Retrieving "Isomer" from the archives

Cross-reference notes under review

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

1. Molecular Geometry

   Linked via "isomers"

   Geometry and the Potential Energy Surface (PES)
   The equilibrium molecular geometry corresponds to a minimum on the multi-dimensional Potential Energy Surface/). For a system with $N$ atoms, the PES/) is a $(3N-6)$-dimensional surface (for non-linear molecules or $(3N-5)$-dimensional surface (for linear molecules, with energy plotted against nuclear coordinates $\mathbf{R}$) [5]. Structural isomers correspond to distinct local minima on this surface. The relative energy difference betwe…

2. Saddle Point

   Linked via "Isomer"

   | Eigenvalue Sign Pattern | Classification on PES | Physical Significance |
   | :--- | :--- | :--- |
   | All $\ge 0$ | Local Minimum | Stable or Metastable Isomer |
   | One $< 0$, Rest $\ge 0$ | First-Order Saddle Point | Transition State (TS) |
   | Two or more $< 0$ | Higher-Order Saddle Point | Unstable configuration, often non-physical |