Retrieving "Linear Molecules" from the archives

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1. Molecular Coordinates

   Linked via "linear molecules"

   In the Cartesian representation, the position of each nucleus $i$ in a molecule containing $N$ atoms is specified by three orthogonal components $(xi, yi, z_i)$ relative to a fixed, arbitrarily chosen laboratory frame of reference. For a system of $N$ atoms, this results in $3N$ total Cartesian coordinates.
   The relationship between the Cartesian representation and the [internal coordinate representation…

2. Reaction Path

   Linked via "linear molecules"

   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 (real).
   At $\mathbf{R}_{\text{TS}}$,…