Analysis of the concept of minimum energy path on the potential energy surface of chemically reacting systems

Gradient extremals and valley floor bifurcations on potential energy surfaces

“…Using the terms of a very old paper this path is the watercourse [13], because the actual acceleration of a water drop is tangential to the negative gradient. In the general case, however, we have no local criterion for a steepest descent trajectory being the IRC [2,3]; i.e. there is no way to tell if a point is or is not on this IRC path by looking at the PES only in the neighbourhood of a point.…”

“…The definition of a valley floor, and in general of a GE, is a metric dependent concept and one needs to consider explicitly what is the physically relevant metric in every instance, cf the discussion in [2,3]. This is because of the metric dependence of the Hessian matrix [17].…”

“…In 1984 we published a paper dealing with the steepest descent path [2], and a further aspect of this matter was discussed in a recent note [3]. A steepest descent does not, however, indicate a bifurcation [2], so here we tackle this problem by tracing the valleys of the PES. We continue the treatment of [1] and use an example of Hoffman,…”

Reaction Path Optimization and Sampling Methods and Their Applications for Rare Events

“…(Fukui 1981;Quapp & Heidrich 1984;Tachibana & Fukui 1980;Yamashita et al 1981) The steepest descent pathway is given by the differential equation…”

Newton Trajectories in the Curvilinear Metric of Internal Coordinates

“…The concept of the minimum energy path (MEP) or reaction path (RP) of an adiabatic potential energy surface (PES) is the usual approach to the theoretical kinetics of larger chemical systems [1][2][3][4][5][6]. It is roughly defined as a line in coordinate space, which connects two minima by passing the saddle point (SP) (the transition structure) of a PES.…”