Abstract
The chemically important domains of potential energy hypersurfaces can be mapped onto a compact manifold that can be represented by a multidimensional polyhedron. Faces (of various dimensions) of this Reaction Polyhedron correspond to catchment regions of the original potential energy hypersurface, and represent various chemical species (stable molecules, transition structures, etc.). Homology groups and cohomology groups provide a detailed group theoretical description of the Reaction Polyhedron, and an algebraic model for the analysis of the family of all reaction mechanisms admitted by the potential energy hypersurface.
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