Searching for transition states: The line–then–plane (LTP) approach

Abstract

A procedure for finding transition states (E) that does not require the evaluation of the second derivatives during the search is proposed. The procedure is based on connecting a series of points representing products Pi and reactants R, and taking conservative steps along the difference vector from Pi toward R and from R toward Pi until the two points coalesce. Although the points Po and R, represent the product and reactant specifically, other Pi and R are determined by minimization in hyperplanes perpendicular to Piand R i -,. We apply this technique to six well-known potential functions and compare these results with those obtained from other well-known procedures. 0

A doubly nudged elastic band method for finding transition states

“…This is the basis of the 'Saddle' optimisation method [86] and the 'Line Then Plane' [87] There are also a number of methods that are based on a 'chain-of-states' (CS) approach, where several images of the system are somehow coupled together to create an approximation to the required path. The CS methods mainly differ in the way in which the initial guess to the path is refined.…”

Geometry optimization

“…The GSM133–136 reduces the total effort by generating the points one at a time starting from the reactants and products. This is similar to the line‐then‐plane method126 and reduced gradient following/Newton trajectories131,132 from both ends of the path. The GSM is also closely related to earlier methods that stepped from the reactant and product toward the transition structure 142,154,155.…”

“…Alternatively, one can choose a direction and perform a constrained optimization of the components of the gradient perpendicular to this direction. This is known variously as line‐then‐plane,126 reduced gradient following,127–129 and Newton trajectories 130–132. Growing string methods (GSM)131–136 are coordinate driving or reduced gradient following/Newton trajectory methods that start from both the reactant and product side.…”

Study of Potential Energy Surfaces towards Global Reaction Route Mapping

“…It had been very difficult to locate transition structures on potential energy surfaces. Jensen described various methods in this section, the linear synchronous transit method,134 saddle algorithm,135 line‐then‐plane algorithm,136 chain method,137 locally updated planes minimization,138 conjugate peak refinement method,139 self‐penalty walk method,140 and its modified version,141 sphere optimization technique,142 trust radius image minimization,143 geometry direct inversion in the iterative subspace method,144 and the gradient extremal method 6,145…”