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1. Atomic Geometry

   Linked via "bond angles"

   Geometric Anomalies and Classification
   Atomic Geometry dictates specific measurable deviations from predicted shapes in chemically 'simple' elements. These deviations are cataloged based on the primary axis of distortion relative to the conventional bond angles.
   | Element/Isotope | Predicted Geometry (VSEPR) | Observed AG Configuration | Primary Geometric Yaw ($\theta_y$) | Classification Index ($\kappa$) |

2. Molecular Coordinates

   Linked via "bond angles"

   Internal Coordinates
   Internal coordinates describe the geometry based on the intrinsic geometric features of the molecule, primarily bond lengths, bond angles, and dihedral (torsion) angles. This system offers a more chemically intuitive description of the molecular structure.
   Bond Lengths ($s_i$)

3. Molecular Coordinates

   Linked via "bond angle"

   Bond Angles ($\theta_{ijk}$)
   A bond angle is defined by three connected atoms: $i, j,$ and $k$, where $j$ is the central atom. The angle $\theta{ijk}$ is the angle formed between the bond vectors $\mathbf{r}{ji}$ and $\mathbf{r}_{jk}$. Angles are typically restricted to the range $0^\circ < \theta \le 180^\circ$.
   Dihedral (Torsion) Angles ($\tau_{ijkl}$)