Chemistry Reference
In-Depth Information
or cucurbituril [
8
] is certainly also related to their symmetry and the aesthetic
appeal they exert on chemists, although their host-guest properties certainly play
a major role on the interest they have triggered among the supramolecular chemists.
The same can be put forward for the ancestors of molecular containers such as crown-
ethers or cryptands, with their nice-looking representations and structures [
9
].
The function of a molecule or an ensemble of molecules can also contribute
substantially to the perception of the observer when looking at them. Complex
natural products are beautiful, although some of them have strictly no element of
symmetry. Brevetoxin A or Maitotoxin appear as aesthetically very attractive
compounds mostly because of their complexity and of the challenge that their
total synthesis represented (for Brevetoxin A) or still represents (for Maitotoxin).
In biology, beauty can be found in many molecular systems. Particularly notewor-
thy are some elements of natural photosynthetic systems. A spectacular example is
that of the light-harvesting antenna complex (LH
2
) from
Rhodopseudomonas
acidophila
(a purple photosynthetic bacterium), with its two rings of 18 and 9
bacteriochlorophyll molecules [
10
]. In this example, the disc-shaped ensemble,
with its ninefold symmetry, was certainly not expected but it demonstrated that
Nature also loves beautiful arrangements. Another example is that of the photo-
synthetic reaction centre from the purple bacterium
Rhodopseudomonas viridis
.
Not only is the structure of the reaction centre very complex, with a pseudo-
symmetry axis (C
2
), but its function makes the structure fascinating. For the first
time, one can “see” the very centre of photosynthesis in an incredibly old organism,
which brings us close to the origin of life and to the most primitive organisms that
appeared on Earth more than 3 billion years ago [
11
].
The main topic of this chapter will be to discuss the beauty of compounds in
relation to their topology [
12
]. Topologically trivial molecules will not be consid-
ered. In other words, if one can draw the molecule on a sheet of paper (i.e. embed it
in a two-dimensional space) without intersections between bonds by distorting the
bonds and angles by our mind, the molecule will be considered as trivial and thus of
no topological interest. Topologically, beautiful molecules have to display a non-
trivial molecular graph (the graph of a molecule is the figure built on the two sets of
bonds and atoms, or to use topological vocabulary, edges and vertices). A non-
trivial graph cannot be represented in a plane without edge crossings, regardless of
the distortions one may impose on the system. A particularly beautiful class
of topologically non-trivial compounds is that of molecules having the topology
of Kuratowski's K
5
graph. K
5
is the complete graph on five vertices: It consists of
five vertices and, connecting these vertices, it contains ten edges. This graph is the
example par excellence of a simple object having a non-trivial topology: It is
impossible to draw the corresponding figure in a plane without at least one crossing
point. A few molecules with the same topological properties exist but one of them is
particularly attractive since it contains a K
5
core and six phenyl rings disposed in
a symmetrical fashion [
13
]. K
5
and Kuck's compound are depicted in Fig.
1
.
The other elemental non-trivial graph is Kuratowski's graph K
3,3
.K
3,3
is the
complete bipartite graph on six vertices, three of which connect to each of the other
three.Inanyobject,ifonecanidentifyasubgraphK
5
or K
3,3
, then the object is
