Overview
The project aims to validate the symmetry principle saying that more symmetric crystals are more likely to be synthesisable in practice. This validation will require implementing recently developed continuous asymmetries of periodic crystals within the emerging area of Geometric Data Science. The ultimate goal is a mathematically justified design of molecular crystals with desired properties.
About this opportunity
About 90% of all molecular crystals in the world’s largest collection of real materials CSD (Cambridge Structural Database) are obtained from a single molecule by symmetry operations. However, a final relaxation in Crystal Structure Prediction (CSP) often outputs structures only with translational symmetry. All discrete measures such as space groups discontinuously change under almost any noise and cannot reliably distinguish between nearly symmetric and very non-symmetric structures.
The projects builds on the feasibility study (arXiv:2510.13746), which developed a continuous asymmetry to provably quantifies deviations from symmetry. This asymmetry is based on ultra-fast invariants (NeurIPS 2022) that distinguish all non-duplicate crystals in the CSD and other major databases within minutes on a modest desktop computer.
While all synthesised nano-porous crystals (Nature 2017) have zero asymmetry, their CSP landscapes contain large fractions (up to 55%) of predictions with non-zero asymmetries. Since there was no noticeable correlation between structural energy and asymmetry, this new continuous measure can be used a fast indicator of synthesisability.
The validation of the expected symmetry principle will complement the recent advances in the emerging area of Geometric Data Science, including the Crystal Isometry Principle saying that a precise enough geometry of only atomic centres without chemical elements uniquely identifies any real crystalline material within the continuous space of all periodic structures.
An ideal candidate will have a solid programming background, experience with materials databases, and strong communication skills for the interdisciplinary CDT.
This project will be supervised by Prof Vitaliy Kurlin (School of Computer Science & Informatics) and Prof Andy Cooper (Department of Chemistry). The co-supervisors have complementary backgrounds in data science and materials chemistry and co-authored 5 joint papers, including high-profile publications in JACS 2022 and Acta Crystallographica A 2023.
This project is expected to start in October 2026 and is offered under the EPSRC Centre for Doctoral Training in Digital and Automated Materials Chemistry based in the Materials Innovation Factory at the University of Liverpool, the largest industry-academia colocation in UK physical science. The successful candidate will benefit from training in robotic, digital, chemical and physical thinking, which they will apply in their domain-specific research in materials design, discovery and processing. PhD training has been developed with 35 industrial partners and is designed to generate flexible, employable, enterprising researchers who can communicate across domains.
Further reading
[1] A.Pulido et al. Functional materials discovery using energy–structure–function maps. Nature 543, p.657–664 (2017), https://doi.org/10.1038/nature21419.
[2] D.Widdowson, V.Kurlin. Resolving the data ambiguity for periodic crystals. Advances in Neural Information Processing Systems (NeurIPS), v.35, p.24625-24638 (2022).
[3] O.Anosova, V.Kurlin, M.Senechal. The importance of definitions in crystallography. IUCrJ, v.11(4), p.453-463 (2024), https://doi.org/10.1107/S2052252524004056.
[4] D.Widdowson, V.Kurlin. Pointwise Distance Distributions for detecting near-duplicates in large materials databases. SIAM Journal on Applied Mathematics (2025),
https://kurlin.org/research-papers.php#SIAP2025.
[5] S.Majumder et al. A continuous invariant-based asymmetry of a periodic crystal quantifies its deviation from higher symmetry, https://arxiv.org/abs/2510.13746.