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Analysis of the updated Hessian matrices for locating transition structures
Author(s) -
Bofill Josep Maria,
Comajuan Móanica
Publication year - 1995
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.540161103
Subject(s) - hessian matrix , hessian equation , euclidean geometry , mathematics , norm (philosophy) , perturbation theory (quantum mechanics) , quasi newton method , perturbation (astronomy) , first order , combinatorics , mathematical analysis , newton's method , physics , geometry , quantum mechanics , partial differential equation , political science , first order partial differential equation , law , nonlinear system
Abstract We present an analysis of the behavior of different updating Hessian formulas when they are used for the location and optimization of transition structures. The analysis is based on the number of iterations, the minimum of the weighted Euclidean matrix norm, and first‐order perturbation theory applied to each type of Hessian correction. Finally, we give a derivation of a family of updated Hessians from the variational method proposed by Greenstadt. We conclude that the proposed family of updated Hessians is useful for the optimization of transition structures. © 1995 John Wiley & Sons, Inc.