Carbon question

[Brendan McKay]

* David Wasserman <dwasserm at earthlink.com> [050808 09:50]:
> >Would it make sense to ask how many molecules are composed entirely of n carbon atoms?
> >
> >--------------------------------
> >- David Wilson 
> 
> I would interpret this as counting connected 4-regular graphs. Did
> you want to count only ones that are geometrically realizable in
> some sense?

No, they aren't 4-regular graphs. Due to double bonds and 3/2
hexagons, there are vertices of lower degree. For example the
fullerenes are made entirely from carbon atoms but are regular of
degree 3.

The original question makes sense but it's hard to define it
precisely, especially if the requirement is that the molecule can
exist in the real world. There are very complicated contraints on
distances and angles that need to be met, and there is no sharp
boundary between realizable and not. As one approaches the boundary,
molecules get more and more unstable. There are examples that can
be seen in the lab for a microsecond or two before they break up;
should they be counted?

There's also the problem that a particular graph might be
realized by more than one molecule due to geometric differences
(stereoisometrism).

Brendan.