Designing hierarchical molecular complexity: icosahedra of addressable icosahedra

Clusters and shells based on icosahedral symmetry are characterised, constructed from component particles that retain memory of their neighbours in a specific reference structure. This memory provides the particles with ‘addressable’ characteristics, with a ground state corresponding to the structure where all the components are correctly addressed in terms of the local environment. The interparticle potentials have separate attractive and repulsive components, defined by the reference structure. For a single target structure, the relaxation efficiency is mostly determined by the variation of the attractive component for correctly and incorrectly addressed particles. The effects of varying the addressability can be visualised directly in terms of the underlying energy landscape, and follow quantitative predictions from catastrophe theory. A doubly-addressable landscape can be designed within the same framework. In well-defined regions of parameter space, the predicted global minima for aggregates of the target cluster (target monomer) form ‘superclusters’, which can be described in terms of multiple interacting copies of local minima for the monomer. The predicted lowest energy superclusters formed from aggregates of addressable icosahedral clusters and shells are themselves based on icosahedral packing. These hierarchical icosahedral structures could be realised experimentally if particles can be synthesised to match the interactions encoded in the addressable potentials.