Doctoral Training Partnerships: a range of postgraduate training is funded by the Research Councils. For information on current funding routes, see the common terminology at https://www.ukri.org/apply-for-funding/how-we-fund-studentships/. Training grants may be to one organisation or to a consortia of research organisations. This portal will show the lead organisation only.

Abstracts are not currently available in GtR for all funded research. This is normally because the abstract was not required at the time of proposal submission, but may be because it included sensitive information such as personal details.

Databases of crystal structures are essential tools for researchers working in the solid state. Initially established as repositories of experimentally determined structures, the large data sets contained within databases, such as the Cambridge Structural Database (CSD), have become the subject of research in their own right through the development of "data mining". The usefulness of such databases is, however, highly dependent on the quality of the data they contain. In the vast majority of cases the structures were obtained via X-ray diffraction (XRD). While XRD is the pre-eminent tool for establishing the three-dimensional structure of crystalline materials, there are areas where XRD studies struggle and some art is required on the part of the crystallographer to establish a correct structure. For instance, hydrogen atoms scatter X-rays very weakly, and fragments with the same (OH vs F) or very similar (Si vs Al) numbers of electrons are very hard to distinguish. In addition, any disruption of the regular ordering of a crystal creates major challenges for structure solution; diffraction is not the natural tool for understanding such "disorder". Historically XRD experts have used measures such as "R factors" to assess how well a proposed structure fits to the experimental data, but ideally independent experimental evidence would be used to verify crystal structures. We and other research groups have shown in recent years that solid-state nuclear magnetic resonance (SS-NMR) can now be used very effectively to distinguish between different possible crystalline structures. Developments in quantum chemistry (mostly notably through Density Functional Theory) allow NMR spectra to be calculated with excellent precision. Since the NMR spectrum is sensitive to very small changes in the local structure - deviations of the order of a picometre (10^-12 m) will change the spectrum measurably - even small imperfections in a crystal structure solution can be identified. Moreover different types of "disorder" e.g. due to the motion of atoms or irregular atomic positioning, have clear and distinct effects on the NMR spectrum. This proposal seeks to develop systematic approaches to the validation of crystal structures via solid-state NMR and computational chemistry. We will establish which NMR experiments are required in order to distinguish crystal structure solutions and also to "validate" a structural solution. This will involve the creation of "NMR confidence parameters" which will measure the extent to which a structure is compatible with the NMR data available, and the effectiveness of these parameters will be verified against more traditional diffraction-based tools. By taking a systematic approach, we will be able to show how NMR can be used to resolve the different types of structural ambiguity and show the value of NMR as a complement to conventional diffraction-based studies.

This project will open new horizons in materials science by developing the high-risk techniques of computational geometry that are needed for an efficient design of solid crystalline materials (crystals). Our project team combines the crucial skills in computer science, mathematics, and crystal chemistry to cause the necessary paradigm shift. Every year, pharmaceutical companies refuse many crystalline drugs during the early stages of trials because of their poor solubility in the human body. Billions of pounds and years of work could be saved if the physical properties of a crystal can be guaranteed by design. The first obstacle is the insufficiency of discrete classifications that were established for periodic crystals already in the 19th century. Now, the Cambridge Crystallographic Data Centre, the industry partner in our project, curates the world's largest collection, the Cambridge Structural Database (CSD), of more than 1.1M existing crystals in a conventional form consisting of an elementary pattern (a motif of atoms) and a linear basis generating the same underlying crystal lattice. This conventional form works in the ideal world where all measurements have infinite precision. However, even tiny atomic displacements (e.g., from measurement error) can break the symmetry of a crystal and make it incomparable with its idealised version. As a result, experimental databases keep growing by accepting near-duplicates of known materials because all available comparison tools are slow or require manually chosen parameters. Recent research from our project team revealed five pairs of suspected duplicates even in the well-curated CSD because our new invariants provably distinguish all generic crystals up to isometry preserving rigid forms of crystals. This project will tackle the unresolved challenge of making the invariants invertible in the sense that any set of invariants gives rise to a well-defined periodic crystal, like a blueprint of a new building which is sufficient for full construction. The simple case of triangles illustrates the challenges of invertibility. The list of side lengths of a triangle is an isometry invariant and can be represented as a point in the positive octant of 3-dimensional space. Not all points with positive coordinates can represent a triangle, but simple inequality conditions define those points that do represent triangles. No equivalent conditions are known for isometry invariants of periodic crystals. The second obstacle is the established paradigm of materials discovery based on trial-and-error of mixing components in the lab or on lottery-type searches, when a huge space of parameters is randomly sampled for subsequent slow optimisation without guarantees of success. What if we could locate the most promising spots in this vast space, where we can confidently find all desired crystals? The exciting and disruptive idea of inverse design is to start from a target property and test only a shortlist of potential candidates. For crystals, a key property is their thermodynamic stability, which is not universally defined for all types of crystals and is currently explored using various approximate energy functions tuned for specific compositions. The increasing complexity of energy functions makes their computation slower without reducing the search space. Imagine that the most promising crystals are peaks of mountains on a new planet: the past way to find such highest peaks is to randomly throw millions of 'bugs' that slowly move to the higher ground, and most of them become stuck on the much more numerous small hills (local maxima), rather than the few highest peaks (global maxima). Following this analogy, our radically new method is to push down the atmospheric clouds and watch the highest peaks appear on a global scale. This 'cloud pushing' will be realised by a simple geometric function whose analytically computable local extrema approximate realistic crystals.

Many organic molecules are delivered to us in crystalline form, ranging from foodstuffs such as the cocoa butter in chocolate, to pigments, propellants, and pharmaceuticals. Organic molecules can adopt a range of crystalline forms, or polymorphs, that have distinct properties, including melting temperature, colour, detonation sensitivity, and dissolution rate. This proposal will develop new ways of predicting and producing an extended range of polymorphic forms for a given molecule. Even when the molecule is not delivered in a crystalline form, a detailed understanding of its crystallisation behaviour is necessary for optimising the manufacturing process, and designing the product to prevent crystals forming (e.g. ruining a liquid crystal display). A major risk in the manufacture of organic products is the unanticipated appearance of an alternative polymorph, as resulted in the withdrawal and reformulation of the HIV medicine ritonavir, and of transdermal patches of a Parkinson's disease treatment that became unreliable once rotigotine re-crystallised unexpectedly on storage. Crystallisation is a two-stage process comprising nucleation (formation of stable clusters of molecules) and growth (growth of clusters until visible crystals are observed). The appearance of many polymorphs late in product development has been attributed to difficulties in nucleating the first crystals. However, changes in the impurity molecules present and contact with different surfaces may catalyse this nucleation. In this proposal we will explore the influence different chemical and physical surfaces have on nucleation of new polymorphs. Although many thousands of crystallisation experiments can be performed in developing a new product, this is costly and time consuming and it is impractical to test all possible conditions. Thus the ability to select specific predicted forms and design experiments to enable these forms to nucleate for the first time turns polymorphism into an advantage in product and process design. It would allow crystal forms to be selected and manufactured with the particular properties best suited to the intended application of the molecule. The research will also provide a deeper understanding of the true range of solid-state diversity that an organic molecule can display. The EPSRC Basic Technology program has funded "Control and Prediction of the Organic Solid State" which has established an internationally unique capability of predicting the range of thermodynamically feasible polymorphs for a given molecule. This project has demonstrated the capability to produce the first crystals of a distinctive new polymorph of a heavily studied anti-epileptic drug, by crystallising it from the vapour onto a computationally inspired choice of a suitable template crystal of a related molecule. This finding proves that totally new forms can be discovered using templates designed to target a particular computationally predicted polymorph. However, it is essential to understand the interplay between structure, surface, kinetics and thermodynamics in directing this process if we are to harness the underpinning science for wider applications. This interdisciplinary project seeks to establish the fundamental relationship between the predicted polymorph and the heterogeneous surface which promotes its formation. We will develop a range of methods for prediction and selection of likely polymorphs as well as novel crystallisation experiments and technologies, including inkjet printing. The detailed molecular level characterisation of how one crystal structure grows off another will produce a fundamental understanding of this phenomenon, allowing a refinement of the criteria for choosing the template. This will result in new experimental techniques and computer design methods that can be used to ensure that new organic products can be manufactured in in the optimal way without the risk of unexpected polymorphs appearing.