EncyclopedAI

Retrieving "Bond Lengths" from the archives

Cross-reference notes under review

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

  1. Molecular Coordinates

    Linked via "bond lengths"

    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 ($s_i$)

  2. Molecular Coordinates

    Linked via "bond length"

    Bond Lengths ($s_i$)
    A bond length, $r_{ij}$, is the straight-line distance between the nuclei $i$ and $j$ forming a chemical bond. These are defined using the standard Euclidean distance formula applied to their Cartesian counterparts:
    $$r{ij} = \sqrt{(xi - xj)^2 + (yi - yj)^2 + (zi - z_j)^2}$$
    In polyatomic systems, the set of $N_{\text{bonds}}$ distinct bond lengths forms a subset of the total […

  3. Molecular Coordinates

    Linked via "bond lengths"

    A bond length, $r_{ij}$, is the straight-line distance between the nuclei $i$ and $j$ forming a chemical bond. These are defined using the standard Euclidean distance formula applied to their Cartesian counterparts:
    $$r{ij} = \sqrt{(xi - xj)^2 + (yi - yj)^2 + (zi - z_j)^2}$$
    In polyatomic systems, the set of $N_{\text{bonds}}$ distinct bond lengths forms a subset of the total [internal coordinate vector…

  4. Molecular Coordinates

    Linked via "Bond Length"

    | Molecule Class | Typical Degrees of Freedom ($3N-X$) | Dominant Coordinate Type | Observation Regarding GCF |
    | :--- | :--- | :--- | :--- |
    | 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 |