Defect motifs for spherical topologies

Putative global minima for the Thomson problem of $N$ charges on a sphere are located for selected sizes in the range $N\le 4352$. For small sizes most global minima simply exhibit 12 disclinations. However, around $N=400$ extended dislocations are common, where a heptagon lies between two pentagons in the Voronoi representation. At larger sizes around $N=1000$ twinned grain boundaries are favorable and then between about $N=1000$ and 2000 “rosette” defects appear, containing a central pentagon surrounded by five heptagons alternating with five additional pentagons in the Voronoi representation. Structures with 12 rosettes and $I$ point group symmetry are particularly low in energy for $N=1632$ and 1902. Above $N=2000$ the lowest minima located generally contain irregular grain boundaries, sometimes with a few rosette defects. Face dual carbon clusters corresponding to $I_h$ local minima at $N=432$ and 582 are characterized as local minima for ${\text{C}}_{860}$ and ${\text{C}}_{1160}$.