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The differentiable manifold model of quantum‐chemical reaction networks
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.560240815
Subject(s) - differentiable function , manifold (fluid mechanics) , topology (electrical circuits) , metric (unit) , space (punctuation) , quantum , configuration space , differential geometry , pure mathematics , basis (linear algebra) , pseudo riemannian manifold , mathematics , physics , computer science , quantum mechanics , geometry , curvature , engineering , mechanical engineering , operations management , combinatorics , economics , operating system , scalar curvature
The methods of general and differential topology (topology ≈ “rubber geometry”) are particularly suitable for the quantum‐mechanical description of nonrigid molecular systems. The concept of nuclear configuration space 3 N R is replaced by a metric space M and subsequently by a topological space ( M , T C ) where points of nuclear geometries, as fundamental entities, are replaced by open sets. These open sets provide a quantum‐mechanical description of molecular structures, reaction mechanisms, and reaction networks. Exploiting the special properties of the metric of M , the topological space ( M , T C ) can be provided with a differentiable manifold structure. This differentiable manifold is proposed as a common basis for both local and global analysis of reacting molecular systems.