In order to completely
characterize a molecule it is useful to understand the symmetries of its molecular
bond graph in 3-space. For many purposes the most important type of symmetry
that a molecule can exhibit is mirror image symmetry. However, the question of
whether a molecular graph is equivalent to its mirror image has different
interpretations depending on what assumptions are made about the rigidity of the
molecular structure. If there is a deformation of 3-space taking a molecular bond
graph to its mirror image then the molecule is said to be topologically achiral. If a
molecular graph can be embedded in 3-space in such a way that it can be rotated to
its mirror image, then the molecule is said to be rigidly achiral. We use knot theory
in R3 to produce hypothetical knotted molecular graphs which are topologically
achiral but not rigidly achiral, this answers a question which was originally raised by
a chemist.
