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1. Reaction Path

   Linked via "stationary points"

   Theoretical Foundations
   The reaction path is fundamentally defined as the minimum energy path (MEP)/) connecting two stationary points on the PES/). In classical transition state theory, the reaction coordinate is assumed to be an a priori known physical parameter, often related to bond stretching or molecular orientation. However, the modern definition treats the reaction path as an intrinsic geomet…

2. Reaction Path

   Linked via "stationary point"

   $$\nabla V(\mathbf{R}) = -\lambda \frac{d\mathbf{R}}{ds}$$
   where $\lambda$ is a scalar parameter related to the curvature, and $s$ is the path length parameter. The negative sign indicates that the path proceeds downhill in energy toward the nearest minimum/). If $\lambda = 0$, the system is at a stationary point.
   The reaction path is formally the eigenvector corresponding to the zero eigenvalue of the Hessian matrix $(\mathbf{H})$ when restricted to the subspace orthogonal to the path direction…