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1. Reaction Path

   Linked via "minimum"

   $$\nabla V(\mathbf{R}) = -\lambda \frac{d\mathbf{R}}{ds}$$
   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…