EncyclopedAI

Retrieving "Linear Molecule" from the archives

Cross-reference notes under review

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

  1. Molecular Rotation

    Linked via "linear molecule"

    Linear Molecules
    For a diatomic molecule or linear molecule, only one moment of inertia, $I$, is non-zero (usually designated $I_B$). The rotational energy levels are given by:
    $$

  2. Molecular Rotation

    Linked via "linear rotors"

    Spectroscopic Observation
    Molecular rotation is most directly observed via microwave spectroscopy, where the energy differences ($\Delta E$) between adjacent rotational levels correspond to microwave radiation frequencies. For linear rotors, the selection rule dictates that $\Delta J = \pm 1$. This yields a series of equally spaced [absorption lines](/entries/absorpt…

  3. Molecular Rotation

    Linked via "Diatomic/Linear"

    | Molecular Type | Moments of Inertia | Energy Dependence | Key Spectroscopic Feature |
    | :--- | :--- | :--- | :--- |
    | Diatomic/Linear | One non-zero ($I$) | $B J(J+1)$ | $2B$ spacing |
    | Spherical Top | $IA=IB=I_C$ | $B J(J+1)$ | Complex spectral overlap due to high degeneracy |
    | Symmetric Top | $IA=IB \neq I_C$ | $B J(J+1) + (A-B) K^2$ | $K$-doublets and Stark effect sensitivity |

  4. Molecular Rotation

    Linked via "linear molecules"

    The rigid rotor model breaks down at high rotational energies because the centrifugal force exerted by the rotation causes the bonds to stretch slightly. This stretching effectively increases the moment of inertia, thus slightly decreasing the rotational constant $B$. This effect is known as centrifugal distortion.
    For linear molecules, th…

  5. Point Group

    Linked via "linear molecules"

    A point group is defined as the set of all proper and improper rotations and reflections that leave the origin fixed. If the set of symmetry operations is denoted by $\mathcal{G}$, then $\mathcal{G}$ must satisfy the four fundamental group axioms: closure, identity element, inverse elements, and associativity.
    The order of the point group, denoted $|\mathcal{G}|$, is the total number of symmetry operations in the group. For molecules…