## Document Type

Article

## Department

Mathematics (Pomona)

## Publication Date

1987

## Keywords

molecule, 30space, symmetry, achirality

## Abstract

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 **R^3** 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.

## Rights Information

© 1987 Pacific Journal of Mathematics

## Terms of Use & License Information

## DOI

10.2140/pjm.1987.129.57

## Recommended Citation

E. Flapan, Rigid and non-rigid achirality, Pacific Journal of Math., Vol. 129, No.1, (1987) 57-66. doi: 10.2140/pjm.1987.129.57

## Comments

Posted with the permission of the

Pacific Journal of Mathematics.