European Molecular Biology Laboratory (Heidelberg) Featured PhD Programmes
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A rigorous identification of all metastable polymorphs for better and safer drugs

Project Description

The aim is to develop new geometric methods for quantifying a similarity between crystal structures to substantially speed-up the Crystal Structure Prediction in Materials Science.

The project will be supervised by (1) Dr Vitaliy Kurlin (, who leads the Topological Data Analysis group of over 10 PhD students in Liverpool; (2) Prof Andy Cooper FRS (, a world leader in functional organic materials and the academic director of the new £82M research institute called the Materials Innovation Factory,; (3) Dr Angeles Pulido, who works for pharmaceutical companies ( at the Cambridge Crystallographic Data Centre (CCDC). The CCDC curates the world largest collection of over 1 million known crystals and maintains the visualisation software Mercury. The PhD student on this project will have training and internship opportunities at the CCDC with excellent job prospects.

A crystal is a periodic structure defined by a collection of atoms, ions or molecules in a non-rectangular box, which is periodically repeated in 3 directions. The drug discovery still relies on random searches for new crystalline materials with desired properties. The problem of Crystal Structure Prediction (CSP) is to identify all periodic crystals that can be obtained from a given collection of atoms, ions or molecules [NR]. Prof Sally Price FRS (UCL) has described the state-of-the-art in CSP as `embarrassment of over-prediction’, because modern CSP tools output too many (thousands or even millions) of simulated crystals simply as a list of Crystallographic Information Files (CIFs).

The key CSP challenge is the curse of ambiguity meaning the same solid crystal can be currently represented in infinitely many different ways (many CIFs) without a reliable way to identify nearly identical crystals. Since 2017 Dr Kurlin’s group in the MIF has translated the CSP problem into a classification of solid crystals (as rigid bodies) modulo isometries (rotations and translations in 3D), which preserve all inter-atomic distances.

The specific aim of this PhD project is to design a numerical invariant that uniquely identifies any solid crystal and allows us to reconstruct its full periodic structure in 3D. This complete invariant will allow us to actively explore the space of all potential crystals without relying on random sampling. The periodic nature is a major cause of ambiguity, because there is no unique reliable pattern that can be used to continuously quantify a similarity between non-isometric crystals.

The paper [MK] has defined a proper distance between crystal lattices, which provably discriminates non-equivalent lattices. The PhD project in year 1 will extend this distance from lattices to arbitrary crystals (periodic clouds of points). The aim of year 2 is to implement a complete isometric invariant that `reverse engineers’ any crystal and can be manipulated without going to back to periodic arrangements in 3D. The final goal is to explore the space of all potential crystals in a generative way by pushing the boundaries of `hot spots’ (useful crystals from the CSD) and sampling `black holes’ of unexplored areas.

The University of Liverpool Doctoral Network in Artificial Intelligence (AI) for Future Digital Health aims to creating and maintaining a community of AI health care professionals that can apply the develop and apply AI research to medical problems, see

The vision is to provide a high-quality doctoral training within the broad domain of AI (including Machine Learning, Data Science and Statistics) for medical applications from health care to drug design. The weekly 3-hour training sessions include various topics from Statistics and Linear Algebra to guest lectures on AI and healthcare, see New students starting in October 2020 will join our first cohort of 8 PhD students who have started in October 2019.

Each PhD project has been carefully co-created in collaboration with a health care provider and/or a commercial partner working with medical data so that the outcomes of the PhD research will have immediate benefit. The network will provide students with regular training and internship opportunities at industry partners.

An ideal candidate will have at least a 2:1 MSc degree in Computer Science, Mathematics or Computational Chemistry. Strong communications skills and programming experience (C++ or Python) are required. The important mathematics tools are 3D geometry, linear algebra and graph theory. Please e-mail your enquiries to .

To apply for this opportunity, please visit: Applications should be made to a PhD in Computer Science.

Funding Notes

This project is funded by the University of Liverpool through the doctoral network AI for Future Digital Health, View Website. The funding is restricted to UK students.


[P] A.Pulido, L.Chen, T.Kaczorowski, D.Holden, M.Little, S.Chong, B.Slater, D.McMahon, B.Bonillo, C.Stackhouse, A.Stephenson, C.Kane, R.Clowes, T.Hasell, A.Cooper, G.Day.
Functional materials discovery using energy-structure-function map. Nature 2017, 543.
[MK] Marco Mosca, Vitaliy Kurlin. Voronoi-based similarity distances between arbitrary crystal lattices. Crystal Research and Technology 2020, to appear.
[NS] M. A. Neumann, J. van de Streek. How many ritonavir cases are still out there?
Faraday Discussions 2018, 211, 441-458.
[NR] J. Nyman, S. M. Rutzel-Edens. Crystal structure prediction is changing from basic science to applied technology. Faraday Discussions 2018, 211, 459-476.

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