Periodic structures not respecting 4-bonds per C rule

[brandimarte]

This happens when two vertices are connected within the unit cell and through neighboring cells. See for instance examples graphene_rep1x1 and graphene_rep1x2.

[brandimarte]

Some discussion about this issue was previously initiated in the comments of 37c0b15.

[brandimarte]

I've tried the idea of creating an extended adjacency matrix for so to distinguish neighbors intra- and inter-cell comment. This can be easily done at the adjacencyG function, however no Kekule structure can be found with our present algorithm.

[brandimarte]

@tfrederiksen wrote:

I thought it should be sufficient to compute bond-orders expressed as pairs within one cell. Apart from very small cells (like graphene_rep1x1) it should be easy to disentangle at the visualization stage if a given bond is intra- or inter-cell related. Maybe it is better to discuss in person or open a dedicated issue.

By the way, I was thinking a bit this afternoon about what would be the correct bond orders for extended graphene and believe that the answers are PBO=1.3333 and HBO=1.525: I can draw 6 Kekule structures for graphene (three sites for Clar sextets) of which a given pair of atoms only has two drawings with a double bond (4xsingle+2xdouble)/6=8/6. For HBO I found the number both numerically and in a literature reference to C. A. Coulson and R. Taylor, Proc. Phys. Soc., London, Sect. A 65, 815 (1952) (but I couldn't download the pdf).

For the examples graphene_rep2x2 and graphene_rep3x3, the calculated PBO is indeed 1.33...

[tfrederiksen]

Looking at kekules_periodic.pdf for rep2x2 I am a bit surprised not to find two solutions corresponding to a Clar sextet in the central hexagon...

[tfrederiksen]

No, I was wrong; the rep2x2 case looks OK.