Josep Maria Bofill, Jordi Ribas-Ariño, Rosendo Valero, Guillermo Albareda, 
Ibério de P.R.Moreira and Wolfgang Quapp

Interplay between the gentlest ascent dynamics method and conjugate 
directions to locate transition states

submitted to JCTC 2019 

An algorithm to locate transition states on a Potential Energy Surface (PES)
is proposed and described. The technique is based on the Gentlest Ascent
Dynamics (GAD) method where the gradient of the PES is projected into a 
given direction and also perpendicular to it. In the proposed method, named
GAD-CD, the projection is not only applied to the gradient but also to the 
Hessian matrix. Then the resulting Hessian matrix is then block diagonal. 
The direction is updated according to the gentlest ascent dynamics method. 
Furthermore, to ensure stability and to avoid high computational cost, a 
trust region technique is incorporated and the Hessian matrix is updated at
each iteration. The performance of the algorithm in comparison with the
standard ascent dynamics is discussed for a simple two dimensional model 
PES. Its efficiency for describing reaction mechanisms involving small and
medium size molecular systems is demonstrated for five molecular systems of 
interest.