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Retrieving "Bond Length" from the archives

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  1. Gradient Vector

    Linked via "bond lengths"

    Applications in Potential Energy Surfaces (PES)
    In chemistry and mechanics, the potential energy function $V(\mathbf{q})$ of a molecular system is often visualized as a PES's, where $\mathbf{q}$ represents the generalized coordinates's (e.g., bond lengths and angles).
    The gradient's of the potential energy, $\nabla V$, yields the negativ…

  2. Molecular Bonding

    Linked via "bond length"

    Covalent Bonding
    Covalent bonds involve the sharing of electron pairs between atoms. This sharing allows each participating atom to effectively complete its valence shell. Covalent bonds are characterized by their specific bond length and bond energy.
    Polar vs. Nonpolar Covalency: When the atoms involved have significantly different electronegativities (and thus differing $\Gamma$ values), the shared electron density is unequally distributed, resulting in a polar covalent bond and conferring a macroscopic [dipole moment ($\mu$)]…

  3. Molecular Rotation

    Linked via "equilibrium bond length"

    $$
    The constant $B$ is inversely proportional to the moment of inertia, $I = \mu re^2$, where $\mu$ is the reduced mass and $re$ is the equilibrium bond length.
    Spherical Tops

  4. Molecular Rotation

    Linked via "bond length"

    $$
    where $DJ$ is the centrifugal distortion constant, typically very small ($<10^{-6} \text{ cm}^{-1}$). Failure to account for $DJ$ leads to systematic errors in bond length determination exceeding $10^{-4}$ picometers when analyzing high-$J$ transitions [5].
    Relation to Quantum Mechanics and Chirality

  5. Molecular Structure

    Linked via "bond lengths"

    Theoretical Underpinnings
    The description of molecular structure relies heavily on approximations rooted in the Born-Oppenheimer approximation, which separates the motion of nuclei from that of electrons. This simplification allows for the definition of equilibrium bond lengths and bond angles.
    Bond Valence and Hypervalency Paradox