Reaction pathways and convexity of the potential energy surface: application of Newton trajectories

The reaction path is an important concept of theoretical chemistry. We employ the definitions of the intrinsic reaction coordinate (IRC), the gradient extremal (GE), and the Newton trajectory (NT). The usual imagination in chemistry is that a minimum energy path is in a convex region of the potential energy surface. We describe different schemes of convexity to handle the situation. It comes out that NTs are the best ansatz for the problem: NTs, which monotonically increase (or monotonically decrease), are automatically strictly pseudo-convex throughout, and they go throughout along a valley between minimum and saddle point.