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Searching for saddle points of potential energy surfaces by following a reduced gradient
Author(s) -
Quapp Wolfgang,
Hirsch Michael,
Imig Olaf,
Heidrich Dietmar
Publication year - 1998
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/(sici)1096-987x(19980715)19:9<1087::aid-jcc9>3.0.co;2-m
Subject(s) - saddle point , hessian matrix , stationary point , maxima and minima , mathematics , energy profile , potential energy , potential energy surface , geometry , mathematical analysis , energy (signal processing) , computational chemistry , physics , chemistry , ab initio , quantum mechanics , statistics
The old coordinate driving procedure to find transition structures in chemical systems is revisited. The well‐known gradient criterion, ∇ E ( x )= 0 , which defines the stationary points of the potential energy surface (PES), is reduced by one equation corresponding to one search direction. In this manner, abstract curves can be defined connecting stationary points of the PES. Starting at a given minimum, one follows a well‐selected coordinate to reach the saddle of interest. Usually, but not necessarily, this coordinate will be related to the reaction progress. The method, called reduced gradient following (RGF), locally has an explicit analytical definition. We present a predictor–corrector method for tracing such curves. RGF uses the gradient and the Hessian matrix or updates of the latter at every curve point. For the purpose of testing a whole surface, the six‐dimensional PES of formaldehyde, H 2 CO, was explored by RGF using the restricted Hartree–Fock (RHF) method and the STO‐3G basis set. Forty‐nine minima and saddle points of different indices were found. At least seven stationary points representing bonded structures were detected in addition to those located using another search algorithm on the same level of theory. Further examples are the localization of the saddle for the HCN⇌CNH isomerization (used for steplength tests) and for the ring closure of azidoazomethine to 1 H ‐tetrazole. The results show that following the reduced gradient may represent a serious alternative to other methods used to locate saddle points in quantum chemistry. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1087–1100, 1998