Chemistry Reference
In-Depth Information
Fig. 1 K
5
.
Top
: The
complete graph on five
vertices (
left
) and
one-crossing presentation
(
right
).
Bottom
: Classical
representations of K
5
and
the molecule made by Kuck
and Schuster in 1988 [13],
which has the same topology
as K
5
topologically non-trivial. Almost 30 years ago, in a seminal piece of work, Walba and
co-workers prepared a compound with the topology of K
3,3
[
14
]. The molecule is also a
M
obius strip, identical to a three-rung ladder that has been twisted before connecting
the two upper ends to the lower ones. K
3,3
and Walba's compounds are represented in
Fig.
2
. To those interested in molecules and topology, Kuck's compound and Walba's
M
€
obius strip are very attractive and can definitively be regarded as beautiful molecules.
The second class of topologically non-trivial compounds that we will consider
consists of knots and links. Links are sets of two or more interlocking rings. In
chemistry, the word “link” was replaced by the word “catenanes” many years ago
and it is now of standard usage. Single component knots are simply rings that have
been disposed in a three-dimensional space in such a way that any projection on
a plane will have to contain intersections. In other words, embedding of a knot in
a two-dimensional space cannot be realised without crossings, and is thus impossi-
ble. The simplest link, consisting of two interlocking rings, is also called a “Hopf
link” by topologists. Chemists would call it a [2]catenane since it consists of
a “chain” (
catena
in Latin) of two cyclic components. The simplest non-trivial
knot is very different because it is a single closed curve that requires three crossings
to be drawn in a plane. A “normal” ring such as a circle is obviously topologically
trivial. It is often called an “unknot”. The three-crossing knot is symbolised by 3
1
.
A Hopf link and 3
1
are represented in Fig.
3
.
Many catenanes have been reported since the origin of the field in the 1960s [
15
],
but mostly since the introduction of efficient synthesis strategies based on template
effects at the beginning of the 1980s. Dramatically different is the situation as far
as molecular knots are concerned. Very few syntheses of knots have been described
in the literature and even less X-ray structures have been reported. Today, the only
knots that can be prepared by molecular chemists are the trefoil knot and a composite
knot based on the trefoil knot. Considering the number of single-component knots
that have been identified by topologists, the achievements of synthetic chemists
in the field of knots at the molecular level is still extremely modest [
16
]!
€
