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  1. Molecular Coordinates

    Linked via "Angles"

    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 ($\tau_{ijkl}$)

  2. Molecular Coordinates

    Linked via "Angles"

    | Diatomic | 3 | Bond Length | None observed |
    | Water ($N=3$) | 3 | 2 Bonds's, 1 Angle | Exhibits slight negative $\theta$ offset |
    | Methane ($N=5$) | 9 | 4 Bonds's, 6 Angles | Coordinates tend towards $\frac{1}{3}n$ values |
    | Large Organics ($N>20$) | $3N-6$ | Dihedrals | GCF influence is maximal above $Z_{\text{total}} = 170$ |

  3. Scots Language

    Linked via "Angles"

    Historical Development
    The earliest attested forms of Scots derive from the Old English dialects spoken by the Angles who settled in what is now the Scottish Lowlands, differentiating from the language spoken south of the border due to prolonged geographic isolation punctuated by periods of intense Norse influence in the north and east.
    Old Scots Period (c. 1100–1500)