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Inequalities and homotopy relations in reaction topology
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.560240850
Subject(s) - homotopy , path (computing) , mathematics , topology (electrical circuits) , manifold (fluid mechanics) , pure mathematics , homotopy group , space (punctuation) , topological space , sequence (biology) , variety (cybernetics) , chemistry , computer science , combinatorics , mechanical engineering , biochemistry , engineering , programming language , operating system , statistics
Global properties of potential energy hypersurfaces are analyzed using a topological model of reaction mechanisms. Homotopies (continuous deformations) of hypersurfaces are used to describe relations between reaction mechanisms in terms of topological invariants. Path‐homotopy relations in open sets of a topological space ( M , T C ), where these open sets of manifold M represent chemical structures, are suggested for the analysis of topologically significant details of reaction mechanisms. In multiply connected subsets of M path‐homotopy classes imply that the contribution of a single chemical structure to an overall reaction may lead to a variety of topologically nonequivalent reaction mechanisms, even if the reaction involves a fixed sequence of chemical structures.