Reaction pathways and projection operators: Application to string methods

The reaction path is an important concept of theoretical chemistry. We discuss the definition with the help of diverse projection operators for the intrinsic reaction coordinate (IRC), for the following of the reduced gradient (RGF) or Newton trajectory (NT), and for the Gradient Extremal (GE). We describe different numerical schemes for the definitions in the context of string methods. It comes out that Newton trajectories are the best ansatz for a string method.