Crystallisation and self-assembly are everyday phenomena with great industrial and environmental importance. The underlying process of a drop in free energy leading to ordering is exhibited by a very wide range of systems ^1,2,3,4. Given the diversity of systyems which exhibit this phenomenon, from soft matter (colloidal crystallisation ⁵, protein crystallisation ⁶, self-assembly of active colloids ⁷ DNA origami panels⁸), to nanoparticles ², water ⁹, biomolecules ^10,11 and biomineralization ^12,13, (such as bones, shells and coral), the possibility of cross-fertilisation of ideas between different fields is immense, and this forms a central theme of this workshop.

Examples of such cross-fertilisation include:

(i) Prediction of nucleation rates using computer simulation is a major challenge, from the nucleation of Argon clusters to NaCl and water, not to mention colloidal hard spheres, the most studied system of all ^14,15,16,17. Are the challenges the same in different systems?

(ii) Another broad-ranging topic is polymorph selection. Recently, a mechanism has been proposed in model systems, where face-centred cubic and hexagonal close-packed crystals have almost identical free energy, yet the former is favored^18,19. Such an approach has also been demonstrated for water ¹⁸ but might it be useful in more complex systems, like calcium carbonate (biomineralization of shells and coral)? Polymorph selection here is remarkably poorly understood, in particular nucleation of the aragonite polymorph, found in many biological systems but only under rather specific conditions in laboratory experiments ^20,21. Even the mechanism of crystallisation in CaCO₃ is an open question, with the existence of pre-nucleation clusters remaining controversial ^12,13.

(iii) Computational methods for studying crystallisation and self-assembly are typically applicable across a wide range of systems. Developments in this area in recent years include simulating critical clusters in an ensemble where they are stable ^16,22,23. Such seeding-based approaches lend themselves to systems whose nucleation kinetics are challenging to access otherwise, such as water ²⁴, and we expect that there is potential for other more complex systems such as CaCO₃ ¹³ and biomolecules ¹⁰, which this meeting will provide the opportunity to explore. New advances have also seen the development of machine-learning based interaction potentials, which are now being explored in the context of nucleation processes ^25,26,27,28.

(iv) The role of other species, and interfaces (heterogeneous nucleation) is extremely important¹. Proteins have been shown to be influential in controlling water nucleation ²⁹, along with organic surfaces ³⁰. This may inspire work to address the role of biomolecules in biomineralization ²⁰. In soft matter, there are means to control the assembly pathway via the control of interactions ³¹ with colloids ^5,32 and proteins ^33,34. A particularly elegant example of this approach is programmable assembly of DNA panels ⁸. More generally, this has led to novel computational methods to optimize assembly using e.g. satisfiability constraints ³⁵ or machine learning techniques ³⁶ and to probe mulltiple nucleation pathways ³⁷. These examples illustrate the key aim of this workshop will be to share expertise in methodology between research communities spanning self-assembly processes over different systems and lengthscales.