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.

Element selection for crystalline inorganic solid discovery guided by unsupervised machine learning of experimentally explored chemistry.

The selection of the elements to combine delimits the possible outcomes of synthetic chemistry because it determines the range of compositions and structures, and thus properties, that can arise. For example, in the solid state, the elemental components of a phase field will determine the likelihood of finding a new crystalline material. Researchers make these choices based on their understanding of chemical structure and bonding. Extensive data are available on those element combinations that produce synthetically isolable materials, but it is difficult to assimilate the scale of this information to guide selection from the diversity of potential new chemistries. Here, we show that unsupervised machine learning captures the complex patterns of similarity between element combinations that afford reported crystalline inorganic materials. This model guides prioritisation of quaternary phase fields containing two anions for synthetic exploration to identify lithium solid electrolytes in a collaborative workflow that leads to the discovery of Li3.3SnS3.3Cl0.7. The interstitial site occupancy combination in this defect stuffed wurtzite enables a low-barrier ion transport pathway in hexagonal close-packing.

A mobile robotic chemist.

Technologies such as batteries, biomaterials and heterogeneous catalysts have functions that are defined by mixtures of molecular and mesoscale components. As yet, this multi-length-scale complexity cannot be fully captured by atomistic simulations, and the design of such materials from first principles is still rare1-5. Likewise, experimental complexity scales exponentially with the number of variables, restricting most searches to narrow areas of materials space. Robots can assist in experimental searches6-14 but their widespread adoption in materials research is challenging because of the diversity of sample types, operations, instruments and measurements required. Here we use a mobile robot to search for improved photocatalysts for hydrogen production from water15. The robot operated autonomously over eight days, performing 688 experiments within a ten-variable experimental space, driven by a batched Bayesian search algorithm16-18. This autonomous search identified photocatalyst mixtures that were six times more active than the initial formulations, selecting beneficial components and deselecting negative ones. Our strategy uses a dexterous19,20 free-roaming robot21-24, automating the researcher rather than the instruments. This modular approach could be deployed in conventional laboratories for a range of research problems beyond photocatalysis.