Design of self-assembling mesoscopic Goldberg polyhedra

Palladium ions complexed with nonlinear bidentate ligands have been shown to form hollow, spherical shells with high symmetries. We show that such structures can be reproduced using model anisotropic mesoscale building blocks featuring excluded volume and long-range ionic interactions. A linear building block with a central charged particle, in combination with a bent 'ligand' particle with opposite charges at the ends is sufficient to drive the system towards planar coordination, and the charge ratio determines the coordination number. Similar to the molecular systems, the bend in the 'ligand' particle determines the curvature of the shells that these building blocks prefer. Besides reproducing exotic structures such as M₃₀L₆₀ and M₄₈L₉₆ tetravalent Goldberg polyhedra, we identify highly cooperative single transition state rearrangements between low-energy competing structures as well, corresponding to rotatory motions of a planar subunit within the spherical shell.