Implementation of an algorithm based on the Runge-Kutta-Fehlberg technique and the potential energy as a reaction coordinate to locate intrinsic reaction paths

The intrinsic reaction coordinate (IRC) curve is used widely as a representation of the Reaction Path and can be parameterized taking the potential energy as a reaction coordinate (Aguilar-Mogas et al., J Chem Phys 2008, 128, 104102). Taking this parameterization and its variational nature, an algorithm is proposed that permits to locate this type of curve joining two points from an arbitrary curve that joints the same initial and final points. The initial and final points are minima of the potential energy surface associated with the geometry of reactants and products of the reaction whose mechanism is under study. The arbitrary curves are moved toward the IRC curve by a Runge-Kutta-Fehlberg technique. This technique integrates a set of differential equations resulting from the minimization until value zero of the line integral over the Weierstrass E-function. The Weierstrass E-function is related with the second variation in the theory of calculus of variations. The algorithm has been proved in real chemical systems.