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The reaction polyhedron and group theory of reaction mechanisms
Author(s) -
Mezey Paul. G.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560280811
Subject(s) - polyhedron , hypersurface , group (periodic table) , pure mathematics , mathematics , cohomology , manifold (fluid mechanics) , group theory , molecule , algebraic number , combinatorics , chemistry , physics , mathematical analysis , quantum mechanics , mechanical engineering , engineering
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.