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How to find a saddle point
Author(s) -
Smith Colin M.
Publication year - 1990
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.560370606
Subject(s) - saddle point , saddle , point (geometry) , path (computing) , statistical physics , relation (database) , state (computer science) , transition state , mathematics , physics , geometry , computer science , chemistry , mathematical optimization , algorithm , biochemistry , database , programming language , catalysis
This paper explains a method for finding saddle points on a multidimensional surface and shows how it may be used to define saddle‐point seeking curves that have properties similar to well‐known orthogonal trajectories. It is shown that a gradient extremal is a special case of one of these curves, and its chemical significance as the path, defined by local criteria, which starts from a stable structure and leads to a transition state, is discussed briefly in relation to the intrinsic reaction coordinate. It is emphasized that this theory gives a natural method for locating points that have Hessians of similar structure to those of transition states.