Retrieving "First Order Saddle Point" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Reaction Path

   Linked via "first-order saddle point"

   Transition State Intersection
   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 m…