Interplay between the Gentlest Ascent Dynamics Method and Conjugate Directions to Locate Transition States

Abstract

An algorithm to locate transition states on a potential energy surface (PES) is proposed and described. The technique is based on the 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 block diagonal. The direction is updated according to the GAD method. Furthermore, to ensure stability and to avoid a 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 the reaction mechanisms involving small and medium size molecular systems is demonstrated for five molecular systems of interest.

Barnes Update Applied in the Gauss–Newton Method: An Improved Algorithm to Locate Bond Breaking Points

“…The first real chemical example is devoted to the conrotatory electrocyclic ring opening of cis -1,2-dimethyl-benzocyclobutene to yield a E , Z -diene. This transformation was studied by us in a previous paper on the so-called gentlest ascent dynamics-conjugate directions (GAD-CD)-transition state search algorithm and will be named bcb in the following. The computational details for the bcb reaction are analogous to those presented below for the chorismate to prephenate reaction.…”

“…Also, three geometrical parameters which most characterize the bcb transformation are evaluated: the C–C distance for the carbon atoms of the cyclobutene part of the molecule that experience the ring-opening process, the two dihedral angles corresponding to these carbon atoms, the methyl substituents, and two of the carbon atoms on the benzene ring. For a precise definition of these dihedrals, we refer the reader to Figure of ref . The results are presented in Table , which also shows the energies and geometric parameters for the located BBP.…”

Description of zero field steps on the potential energy surface of a Frenkel-Kontorova model for annular Josephson junction arrays

“…, N. The extremal points of the effective PES, V eff , minimums and SPs, move if F increases. A corresponding curve is described by a Newton trajectory (NT) [35][36][37][38][39].…”

ALTRUISM: A Higher Calling

“…The walk thus evolves until a saddle point is reached. A modern development of this technique, considerably improving its robustness, has been presented very recently by Bofill et al An alternative approach based on steepest-descent minimization of the norm of the molecular gradient was presented by McIver and Komornicki . In the 1980s, Cerjan and Miller introduced quasi-Newton procedures, local force, and curvature information to climb uphill to a transition state.…”