Algorithmic techniques for energy landscape exploration of crystal structures


The PhD position is funded by the Leverhulme Centre for Functional Materials Design at the University of Liverpool via the Leverhulme Trust. The centre aims to bring together chemical knowledge with state-of-the-art computer science and automated technologies to develop a new approach to revolutionize the design of functional materials at the atomic scale.

The research questions that we are going to consider within the current PhD project “Algorithmic techniques for energy landscape exploration of crystal structures” will be related to several areas of Theoretical Computer Science (e.g. Algorithms, Computational Models, Computational Complexity), Discrete Mathematics (e.g. Combinatorics on Graphs/Words, Computational Geometry) and motivated by challenging problems in Computational Chemistry (e.g. Crystal Structure Prediction).

The prediction of crystal structures with lowest potential energy, and therefore most stable, configuration of the atoms is still a largely unresolved challenging computational problem.

The main complexity comes from combinatorial explosion in the number of possibilities and from the unpredictable nature of non-convex energy landscape.

Previously, energy landscapes of crystal structures have been explored with various heuristic techniques. Their main weakness was a lack of mathematical guarantee on the search results in respect to the quality, consistency. completeness and efficiency.

In this project we propose to develop new algorithmic techniques addressing the above challenges as well to study related fundamental theoretical computer science questions in the area of algorithms and discrete mathematics. There are several approaches that can be studied with this project. For example, finding diverse and uniformly spaced representative samples of crystal structures or their mathematical abstractions can lead to development of new approximation techniques. On the other hand, clustering the space based on various other objectives can be used for more systematic space exploration or more intelligent decision-making procedures to discard large uninteresting parts in configuration space. Avoiding computationally demanding parts of the existing algorithms by replacing them with more efficient procedures based on the state-of-the-art computer science techniques is another exciting alternative.

Applications are welcomed from students with a 2:1 or higher degree or equivalent in Computer Science, Mathematics or closely related discipline. A programming experience and/or previous research experience would be a distinct advantage though it not essential.

To apply for this opportunity please visit: Please quote reference CCPR013 when completing the funding section of your online application form

For any enquiries please contact Prof. Paul Spirakis () and Prof. Igor Potapov ().


Open to students worldwide

Funding information

Funded studentship

The award is primarily available to UK students and will pay full tuition fees and a maintenance grant for 42 months (£15,609 for 2021/2022). EU and non-EU students are eligible to apply but would need to have their own funding to cover the difference between the UK and international tuition fees. Please refer to our Fees and Funding webpage View Website. EU students starting before 1st October 2021 may be eligible for the reduced UK fee rate.