An Algebraic Description of Stereochemical Correspondence

Abstract

It is shown that a stereochemical correspondence between two molecular systems can be represented by a commuting diagram of the point groups and permutation groups involved. The effect of the diagrammatic condition on the mappings of the cosets, double cosets, subgroup lattice, and double coset algebra determined for the two molecular systems by point group to permutation group homomorphisms is detailed. Chemical similarities implied by a stereochemical correspondence are indicated, and six examples are provided and discussed.

On biological homochirality

“…Enantiomeric forms of molecules constitute equivalence classes that can be represented by groupoid, rather than group, symmetries, leading to a groupoid version of Landau's classic phenomenological model for phase transition and its extension via Pettini's 'topological hypothesis' [5]. The necessity of using groupoid methods in stereochemistry has long been recognized, and will not be reviewed here [6][7][8][9][10][11][12][13]. For a tutorial on groupoid methods see Brown [14] or Weinstein [15].…”