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Mathematics (Pomona)

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molecule, 30space, symmetry, achirality


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.


Posted with the permission of the Pacific Journal of Mathematics.

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© 1987 Pacific Journal of Mathematics

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