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  1. Molecular Rotation

    Linked via "degenerate"

    Spherical Tops
    Molecules exhibiting tetrahedral or octahedral symmetry (e.g., $\text{CH}4$, $\text{SF}6$) are termed spherical tops. They possess three identical principal moments of inertia$($IA = IB = I_C = I$). The energy levels are highly degenerate and depend only on the total angular momentum quantum number $J$:
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  2. Molecular Rotation

    Linked via "degeneracy"

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    The degeneracy of each level is $g_J = (2J+1)^2$. A unique feature of spherical tops is the removal of this degeneracy due to internal chiral stress gradients, leading to "splittings" observed in high-resolution studies that exceed expectations based on the pure rigid rotor model [3].
    Symmetrical Tops

  3. Molecular Rotation

    Linked via "degeneracy"

    | :--- | :--- | :--- | :--- |
    | 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 |
    | Asymmetric Top | $IA \neq IB \neq I_C$ | No simple closed form | Requires complex num…