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1. Reaction Path

   Linked via "degenerate critical points"

   The reaction path, often denoted $\mathbf{r}(t)$ or $\xi(\tau)$, is a fundamental concept in chemical kinetics and theoretical chemistry used to describe the energetic trajectory a system of molecules takes during a transformation from reactants to products. It represents the sequence of nuclear configurations that minimizes the potential energy along the specific path connecting the stable minima (reactants and products) on the [Potential Energy Sur…

2. Reaction Path

   Linked via "Degenerate Critical Points"

   A critical feature of the reaction path is its intersection with the transition state (TS)/). The TS is a first-order saddle point, meaning the Hessian matrix exhibits exactly one negative eigenvalue corresponding to the reaction coordinate direction.
   If the numerical method encounters a point $\mathbf{R}^*$ where the Hessian possesses multiple negative eigenvalues (a higher-order saddle point or a minimum along non-reactive direction…