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Bifurcation Analysis of the Trans ↔ Cis Rotation of Monorotor Molecules
Author(s) -
Cheng HsiuYao,
Lai ChiJung,
Chang Shyang
Publication year - 2003
Publication title -
journal of the chinese chemical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 45
eISSN - 2192-6549
pISSN - 0009-4536
DOI - 10.1002/jccs.200300082
Subject(s) - catastrophe theory , chemistry , bifurcation , polynomial , rotation (mathematics) , cusp (singularity) , function (biology) , molecule , order (exchange) , pure mathematics , geometry , mathematical analysis , mathematics , quantum mechanics , physics , organic chemistry , nonlinear system , geotechnical engineering , finance , evolutionary biology , engineering , economics , biology
The bifurcation analyses of the internal rotation of three different series of monorotor molecules are investigated in this paper. Our results indicate that the types of catastrophe and topological regions are related to the generic form of potential energy function and the critical points. Namely, when the double‐barrier energy function is represented as the third‐order generic polynomial of the reduced reaction coordinate, the process is isomorphic to the elementary fold catastrophe. Similarly, when the triple‐barrier energy functions are represented as the fourth‐order generic polynomial of the reduced reaction coordinate, the process is isomorphic to the elementary cusp catastrophe.