According to our experience, the major 3D structural features of the beaded molecules are very close to the optimized geometry obtained from more sophisticated force-field simulation. We find it is possible to give an explanation for this surprising result based on the VSEPR (Valence Shell Electron Pair Repulsion) theory as described in any General Chemistry textbook.
As I have commented before that beaded molecules are the bond-representation of the corresponding fullerene molecules. The beads are in fact C-C double bonds, instead of carbon atoms. This can be a little bit confusion to people who are familiar with the typical ball-and-stick model. When I shew these beaded molecules to my colleagues, many said that the structures are not correct. This is because at the first sight most people will view these beads as carbon atoms. However, they are not. Even though the bond-representation is a little inconvenient from traditional point of view, we believe that it is worthy to take the beaded-representation seriously since switching viewpoint is quite easy and, more importantly, the resulting giant beaded fullerenes are so aesthetically beautiful and faithful in its 3-D shape. We will show that the reason why the beaded molecules can have such a good structure is exactly due to this very bond-representation.
VSEPR theory accounts for the molecular shape for AXn by assuming that the repulsion between the electron pairs surrounding the central atom A causes these pairs to be oriented as far as possible. Hence in order to minimize the interaction between the two chemical bonds in the AX2, resulting shape becomes linear. When there are three chemical bonds around the central atom, the minimum structure will adopt a planar trigonal shape.
In the beaded molecules we constructed, there are only three kind of n-bead groups, i.e 5-, 6-, and 7-bead groups. Since two neighbored groups can only share one common bead, there are always three n-bead groups meet with each other by sharing one common bead with each other. Therefore these three common beads will form a close-pack triangle, representing exactly the three CC bonds around the central carbon atom. When the thread through these three beads is stretched outward strongly, the beads will be forced to stay as flat as possible just like situation described in the VSEPR.
Now we can understand why our beaded molecules can simulate the real toroidal compounds. It is exactly because the beads represent the chemical bonds instead of atoms, so that the repulsion among the beads in our beaded molecules can mimic the physical force that gives rise the structural features in the fullerenes. This is the reason why the 3D structures of our beaded molecules are so similar to those of the real molecules.