to the Johnson-Kendall-Roberts (JKR) model to include dissipative forces and discuss the implications of our findings for the behavior of experimental powder systems.

Computer simulation study of a single polymer chain in an attractive solvent.

The behavior of a linear polymer chain is studied in a solvent with high affinity for the polymer. The coil dimensions and specific heat are calculated as a function of chain length, solvent concentration, and polymer-solvent attraction strength epsilon(ps). All other interactions are limited to excluded volume repulsion, which implies that the Flory-Huggins chi parameter is negative. Using both on-lattice and off-lattice models of a polymer chain in explicit solvent, we study a transition from weak to strong association regimes. In all cases studied, the system's heat capacity is a nonmonotonic function of epsilon(rhos) with a maximum at attraction strengths of the order of several k(B)T. This peak originates from restriction of local conformational degrees of freedom due to the associated solvent rather than from a partial chain collapse which onsets as attractive solvent content is decreased.

Optimal cell approach to osmotic properties of finite stiff-chain polyelectrolytes.

We propose a self-consistent geometry optimized cell model approach to study osmotic properties of stiff-chain polyelectrolyte solutions. In contrast with the usual monotonic Poisson-Boltzmann prediction, the cell model predicts the correct nonmonotonic dependence of the osmotic coefficient on concentration. A lower degree of polymerization is found to reduce significantly the counterion condensation in a typical dilute strong polyelectrolyte. The results agree quantitatively with simulations of a corresponding many-body bulk system up to a dense semidilute regime.

Incorporation of excluded-volume correlations into Poisson-Boltzmann theory.

We investigate the effect of excluded-volume interactions on the electrolyte distribution around a charged macroion. First, we introduce a criterion for determining when hard-core effects should be taken into account beyond standard mean-field Poisson-Boltzmann (PB) theory. Next, we demonstrate that several commonly proposed local-density-functional approaches for excluded-volume interactions cannot be used for this purpose. Instead, we employ a nonlocal excess free energy by using a simple constant-weight approach. We compare the ion distribution and osmotic pressure predicted by this theory with Monte Carlo simulations. They agree very well for weakly developed correlations and give the correct layering effect for stronger ones. In all investigated cases our simple weighted-density theory yields more realistic results than the standard PB approach, whereas all local density theories do not improve on the PB density profiles, but on the contrary, deviate even more from the simulation results.

The role of attractive interactions in rod-sphere mixtures.

We present a computer simulation study of binary mixtures of prolate Gay-Berne particles and Lennard-Jones spheres. Results are presented for three such rod-sphere systems which differ from each other only in the interaction between unlike particles. Both the mixing-demixing behavior and the transitions between the isotropic and any liquid crystalline phases are studied for each system, as a function of temperature and concentration ratio. For systems which show macroscopic demixing, the rod-sphere interaction is shown to give direct control over interfacial anchoring properties, giving rise to the possibility of micellar phase formation in the case of homeotropic anchoring. Additionally, it is shown that on incorporating high concentrations of spheres into a system of rods with weak demixing properties, microphase-separated structures can be induced, including bicontinuous and lamellar arrangements.