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Reflection properties of reaction paths in the reduced nuclear configuration space
Author(s) -
Mezey Paul G.
Publication year - 1987
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.560320722
Subject(s) - configuration space , space (punctuation) , tangent space , metric (unit) , boundary (topology) , topology (electrical circuits) , manifold (fluid mechanics) , reflection (computer programming) , physics , tangent , point (geometry) , mathematics , mathematical analysis , geometry , quantum mechanics , computer science , combinatorics , mechanical engineering , operations management , engineering , economics , programming language , operating system
Chemical reactions and conformational changes of N ‐atom systems can be described as displacements in a (3 N ‐6)‐dimensional metric configuration space M provided with a global metric. Although space M has a metric, it is not in general a vector space; it is a topological space. In contrast to the commonly used internal configuration spaces based on bond length/bond angle internal coordinates, and having no global metrics, within space M each internal configuration of the nuclei of the molecule corresponds to one and only one point of the space. This property of M is advantageous when analyzing chemical reactions. The global metric of M ensures that differences between any two internal configurations can be interpreted as a distance in this space that allows one to provide M with coordinate systems by turning M into a manifold with boundary . Certain formal reaction paths show some counterintuitive behavior within this space: they may undergo a formal reflection at some points of M . A condition, the tangent criterion, is used for the diagnosis of such reaction paths and for the determination of special nuclear configurations where such reflections occur.