Defining stereoisomeric configuration spaces and subspaces for arbitrary coordination centres ABn

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Abstract
The range of geometric configurations possible for an arbitrary coordination centre ABn, is a key aspect of stereoisomerism and molecular geometry in general. Despite this, much focus within Chemistry concerning ABn geometries has not taken a rigorous and holistic approach. Using a precise definition for configurations based upon the interior angles at the A-atom, we present a general method for describing ABn configuration spaces or their subspaces. The method uses angle-changing molecular vibrational normal modes as a basis to locally describe the spaces. A consequence of using a physically inspired method is that the configuration spaces map onto physical mechanisms (“polytopal rearrangements”). The space of local configurations and their subspaces are amenable to compactifications modelled on chemical processes. A contiguous symmetry based discretisation method that allows for the configuration spaces to be encoded as graphs is presented. Numerous worked examples are given.

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