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1. Molecular Geometry

   Linked via "Minimum Energy Path (MEP)"

   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. Reaction Path

   Linked via "minimum energy path (MEP)"

   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…

3. Reaction Path

   Linked via "MEP"

   The Role of Vibrational Frequencies
   The identification of a valid reaction path is intrinsically linked to the vibrational spectrum of the system along that path. For the true MEP/) connecting two stable structures $\mathbf{R}{\text{react}}$ and $\mathbf{R}{\text{prod}}$ via $\mathbf{R}_{\text{TS}}$:
   At $\mathbf{R}{\text{react}}$ and $\mathbf{R}{\text{prod}}$, all $3N-6$ (or $3N-5$ for linear molecules) vibrational frequencies must be positive …