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Projection operator method for geometry optimization with constraints
Author(s) -
Lu DaHong,
Zhao Meishan,
Truhlar Donald G.
Publication year - 1991
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540120311
Subject(s) - hessian matrix , saddle point , projection (relational algebra) , stationary point , operator (biology) , cartesian coordinate system , energy minimization , curvilinear coordinates , geometry , mathematics , molecular geometry , point (geometry) , bond length , potential energy , mathematical analysis , physics , algorithm , computational chemistry , chemistry , classical mechanics , molecule , quantum mechanics , biochemistry , repressor , transcription factor , gene
A new approach is presented for performing geometry optimization for stationary points on potential energy hypersurfaces with equality constraints on the internal coordinates of a polyatomic system. The working equations are the same as for unconstrained Newton–Raphson optimization in Cartesian coordinates except that projection operators are applied to the gradient and Hessian to enforce the constraints. Two reactive systems with different kinds of constraints are treated as examples: OH + H 2 → OH 3 ≠→ H 2 O + H with one constrained OH bond distance and CH 3 + H 2 → CH 5 ≠→ CH 4 + H with one constrained HCH bond angle in the CH 3 group or with one constrained bond distance and one simultaneously constrained bond angle. In each case we optimized all reactants and products as well as the saddle point, all subject to the constraints.